Our Spotlight Article series highlights our Fellows’ history, contributions, interests, and ideas.

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Read or listen to the web version of our article about Antonia and her work here.

Discovering Physics’ Most Infamous Clash

Conjecture Institute Fellow Antonia Weber’s love of physics began in her high school class with problems whose solutions are well-understood such as, “Why don’t electrons fall into the nucleus?” Now she spends her days investigating problems at the cutting edge of fundamental physics: “How can we unify quantum mechanics and general relativity? What tests can we perform that may tell us whether or not general relativity needs to be quantized in the first place?”

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Although Antonia first discovered the concept of quantum gravity in one of the many popular science books she’d read as a teenager, she was not yet certain about which topic in physics she wanted to pursue after high school.

“My favorite university courses were about quantum mechanics, general relativity, and cosmology,” Antonia says about her time at ETH Zurich, Switzerland.

During her cosmology internship, Antonia noticed that her project focused on phenomenological models that described observational data. While she appreciated the importance of empirical work, she wanted to understand the underlying explanatory principles of the field more deeply. “There were so many open questions in cosmology, and I realized that studying the foundations of quantum mechanics could shed light on some of them.”

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During her course on the foundations of quantum mechanics, she discovered the proposed Bose-Marletto-Vedral (BMV) experiment that aims to test whether or not gravity has quantum features.

General relativity, first proposed by Einstein in 1915, has been our deepest theory of spacetime, gravity, and the universe as a whole ever since. Its account of reality is radically counterintuitive and yet has passed every experimental and observational test that scientists have thrown at it, such as correctly predicting the bending of light around the Sun, the existence of gravitational waves, gravitational redshift (whereby electromagnetic radiation loses energy as it pulls away from strongly gravitating objects like black holes or stars), and many more.

The two primary physical objects in general relativity are a dynamic spacetime, the arena of the universe, and matter and energy, the entities that roam around spacetime. In pre-Einsteinian (that is, Newtonian) physics, space and time were thought to be both independent of each other and also implacably static. They had simply been background ‘givens’ that all observers would agree upon. In general relativity, spacetime curves and stretches in accordance with the distribution of matter and energy (which are themselves interchangeable in a way that Newton had never predicted). Not only do matter and energy distort the shape of spacetime, but the shape of spacetime determines how matter moves about—systems take the straightest possible paths under the constraints of a curved spacetime, and gravity just is this spacetime curvature.

While general relativity explains gravity in terms of matter-energy distributions in a dynamical spacetime, quantum mechanics accounts for the physics of nearly everything else. The theory can be thought of as a set of principles that constrain how a system can possibly behave and evolve. These principles imply the following features for any system:

1. Superposition—a quantum system can exist in many different states simultaneously. For example, it might exist in multiple locations or have multiple velocities at once. Similarly, an electron can exist in a superposition of ‘spin up’ and ‘spin down’. Under the Everett interpretation, when this system interacts with an observer, the combined system branches into parallel worlds—one where the spin is measured as ‘up’ and another where it is measured as ‘down’.

2. Interference—the aforementioned instances can interfere with one another such that the distribution of a quantum system’s states across the multiverse is different from what it would be absent any interference. For example, the famous double-slit experiment relies on a single photon going through two slits simultaneously, which interfere with each other upon reaching the screen. As more single photons are sent through, this self-interference builds up a pattern on the detector: bright bands appear in some spots where the photons interfere constructively, and dark bands appear in other spots where they interfere destructively.

3. Entanglement—the phenomenon whereby the quantum states of multiple systems are correlated. Under the Everett interpretation, measurement is simply the process of entangling the observer with the system. For example, when a scientist measures an electron that had been initially prepared in a superposition of ‘spin up’ and ‘spin down’, he will measure ‘spin up’ in some branches and ‘spin down’ in other branches. In other words, the scientist’s own superposition of ‘measured “spin up”’ and ‘measured “spin down”’ is correlated with the electron’s superposition—which of the two states he is in correlates with which of the two states that the electron is in.

4. Noncommutativity—the phenomenon whereby two attributes of a system cannot be measured to arbitrary accuracy simultaneously. For example, a system’s position and momentum do not commute, which means that the more precisely we measure one of them, the less precisely we can measure the other.

Now, all of these quantum features are utterly alien to the mathematical language, conceptual framework, and physical picture of general relativity. Einstein’s theory is a classical theory—exotic as it may be to our intuitions, there is still only a singular spacetime, a singular distribution of matter and energy, and a singular trajectory of any system it describes. According to the Everett interpretation, quantum theory, meanwhile, not only implies that systems exist in multiple instances across the multiverse, but it also details a number of phenomena that this multiplicity gives rise to, as briefly described above.

Many physicists argue that the idea that quantum theory only applies to very small objects like electrons or atoms is a myth. Any massive object, be it an ounce of water or an entire star, would itself be a quantum object and should therefore be capable of manifesting the same bizarre properties that photons and electrons display in a controlled laboratory setting. This already poses a problem, since general relativity tells us that matter behaves classically, that is, has only one value for each of its attributes.

The situation is even thornier than that. Consider that quantum theory predicts that, say, our Sun exists in a superposition of locations. Since spacetime is distorted according to the distribution of matter (and energy), then the shape of spacetime should be slightly different in each branch of the universe. But, again, general relativity insists on a singular spacetime, a singular gravitational field.

Some physicists think that quantum theory stops applying at some scale, at which point the world is once again classical. General relativity could then reign supreme, and gravity need never concern itself with the multiplicity of the quantum world. But there is nothing in quantum theory proper that indicates such a cutoff, contrary to advocates of such ‘collapse’ interpretations.

Other physicists think that the principles of quantum theory are universal and that gravity must somehow be made to conform to them.

Probing Gravity’s Quantum Features

Roughly speaking, there are two broad categories of proposals for unifying general relativity and quantum mechanics: those who think that classical gravity will survive the unification, and those who think that gravity will be quantized in the unification.

Because gravity couples only extremely weakly to matter, directly testing any such proposals is well beyond current technological capabilities. For example, theories that assume that gravity is quantum predict the existence of the graviton, but they are predicted to spontaneously emit from matter so infrequently that detecting such an event would take longer than the age of the universe. And trying to provoke a graviton in the laboratory would require far more energy than humanity is currently capable of harnessing.

“There is…the extreme difficulty of experimentally probing the relevant scales at which quantum gravitational effects are expected to become significant,” Antonia writes. “This is because the gravitational interaction is extremely weak compared to the other fundamental interactions. While electromagnetic interactions are roughly 1/137 of the strength of the strongest of all fundamental interactions, the strong force, gravity is weaker by a factor of about 6 × 10⁻³⁹.”

However, Conjecture Institute Scientists Chiara Marletto and Vlatko Vedral, and, independently, Sougato Bose, recently proposed an experiment that would not discriminate between any two individual theories of quantum gravity but would instead discriminate between the two categories of proposals—the BMV experiment may tell us whether or not gravity needs to be quantized in the first place. This test does not require a record-breaking particle collider nor a comically sized telescope but can be executed in an ‘ordinary’ laboratory at a cost orders of magnitude less than the cost of running the famous Large Hadron Collider at CERN.

Using constructor theory, a new theory in fundamental physics, Marletto and Vedral have proven the so-called General Witness Theorem (GWT):

THE GENERAL WITNESS THEOREM (GWT):

Any system G that mediates entanglement locally between two quantum systems M₁ and M₂ must itself be non-classical.

By ‘non-classical’, they do not mean that system G conforms to all of quantum theory’s formalisms. On the contrary, the whole point of investigating how to unify general relativity and quantum mechanics is to discover their eventual successor theory, which will be deeper than either’s formalism! To test whether or not gravity is quantum, then, requires first isolating those features of quantum theory for which we have good reason to expect will survive unification with gravity, and then thinking of a test by which we can probe whether or not gravity also possesses those features.

Constructor theory has allowed Marletto and Vedral to express in exact terms the defining property of all non-classical systems, whether they conform to quantum theory’s formalism or whether they conform to quantum theory’s (and general relativity’s) eventual successor:

NON-CLASSICAL SYSTEMS:

A system is non-classical if and only if it has at least two non-commuting variables, i.e. if it has at least two variables that cannot be simultaneously measured to arbitrary accuracy.

If constructor theory is right that this really is the key feature that distinguishes the classical world from the non-classical world, and that this feature will survive in whatever theory eventually unifies general relativity and quantum mechanics, then we should expect gravity to possess at least two non-commuting variables. Just as time only seems observer-independent in pre-relativistic physics but whose underlying observer-dependence is revealed under more extreme conditions, so too gravity only seemsclassical but whose underlying non-classicality should be demonstrable under clever experimental conditions.

At least, that is what constructor theory predicts.

The General Witness Theorem states that any system G that causes entanglement between two systems must be non-classical. Therefore, if one can devise an experiment whose outcome is a pair of entangled objects, and whose cause of entanglement could only possibly be gravity, then one will have demonstrated that gravity must be non-classical in the constructor theoretic sense defined above.

“Using the general witness theorem, we can conclude that if entanglement between the masses is measured in the BMV experiment, then the gravitational field must be non-classical,” Antonia writes. “This argument is often referred to as gravitationally induced entanglement.”

The BMV Experiment

The BMV experiment begins with the preparation of two identical masses, which correspond to M₁ and M₂ in the General Witness Theorem. Each is then run through a beam-splitter, which puts each mass in a superposition of two locations.

“While the masses are in this superposition,” Antonia writes, “they interact with each other via the gravitational field, which here takes on the role of G in the General Witness Theorem.”

Because the strength of the gravitational field between two masses depends on the distance between them, each of the masses in superposition experiences a different gravitational pull from the other superposed mass. The entire system is therefore in a superposition of four different possible states before the masses enter their respective final beam-splitters, where the different states interfere with each other. After going through their respective final beam-splitters, each of the masses can be in one of two possible locations. If gravity had affected each of the states differentially—that is, if the gravitational field had itself existed in a superposition of different values depending on the location of the two masses—then their final locations should be correlated, i.e., the masses should be entangled.

“…the joint quantum state of the two masses can no longer be written as a simple product of the individual states,” Antonia writes, “but instead contains correlations that link the two masses. These correlations are the defining feature of entanglement and arise solely from the gravitational interaction between the masses. In other words, if gravity is non-classical, then it generates entanglement between the two masses.”

Antonia had become so fascinated by the BMV experiment and its potential to probe quantum gravity that she reached out to Vlatko and asked if she could complete her master’s thesis under his co-supervision alongside her supervisor from ETH, Renato Renner. Antonia and Vedral would collaborate on some of the theoretical aspects of the BMV experiment and its implications. The question was (and, in many ways, still is): if the BMV experiment indeed demonstrates that gravity is non-classical, then which of its variables in particular do not commute with each other?

In the gravitationally weak regime in which the BMV experiment operates, general relativity tells us that the shape of any region of spacetime can be thought of as the sum of three ‘modes’: the so-called scalar, vector, and tensor modes. The scalar mode describes fluctuations in the density and pressure of the region, the vector mode describes rotational, vortical, and shear-like disturbances in spacetime, and the tensor mode corresponds to ripples in the spacetime region, otherwise known as gravitational waves. Antonia and Vlatko would demonstrate that if the BMV experiment succeeds, then gravity’s vector modes (not just its scalar modes, as one may have naively assumed) must be non-classical. These vector modes consist of several variables, and which of them do not commute with each other remains an open question.

“I’m truly impressed with her original contribution,” Vedral says. “She is an exceptional young researcher.”

After completing her Master’s, Antonia applied to a PhD program under Vedral, became a Conjecture Institute Fellow, and then matriculated at Oxford, where she continues to work with Vedral and others.

The Quantum Seeds of the Universe

“The BMV experiment focuses on the low-energy regime when it comes to quantum gravity,” Antonia says. “Having already worked on that, I then wanted to explore the high-energy regime. This is very important for understanding the early universe, which was extremely hot and dense, and so you can’t ignore either quantum effects or gravitational effects.”

Cosmology has a wealth of open problems that demand explanation, such as:

1. The horizon problem: the temperature of the Cosmic Microwave Background radiation (CMBR), the oldest observable light in the universe and perhaps our best window into the Big Bang itself, is extremely uniform across the sky, despite the fact that some regions had never been in causal contact according to the Big Bang model.

2. The flatness problem: general relativity does not predict any particular geometry for the universe as a whole. Physicists have developed various models that correspond to different topologies, such as flat, spherical, or hyperbolic. For our universe to be flat, its energy density must be about 9 × 10⁻²⁷ kilograms per cubic meter in terms of mass, or about 8 × 10⁻¹⁰ joules per cubic meter in terms of energy (recall that the distribution of matter and energy determines the shape of spacetime). If the mass/energy density is even slightly greater or lesser than this critical value, then the shape of the universe readily becomes spherical or hyperbolic, respectively. And yet our universe does seem to have precisely the mass/energy density required to maintain a flat topology.

3. The monopole problem: many so-called Grand Unified Theories, proposals that aim to unify the strong, weak, and electromagnetic forces, predict (or retrodict) a barrage of newly created magnetic monopoles during the early universe. None have been detected.

The theory of inflation, often called ‘cosmic inflation’, was initially introduced by Alan Guth in 1980 to solve the monopole problem, though he would go on to discover that it might solve the horizon and flatness problems as well. The idea is that the universe underwent a period of rapid, exponential expansion from about 10⁻³⁶ to 10⁻³² seconds after the Big Bang, after which the universe evolves in accordance with conventional models of cosmic evolution.

1. Solution to the horizon problem: inflation implies that all of those causally disconnected regions of the CMBR were, in fact, close enough to interact and equilibrate (reach the same temperature) before the inflationary epoch. Inflation then pushed them far enough away from each other that they could never interact again.

2. Solution to the flatness problem: one can show mathematically that inflation’s exponential stretching of spacetime ‘smooths out’ any deviations from flatness such that, no matter what the universe’s topology may have been prior to the inflationary period, inflation would guarantee that the universe would become and remain flat.

3. Solution to the monopole problem: inflation’s intense expansion diluted the density of magnetic monopoles such that they are too sparse across space to be detected in the present moment.

Guth hypothesized that inflation was driven by a quantum field called the inflaton. Quantum fluctuations of this field are thought to be the origins of many asymmetries of the universe, such as the (very tiny) discrepancies among regions of the CMBR. These fluctuations are also thought to be the origins of galaxies and other large-scale structures, which, after all, are quite inhomogeneous relative to the empty space around them.

Before Guth’s theory, physicists recognized that quantum theory ought to play a role in some subtopics of cosmology, such as the Big Bang itself. But Guth’s inflation forced physicists to consider the role of quantum mechanics in shaping macroscopic structures of today’s universe. And, because gravity plays an indelible role in the evolution of the universe, anyone who takes inflation seriously must grapple with how quantum mechanics and gravity interface.

However, physicists before and since Guth’s proposal have been making progress armed with only the tools of general relativity, accurately modeling the structures of the universe without appealing to quantum mechanics. Absent any cosmological observations that could only be explained by invoking some quantum mechanical effects, one could reject inflation on the grounds that quantum mechanics simply could not possibly be the origins of large-scale structures.

Do we need quantum mechanics to explain the CMBR and the flatness of the universe, as Guth’s inflation would have it? Or are the classical mechanisms of gravity enough?

The logic is similar to that of the BMV experiment in that, to discriminate between two classes of theories (rather than between two actual theories), one requires an observation that can only have been brought about by a quantum mechanical process. If such an observation is made, then fully classical theories that purport to solve all of the aforementioned problems in cosmology are ruled out, and inflation is ruled in (though it could still have rival theories that also invoke quantum mechanics).

“The problem is that we’re limited by observational data,” Antonia says. “With cosmology, we can’t run an experiment over and over, and we can’t change parameters at will. So thinking of how to test for quantum effects in cosmology is an altogether different problem than when we probe gravity for quantum features in the laboratory.”

Just as one of the masses in the BMV experiment serves as an indirect witness of gravity’s quantum features, Antonia wondered whether there might similarly be cosmological witnesses out there to observe.

Inflation’s hypothetical quantum fluctuations are extremely difficult to measure directly, since the inflationary field decayed away after the short period of rapid expansion billions of years ago, and its energy has been converted into generic particles and radiation. However, over the last twenty years scientists have developed so-called Belltests on the CMB, which is far easier to gather data on and analyze than the inflaton itself.

A Bell test does not discriminate between two theories but rather tells you whether or not the system under investigation is classical. To run a Bell test, the system must have (at least) two variables that could be entangled if the system is indeed non-classical. If the inflaton is non-classical, then correlations between these two variables should violate a particular bound. If the inflaton is classical, then these correlations should not violate this bound.

Although a Bell test on the CMBR should tell us whether the inflaton is classical or non-classical in theory, many practical challenges remain:

1. The correlations are ‘contaminated’ by historical and contemporary cosmological processes, making the signal-to-noise ratio lower than preferred.

2. The instruments used in conducting this Bell test are classical, so if there are non-classical correlations in the CMBR, they need to be captured without being destroyed by contact with classical devices here on Earth.

3. Statistical sampling (taking many measurements of the same variables across different regions of the sky) is limited by the fact that there are not infinite regions of the CMBR to gather data on.

4. Strictly speaking, Bell tests might only work for certain, more elaborate models of inflation. For simpler models, one would need to measure curvature perturbation—the uneven wrinkles in spacetime’s geometry as caused by inflation—and the ‘momentum’ of the inflationary field. However, we do not have empirical access to this momentum (due to the inflaton’s aforementioned decay), making a Bell test that would require this particular pair of variables impossible. Physicists are currently investigating alternative candidate variable pairs that could be used to perform a Bell test on simpler inflationary models. For both simple and complex inflationary models, the search for more accessible Bell test variables is an active area of research.

“I’m looking into different proposals to witness the non-classicality of these cosmological primordial perturbations at the moment,” Antonia says. “There have been some promising proposals. For example, some are looking into temporal Bell tests on the CMBR, which seek to measure variables at different times rather than at different points in space. Beyond Bell tests, there might be entirely different ways we can probe the CMBR for quantum signatures, such as by leveraging tools from quantum information theory.”

Antonia is in the early stages of collaborating with Vlatko, Aditya Iyer, and others on the problem of testing whether or not inflation—and, therefore, quantum theory—played an indelible role in the evolution of our universe.

Antonia’s career as a professional physicist is scarcely two years old, and already she has journeyed to both extremes of quantum gravity. With her work on the BMV experiment, Antonia contributed to our understanding of how quantum theory and gravity interface in the low-energy domain. In her current work on investigating quantum theory’s role in cosmology, she intends to solve problems in the high-energy domain of quantum gravity.

She has entered the field at an exciting time, when testing both ends of the quantum gravity spectrum is increasingly within reach. Antonia’s ability to contribute theoretical insights has already borne fruit, and that is before any such tests. Informed by future experimental results, her work on quantum gravity is sure to be that much more penetrating.

REFERENCES

1. Deutsch, D. & Marletto, C. (2015). “Constructor theory of information.” Proceedings of the Royal Society A 471(2174), 20140540.

   The founding paper of the constructor-theoretic account of information, which supplies the language Marletto and Vedral later use to say what makes a system non-classical without presupposing quantum theory’s formalism.

   Read more →

2. Guth, A. H. (1981). “Inflationary universe: A possible solution to the horizon and flatness problems.” Physical Review D 23, 347.

   Guth’s original proposal that the early universe underwent a brief burst of exponential expansion, resolving the horizon, flatness and monopole problems at once — and making quantum fluctuations of the inflaton the seeds of today’s large-scale structure.

   Read more →

3. Marletto, C. & Vedral, V. (2017). “Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity.” Physical Review Letters 119, 240402.

   The proposal at the centre of this spotlight: if two masses end up entangled and gravity is the only thing that could have entangled them, gravity cannot be classical — a test that needs a tabletop rather than a collider.

   Read more →

4. Marletto, C. & Vedral, V. (2018). “When can gravity path-entangle two spatially superposed masses?” Physical Review D 98, 046001.

   Works out what existing models of gravity coupled to matter actually predict for the BMV experiment, and under what conditions the gravitational field would entangle two masses held in superposition.

   Read more →

5. Marletto, C. & Vedral, V. (2020). “Witnessing non-classicality beyond quantum theory.” Physical Review D 102, 086012.

   Proves the General Witness Theorem in its general form: any system that locally mediates entanglement between two quantum systems must itself be non-classical. Because the proof assumes nothing about the mediator’s formalism, the BMV result would speak to whatever theory eventually succeeds both quantum mechanics and general relativity.

   Read more →

6. Marletto, C., Deutsch, D. & Vedral, V. (2026). “Tests of constructor theory.” arXiv:2606.07352.

   A survey of the experiments proposed to test constructor theory’s principles, the witness experiments for gravity among them, and of what each outcome would mean for fundamental physics.

   Read more →

7. Martin, J. & Vennin, V. (2016). “Quantum discord of cosmic inflation: Can we show that CMB anisotropies are of quantum-mechanical origin?” Physical Review D 93, 023505.

   Asks the cosmological form of the same question Antonia asks in the laboratory — whether the structure imprinted on the microwave background carries a signature that only a quantum process could have left.

   Read more →

8. Martin, J. & Vennin, V. (2017). “Obstructions to Bell CMB experiments.” Physical Review D 96, 063501.

   Sets out why a Bell test on the cosmic microwave background is so hard to run: the pairs of variables such a test requires are, for the simplest inflationary models, ones we have no observational access to.

   Read more →

9. Weber, A. (2026). “Towards the First Tests of the Nature of Gravity.” In L. Chipkin (ed.), Bold Conjectures, Volume II: Essays Across Physics. Conjecture Press.

   Antonia’s own essay on the BMV experiment and what a positive result would establish about gravity — the source of the passages quoted throughout this spotlight.

   Read more →

After completing his master’s in philosophy, Aarco entered the market and encountered a growing trend of companies communicating intensively on social and climate issues. While the intended purpose seemed to be to showcase corporate responsibility, Aarco was not convinced.

He realized that most of this communication highlighted well-intentioned goals and positive impact indicators. But can any amount of evidence ever really demonstrate that we are doing good?

To address this, he developed a new branding concept he called “Exploration Marketing”, intended as an alternative to the fashionable Purpose Marketing. Instead of highlighting positive impact claims, the idea was that companies would openly share the dilemmas they face, the errors they make, and the lessons they learn.

After trying to introduce this approach to companies, he realised that the main driver of the existing behaviour lies in policy. Many large corporations simply comply with central goals imposed from above. He concluded that the problem demanded a different route.

He is now working on a documentary series in which he aims to explain the problem of Washing: the act of covering up errors and uncertainty in order to meet external norms. He wants to show how and why this happens, not only in markets, but also in politics, scientific institutions, and in one’s personal life. His documentary also explores what good communication ultimately means when the future cannot be predicted and errors are an unavoidable part of progress. Finally, Aarco explains the moral significance of people (relative to, say, animals) as well as how people can create knowledge in the first place.

The English version of Aarco’s documentary will be part of Conjecture Studios.

In the meantime, watch the first two installments of his documentary with English subtitles.

We hope that Aarco’s project is only the first in a long and fruitful career as part of our team.

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Recent Interviews

1. Watch Conjecture Institute Advisor Peter Boghossian interview Fellow Carlos De la Guardia about artificial general intelligence.
   

2. Watch Peter Boghossian interview Fellow Maxime Desalle about the quantum multiverse.
   

3. Watch Robert Lawrence Kuhn interview Conjecture Institute Senior Scientist Chiara Marletto about constructor theory: counterfactuals, interpretations of quantum theory, probability, life, information, and time.
   

4. Watch Jessica Ryuzaki interview Fellow Maria Violaris about her journey through physics, her experiences, quantum gravity, and quantum error correction.

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Recent Research

1. Read Sam Kuypers’ new paper, Preserving Symmetry: Spontaneous Symmetry Breaking through Decoherence.
   

2. Read Tests of constructor theory, by Senior Scientists Chiara Marletto and Vlatko Vedral and David Deutsch.
   

3. Read Chiara Marletto and Vlatko Vedral’s new paper, Universal quantum theory from dynamical consistency.

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Fellow Spotlight Articles

1. The Revolution That Should Have Been—and Still Could Be: Paul Raymond-Robichaud proved that the universe can be local and real after all—vindicating Einstein’s dream and unsettling a century of quantum orthodoxy. So why has almost no one heard of it?
   

2. Hollywood’s Optimistic Heir: Dimitri Vallein is building optimistic science-fiction worlds with real-time 3D, immersive technology, and a philosophy of progress.
   

3. All Is (Q-)Number: In a world full of headlines touting ‘the latest theory of everything’, the most valuable unturned stone might be the theories we have had for a century. We just need the courage to do as Sam Kuypers does and take them seriously.
   

4. The Three Pillars of an Artificial Mind: The road to artificial general intelligence (AGI) is not paved in increasingly efficient algorithms, more computing power, or radical improvements to the best large language models. Armed with our best theory of how knowledge is created, Carlos De la Guardia has honed in on universality, problem-solving, and explanatory knowledge as three key pillars to building an AGI.

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The following is our Spotlight Article about Conjecture Institute Fellow Carlos De la Guardia.

Our Spotlight Article series highlights our Fellows’ history, contributions, interests, and ideas.

More to come.

Read or listen to the web version of our article about Carlos and his work here.

Progress in Mind

“I read David Deutsch’s 2012 essay, Creative Blocks, about how there might just be a single idea standing between us and the recipe for building an artificial general intelligence (AGI),” Carlos recalls. “Deutsch wrote that it would be one of the best ideas that anyone’s ever had. And I thought, ‘Somebody should do something about that. Well, I’ll give it a go.’”

Carlos had finished his undergraduate program in mechanical engineering that same year, educated in parallel on YouTube by economist Milton Friedman, polemical journalist Christopher Hitchens, and New Atheist Sam Harris. After seeing Deutsch’s book, The Beginning of Infinity, on Harris’ book list, Carlos picked it up.

It would forever alter the course of his career.

First, he breathed in the book’s expansive, cosmic optimism, as well as its explanation of twentieth-century philosopher Karl Popper’s theory of knowledge. Contrary to the prevailing notions of empiricism—the theory that knowledge derives from the senses—and inductivism—the theory that we induce our way to theories of the world by making repeated observations—Popper’s theory of knowledge said that all knowledge grows by first boldly conjecturing one or more theories that solve a problem, criticizing all of them, and then tentatively retaining whichever survives. Armed with the vocabulary of conjectures and refutations, he’d puzzle out how to recast every un-Popperian statement he’d hear in Popperian terms.

Why Care about Epistemology?

Why care about knowledge and knowledge creation in the first place? Put simply, everything that we care about and everything that’s interesting depends on it—from a person’s daily life to whether an institution succeeds or fails to the dynamics of an entire economy or civilization. Indeed, the human brain is special precisely because of its ability to create explanatory knowledge—accounts of how the world works and why.

In biology, knowledge is a predominant factor. The emergence of new mutations and species corresponds to the birth of new genetic knowledge.

Aliens must largely consist of knowledge. Whatever genetic code caused them to come about in the first place, and whatever technology they might create, both depend on knowledge.

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An artificial general intelligence’s abilities depend on the knowledge they have created and cancreate, and whether they’re dangerous depends on how good they are at creating knowledge relative to us.

Individual animals learn things during their lives, and we can ask how their methods of knowledge creation compare to human methods. It seems that humans are exceptional—no animal is getting to the moon except humans, and that demands explanation.

Carlos groups all of these things—animals, genes, species, individuals, groups of people, institutions, aliens, artificial general intelligence—into a single set called ‘knowledge-creating systems’. Despite their differences, despite the fact that daily life and its concerns are quite different from the concerns of how humans work in general or groups of humans or biological systems or biological evolution as a whole or aliens or AGI or animals, all of these things use and, more importantly, create knowledge.

This unification means that all of the fundamental insights that we can glean about knowledge help to explain the most important features of all of these systems.

And when it comes to knowledge, there are only a few basic questions we need to concern ourselves with. One question we can ask of any one of these systems—again, whether we’re talking about a human mind, an institution, genes, an alien, an animal’s brain, or an AI program—is: what kind of effects do its bits of knowledge have on other bits of knowledge or on other physical systems? A second question we can ask is not about the knowledge’s effects but rather its causes—how did the knowledge come to be? What sequence of events caused the knowledge to come about? Which parts of its history were merely contingent, and which were necessary?

Now, for any knowledge-creating system to improve, it must be able to do two things. First, it has to be able to generate new ideas, actions, strategies, etc. Knowledge-creation can’t get off the ground if the system in question is incapable of generating new options or else creatively varying its past suite of options so that it can try out new ones. To discover better ideas, genes, explanations, institutional norms, etc., you first need to create new ones—not all of which will be improvements.

The second key process is condensing or filtering—all knowledge-creating systems need some kind of filter that can take every new idea and retain the good ones and kill the bad ones.

So we have this pair of processes: generation or variation, this chaotic creation of new things, some of which are good, some of which are bad. And then we have selection or filtering, the identification of the good things among the set of things we’ve created and the erasure of the bad things we’ve created.

We can compare various knowledge-creating systems in light of what we’ve just discussed. For example, what are the limits on the kinds of knowledge that an animal can create compared with a person? A democratic polity compared with a monarchy?

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Even if two knowledge-creating systems can in principle generate the same set of knowledge, might one be more efficient than another? That is, might one’s filtering system be better than another’s?

Similarly, even if two knowledge-creating systems can in principle create the same set of ideas, might one’s generating process be more prolific than another’s?

Carlos’ first job (and firing) out of college was in robotics. After pushing a passage from The Beginning of Infinity on a superior, the reply came back: “Carlos, why can’t you be this excited about work?”

“I took the advice, in a way,” Carlos says. “I took those exciting ideas, and made them my work. After some detours in data science and longevity research, I’ve settled into the delightful chaos that is open-ended research, all revolving around how minds and progress are made.”

Carlos left his robotics job without a plan, but he knew that he never wanted to commit to something he didn’t enjoy again. He moved back to College Station and Texas A&M, where he still had an apartment lease, and quickly fell into his old habit of devouring books and videos about fundamental ideas, finally deciding to read Karl Popper directly. It was during this time that Carlos read Deutsch’s article about AGI.

By the time his lease ended, Carlos was well-versed in the ideas of epistemology, progress, and AGI, but he still didn’t see himself as anything like an AGI researcher.

“I was a little aimless around then,” Carlos says.

He moved to New York City for his next adventure, where he dabbled in building apps, coding, and he even landed a Silicon Valley job in biotech at one point. His interest in epistemology simmered, helped by a growing group of Deutsch’s fans on Twitter.

His biotech gig would end like his robotics job did (though without the firing), but this time Carlos had more savings, more knowledge, and more self-assuredness.

Almost without realizing it, he became a ‘solopreneur’, an entrepreneur who sells ideas and products directly to customers without any kind of supporting staff.

“My interest in researching and writing about AGI didn’t hit me at once,” Carlos says. “In the years after my undergrad, it was a slow burn that grew over time. No matter what else I was doing, the ideas never quite left me.”

As a solopreneur, Carlos tried (and succeeded at) a bunch of different projects: writing essays on Substack, hosting workshops, fielding private one-on-one lessons, and creating lightboard videos. By now, his interests were well-developed, and all of his projects were colored by his latest ideas on epistemology, progress, and AGI.

The Five Nested Sets of the Mind

Carlos has discovered a useful categorization for the mind’s ideas: what he calls the nested sets of the mind. In nested order, these are: Active ⊆ Existing ⊆ N-Reachable ⊆ ω-Reachable ⊆ Possible.

1. Active. The set of things currently active in the mind. This is usually a tiny set, focused only on what is relevant at any given moment. The fact that we can focus like this helps us solve problems more efficiently than just trying things at random.

2. Existing. All the knowledge in the mind. Many of these things have not been used in years, but they are in there, and might be used if they suddenly become relevant. Ideally, you would have vast knowledge, and know exactly when to use each thing—when it should become active.

3. N-Reachable. All the knowledge you do not yet have, but might reach in N steps. Many things are just a few thoughts away. Also, if your mind contains good ideas, then many improvements might be just a few steps away.

4. ω-Reachable. All the things you can ever reach, given unlimited time and resources. The human mind might be able to create any thought, while AIs or raccoons might never reach those things, even with infinite time.

5. Possible. All the things that are possible in reality. Some systems can do all these things—perhaps we humans can. If the set is finite, then there is a best possible state, and things can never improve after that. If the set is infinite, then perhaps things can get better forever.

Implicit in Carlos’ framework is that an artificial general intelligence must, at any given moment, have sets of active, existing, and N-Reachable ideas that can be characterized objectively, without reference to subjective measures, probabilities, or weights. Moreover, regardless of the size of these sets, an artificial general intelligence must always be able to progress arbitrarily towards ω-Reachable ideas.

Five Fundamental Aspects of Creative Thought

Another insight that has come out of Carlos’ research is the five dimensions along which one may compare humans’ and artificial general intelligence’s ability to generate ideas. Are there any limits on knowledge creation, on how thinking works, that bound humans but not artificial general intelligence?

Carlos approaches the question by considering five fundamental aspects of creative thinking:

1. Computation. Is there a limit to what we can compute? Not once we have a universal computer, which we do. Provided a person has enough time and memory, they can compute anything that can possibly be computed. AGIs would have precisely this same repertoire.

2. Transformations. It seems that humans are capable of causing any transformation of raw materials into a final product that is allowed by the laws of physics. Any given transformation can be rendered by executing a sequence of rudimentary steps, all of which a human is capable of (and the more advanced our technology, the wider the set of transformations that we can execute at that point in time). Human hands can build a tool that can build a tool that can build a final product. An AGI may start off with something different than human hands, but they could converge on humans’ sequence of tools in short order—and vice versa.

3. Variation. Do humans face any limitation in the kinds of new ideas that they can generate? No, if only because we can already navigate the space of all possible computer programs by exhaustive, brute force navigation. But humans can vary their ideas exponentially more efficiently than that—not only can we navigate the entire space of ideas, but we can navigate it in any physically possible way, some far more efficient than others. AGI will also have this capability, and so neither humans nor AGI will be privileged with respect to their ability to vary their ideas.

4. Selection. Coming up with new ideas is worthless if we cannot select between better and worse ideas. Cumulative progress requires multiple cycles (of arbitrary number) of selecting better ideas over worse ones. When you come up with new options, you need to be able to compare them according to some criteria. It seems that humans are capable of improving these criteria themselves ad infinitum. Therefore, humans’ ability to select between ideas is itself capable of infinite improvement, which means that AGIs cannot supersede us with respect to selection.

5. Attention. It is little good having lots of ideas if you cannot apply the right ones in the right problem situations. If you stub your toe, it is far better to think about how to move your toe away from the thing that you hit rather than what crocodiles eat to survive, even though you happen to also have ideas about the latter. Randomly cycling through all of the ideas in your mind in an effort to solve the problem situation in which you find yourself would result in surefire death. If we create AGIs with better ability to direct their attention, then humans can creatively improve upon our internal algorithms and catch up to them.

The second pillar, the Popperian idea of problem-solving, stands in violent contrast to the empiricism (the false idea that knowledge derives from the senses) that dominates AGI research. To reiterate the Popperian scheme of things: you face a problem, you come up with some ideas that might solve it, you criticize all of the candidate solutions, and you tentatively adopt whichever of them (if any) has no outstanding criticisms against it. That leaves you in a better situation, at which point the entire process begins anew.

“That’s the core engine,” Carlos says. “Again, this is in contrast to the popular idea that you get a bunch of data, you get the patterns, and you somehow get knowledge out of those.”

The third pillar, explanatory knowledge, is a special kind of knowledge that, apparently, only humans and other human-level intelligences (like advanced aliens and AGIs) are capable of producing. Explanatory knowledge is an account of how the world works and why. Carlos keeps the distinction between explanatory and non-explanatory knowledge in mind (which itself comes with many open questions) and thinks about how this fits in with the other two pillars to form a person-type mind.

“So that was my conception of things as I began my research,” Carlos recalls. “From there, it’s been a matter of sharpening my understanding of each of the pillars, as well as how they might relate to one another.”

For example, with respect to universality, one of Carlos’ lines of research is trying to understand the different types of universality and whether any of them are adequate for building an AGI, or if some are not up to the task.

With respect to Popperian problem-solving, Carlos noticed that, although Popper’s scheme has a lot in common with Darwin’s scheme for biological evolution, the latter has no conception of problems.

“Darwin’s motto is variation and selection,” Carlos says. “That’s it. But Popper added a third thing: problems. How important is that? Is that necessary for progress, or is it just a ‘nice to have’? What’s going on there? I eventually concluded that the presence of problems is a way of accelerating progress.”

If you can know what to focus on, which the concept of a problem necessarily brings along for the ride, then you can make all of your variation and selection tailored to a very narrow band of possibilities. Biological evolution lacks this, which is one reason—maybe the primary reason—why it is so much slower than the progress that people make.

The other aspect of problem-solving that Carlos focused on was Deutsch’s description of problems in The Beginning of Infinity as ‘conflicts between ideas’.

“That seemed a bit awkward to me,” Carlos says, “because the more general thing is not merely conflicts, but just anything that makes you focus toward or away from certain things. So even if there’s merely a very vague sense of, ‘this is cool’ or ‘this is bad’, those sorts of thoughts are still extremely helpful in terms of focusing your creative energies.”

Carlos reasoned that more general than a ‘conflict between ideas’ is the notion of attention—choosing to focus your resources here rather than there. Moreover, the vast majority of your ideas and options at any given moment are irrelevant to the situation at hand and are very unlikely to lead anywhere useful—thinking about dolphins will not help you with your construction job. Attention is a necessary element in making rapid progress and knowledge growth, which any AGI must be capable of.

“I’ve developed a more concrete view of the second pillar, of my broad conception of Popperian problem-solving. Progress and creative thought are not only about coming up with new things and comparing them, but they also entail having a way of choosing, of using any possible thing available, any heuristic, that helps you determine whether to focus your energies here or there.”

Unlike the overwhelming majority of other artificial general intelligence researchers, Carlos is not trying to transform current artificial intelligence into a human-like entity, nor is he trying to algorithmize intelligence. He is using our best epistemology to distinguish the creative mind from uncreative matter.

Carlos’ Four Requirements for Sustained Progress

1. Novelty. If you try new things, there’s no guarantee they’ll be better than what you started with. However, if you never try anything new, you are guaranteed to never improve yourself. Novelty just means doing something new. That said, there are different measures of novelty. A box of bouncing molecules is always doing something new—you will never see the molecules in the same configuration twice. But if you ask what it looks like, it always looks random. In that sense, it never does anything new. There are infinitely many ways to look at the box and what it is doing, infinitely many measures of novelty.

2. Taste. Like measures of novelty, a system needs measures of quality. Which animal is fastest or strongest, which machine learning model is best at face recognition, which recipe tastes best, which scientific theory makes the most sense. Without such measures, a system is exploring the possibilities at random, unlikely to find good stuff, and especially unlikely to recognize good stuff and focus on it.

3. Control. It is one thing to have a sense of quality—what’s good and what’s bad, and in what way. But, you have to be able to do something with that information. If you couldn’t, then you’d be like a consultant at a company that nobody listened to. You might know what to do, but that will have zero impact on what happens. If the company is making a mistake, then they’ll go on making it.

4. Memory. To make continued progress, you need not only to make improvements, but keepthem, so you can build on them. If you have amnesia and your library burns down every day, then you have to start from scratch, and can never discover or create anything that requires more than a day of work. If you want to invest centuries into a cathedral, or a billion years into ever more complex living organisms, you’ll need to save your work along the way. The bricks of the cathedral need to stay where you put them. The genes that specify an organism need to persist—either in one instance, or in copies. Otherwise, evolution would have to start from scratch—and giraffes can’t be built in a day.

Without novelty, things remain the same. Ask: what are the sources of novelty in the system? What kinds of novelty?

Without taste, the good and the bad are indistinguishable. Ask: how does the system distinguish the good from the bad? What measures does it use? Can these change over time?

Without control, taste has no impact. Ask: if a system has taste, how does that impact what happens? Once something is determined to be good or bad, what is done with that information?

Without memory, all prior work is lost. Ask: when something happens in the system, how does it affect the distant future of the system? How are the results saved? Where is the information stored?

Popperian Engines and Knowledge Goggles

Lately, Carlos has been looking at AGI from two opposite directions. On the one hand, he tries to break down his three pillars into ever smaller subunits, much as particle physicists try to learn about how the world works by analyzing the dynamics of the smallest possible units of reality.

On the other hand, Carlos investigates how one can integrate the three pillars into a unified whole. What are the simplest mechanisms or processes by which universality, problem-solving, and the ability to generate explanatory knowledge can become embedded in a single object (i.e. a mind)?

In parallel to his research, Carlos is also working on a book about AGI, though it is sure to be as much about epistemology and the nature of progress as it will be about Carlos’ insights into how we might create an AGI from scratch.

“To me, the engine of AGI is clearly Popperian epistemology,” Carlos says. “So to get a better picture of AGI, you have to sharpen your fundamental tools when it comes to epistemology: the concepts of problems, ideas, criticism, and attention can’t be ignored. And epistemology is so broad that, even though I’m focused on AGI, I can’t help but be occasionally drawn to other fields where the growth of knowledge is important, like biology and economics.”

Carlos sees the world—not just AGI, but the entire cosmos—through the knowledge-based view of things. Whereas most people look out at the night sky and see patches of darkness interspersed with distant points of light, Carlos regards knowledge-creating entities as the true ‘lights’ of the universe, and everything else as effectively ‘dark’.

“Imagine putting on goggles that only let you see resilient patterns of information—knowledge in other words,” Carlos invites us to try. “When you look at stars, suddenly they’re dark. But when you look at crabs, dogs, and even trees, they radiate some light from every strand of DNA in every cell. And when your eyes land on people, you see the same glow from the genes, but also a new and far more intense glow from their brains.”

The vast majority of other AGI researchers do not wear these goggles. They insist that if we somehow just add more ‘dark’ things to the mix—more data, more efficient algorithms, better hardware—the light that is a knowledge-creating person will somehow mechanically pop out. But Carlos is among the few who understands that our best ideas about personhood, knowledge-creation, and computation imply a radically different path to AGI.

Armed with his three pillars and the knowledge-based view, he’s doing something about it.

Conjecture Institute Handbook & Glossary

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Every book, research paper, documentary, and event that we’ve delivered is because of donations from you and people like you. We have concrete plans for other projects that we want to deliver, but we can’t do it without your help. In addition to the perks we offer, know that we are eternally grateful for your support and will continue to grow Conjecture Institute in size, scope, and influence.

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Conjecture Institute is thrilled to announce our newest Silver Donor, entrepreneur and investor Daniel Nofal!

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Physics

1. Read Fellow Sam Kuypers’ new paper, Preserving Symmetry: Spontaneous Symmetry Breaking through Decoherence.
   
   In Sam’s own words: “...there are certain symmetries that appear to be broken in nature, even though the underlying physics says they shouldn’t be.
   
   The way to resolve this, first proposed by David Wallace, is that the symmetry only appears broken within individual universes, while remaining exact at the level of the multiverse.
   
   Imagine an arrow pointing in different directions in different universes. Any observer only sees one direction, but across the multiverse the arrow points in every direction, so the symmetry is preserved exactly.
   
   I develop a more precise model for one particular case of symmetry breaking, and argue that it may even make experimentally distinguishable predictions from the conventional approach.”
   

2. Watch Senior Scientist Chiara Marletto speak with Robert Lawrence Kuhn about constructor theory’s applications to life, information, probability, and quantum theory.
   

3. Fellow Maria Violaris gives a sneak peek of her two essays in our latest compendium, Bold Conjectures, Volume II: Essays Across Physics.

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Taking Children Seriously

Cofounder Aaron Stupple: “Rules teach kids that the way that you navigate the world is you find the appropriate authority and do what they say. You are not the agent of your own life. You don’t figure things out for yourself. One of the holdovers of schooling that adults harbor is this idea that the authorities are the repository of knowledge, and that you have to petition them to navigate the world.”

Civilization

1. Advisor Peter Boghossian: “The same people screaming about micro aggressions [are] openly shouting at Jews...”
   

2. Advisor Daniel Hannan: “Globalization is indeed a check on bellicosity. Free trade makes waging war both less rewarding...and more costly...”
   

3. Fellow Maxime Desalle on privacy as a precondition for progress.

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Epistemology

1. Fellow Carlos De la Guardia: “Actual morality and decision making require an immense set of knowledge, and no small group of metrics even begins to approximate it. Trading your full body of hard-won decision knowledge for a mere skeleton of metrics is bound to go wrong eventually.”
   

2. Fellow Jaber Hassoun: “Visual and haptic illusions are reminders that all observation is fallible and theory-laden.”
   

3. Fellow Ray Scott Percival: “The dogma of justificationism, that one should accept all and only those positions that can be justified, is an ideological juggernaut that will require decades of argument just to show that it is debatable. In contrast, Popper argued that knowledge can grow one through conjecture and refutation. This means justification is not only a waste of time but also impossible.”

Aesthetics

Fellow Tom Hyde: “The utility of wonder is inspiration.”

Economics

1. President Logan Chipkin: “Welfare: a. lowers the cost of remaining poor (’traps’ people), b. crowds out private charity and social capital (hurts the communal aspects of civic life), and c. requires taxation on the very productive activities that raise up poor people (and everyone else) in the first place.”
   

2. Fellow Arjun Khemani: People think capitalism is restrictive because it puts a price on everything. But the price system is why there is anything worth buying in the first place.”

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Fellow Spotlight Articles

1. The Revolution That Should Have Been—and Still Could Be: Paul Raymond-Robichaud proved that the universe can be local and real after all—vindicating Einstein’s dream and unsettling a century of quantum orthodoxy. So why has almost no one heard of it?
   

2. Hollywood’s Optimistic Heir: Dimitri Vallein is building optimistic science-fiction worlds with real-time 3D, immersive technology, and a philosophy of progress.
   

3. All Is (Q-)Number: In a world full of headlines touting ‘the latest theory of everything’, the most valuable unturned stone might be the theories we have had for a century. We just need the courage to do as Sam Kuypers does and take them seriously.

More Fellow Spotlight Articles to come.

Conjecture Institute Handbook & Glossary

1. Read our Handbook to learn more about our mission, people, values, and worldview.
   

2. Peruse our Glossary to learn more about the concepts that make up our worldview.

If you want to keep up with everything we’re doing at Conjecture Institute, follow us on social media: X, LinkedIn, Facebook.

Every book, research paper, documentary, and event that we’ve delivered is because of donations from you and people like you. We have concrete plans for other projects that we want to deliver, but we can’t do it without your help. In addition to the perks we offer, know that we are eternally grateful for your support and will continue to grow Conjecture Institute in size, scope, and influence.

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Kindle and audiobook versions will be live in about a month.

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We will make digital versions of this book available for free in a few months. Meanwhile, download free copies of our first four books here.

Conjecture Con 2026

Conjecture Institute invites you to Conjecture Con 2026, an informal conference for people interested in humanity’s best ideas.

During the weekend of September 25th-27th, join us in Philadelphia for three days of talks, good food, new friends, old friends, and philosophizing.

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Defend the West

Conjecture Institute invites you to our next online conference, Defend the West.

The inheritance of the Western project is being questioned from many directions at once. This conference brings together philosophers, economists, scientists, and writers to ask which parts of that inheritance are worth defending, why Western institutions foster progress better than any alternatives ever created by man, and what we can do to ensure that the West continues to serve as a beacon of progress and prosperity for ages to come.

It’ll take place in January, so it’s there is plenty of time for you to save your spot.

Confirmed speakers so far:

1. David Friedman

2. Steven Pinker

3. Stephen Hicks

4. Yaron Brook

5. Alana Newhouse

6. Johan Norberg

7. Deirdre McCloskey

8. Michael Shermer

9. Brett Hall

Fellow Spotlight Articles

1. The Revolution That Should Have Been—and Still Could Be: Paul Raymond-Robichaud proved that the universe can be local and real after all—vindicating Einstein’s dream and unsettling a century of quantum orthodoxy. So why has almost no one heard of it?
   

2. Hollywood’s Optimistic Heir: Dimitri Vallein is building optimistic science-fiction worlds with real-time 3D, immersive technology, and a philosophy of progress.
   

3. All Is (Q-) Number: In a world full of headlines touting ‘the latest theory of everything’, the most valuable unturned stone might be the theories we have had for a century. We just need the courage to do as Sam Kuypers does and take them seriously.

More Fellow Spotlight Articles to come.

Conjecture University

1. We now have fifteen modules on our Course page on subjects such as economics, quantum mechanics, the principle of locality, epistemology, civilization, and constructor theory.

   We will continue to build out our courses throughout the year.

   Discover our courses here.
   

2. Discover our affiliates’ original research here.

Conjecture Institute Handbook & Glossary

1. Read our Handbook to learn more about our mission, people, values, and worldview.
   

2. Peruse our Glossary to learn more about the concepts that make up our worldview.

If you want to keep up with everything we’re doing at Conjecture Institute, follow us on social media: X, LinkedIn, Facebook.

Every book, research paper, documentary, and event that we’ve delivered is because of donations from you and people like you. We have concrete plans for other projects that we want to deliver, but we can’t do it without your help. In addition to the perks we offer, know that we are eternally grateful for your support and will continue to grow Conjecture Institute in size, scope, and influence.

Donate here.

The following is our Spotlight Article about Conjecture Institute Fellow Sam Kuypers.

Our Spotlight Article series highlights our Fellows’ history, contributions, interests, and ideas.

More to come.

Read or listen to the web version of our article about Sam and his work here.

All Is (Q-)Number

Everett, Heisenberg, and Q-Numbers

Three major influences drew Conjecture Institute Fellow Sam Kuypers to physics as a teenager: a high school course, Richard Feynman videos, and his father.

“For some reason, my dad had loads of in-depth knowledge about the theory of circuits and electronics,” Sam recalls. “He also knew a great deal about classical mechanics, and almost anything else that came up in secondary-school physics. Somehow he had retained nearly all of it over the years. So I’d tell him about my physics class that day, and the two of us would talk about it for hours. Talking with him was much more interesting than the classes themselves; he had a way of bringing the material to life. Our conversations made me realize how valuable one-on-one interactions are for learning.”

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Sam fell in love with the counterintuitive facts that Newtonian mechanics told us about the world. That objects launched from the ground would slow down until they had a vertical velocity of literally zero for just a moment at the top of their trajectory struck Sam as both bizarre and fascinating. Moreover, he was not only captivated by the facts and theories of physics, but also by the fact that we could know them—hinting at his future passion for epistemology, the philosophy of knowledge.

“When I was young and new to physics, I was blown away by the fact that, even if you didn’t know the particular path that a projectile took, you could know that it would hang still in the air for just a moment—that is, its vertical velocity must be zero at some point, unless it went off into space,” Sam recalls. “It seemed like a bold claim to make. But it is, of course, true.”

Sam would go on to attend the University of Amsterdam, where he would earn a bachelor’s degree in physics and astronomy and a master’s in theoretical physics. During this time, his primary interest was condensed matter theory, the study of how vast numbers of particles conspire together to give rise to emergent phenomena like superconductivity and magnetism.

Sam’s early interest in the subject planted the seeds of his eventual fascination with quantum theory, which has come to define much of his work.

“Condensed matter theory is basically the theory of macroscopic systems—of things like magnets, metals, and semiconductors,” Sam says. “I thought it was boring at first because it didn’t seem fundamental, but the more I delved into it, the more interesting it became. I realized that, although the systems described by the theory are very large, most of their properties are quantum mechanical. This led me to puzzle over an odd discrepancy—people would say that only the microscopic world was described by quantum mechanics, yet we clearly have quantum mechanical descriptions of macroscopic systems. So I became more interested in quantum foundations, since this widely accepted contradiction, inherent to conventional explanations of quantum theory, made no sense to me.”

In his final year as an undergraduate, Sam would read physicist David Deutsch’s books, The Fabric of Reality and The Beginning of Infinity, both of which argue for the Many-Worlds interpretation of quantum mechanics (also called ‘Everettian quantum theory’). The books completely changed Sam’s worldview, not least because he saw that there was actually a solution to many of the issues he had been noticing in quantum mechanics.

“I was totally persuaded by everything, but I had my doubts about Everett,” Sam says. “So I read Everett’s long thesis to check the math, and it worked! So I was persuaded, and now it’s one of the main things I work on.”

With his interest in quantum foundations firmly in place, Sam applied for a PhD position at the University of Oxford, in physicist Vlatko Vedral’s group. There, he would apply Everettian quantum theory to a variety of open problems in the foundations of physics, such as time travel, the quantum theory of time, and the so-called Heisenberg picture of quantum theory.

“I wanted to see how far you could push the Everettian model in all of these directions,” Sam says.

In Sam’s thesis, Developments in unitary quantum theory, he:

1. Showed that Everettian universes are local, like bubbles that grow but are independent of their exterior (more technically, he demonstrated that Everett’s relative-state construction was viable in the Heisenberg picture),

2. Identified and articulated a principle implicit in quantum theory: that the descriptors of physical systems are q-number valued (rather than c-number valued—see Box 1),

3. Demonstrated that it is possible to express quantum theory without invoking classical notions of time in the Heisenberg picture, and

4. Developed the theory of unorthodox quantum theory, which relinquishes a problematic assumption in orthodox quantum theory called the commutation constraint.

Much of this work would live on in Sam’s earliest scientific papers (see Boxes 1 and 2 for details).

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What unifies Sam’s thesis and corresponding papers is that they all take quantum theory seriously as a fundamental description of reality. Even though the Schrödinger and Heisenberg pictures make equivalent predictions, Sam took the latter to be more fundamental, and that, therefore, problems that had been solved only in the Schrödinger picture needed solving in the Heisenberg picture, too. And even though collapse models of quantum theory ‘worked’ for most practical purposes, only Everett’s relative-state construction and corresponding Many-Worlds interpretation actually made sense of quantum theory. Combining these two explanatory improvements to traditional views of quantum theory—the Heisenberg picture over the Schrödinger picture and Everett’s relative-state construction over collapse models—Sam solved problems in physics’ theoretical edifice for which the older perspectives on quantum theory never could.

Quantum Time and the Fundamental Principle of Quantum Theory

In any classical theory, such as Newtonian mechanics, Maxwell’s (pre-quantum) theory of electromagnetism, or Einstein’s general relativity, physical quantities such as position, momentum, electric charge, or the metric tensor are all characterized by c-numbers (or c-number descriptors), which are the commonsensical, single-valued numbers (or functions more generally). Critically, c-numbers commute with each other, which means that the order in which you measure them does not matter. For example, it does not matter whether you first measure the velocity of a car and then its position or vice versa—the order in which you make the measurements will not change the numbers you read for the car’s velocity and position. At each moment in time, the car has only one possible value of velocity and position. The same goes for a classical electromagnetic system or a system described by general relativity.

One of the hallmarks of quantum theory is a radical departure from the intuitive logic of c-numbers. The theory tells us that all physical quantities (also called observables) are characterized by q-numbers (or q-number descriptors), which are not single-valued and whose order of measurement does matter in general. Mathematically, q-numbers correspond to matrices or operators. Whereas the velocity of an object in Newtonian mechanics might be 10 m/s, the velocity of an object in quantum mechanics might be 9 m/s, 10 m/s, and 11 m/s all simultaneously (see Box 2 for a discussion on what this means). Moreover, the order of measurement matters for quantities described by q-numbers. For example, imagine you prepare many instances of an electron, all prepared in the same initial state. For half of them, you measure their position first and their velocity second, and vice versa for the other half. Because the order of measurement matters, you will have different statistical outcomes for each subgroup of electrons.

According to Sam, the fact that all physical systems in quantum theory are characterized by q-numbers is the fundamental principle of quantum theory.

The Pythagoreans made a valiant attempt at describing the world and were right to consider it a principle that “All is number”, i.e. that the physical world ought to be describable by numbers. At the same time, their own parochial conception of numbers led them to conclude that only rational numbers were valid descriptors and that, for instance, irrational numbers (numbers that cannot be expressed as the ratio of two integers) were somehow illegitimate.

Many refinements of the Pythagoreans’ basic thesis have taken place over the course of thousands of years, as mathematicians and physicists have discovered ever broader classes of numbers that are both internally consistent and capable of describing the physical world.

Sam’s refinement is that, in light of his proposed fundamental principle of quantum theory, the Pythagorean mantra “All is number” should be replaced by: “All is q-number.” According to Sam, the fact that all physical systems in quantum theory are characterized by q-numbers is not merely a feature of the theory’s mathematical formalism, but its fundamental physical principle.

Until 1983, there had been an awkward violation to this principle—time. All of a system’s q-number-described observables had been assumed to evolve relative to a c-number-described time, ruining the universality of Sam’s principle. Moreover, this c-number time is necessarily unphysical, as it has no physical relationship with any of a system’s q-numbers. Instead, “This c-number time is…an unphysical backdrop against which quantum systems can change. In fact, c-number time is all but identical to Newton’s absolute time…”

This problematic c-number time may be contrasted with clock time, which is the straightforward and commonsensical measurement of the change of a clock. While c-number time is thought to ‘flow’ uniformly and independently of the behavior of quantum systems as a kind of god-like background of the universe, clock time is a definite, physical component of a system and, as Page and Wootters had shown in 1983, can be characterized by q-numbers.

As Sam writes, “To make clear the distinction between clock time and c-number time, consider a hypothetical situation in which all physical systems in the universe suddenly ‘freeze’ relative to c-number time. Clocks are physical systems and would be stationary during this ‘freeze’, which makes the ‘freeze’ and its duration completely undetectable to any observer in the universe. C-number time must therefore be just as unmeasurable as the duration of the ‘freeze’.”

The Page and Wootters resolution of the conflict between the fundamental principle of quantum theory and c-number time is limited by the fact that they developed their model using the Schrödinger picture of quantum mechanics, rather than the Heisenberg picture. While both formulations yield the same predictions, they are conceptually distinct. Moreover, Sam and others argue that the Heisenberg formulation is more fundamental—for example, only the Heisenberg picture makes explicit quantum theory’s consistency with the principle of locality (the idea that systems can only affect other systems in their immediate vicinity). Therefore, one could argue that, while Page and Wootters had successfully excised c-number time from the Schrödinger formulation of quantum mechanics, perhaps it could not possibly be excised from the Heisenberg formulation. In that case, perhaps Sam’s fundamental principle of quantum theory would be mistaken, after all.

Sam went on to demonstrate that, in fact, it is possible to replace c-number time with clock time in the Heisenberg picture. All of the conceptual and mathematical issues that a classical conception of time had brought to the quantum world could indeed be done away with.

In the conclusion of his paper, Sam drew attention to striking similarities between the clocks in his version of the Page-Wootters model and some fundamental properties of spacetime manifolds—mathematical objects that describe the geometry of regions of the universe in general relativity. He conjectures that the similarities are not a coincidence and that, in fact, “the properties of a [spacetime] manifold can be formulated in terms of q-numbers.” Sam’s conjecture, if true, drastically constrains the space of viable candidates for the long-sought solution to the problem of unifying general relativity and quantum mechanics.

Nor was it enough for Sam to think of quantum theory as ‘just’ an equation that described the evolution of physical systems over time—his fundamental principle of quantum mechanics is a deeper characterization about what the theory is all about than any single algebraic equation could possibly be. As he writes, “‘quantum theory’ is better thought of as a collection of theories that comply with this fundamental principle…The reason why quantum theory is better thought of as a set of principles is that it does not describe particular systems…Quantum theory is not about any of those systems in particular [atoms, photons, superconductors, quantum computers], but about all of them—or rather, it is about what kinds of theories can describe physical objects.”

Sam had been quite fortunate to earn his PhD under Vlatko, who had been laissez-faire with respect to what sort of research Sam could or could not pursue. Even so, the university itself had a different, more paternalistic philosophy.

“There was a stark contrast between Vlatko’s wonderful willingness to just let me work on anything I wanted and Oxford’s policies,” Sam remembers. “For example, every few months I’d have to regularly justify my research to a person in charge of research students. These online check-ins gave me mild anxiety—after all, what if I hadn’t made enough progress since our last meeting to satisfy him? Or what if he didn’t approve of what I had been working on?”

Everettian Relative States in the Heisenberg Picture

The so-called ‘collapse postulate’ was introduced by Werner Heisenberg in 1927, formalized by John von Neumann in 1932, and has been a hallmark in mainstream textbooks, university courses, and research groups ever since. The idea is that the principles and equations of quantum mechanics apply to a system until it is observed or measured. Before then, quantum mechanics seems to imply that the system has many values at once for its observables—for example, it would not have a single value for its position but rather a series of well-defined values, all equally real or equally probable. Once the system is observed or measured, though, the system ‘collapses’ such that only one of its many possible outcomes remains—the one that is observed.

The collapse postulate does not sit comfortably with the other principles of quantum mechanics. Not only do the rest of the principles already cohere to form an explanatory theory (i.e., the collapse postulate is not needed to make the theory ‘work’), but the collapse postulate in fact adds problems that had not existed: what counts as a measurement? How do we square the continuous, deterministic, and reversible nature of quantum theory’s central equation with the collapse postulate’s introduction of instantaneity (collapse takes no time to occur), indeterminism (whichever outcome the system collapses to is intrinsically random), and irreversibility?

Why ought we insist on collapse at all?

In his 1957 PhD thesis, Hugh Everett III considered what the world would be like if quantum theory was a truly universal theory, one that applied at all scales and whose equations did not collapse upon measurement.

As Sam and David Deutsch put it, “The arbitrariness, non-locality, vagueness, inelegance and anthropocentricity of this supposed exception [measurement events] has caused many misconceptions and confusions both in theoretical physics and in philosophy, despite the work of Everett (1973), including his relative-state construction, which eliminated the exception.”

Consider a particle that has been carefully prepared such that, should a scientist measure its spin, quantum theory tells us that he will measure ‘spin up’ with 50% probability and ‘spin down’ with 50% probability. Collapse models would describe the particle before having been measured as being in a superposition of the two possibilities. Upon measuring the particle as being in the ‘spin up’ state, collapse models would say that the superposition has collapsed and that the 50% probability of the particle being in the ‘spin down’ state has utterly disappeared—there is only the scientist, his measuring device, and the particle in its ‘spin up state’.

Everett’s analysis drops the collapse assumption altogether. Rather than insist that the scientist and his measurement apparatus are ‘too macroscopic’ to be quantum objects, he takes quantum theory to be a universal theory of Nature: just as the particle exists in a superposition of ‘spin up’ and ‘spin down’, so do the scientist, the measurement apparatus, and every other physical system in reality.

Everett realized that the particle does not collapse into either ‘spin up’ or ‘spin down’. Instead, half of the copies of the scientist measure ‘spin up’, while the other half measure ‘spin down’. So, after the measurement event, the state of the particle is ‘spin up’ relative to the state of the scientist being ‘measured ‘spin up’’ and the state of the particle is ‘spin down’ relative to the state of the scientist being ‘measured ‘spin down’’. Naturally, Everett called this scheme the Relative State Formulation.

As Sam writes, “His primary technical innovation was to analyse quantum measurement processes by treating not only the system being measured but also the measuring apparatus or instrument (or measurer, for short) jointly as [an] evolving quantum system.”

The implication was clear—reality consists of a mindbogglingly large number of branches (or universes, or worlds) that are constantly splitting and differentiating from each other (they occasionally interact as well, but such processes do not concern us here).

Everett’s advisor, John Wheeler, encouraged Everett to heavily edit down his consensus-defying thesis, as Wheeler was concerned over the physics community’s reaction. It would not be until 1973 that Everett’s uncut version saw the light of day, when Bryce DeWitt included it in his anthology, The Many-Worlds of Quantum Mechanics. It was DeWitt, not Everett, who would bring the phrase ‘Many-Worlds’ to the fore.

While Everett’s construction and its implications have solved a host of problems that the collapse postulate had introduced (and then some), until 2020 all such work had been confined to the Schrödinger formulation of quantum mechanics. The logic of the situation is similar to that of quantum time (see Box 1): if Everett’s construction could not be formulated in the more fundamental Heisenberg picture, then perhaps the Everettian approach and its implications of many worlds were not viable in the first place.

In 2020, Sam and David Deutsch successfully formulated Everett’s relative-state construction in the Heisenberg picture. Not only is their formulation explicitly local (as one would expect, since Heisenberg quantum mechanics is local), but the branching of universes occurs at the speed of light or less (also as one would expect if Einsteinian relativity and the Many-Worlds picture of reality are to one day unify).

Academia’s Boundary Conditions

After graduating with his PhD, Sam acquired a postdoctoral position in Lugano, Switzerland, working under quantum information scientist Stefan Wolf. Conjecture Institute Fellow Charles Bedard had been working under Wolf at the time, and he had gladly helped to earn Sam the position. While in Lugano, Sam would continue his work on the quantum theory of time, co-authoring a second paper on the subject alongside Simone Rijavec titled “Measuring time in a timeless universe”.

“It was a really nice group, and I enjoyed my many discussions with Charles,” Sam recalls. “I was able to continue working on problems that I was interested in.”

Following his time in Lugano, Sam took a second postdoctoral position under quantum information scientist Gilles Brassard at the Université de Montréal. It was here that he became close with another Conjecture Institute Fellow, Paul Raymond-Robichaud, who lived nearby.

“We saw each other quite a lot,” Sam says. “And he persuaded me that mathematics was not taken seriously enough by physicists. As a whole, physicists tend to use mathematics rigorously enough to get by, but Paul explained to me why physics would benefit from holding their work up to the standards of mathematicians when developing their proofs and theorems. Ever since, I’ve tried to do exactly that in my work.”

Sam was not merely persuaded by Paul’s general arguments, but also by Paul’s own work on formalizing the notion of local-realism. Sam and Conjecture Institute Fellow Maria Violaris are now applying Paul’s formulae to the physics of information. In particular, they are taking both Paul’s notion of local-realism and the constructor theory of information to solve problems having to do with differences between locally accessible information and locally inaccessible information.

Paul’s influence on Sam would also be felt in Sam’s chapter contribution to Alyssa Ney’s compendium, Local Quantum Mechanics: Everett, Many Worlds, and Reality, which he also wrote during his time in Canada. His chapter, ‘Restoring Locality: The Heisenberg Picture as a Separable Description of Quantum Theory’, explains how local realism is respected in quantum theory, despite appearances and the popular consensus. Something of a review, Sam walks the reader through the historical context of the problem, how it was eventually solved by Deutsch and Patrick Hayden in 2000, and Paul’s original contributions a couple of decades later.

Throughout his academic career, Sam experienced pressure by academic bureaucracy and funders alike to stick to a preset list of research topics. Any public funding he received during that time came with an expectation that he would satisfy some particular goal. But the questions Sam asks in his research do not yet have known solutions—that is why he pursues them in the first place! And if the solution cannot be known before the question is pursued, then neither can any arbitrary goal.

For example, Kuypers and Deutsch successfully provided a local account of branching using the Heisenberg picture, allowing them to describe universes that exist at remote locations from one another as separate systems with independent dynamics. But, strictly speaking, whether such a description was possible was not known beforehand, and so nobody could have known how this research would pan out. Conceivably, no local description of branching existed, in which case demonstrating that could itself have become a research project, which would have opened up further problems to work on. For example, it could have laid bare a fundamental discrepancy between the Schrödinger and Heisenberg pictures, in that in this hypothetical scenario one would support the relative-state construction while the other would not. This discrepancy would itself demand explanation.Now, this entire sequence of events would have been genuine progress in fundamental physics—and yet, most criteria that a funder would have attached to their funding of Sam, or guidelines insisted upon by the university system, could not have possibly been satisfied by both this outcome and the outcome that Sam actually achieved.

A New Quantum Mechanics: Textbook and Application

Since Sam became a Conjecture Institute Fellow in 2025, he has so far pursued two main projects.

The first is that he has continued to co-write a much-needed textbook on quantum mechanics alongside Deutsch and Conjecture Institute Senior Scientist Chiara Marletto. The Heisenberg picture and the Everett interpretation are both drastically underappreciated in the halls of academia, yet they have been and will continue to be vital for making progress in fundamental physics. The overwhelming majority of quantum mechanics textbooks downplay the Heisenberg picture and equivocate on the Everett interpretation at best and endorse an instrumentalist view of quantum physics at worst. They also tend to use unnecessarily complicated examples such as, say, the hydrogen atom and harmonic oscillators that require the reader to grok concepts and mathematical superstructures that are not intrinsic to the principles of quantum theory. Imagine if our best textbook on evolutionary theory today was written before the revolution of the selfish gene model, or if our best textbook on special relativity was written before the Minkowski spacetime was invented. That is precisely where we are with respect to quantum mechanics textbooks—there is scope for an update. To that end, Deutsch, Marletto, and Sam are writing a quantum mechanics textbook that fully incorporates the latest developments on the Heisenberg picture, the Everett interpretation, and quantum information theory.

Sam’s recent preprint, “Preserving Symmetry: Spontaneous Symmetry Breaking through Decoherence”, was written during his time as a Conjecture Institute Fellow. As is the theme in so much of his research, Sam addressed a longstanding problem in quantum physics by looking at it through a Many-Worlds lens. In condensed matter theory, the field in which Sam began his research career, there is a conventional explanation for how solid objects obtain a definite position. Solids are ‘translationally symmetric’–-when considered in isolation, they have the same energy regardless of where in space they are positioned; due to the physics of symmetries, this precludes them from being localised at any particular location, requiring them instead to be in a superposition that is spread out over all of space. Yet this is not how actual objects like tables and chairs seem to behave: they occupy definite locations.

The conventional solution is to introduce a classical environment that pins the system to a particular location. In the conventional account, known as spontaneous symmetry breaking, this classical environment is a mathematical artifact that is later removed by hand once the symmetry has been broken. Scientific realists might therefore object that the classical environment is doing real work, even if it is later brushed under the carpet.

As David Wallace had previously shown, the environment can instead be treated as a quantum system, restoring the symmetry so that the environment and the system are jointly completely spread out over space. Yet in different branches of the multiverse, the symmetry appears to be broken: a system can have a definite position in a particular universe relative to a quantum environment. Sam’s contribution was to develop a specific model of this for translational symmetry and derive experimental signatures that distinguish the conventional account from the fully quantum one.

“What Wallace—and, separately, Zeh—showed is that you can have your cake and eat it too,” Sam says. “We can preserve the symmetry at the level of the multiverse while breaking it within branches. This is a natural solution to the problems with the conventional account, but it requires both a realist interpretation of physics, in which the mathematical artifacts correspond to something real, and the Many-Worlds interpretation, because the whole description hinges on the multiverse being taken seriously. We need the other branches—the ones that we don’t see—to restore the symmetry.”

“It tackles a more conventional problem than my previous papers, which is a good thing to do every once in a while,” Sam says. “It’s still Many-Worlds, and I hope that it reaches a broad audience and maybe plants some Everettian seeds.”

It was one of the most fun papers that Sam has ever written. “It helped that, as a Conjecture Institute Fellow, I didn’t have to worry about fitting my work into exactly this or that bucket. Traditional academia had never granted me such creative freedom.”

The Courage to Take Our Existing Principles Seriously

One of the most famous outstanding problems in physics is the clash between quantum mechanics and general relativity, the theory of spacetime, gravity, matter, and interactions between them. Each is a beautiful, deep, and wide explanation in its own right, and, despite contradicting each other, each can be used without referencing the other in many contexts. For example, the physics of planetary motion can be modeled by general relativity without considerations of quantum mechanics, and the trajectory of an electron in an atom can be modeled by quantum mechanics without considerations of general relativity. Yet there are physical phenomena whose behavior cannot be explained by just one or the other theory—events such as the Big Bang, and objects such as black holes, are dominated by both gravity and by quantum phenomena such as interference and superposition. Until we unify these two pillars of fundamental physics, then, much of reality is necessarily left unexplained.

Now, much of the effort that has gone into trying to marry quantum theory with general relativity has taken most or all of the traditional views on quantum theory for granted: collapse models, the Schrödinger picture, and the fundamentality of c-numbers. But if Sam is right that literally all of these aspects have to be replaced, then perhaps most of the attempts to unify general relativity with quantum mechanics had been doomed from the start.

If we follow Sam in accepting Many-Worlds quantum theory, what does the conceptual problem between physics’ two pillars look like? Consider massive objects like the Sun and the planets that revolve around it. Everettian quantum theory tells us that they will all follow different trajectories (or positions at a given point in time) in different branches of the multiverse. General relativity, meanwhile, tells us that they must curve spacetime differently in each branch, since the exact shape of spacetime’s curvature depends on the distribution of mass. But general relativity is a theory of c-numbers, and so, as explained in Box 1, it cannot handle something like a superposition of different spacetime curvatures. Everettian quantum theory alone tells us that masses can exist in a superposition of trajectories (or positions) across the multiverse; general relativity alone tells us that masses curve spacetime. Taken together, they imply that spacetime must be able to exist in a superposition of different curvatures, but general relativity’s mathematical machinery of c-numbers cannot handle such a thing.

But Sam has already argued that we ought to drop c-numbers from physics, anyway. If c-number spacetime is the logjam preventing unification between quantum theory and general relativity, then Sam’s fundamental principle of quantum theory gives us a natural path forward: express spacetime in terms of q-numbers.

We have seen that time has been incorporated into quantum theory as an emergent property, initially by Page and Wootters and then by Sam. What remains, then, is to do the same for space.

As Sam summarizes in an upcoming essay for an original Conjecture Institute compendium, “Now that time is understood as emerging naturally from quantum theory, such that it does not have to appear as a classical parameter put in by hand, it becomes difficult to treat space any differently. Likewise, it is equally difficult to maintain interpretations of quantum theory that rely on external classical structures, as all non-Everettian interpretations do. On this view, the many-worlds interpretation is not an optional philosophical gloss but a natural completion of the quantum description of reality. We are still left with the quest of unifying quantum theory and gravity, which has hitherto eluded us. But these recent advances point to a clear path forward for how to give a quantum description of not just time but potentially also space and ultimately spacetime. Hence, it might be that what is needed to understand quantum gravity is not just new ideas, but also the courage to take our existing principles seriously.”

Sam’s insistence on first taking our current ideas seriously before endeavoring to think up radically new ones is a kind of radical conservatism—conservative, because he argues that our best ideas already have much more fruit yet to bear if only we are willing to accept them; and radical, because so many other scientists shy away our deepest theories’ implications.

In a world full of headlines touting ‘the latest theory of everything’, the most valuable unturned stone might be the theories we have had for a century. We just need the courage to take them seriously.

Summary

References

1. Chipkin, L. “The Revolution That Should Have Been—and Still Could Be.” Conjecture Institute Fellow Spotlight.
   The companion spotlight on Conjecture Institute Fellow Paul Raymond-Robichaud, whose local-realistic model of quantum theory informs Sam’s own work on locality.
   Read more →

2. Kuypers, S. (2022). “Developments in unitary quantum theory.” DPhil thesis, University of Oxford.
   Sam’s doctoral thesis, drawing together his work on the Heisenberg picture, Everettian branching, and the emergence of time into a single collapse-free account of quantum theory.
   Read more →

3. Kuypers, S. (2022). “On unorthodox qubits, with an application to the closed timelike curve problem.” arXiv:2205.02797.
   Drops the orthodox assumption that observables of distant systems must commute, and uses the resulting ‘unorthodox’ qubits to model closed timelike curves without paradox.
   Read more →

4. Kuypers, S. (2022). “The quantum theory of time: a calculus for q-numbers.” Proceedings of the Royal Society A 478(2263), 20210970.
   Builds a calculus in which time itself is a q-number, showing that the classical time parameter can be dispensed with in quantum theory altogether.
   Read more →

5. Kuypers, S. (2026). “Restoring Locality: The Heisenberg Picture as a Separable Description of Quantum Theory.” arXiv:2601.06522. Forthcoming in A. Ney (ed.), Local Quantum Mechanics: Everett, Many Worlds, and Reality (Oxford University Press).
   Sam’s contribution to the Ney volume: a walk through how the Heisenberg picture restores local realism to quantum theory, from Deutsch and Hayden’s 2000 proof to Raymond-Robichaud’s later work.
   Read more →

6. Kuypers, S. & Deutsch, D. (2021). “Everettian relative states in the Heisenberg picture.” Proceedings of the Royal Society A 477(2246), 20200783.
   Recasts Everett’s relative-state construction in the Heisenberg picture, giving a fully local account of how the multiverse branches.
   Read more →

7. Kuypers, S. & Rijavec, S. (2025). “Measuring time in a timeless universe.” Physical Review D 112, 063544.
   Shows that a clock in a Page-Wootters timeless universe can actually be read and synchronised with other clocks, rather than having to remain isolated and unreadable.
   Read more →

8. Ney, A. (ed.) (2026). Local Quantum Mechanics: Everett, Many Worlds, and Reality. Oxford University Press.
   The forthcoming compendium on locality and the Everett interpretation to which Sam contributed a chapter.
   Read more →

The paper back version of Bold Conjectures, Volume II: Essays Across Physics, is live! Kindle and audiobooks are forthcoming.

Get your copy here.

If we really do live in a quantum multiverse, then where does gravity fit into that picture? How does quantum theory solve the problem of time? How can the world be truly local, despite quantum theory’s notorious and bizarre properties? Can we ever settle the debate over whether entropy is subjective or objective? What is the relationship between probability and fundamental reality?

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Bold Conjectures, Volume II: Essays Across Physics consists of essays by physicists who explore and answer questions such as these. Drawing from their own careers as researchers, contributors to this entry in our Bold Conjectures series either explain cutting-edge developments in physics that most people are not yet aware of, or they clarify a key idea that popular culture tends to get wrong.

In this compendium, you’ll also read about novel ways by which we may test for quantum effects in biology, the history of string theory, the philosophy of effective realism, a new way to test the nature of gravity, and what constructor theory of theory may tell us about how to bring together general relativity and quantum theory.

Each essay may be read independently of the others, though often you will discover that ideas in one essay reinforce those in another. Like the human project that is science itself, Bold Conjectures, Volume II: Essays Across Physics has no singular starting point or end point but rather consists of a collection of explanations, advancements, and open problems that the reader is encouraged to explore as he or she sees fit.

What You’ll Find in Bold Conjectures, Volume II: Essays Across Physics

1. The Fate of Spacetime: What Many Worlds Means for Gravity, by Conjecture Institute Fellow Sam Kuypers

2. Controversial Coffee: Is Entropy Subjective? by Conjecture Institute Fellow Maria Violaris

3. Can Quantum Mechanics under the Copenhagen Interpretation Be Experimentally Tested? by Conjecture Institute Fellow Maria Violaris

4. Another Triumph of Locality: Colliding Histories Skew Handshakes, by Conjecture Institute Fellow Charles Bedard

5. Sherlock Photon: A Quantum Witness to Non-Classicality in Biology, by Conjecture Institute Fellow Giuseppe Di Pietra

6. Quantum Physics and General Relativity as Superinformation, by Conjecture Institute Senior Scientists Chiara Marletto & Vlatko Vedral

7. Towards the First Tests of the Nature of Gravity, by Conjecture Institute Fellow Antonia Weber

8. Beyond Elegance: String Theory and the Seduction of Mathematical Elegance, by Aditya Varna Iyer

9. The Quantum Solution to an Ancient Problem, by Simone Rijavec

10. Why We Can’t Understand Probability without Many-Worlds Quantum Theory, by David Wallace

11. Thermodynamic Witnesses of Entanglement: A New Way to Probe the Quantum World, by Mia Stamatova

12. Effective Field Theory and the Shape of Realism, by Abdullah Afzal & Hassaan Saleem

13. Gravity without Absolutes, by Julian Barbour

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Our Spotlight Article series highlights our Fellows’ history, contributions, interests, and ideas.

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Read or listen to the web version of our article about Dimitri and his work here.

Hollywood’s Optimistic Heir

A New Philosophy for Hollywood’s Successor

After New Specimen, Dimitri did not want to create a fourth short film that might only be incrementally better than his first three. He had grown comfortable, almost bored, with the tools he had used thus far. Now he wanted to jump into a new paradigm entirely: an immersive experience.

“I asked myself, ‘What’s next? What is the next step?’” Dimitri says. “But I quickly realized that the next step wasn’t the most interesting question. The more interesting question was: ‘What is the final step?’ And to me, the answer was immersive technology, specifically virtual reality. The idea that you could be inside a simulated world, inside a story, surrounded by its characters and environments, rather than just watching it in 2D from the outside. That was an exciting turning point for me. I felt like I was starting to work on something the future was pointing toward, and I wanted to play an active role in popularizing it.”

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Not only did Dimitri want to evolve the technological aspects of his craft, but he thought a lot about the content of his future stories. He was disappointed with the philosophical pessimism that had dominated Hollywood for decades, especially in his own genre of science fiction. Nearly every such film was about why humanity was doomed, or else it imagined some hellscape future: humanity at war with technology, humanity enslaved by machines, humanity at the edge of survival because of its own mistakes.

“That is not what I want to create,” Dimitri says starkly. “Those movies are always about the end of humanity as we know it. Maybe a biological weapon wiped most of us out, or maybe we’re stuck living indoors following a nuclear war and can no longer see the blue sky, or maybe much of humanity has transformed into cannibalistic zombies.”

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To be sure, Dimitri does not have interest in creating the mirror image of dystopian films. Stories of some problem-free utopia strike him as uninspiring and misleading, since there is no such thing. Rather, Dimitri is interested in protopian storytelling, tales of how humanity can and should make progress, regardless of current circumstances. Neither doomerism nor perfection would define Dimitri’s future work, but rather the possibility and desirability of progress.

Dimitri rightly recognizes that it is ideas, not any particular technology, that determine the fate of humanity. For example, if people one day find themselves fighting mindless robots, then humans will either create knowledge of a viable strategy for defeating, taking shelter from, neutralizing, or transforming the robots, or else they will fail to create such knowledge and possibly go extinct. Either outcome depends on the ideas that they may or may not create. As Dimitri thought about the philosophy that would define his future projects, he realized that, fundamentally, all human conflict is about conflicting ideas, and better ideas could always win out, in principle.

“Humans are never actually at war with machines,” he explains. “Rather, there are factions of different ideas that are at war with each other. So many interesting science fiction stories can be told through that lens: what principles are the different factions based on? Why do some factions ally and some go to war? How have these factions evolved over time? How might the conflicts resolve? Which factions foster progress, and which inhibit progress? It’s extremely rare for mainstream films to explore these sorts of questions.”

Putting aside the content of his philosophy, Dimitri came to appreciate that many of the biggest studios, such as Pixar, have a singular philosophy that drives all of their projects. While each individual movie produced by Pixar tells its own story, they all speak with a similar voice, and their messages for the world fall under one philosophical umbrella. Dimitri decided that it was time for his art to do the same, so that the world would instantly recognize a Dimitri Vallein creation as uniquely his, in pathos, ethos, style, and worldview.

Dimitri’s next film, The Day I Met You, will be the first visual manifestation of the philosophy that he wanted to see in the world. His most ambitious project to date, this twenty-minute film fuses a romantic tale with cutting-edge science, quantum computing and the multiverse in particular.

And he is well aware that the themes of progress and optimism grate against the tide. “Hollywood has become repetitive, pessimistic, and mechanical, addicted to the same franchises,” Dimitri says. “They’ve stopped developing bold new ideas that push the boundaries of our imagination. There’s an opportunity here for the new generation of filmmakers to create innovative films by harnessing optimism, new technologies, and our deepest scientific ideas. So this next project will focus on a hopeful future, one where scientific discovery moves civilization forward.”

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The Day I Met You is scheduled for a late 2026 release.

With the desire to create immersive films colored by philosophical optimism firmly set in his mind, Dimitri plotted his next move.

Ideas, Knowledge, and Dreams

Dimitri could have continued to operate completely on his own, but he decided that a company would be a far more effective vehicle for implementing his two-pronged innovative approach to film. In 2026, he founded Revery, which is currently in stealth mode. Part-storytelling company, part-technology company, Revery is already serving as a kind of creative incubator for Dimitri and his team as they play around with the latest software, 4D Gaussian splatting and VR, AI, and other algorithmic gadgets with which they can push their medium forward.

“Artists have been playing around with the latest technological tools since art began,” Dimitri says. “And the technology shapes the medium. We can’t tell the best stories if we’re not up to date on the best tools available.”

Revery’s first film is already in preproduction. Longer than any of Dimitri’s earlier solo ventures, Memetics will be about ninety minutes long. The script is currently in development, and production is just around the corner.

True to Dimitri’s newfound drive to explore philosophical optimism and the centrality of ideas, Memetics tells the story of a young man, Arya, who discovers a simulator that allows users to visit societies across the past, present, and future. Throughout the story, Arya learns about the ideas and memes that have shaped history, and he discovers why certain ideas protect humanity while others threaten the emergence of a better future.

Dimitri and his team are currently developing tools to make the story fully immersive, with NPCs embedded in the environment and trained on their own philosophical framework, allowing them to approach and speak directly to the viewer. The result may become a hybrid between film and video game.

Dimitri sees Memetics as a way to tell the world about important philosophical and scientific ideas they may not have heard about. “So many great ideas have been written about in books and articles,” Dimitri says, “but lots of them haven’t made it into mainstream culture. There’s too much logos in the way that those ideas are usually conveyed. With our immersive storytelling, we hope that the pathos we imbue our work with will make the ideas more interesting for laypeople.”

In particular, Dimitri wants to tell the world the fascinating truths about how ideas spread, why some ideas foster progress and others foster stasis, and how humanity’s knowledge grows in the first place. These are largely issues from the field of epistemology, the philosophy of knowledge. It is not well understood or appreciated in the culture despite being relevant in everything from morality to economics to science to beauty. With Memetics, Dimitri is taking what people might regard as dry ideas and bringing them to life.

At Revery, Dimitri and his team consciously package logos and pathos together to form what they call mythos. They hope that their films catalyze the spread of myth-like stories for the modern era that inject good and true ideas pertaining to the philosophy of optimism, progress, and humanism into the culture.

Memorable stories, whether fictional or true, have changed the world before. The tale of Newton discovering his law of universal gravitation after an apple fell upon his head is surely false, and yet it continues to spread and bring along with it actual facts about Newtonian physics. And in the realm of human affairs, Frederick Douglass’ written account in 1845 about his life as a former slave humanized the African-American experience to the free whites, significantly contributing to the abolition of slavery only decades later.

There is no reason that Dimitri and his team cannot do the same for optimism and other ideas about the nature of progress.

“A well-told story sticks with you after you watch it. Maybe you tell your friends about it, maybe it leads to fruitful discussion. That’s how we can change the culture for the better.”

Read or listen to the entire article about Dimitri and his work here.

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Conjecture Institute Handbook & Glossary

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But it should not be only American citizens who celebrate her birthday, as much of the rest of the world has benefited enormously from the American experiment. Others have emulated her institutions, adopted her inventions, and built upon her scientific breakthroughs.

Not everyone is American, but America—her example, her ideas, her ingredients for progress—is for everyone.

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Recent Talks and Discussions

Several Conjecture Institute Fellows and our Senior Scientists have recently given talks or participated in recorded discussions:

1. Fellow Ray Scott Percival at Conjecture Con Europe: Why False Ideas Persist Among Rational Agents
   

2. Fellow Tom Hyde at Conjecture Con Europe: An Aesthetic Theory of Romance
   

3. Fellow Maxime Desalle at Conjecture Con Europe: Doges, Futarchy, and Error-Correcting Governance
   

4. Fellow Maria Violaris at Conjecture Con Europe: Can We Communicate Across the Multiverse?
   

5. Fellow Sam Kuypers at Conjecture Con Europe: Problem Solving in the Foundations of Quantum Mechanics
   

6. Fellows Maxime Desalle and Sam Kuypers discuss the physics of the multiverse
   

7. Fellow Maria Violaris at The Royal Institution: Quantum Paradoxes: 5 Ways to Test the Multiverse
   

8. Senior Scientist Vlatko Vedral at the World Science Festival with Brian Greene: Can We Test Quantum Gravity?
   

9. Watch all talks from our recent conference, Advances in Physics
   

10. Fellow Arjun Khemani and economist and anarcho-capitalist David Friedman discuss the economics of longevity, ‘overpopulation’, cryptocurrency, Javier Milei, and more

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Conjecture Institute Handbook & Glossary

1. Read our Handbook to learn more about our mission, people, values, and worldview.
   

2. Peruse our Glossary to learn more about the concepts that make up our worldview.

If you want to keep up with everything we’re doing at Conjecture Institute, follow us on social media: X, LinkedIn, Facebook.

Every book, research paper, documentary, and event that we’ve delivered is because of donations from you and people like you. We have concrete plans for other projects that we want to deliver, but we can’t do it without your help. In addition to the perks we offer, know that we are eternally grateful for your support and will continue to grow Conjecture Institute in size, scope, and influence.

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Fellow Spotlight Article: Paul Raymond-Robichaud

Learn more about how Fellow Paul Raymond-Robichaud’s fulfilled Einstein’s dream here.

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Our Spotlight Article series highlights our Fellows’ history, contributions, interests, and ideas.

More to come.

Read or listen to the web version of our article about Paul and his work here.

“Paul’s theory is the single most important discovery in quantum foundations so far in the twenty-first century,” says Gilles Brassard FRS, co-inventor of quantum cryptography and quantum teleportation and recipient of the Wolf Prize, Breakthrough Prize, and Turing Award.

It is poetic justice that the mathematician under whom Conjecture Institute Fellow Paul Raymond-Robichaud began his PhD and learned mathematics, Gert Sabidussi, was a colleague of Albert Einstein at the Institute for Advanced Study in Princeton, New Jersey. The greatest physicist of the twentieth century famously opposed quantum mechanics twice over: he refused to accept a random world (“God does not play dice”), nor one that allowed for so-called “spooky action at a distance”. He thought that quantum physics could not possibly be complete, that some deeper, complete theory would recover a deterministic and local universe. The debate over local-realism—the philosophical position that the universe is made of real systems with real properties, and that those properties can only be influenced by nearby events noninstantaneously—has dominated the foundations of physics community for about a century.

At long last, Paul has vindicated Einstein’s dream.

Paul’s work should have ended the debate in favor of local-realism. The countless hours and hundreds of millions of dollars (possibly billions, depending on how you count) that go into ‘nonlocal’ research should have been redirected by now.

But the world has not yet heard of Paul’s work. The foundations of physics community is still arguing about what should be a settled matter, like post-Darwinian biologists still arguing over whether or not species share a common ancestor.

Conjecture Institute exists to change that.

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Constraints, Shallow and Deep

One of the most well-known applications of scientific theories is the derivation of predictions: the scientific community was amazed at Newton’s ability to predict the trajectories of the planets from the foundational tenets of his theory, for example. Such a result gives us the specific data about certain systems ‘for free’—they follow from direct application of the theory.

Less well-known is the rare but beautiful derivation of a universal statement from a theory’s core tenets. For example, one can prove from quantum computation that it is impossible (always and everywhere) to copy an unknown quantum state from one medium to another. This sort of result, deeper than the trajectories of the planets, tells us about the kinds of things we can and cannot do to any quantum mechanical system. We will immediately know ‘for free’ that, if a system is described by quantum mechanics, then it obeys this so-called no-cloning theorem.

And even less well-known, rarer, yet deeper than that is the discovery of an extremely general result that does not give us data about a particular system, nor even the kinds of things we can do to systems that obey a particular theory. The result I am referring to is a theorem that has the logic of a theory of theories—it gives us constraints that all theories, both known and unknown, must conform to. For example, the principle of conservation of energy is thought to be respected both by accepted theories like quantum mechanics and general relativity, but also by their eventual successors.

Conjecture Institute Fellow Paul Raymond-Robichaud discovered precisely such a constraint—under extremely general assumptions that we will review, all theories, both known and unknown, are expressible in entirely local terms. Spooky action at a distance and all other forms of apparently nonlocal action in the universe are just illusions or relics of how we express our theories. And, as we will see, Paul’s work did more than ‘just’ constrain all theories in physics that satisfy very general criteria—he showed how to find the underlying local reality behind such theories.

In a single stroke of mathematics, Paul should have put to bed all debates having to do with whether or not physics is local, and all lines of thought that insist on nonlocality. And yet there continue to be entire research groups dedicated to subjects such as ‘quantum nonlocality’ and entire careers dedicated to proposed theories of quantum gravity that presume nonlocality.

The Era-Defining Debate in Quantum Foundations

The debate began, not over locality, but over determinism and quantum theory’s completeness. At the famous Solvay Conference in 1927, Albert Einstein argued to the other founders of quantum mechanics that quantum mechanics must have been logically and physically inconsistent. Einstein thought that the theory as it was currently constituted implied a nondeterministic universe, and he refused to accept such a world. The titan of science would present thought experiments to his colleagues at breakfast that he had hoped would persuade them of quantum mechanics’ inconsistency, but Niels Bohr would rebut them by dinnertime, often by exposing details that Einstein had failed to account for.

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By the 1930s, Einstein had given up on proving quantum mechanics’ inconsistency, but he remained dissatisfied with the state of the theory. So he changed tack, now arguing that it was incomplete, and that ‘completing’ it would surely bring determinism back into the fold.

In 1935, Einstein, Podolsky, and Rosen (EPR) threw down the gauntlet with their famous paper, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” They considered two interacting particles that are separated by some distance—a state Erwin Schrödinger would soon dub “entangled.” Since measuring the position of one particle allowed an observer to instantly predict the position of the other, and measuring its momentum did the same for the other’s momentum, the authors presented a strict logical dilemma: either the quantum mechanical description of reality was incomplete, or incompatible quantities (like position and momentum) could not be simultaneously real.

Because the authors assumed that local-realism was true—that distant measurements cannot affect each other instantaneously, and that reality exists independent of observation—they argued that both position and momentum must have simultaneous reality. They concluded that quantum mechanics could not be the final story, and that a complete theory (one explaining quantum phenomena with an underlying local-realistic model) had to exist. The tension the authors highlighted has been known as the EPR paradox ever since.

The EPR paper was largely ignored by the mainstream physics community for almost twenty years, as most working physicists were satisfied with Bohr’s Copenhagen interpretation of quantum mechanics and the ‘shut up and calculate’ mindset when approaching problems.

A tiny minority of physicists who sympathized with Einstein and his colleagues posited that there must be a so-called ‘local hidden variables theory’ behind quantum mechanics that would bring determinism and locality back into physics (Einstein himself did not use the phrase, nor is it clear that he would have advocated for a hidden variables theory as the solution to the EPR paradox). The idea was that, if we only knew these hidden variables, then we could predict the outcomes of quantum mechanical experiments with certainty, that the bizarre unpredictability of quantum measurements would vanish.

Then, in 1964, John Stewart Bell demonstrated that any local hidden variables theory must conform to specific inequalities on correlations between measurements. He also showed quantum theory violated these inequalities. In other words, Bell proved that local hidden variables theories and quantum mechanics make mutually exclusive predictions that one can check via experiment. If the numbers did not violate ‘Bell’s bound’ or ‘Bell’s inequality’, then quantum mechanics would be shown to be false, and a local hidden variables theory could instead be viable. If the experimental results did violate Bell’s bound, then there would be no hope for a local hidden variables theory.

The first tests using Bell’s inequality came in 1972, when John Clauser and Stuart Freedman used photons to demonstrate that quantum mechanics indeed violated Bell’s bound. But critics pointed to loopholes in the experiment, thereby rendering the results inconclusive. In the next decade, Alain Aspect conducted more sophisticated experiments that were not exposed to the loopholes of his predecessors. Again, Aspect’s work seemed to confirm that quantum theory violated Bell’s bound. In 2015, three more independent experiments appeared to demonstrate the same, this time with even more advanced technology.

In 2022, Aspect, Clauser, and Anton Zeilinger won the Nobel Prize in Physics for their work on these era-defining experiments. Einstein’s insistence on local-realism seemed to lose to the idea that quantum mechanics and the wider physical world were, in fact, nonlocal, that spooky action at a distance was just a brute fact that we had to accept.

But evidence never speaks for itself. Many physicists, perhaps the majority, interpret the experimental results to mean that local-realism is untenable. They claim that, at most, followers of Einstein could hold onto the fact that locality and realism cannot hold simultaneously, but that one of them might still be true. Some side with locality over realism, others with realism over locality, and nearly everyone proclaims Einstein’s dream of local-realism dead and buried.

Paul discovered the simplest possible thought experiment that showed that, in fact, theories that violate Bell’s inequality are perfectly capable of conforming to local-realism—that the very meaning of a Bell inequality violation had been misinterpreted for all those decades. It is true that a system that violates Bell’s inequality cannot be described by a hidden variables theory, but that alone does not imply that the theory is not local-realistic!

“Paul’s work shows that there are other ways to be local-realistic than via a local hidden variables theory,” Brassard explains.

And that, as we will see, was the least of what Paul would go on to prove.

The debate that has dominated the foundations of physics community should have ended in 2021, when Paul published his complete results (he had published an earlier, slightly incomplete version in 2017).

It is the revolution that should have been—and still could be.

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Threefold Locality

Paul had begun his academic career in 2007, pursuing a bachelor’s degree at the Université de Montréal with the intention of becoming a pure mathematician (as opposed to an applied mathematician). Under the advisory of Sabidussi, Paul studied a wide range of topics, such as group theory, discrete mathematics, and graph theory. He wanted to understand the nature of mathematics and so was quickly attracted to foundational subfields, such as set theory, logic, and philosophy of mathematics.

“Mr. Sabidussi invited me to visit him every week to discuss mathematics and work on problems,” Paul says. “He taught me all kinds of theorems. He’d also tell me tales of his encounters with Gödel, Einstein, and other legends from a forgotten era. My private sessions with Sabidussi made me feel so alive for mathematics.”

Paul eventually realized that understanding the foundations of mathematics would require that he learn the foundations of computer science, including the theory of computation and formal languages.

By 2009, Paul’s interest in computer science had driven him to attend Brassard’s course on classical (pre-quantum) computation. Paul would switch his advisor from Sabidussi to Brassard in 2011.

In 2012, he signed up for Brassard’s course on quantum information and computation, and it is here where the story of his proofs really starts.

“Gilles impressed upon me that information is physical,” Paul says. “I realized that to understand the nature of computation and information, learning about classical computers would not be enough; I needed to study quantum computation. And to understand that deeply, I realized I had to study quantum foundations.” Thinking back on his path, Paul adds that “things came full circle. It turned out that my unusual background in algebra and the foundations of mathematics gave me the tools I needed to understand the foundations of physics, and in particular the foundations of quantum theory.”

During a particular lecture, Brassard presented the standard argument for why Nature must be nonlocal: quantum theory makes it possible to implement a so-called nonlocal box with about an 85% probability of success, whereas a local hidden variables theory would allow for only a 75% probability of success (the logic of the argument is similar to that of Bell’s theorem as outlined earlier).

A few days after the lecture, Paul approached Brassard and told him that he had created a toy model that proved Brassard wrong—Paul had invented a universe in which a nonlocal box could be implemented to have a 100% success rate even though Paul’s world was entirely local-realistic.

“It was one of the most magical moments of my life,” Brassard says. “Paul’s counterexample changed me profoundly for the better. I’d been teaching and explaining something that simply wasn’t true, that quantum theory was necessarily nonlocal. In hindsight, I was just repeating what everyone else was saying. Once Paul showed me that I’d been wrong, it became my duty to get things straight, not just for myself but for anyone who’d listen.”

Paul’s Local-Realistic World of Nonlocal Boxes

In Paul’s world, Alice and Bob each have a nonlocal box, and each box has two buttons—0 and 1. If Alice pushes either button, her box will flash either green or red with equal probability, regardless of what Bob pushes. Bob faces the same situation. If both Alice and Bob push 1, then they will always see different colors. Any other combination of buttons results in Alice and Bob seeing the same colors.

This cannot be explained by the boxes being preprogrammed, i.e. by a local hidden variables theory. Why not? Any box that outputs the proper results over 75% of the time is not describable by a local hidden variables theory. In Paul’s toy model, the results are correct 100% of the time.

Imagine that Alice and Bob are with their boxes, and whenever Alice pushes an arbitrary button, she splits into two Alices. One has seen green and the other has seen red. These two Alices will never talk to each other and do not even know that the other exists. The split ripples through space but not faster than light, hence locality is respected. In particular, there is no instantaneous effect on Bob whatsoever.

What if Bob pushes an arbitrary button? Then he splits and, again, it is purely local and does not affect Alice.

Now there are two Alices and two Bobs, all independent from one another.

What if Alice and Bob decide to meet and compare their results? The (entirely local) rules determine which version of each person interacts with which version of the other person. For example, if Alice had pushed 1 and Bob had pushed 0, then ‘Alice who saw red’ will see only ‘Bob who saw red’ and ‘Alice who saw green’ will only see ‘Bob who saw green’. This proves that it is wrong to claim that any world that cannot be described by a local hidden variables theory is nonlocal.

Not being describable by a local hidden variables theory, Paul had shown, did not imply that a theory was nonlocal:

1. It is possible to construct a world that cannot be described by local hidden variables and is entirely local-realistic.

“I was new to physics,” Paul says. “This was my first course in quantum theory. In less than a week, I learned about nonlocality and came up with a way to make the ‘nonlocal’ box local, after all. And my proof is extremely mathematically simple.”

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“I listened, and in a few minutes, my entire perception of reality shattered,” Brassard recalls. “It was so straightforward. Once you see it, it’s impossible to believe anymore that a violation of Bell’s inequality implies nonlocality.”

Before Paul’s proof, nearly everyone had taken that implication for granted. But Paul’s imaginary world demonstrated that the scientific community’s assumption was flat-out false.

Paul and Brassard then coauthored a paper presenting Paul’s ideas, but his resurrection of locality had only just begun. After all, while showing that a local-realistic world can give the superficial appearance of nonlocality, Paul had not yet applied his thinking to the actual world, which is described by quantum theory.

Even after understanding Paul’s initial proof, one could cling to the possibility that quantum theory was nonlocal, taking refuge in the fact that, although a Bell test could no longer be taken to be a guarantor of its nonlocality, perhaps quantum theory was nonlocal regardless.

A proof of concept is nice. An actual solution for quantum theory is even better.

“It was clear that the path would be similar,” Paul recalls.

Having already made a monumental contribution, Paul decided to explore the topic of locality for his PhD (he would complete his thesis in 2017). He learned more quantum theory and then decided to generalize what he had done in his toy universe to the actual quantum world in which we live.

“I barely know about electrons and other common quantum systems,” Paul says. “The version of quantum theory that I know is quite different from the ones physicists know. Mine is more abstract, mathematical.”

Paul was burning to take the natural next step, which was to carry over his local-realism proof from his toy model to actual physics.

But before he could dive fully into his problem, Paul was forced to endure a “horrible” predoctoral exam. “My committee wanted me to do a literature review,” he recalls. “I had to write about things that did not exist. There was no literature [on locality in quantum theory] beyond the paper by Deutsch and Hayden [more on their work below]. I didn’t care about the committee’s request, since I’m not a historian. I wanted to work on my problem, and what could I possibly write for them? The problem was still undefined, and no clear mathematics on it had existed before I approached it.”

Paul was given an impossible bureaucratic task that he chose not to take up. Rather than write up any historical comments that the committee had requested, he wrote a long rant about why quantum theory was local. They could have failed him, but they ultimately decided that he should not waste any more time on such inert reports.

“I do not want to play these games,” Paul says.

Instead, he played the real game of ideas—he continued to solve problems.

Paul proved that:

2. There exists a local-realistic model of quantum theory, even though it violates a Bell inequality.

Initially, Paul had not realized that physicists David Deutsch FRS (father of quantum computing and recipient of the Dirac Prize and Breakthrough Prize) and Patrick Hayden had already demonstrated this, since the literature hardly cited their result. He would learn about their work as he developed his own proof. Still, Paul strengthened their earlier results by formalizing the notion of local-realism.

“I wanted to prove it in my own way, because the math used by Deutsch and Hayden was underdeveloped,” Paul says. “Their proof was intuitively correct, but it was missing some details that I filled in. My proof used different math than they did as well, so mine was different from theirs. I also developed a mathematically precise definition of local-realism, which had been lacking in the literature.”

It was humanity’s first formal and complete proof that quantum theory is local-realistic.

Paul realized that he could abstract some elements of his proof away such that it would apply not only to quantum theory but in general. Armed with the mathematically precise definitions of his own making, he proved that:

3. Any theory with reversible dynamics and a no-signalling theorem is necessarily local-realistic.

More than that, Paul’s mathematical machinery takes in such a theory and outputs a model that shows precisely how the theory is local-realistic. In this sense, Paul’s result is even more informative than a ‘mere’ constraint like the principle of conservation of energy.

Deutsch and Hayden had previously demonstrated that the flow of quantum information is local, but they did not fully explain why this must be the case. Paul’s general proof, on the other hand, explained precisely which elements of quantum theory are necessary to establish its locality—namely, that its dynamics are reversible and that it is a no-signaling theory (more on this below).

From the moment Paul attended Gilles’ lecture, it would take Paul a full nine years to develop all of the mathematical details he would need to complete his three-layered proof of local-realism. Because he was in the process of creating new fundamental knowledge that had never before existed, there was no way to predict where his work was heading. There were even long stretches of time when Paul did not make any progress or otherwise went down blind alleys. Neither Paul nor any checkbox-insistent administrator could have possibly known just how long Paul’s research would take, whether or not it would bear any fruit, or if the final outcome would be ‘worth’ any particular grant. Yet with only the freedom to pursue his interests, Paul delivered.

“Many people didn’t consider me ‘productive’ during that time,” Paul says. “Often I would just learn about this or that piece of math that had nothing to do with local-realism. I’d go months without writing anything. I would just explore fundamental mathematics for the fun of it. Often I’d get lucky, and something I’d learned ended up being useful in my work, as happened with algebra.”

It is worth noting that the output of the titans of science would not survive today’s publish-or-perish culture. Charles Darwin took two decades to publish his theory of evolution by natural selection, and Isaac Newton needed about as much time before releasing his own theory of classical physics. Had they been pressured to release their work at arbitrary times and in arbitrary chunks, the world may have rejected their work as being too half-baked—which it would have been, precisely so as to appease those who demand mechanical output over genuine solutions.

“Paul is determined to find the truth,” Brassard says. “I’m very proud to have been by his side during all those years and beyond. My role was and is to advocate for his world-changing ideas, even when too many people are still not ready to hear them.”

Paul is incredibly grateful for Brassard’s mentorship and allieship. “I don’t think my work would have been possible without such a friend,” he says. “To have someone who was willing to listen to new ideas and change his mind accordingly, and someone who’d stand by my ideas even though they’re unpopular, meant everything to me.”

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Why the Silence?

“The results were crickets from the mainstream,” says Paul about the period after he published his work.

Science has been here before. Mendel’s theory of genetics was published in an obscure journal in the 1870s and was ignored or considered irrelevant as it pertained to Darwin’s theory of evolution. Only about 35 years later was it rediscovered, integrated into Darwinism, and accepted by the mainstream. In 1912, Alfred Wegener proffered the theory of continental drift, or plate tectonics, but geologists considered it to be nonsense. It gained acceptance only about four decades later.

Mendel was ignored not only because his work was published in obscurity, but also because his mathematical approach was little appreciated by scientists of the day, and because his theory conflicted with Darwin’s theory of blended inheritance. Wegener was dismissed because he lacked both an explanatory mechanism and evidence in favor of his theory of continental drift. When both were uncovered, the communal tide turned in his favor.

Paul’s case is closer to Mendel’s than to Wegener’s: Paul’s work contradicts certain ideas that today’s scientists take for granted. Why, then, can we be so confident that Paul is correct and the popular consensus is wrong?

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Because Paul’s work takes quantum mechanics seriously, while his critics do not.

The central equation of quantum theory, the so-called Schrödinger equation, is inherently universal—by its nature, it applies to all systems. Just as Darwin’s theory of evolution logically implies that humans and gorillas share a common ancestor, the Schrödinger equation’s universality implies that our world is but one of many, often in parallel and sometimes interfering with each other. And, just as there was a sociological backlash to the implications of Darwin’s theory with respect to what it told us about human origins, so too there has been a backlash to quantum mechanics’ implication that reality is far vaster than Newton would have thought.

This is not the place for a full defense of the so-called ‘Many Worlds’ interpretation of quantum mechanics, other than to say that it is the only interpretation of quantum theory that does not introduce arbitrary cutoffs into an otherwise seamless, universal, and nonarbitrary framework.

“In my work, I took for granted that quantum mechanics is unitary [that its equations don’t stop applying at some arbitrary scale],” Paul says.

There is also the awkward sociological fact that entire institutes, billion-dollar grants, and thousands of tenure-track careers are currently built on the premise of quantum nonlocality and entanglement as ‘spooky action’. Paul’s proof effectively zeroes out the value of their life’s work. To most researchers who depend on this ecosystem, accepting Paul’s results means accepting that their work is null and void.

Paul’s Maxwellian Moment

As we’d mentioned, Paul also solved another problem in the foundations of physics: until his work, no one had ever offered a mathematically precise definition of what scientists quite meant by local-realism, the intuitive idea that physical systems with definite properties can only affect the definite properties of other physical systems in their vicinity. Famously, Newton’s theory of gravity appeared to violate the tenet of local-realism—for example, his theory said that the Sun’s gravitational field should influence the Earth instantaneously, regardless of the distance between them. Newton himself recognized this as a problem, and Einstein’s theory of gravity would resolve it over two centuries later.

Still, although most scientists have long taken local-realism seriously as a constraint of Nature, it had been more of a qualitative intuition than a rigorous mathematical statement. With some good fortune, scientists can make progress with unrefined intuitions when dealing with particular examples, but eventually one’s luck runs out. For example, Michael Faraday described electromagnetic fields as lines of force and developed visualizations of how magnetism and electricity interact, but he did not explain the relevant physics in greater quantitative detail, which prevented further progress. James Clerk Maxwell took Faraday’s qualitative description and created a robust set of equations that not only captured the dynamics of electromagnetic fields but also unified electricity, magnetism, and light—something that Faraday’s vague pictograms could have never done.

The notion of local-realism had been in roughly the same state as Faraday’s electromagnetic fields before Paul had his Maxwellian moment. Paul clarified the distinction between local-realism and non-signalling (in so doing, Paul also greatly improved upon the meaning of non-signalling, which had previously been in poor shape): the former is a characteristic of the physical world independent of observers, while the latter is a statement about the constraints on what can be observed. Non-signalling in quantum mechanics, for example, means that one cannot use quantum entanglement to transmit information faster than the speed of light.

Taking terminology from Immanuel Kant, Paul distinguished between the noumenal world—the world as it exists, regardless of any observational constraints—and the phenomenal world—the world that can be observed. Local-realism was a noumenal concept, while non-signalling was a phenomenal concept. More specifically, a system’s noumenal state is its complete and local description, while its phenomenal state is a complete description only of what is locally observable—what is accessible by experiment. Crucially, a system’s noumenal state and phenomenal state are in general distinct.

One of the counterintuitive implications of Paul’s more mathematically precise version of local-realism is that if a physical theory forbids any observable nonlocal effects, then the theory is necessarily local-realistic (and vice versa). Before Paul’s work, one could have argued that, even if observation of nonlocality was out of the question, maybe there were still nonlocal effects that were real but beyond the reach of our measuring devices. Paul showed that that is false: the impossibility of observing nonlocality under a given theory immediately implies that the theory is local-realistic.

More than that, Paul’s work shows how to take the phenomenal world according to some theory and produce ‘for free’ the corresponding and underlying local-realistic noumenal world. Paul had solved the problem of determining the noumenal world, the world as it is, for any theory of physics—not just quantum theory, but future theories that we have yet to discover (provided that they are also no-signalling theories).

The EPR paradox has been resolved. Paul has settled the ninety-year-old debate in favor of Einstein’s dream of a local-realistic world. Research into ‘nonlocal physics’ is now moot. All that remains is to tell the world.

“I was flabbergasted by his result, which has made much existing (and continuing!) work in quantum foundations obsolete,” says Deutsch. “But it has received grossly insufficient recognition from the community. They still don’t know what hit them and are still ingeniously discussing nonexistent things like ‘quantum nonlocality’ (and ‘the measurement problem’) in ever greater detail.”

A Free Mind

After his PhD, Paul entered the job market for a postdoctoral position. The job offerings were slim, and those that were available required far too much administrative work that did not interest Paul. Moreover, most of the job postings were for the kind of work that Paul’s discoveries had already rendered moot.

“So many of the job offers I saw are for quantum nonlocal researchers, or to work on ideas that have already been developed,” Paul notes. “Many of them insist that applicants should have already published many highly cited papers. But that’s quite difficult when your papers prove everybody wrong!”

Eventually, Paul discovered an institute whose president had initially let him work on anything he found interesting—a nonnegotiable for Paul. Unfortunately, things would take a bad turn.

“The Board of Directors fired the president,” Paul recalls. “They wanted something very different—whatever was popular, rather than research done for its own sake.”

Because Paul’s work is so deep, it is not the kind of ‘product’ that can easily survive a publish-or-perish or follow-the-hype culture.

“Paul never accepts anything just because it’s in the mainstream,” Brassard says. “He is willing to rebel against the scientific establishment and has one of the freest and most independent minds I’ve ever encountered. He never accepts a mathematical theorem without checking the proof behind it. Nor does he accept a piece of science or mathematics just because it’s been published in a journal.”

When Conjecture Institute discovered Paul, he had been living in a room inside of a rental and eating lentils to save money. He had been jobless for over a year, as he refused to take a job that would make him publish pointless papers or engage in wasteful administrative work. For Paul, it was freedom to do, think, and research on his own terms or bust.

“It was a difficult and anxious period for me,” Paul says. “I’m enormously grateful for Conjecture Institute finding and helping me when they did.”

We saw Paul’s work for what it was—nothing short of revolutionary. That, and a letter of recommendation from Deutsch, convinced us that Paul was precisely the kind of researcher we want to support—one who takes our best ideas seriously and carries them forward, wants to pursue ideas for no other reason than that he finds them fascinating, and puts no weight on the popularity of an idea or lack thereof. We do not care how many papers he publishes nor how he chooses to spend his time. We are confident that Paul will continue to quench his thirst for deep mathematical truths about the nature of reality, knowing that his next great discovery is literally unpredictable.

References

1. Aspect, A., Dalibard, J. & Roger, G. (1982). “Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers.” Physical Review Letters 49, 1804. https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.49.1804

   Summary: A refined Bell test that switched the measurement settings while the photons were already in flight, closing that loophole and again confirming the quantum violation.

2. Bell, J. S. (1964). “On the Einstein Podolsky Rosen Paradox.” Physics 1, 195. https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf

   Summary: Proves that any local hidden-variable theory must obey strict statistical inequalities which quantum mechanics predicts will be violated.

3. Brassard, G. & Raymond-Robichaud, P. (2019). “Parallel Lives: A Local-Realistic Interpretation of ‘Nonlocal’ Boxes.” Entropy 21(1), 87. https://www.mdpi.com/1099-4300/21/1/87

   Summary: Constructs an imaginary world that is fully local and realistic yet cannot be described by local hidden variable theories, debunking the assumption that a Bell violation implies nonlocality.

4. Brassard, G. (2023). “Profile of John Clauser, Alain Aspect and Anton Zeilinger: 2022 Nobel Laureates in Physics.” Proceedings of the National Academy of Sciences 120(23), e2304809120. https://www.pnas.org/doi/pdf/10.1073/pnas.2304809120

   Summary: A profile, by Gilles Brassard, of the three 2022 Nobel laureates whose Bell-test experiments anchor this debate — arguing that such violations do not establish nonlocality.

5. Deutsch, D. & Hayden, P. (2000). “Information Flow in Entangled Quantum Systems.” Proceedings of the Royal Society A 456, 1759 (arXiv:quant-ph/9906007). https://arxiv.org/pdf/quant-ph/9906007

   Summary: Argues, in the Heisenberg picture, that quantum information actually flows locally through entangled systems — an early proof showing that entanglement need not imply nonlocality.

6. Einstein, A., Podolsky, B. & Rosen, N. (1935). “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Physical Review 47, 777. https://cds.cern.ch/record/405662/files/PhysRev.47.777.pdf

   Summary: The founding “EPR” argument that under the assumptions of local-realism, quantum theory was incomplete, and launched the quest for a complete theory.

7. Freedman, S. J. & Clauser, J. F. (1972). “Experimental Test of Local Hidden-Variable Theories.” Physical Review Letters 28, 938. https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.28.938

   Summary: The first laboratory test of Bell’s inequality, using entangled photons, finding the violation quantum mechanics predicts.

8. Giustina, M. et al. (2015). “Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons.” Physical Review Letters 115, 250401. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.250401

   Summary: One of three landmark 2015 experiments to violate a Bell inequality while simultaneously closing loopholes, with overwhelming statistical significance.

9. Raymond-Robichaud, P. (2017). “The Equivalence of Local-Realistic and No-Signalling Theories.” arXiv:1710.01380. https://arxiv.org/pdf/1710.01380

   Summary: Proves the general theorem that every no-signalling theory with reversible dynamics admits a local-realistic model, supplying mathematically precise definitions of both notions.

10. Raymond-Robichaud, P. (2021). “A Local-Realistic Model for Quantum Theory.” Proceedings of the Royal Society A 477, 20200897. https://royalsocietypublishing.org/rspa/article/477/2250/20200897/82347

    Summary: Gives a complete, rigorous local-realistic model of quantum theory itself, showing how to construct the underlying local reality behind quantum phenomena.

Daniel Gilbert is Founder & CEO of Brainlabs, a 1,000-person media agency he started in 2012 from his parents’ attic.

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The founding thesis: better decisions come from testing ideas against reality, not trusting intuition or consensus.

By hiring mathematicians, programmers, and engineers alongside marketers, Brainlabs pioneered an error-correction approach to marketing that earned #1 on the Deloitte Fast50 Tech Track and multiple Agency of the Year awards.

Dan is the author of Don’t Be a Midwit: How to Learn Good Judgement at Work So That AI Doesn’t Replace You.

Published with Conjecture Institute and built on Popper and Deutsch, the book covers how to form conjectures, test them honestly, and kill the ones that don’t survive contact with reality.

It tries to do in one book what most business books split across five: case studies, theory, anecdotes, practical frameworks, and a reading guide.

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Today his focus is almost entirely on AI implementation.

Brainlabs is rebuilding itself as AI-native: not stacking AI on top of how things used to work, but changing how the work gets done.

Skills replacing manual steps, agents running complex systems, practitioners moving faster and closer to clients.

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Learn more about Dan and his upcoming book: dangilbert.ai.

Our Next Conference: Advances in Physics

Our online conference, Advances in Physics, will take place on June 17th.

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What does it mean to take our best theories in physics seriously? What do they tell us about what the world is really like?

This conference gathers researchers who pursue these questions in quantum gravity, foundations of quantum mechanics, and constructor theory.

Attendees are welcome to ask questions, and those who register are free to come and go as they please.

The entire event will be recorded and uploaded to YouTube.

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If you cannot make it but want to ask a speaker a question, please email your question to logan@conjectureinstitute.org.

Speakers and talk titles:

1. Professor of Philosophy of Physics at the University of Oxford and Emeritus Fellow of Merton College Simon Saunders - Probability in Everettian Quantum Theory
   

2. Physicist at the University of Oxford and Conjecture Institute Senior Scientist Chiara Marletto - The Science of Can and Can’t
   

3. Physicist at the University of Oxford and Conjecture Institute Senior Scientist Vlatko Vedral - Portals to a New Reality
   

4. Research Director at INRIM in Turin Marco Genovese - Bell Inequalities: From Conceptual Impact to Technology
   

5. Associate Professor of Physics at Saint Anselm College and Adjunct at Dartmouth College Alexander R. H. Smith - Schrödinger’s Clock: How Time Ticks in the Quantum Realm
   

6. Quantum physicist and Conjecture Institute Fellow Charles Bédard -Explaining Bell Locally
   

7. Quantum physicist and Conjecture Institute Fellow Sam Kuypers -Measuring Time in a Timeless Universe
   

8. Quantum physicist, science communicator at Oxford Quantum Circuits, and Conjecture Institute Fellow Maria Violaris - Is it possible to communicate across the quantum multiverse?
   

9. Professor of Physics at the University of California, Berkeley, and Director of the Leinweber Institute for Theoretical Physics Yasunori Nomura - Eternally Inflating Multiverse and Many Worlds in Quantum Mechanics: Same Concept?
   

10. Professor of Physics at Chonnam National University in Gwangju, South Korea Kicheon Kang - Aharonov-Bohm, Locality, and Quantum Electrodynamics
    

11. Experimental quantum physicist at INRIM in Turin Fabrizio Piacentini - Novel Frameworks in Quantum Mechanics: The Emergence of Constructor-Based Irreversibility
    

12. UKRI Future Leaders Fellow, Visiting Researcher at the University of Oxford, and CEO and co-founder of Allos AI Aditya Iyer - Why We Must Try to Quantize Gravity
    

13. DPhil candidate at the University of Oxford Lodovico Scarpa - On the emergence of irreversibility in isolated quantum systems

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1. Read our Handbook to learn more about our mission, people, values, and worldview.
   

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Every book, research paper, documentary, and event that we’ve delivered is because of donations from you and people like you. We have concrete plans for other projects that we want to deliver, but we can’t do it without your help. In addition to the perks we offer, know that we are eternally grateful for your support and will continue to grow Conjecture Institute in size, scope, and influence.

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The Sovereign Child has now been translated into Chinese, Persian, and French. A Spanish edition will be available soon.

Our Next Conference: Advances in Physics

Our online conference, Advances in Physics, will take place on June 17th.

Register here.

What does it mean to take our best theories in physics seriously? What do they tell us about what the world is really like?

This conference gathers researchers who pursue these questions in quantum gravity, foundations of quantum mechanics, and constructor theory.

Attendees are welcome to ask questions, and those who register are free to come and go as they please.

Share

The entire event will be recorded and uploaded to YouTube.

If you cannot make it but want to ask a speaker a question, please email your question to logan@conjectureinstitute.org.

Speakers and talk titles:

1. Professor of Philosophy of Physics at the University of Oxford and Emeritus Fellow of Merton College Simon Saunders - Probability in Everettian Quantum Theory
   
   

2. Physicist at the University of Oxford and Conjecture Institute Senior Scientist Chiara Marletto - The Science of Can and Can’t
   
   

3. Physicist at the University of Oxford and Conjecture Institute Senior Scientist Vlatko Vedral - Portals to a New Reality
   
   

4. Research Director at INRIM in Turin Marco Genovese - Bell Inequalities: From Conceptual Impact to Technology
   
   

5. Associate Professor of Physics at Saint Anselm College and Adjunct at Dartmouth College Alexander R. H. Smith - Schrödinger’s Clock: How Time Ticks in the Quantum Realm
   
   

6. Quantum physicist and Conjecture Institute Fellow Charles Bédard - Explaining Bell Locally
   
   

7. Quantum physicist and Conjecture Institute Fellow Sam Kuypers - Measuring Time in a Timeless Universe
   
   

8. Quantum physicist, science communicator at Oxford Quantum Circuits, and Conjecture Institute Fellow Maria Violaris - Is it possible to communicate across the quantum multiverse?
   
   

9. Professor of Physics at the University of California, Berkeley, and Director of the Leinweber Institute for Theoretical Physics Yasunori Nomura - Eternally Inflating Multiverse and Many Worlds in Quantum Mechanics: Same Concept?
   
   

10. Professor of Physics at Chonnam National University in Gwangju, South Korea Kicheon Kang - Aharonov-Bohm, Locality, and Quantum Electrodynamics
    
    

11. Experimental quantum physicist at INRIM in Turin Fabrizio Piacentini - Novel Frameworks in Quantum Mechanics: The Emergence of Constructor-Based Irreversibility
    
    

12. UKRI Future Leaders Fellow, Visiting Researcher at the University of Oxford, and CEO and co-founder of Allos AI Aditya Iyer - Why We Must Try to Quantize Gravity
    
    

13. Phil candidate at the University of Oxford Lodovico Scarpa - On the emergence of irreversibility in isolated quantum systems

Conjecture Institute Handbook & Glossary

1. Read our Handbook to learn more about our mission, people, values, and worldview.
   

2. Peruse our Glossary to learn more about the concepts that make up our worldview.

If you want to keep up with everything we’re doing at Conjecture Institute, follow us on social media: X, LinkedIn, Facebook.

Every book, research paper, documentary, and event that we’ve delivered is because of donations from you and people like you. We have concrete plans for other projects that we want to deliver, but we can’t do it without your help. In addition to the perks we offer, know that we are eternally grateful for your support and will continue to grow Conjecture Institute in size, scope, and influence.

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Taking Children Seriously

Watch Cofounder Aaron Stupple talk to Advisor Peter Boghossian about why the moral status of people, including children, is not an empirical question.

Physics

1. Read Senior Scientist Chiara Marletto, Fellow Giuseppe Di Pietra, and Salvator Raia’s new paper, Role of nonclassicality in mediated spatial quantum correlations: “Our results provide a general framework for witnessing nonclassicality of a system via its intrinsic properties, independently of the specifically chosen interaction dynamics.”
   

2. Read Fellow Maria Violaris’ comments to Physics World about quantum computing hardware developments: “The space-efficient [architecture] is mostly based on assuming aspects that have been demonstrated to work individually in state-of-the-art academic labs...meanwhile, the time-efficient one relies on more speculative assumptions that need future innovation.”
   

3. Read Fellow Paul Raymond-Robichaud’s paper, The equivalence of local-realistic and no-signalling theories.

Civilization

1. Advisor Daniel Hannan: “As we lose sight of what the Anglosphere has achieved, we risk losing the institutions that have served to make it what it is.”
   

2. Fellow Arjun Khemani: “Throughout history, freedom has always depended on the tools we had to protect it. The printing press made free speech possible. Before Gutenberg, ideas were chained to scribes and priests, locked away behind the authority of institutions. Printing blew apart that monopoly. Knowledge escaped. Authority collapsed under scale. The monopoly of ideas was gone forever.”

Economics

Read Fellow Arjun Khemani and President Logan Chipkin’s essay, Zcash: Hard Money for a Private World.

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Artificial General Intelligence

1. Watch Fellow Carlos De la Guardia explain the ecosystem view of the mind.
   

2. Watch Fellow Carlos De la Guardia explain the significance of Turing completeness as it pertains to thinking.

Epistemology

1. Ambassador Brett Hall quoting Karl Popper: “One of the main tasks of human reason is to make the universe we live in understandable to ourselves. That is the task of science.”
   

2. Fellow Ray Scott Percival: “Rationality does not lie in how you come up with your guesses, but in how you test them once you have arrived at them.”

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Aesthetics

Watch Fellow Tom Hyde’s talk on Wonderism, his philosophy of Enlightenment and Romanticism, reason and feeling, science and art.

Philosophy

1. Some writings by Conjecture Institute affiliates about physics, philosophy, and free will.
   

2. Watch Advisor Judea Pearl explain the Ladder of Causality.

Conjecture Press

All four of our books are now free to download here.

Conjecture Studios

We are delighted to announce Jaber’s Philosophy Corner, where Fellow Jaber Hassoun will be creating short video content in which he explains various ideas in epistemology and its applications. His first video, Taking Fallibilism Seriously, is live.

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Conjecture University

1. Read or listen to History of Ideas, Module 2: Ancient Greeks: The Pythagoreans, by Logan Chipkin.
   

2. Discover our affiliates’ original research here.

Conjecture Forum

Our first online conference, Advances in Physics, takes place on June 17th. Register here.

Conjecture Institute Handbook & Glossary

1. Read our Handbook to learn more about our mission, people, values, and worldview.
   

2. Peruse our Glossary to learn more about the concepts that make up our worldview.

If you want to keep up with everything we’re doing at Conjecture Institute, follow us on social media: X, LinkedIn, Facebook.

Every book, research paper, documentary, and event that we’ve delivered is because of donations from you and people like you. We have concrete plans for other projects that we want to deliver, but we can’t do it without your help. In addition to the perks we offer, know that we are eternally grateful for your support and will continue to grow Conjecture Institute in size, scope, and influence.

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Ancient Greeks: The Pythagoreans

I swear by the discoverer of the Tetraktys,

Which is the spring of all our wisdom,

The perennial root of Nature’s fount.

-The Pythagorean Oath

“All Things Are Number”

The ancient Greeks did not appreciate our modern boundaries between science, philosophy, mathematics, and spirituality. For example, the Pythagoreans seamlessly wove together serious mathematical investigation with religious reverence for the beauty and power of numbers. Given the time they spent pursuing the magical and metaphysical meaning of numbers, our modern sensibilities would not recognize the Pythagoreans as strict mathematicians. Still, they made objective progress not only in the subject of mathematics but in understanding the relationship between mathematics and the rest of Nature.

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Pythagoras (~572 - 497 BC) himself led this fusionistic charge, simultaneously working as a mathematician, philosopher, and spiritual leader. We do not know which of the Pythagorean school’s genuine contributions were his own. He left no writings, and all of his acolytes attributed their discoveries to Pythagoras himself—possibly because they saw him as a religious leader.

As Mario Livio writes in Is God a Mathematician?, “To the Pythagoreans, numbers were both living entities and universal principles, permeating everything from the heavens to human ethics. In other words, numbers had two distinct, complementary aspects. On one hand, they had a tangible physical existence; on the other, they were abstract prescriptions on which everything was founded. For instance, the monad (the number 1) was understood both as the generator of all other numbers, an entity as real as water, air, and fire that participated in the structure of the physical world, and as an idea—the metaphysical unity at the source of all creation.”

The supposedly divine Tetraktys exemplifies the Pythagoreans’ wedding of mysticism and respect for what we would consider genuine mathematics. This object is a special case of their more general way of representing numbers—they would create symmetrical (equilateral) triangles made out of discrete pebbles. For example, the number ‘1’ would be represented by a single pebble, the number ‘3’ would be represented by a total of six pebbles arranged as a row of one pebble stacked on a row of two pebbles stacked on a row of three pebbles. The Tetraktys is simply the particular arrangement of pebbles that represents the number ‘4’ in accordance with their schema (stacked rows of one, two, three, and four pebbles from top to bottom). Because the total number of pebbles that make up the Tetraktys is ten, the Pythagoreans felt that the object represented nothing short of perfection.

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In typical Pythagorean fashion, they went further in their mystical applications of the Tetraktys. For example, Pythagoreans are rightly credited with having discovered that “dividing a [musical instrument’s] string by simple consecutive integers produces harmonious and consonant intervals.” In particular, they realized that plucking two strings at the same time whose lengths are in a 3:4 ratio with one another creates a pleasurable tune called the ‘perfect fourth.’ Naturally, they associated this seemingly magical harmony between space, music, joy, and number with the Tetraktys.

The Pythagoreans similarly applied their unique blend of rigorous mathematical inquiry and mysticism to the heavens. They were some of the first thinkers to assert that the Earth was a sphere, though at least one of their reasons was simply that spheres were ‘superior’ to other shapes. Perhaps more impressive, they may have been the first school to ever notice that the Sun, the Moon, and other planets move across the sky independently of the supposedly fixed background of stars. The Pythagoreans’ love of the constellations only reinforced their divine view of number and geometry: each was defined by its number of constituent stars and shape that the stars collectively formed.

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The Pythagoreans did not confine the supposed divinity of numbers to inanimate objects but rather thought that they infused the world of people just as much. For example, they thought that odd numbers were masculine, even numbers feminine. They also associated the concept of unity with the number one (understandably) and the concept of justice with the number four (less understandably).

Whether in the small, manmade musical instruments, in the titanic, celestial bodies, or in the abstract world of human ideas, Pythagoreans took for granted the effectiveness of mathematics while insisting that said effectiveness revealed a spiritual dimension of the world. Theirs was an inseparable mess of sound application and ad hoc storytelling.

The Dawn of Pure Mathematics and Proofs

Despite their cloak of mysticism, the Pythagoreans were the first to think seriously about how mathematics relates to both the physical world and human thought. They were also among the first thinkers to (attempt to) explain the order of the universe by harnessing mathematics.

Before the Pythagoreans, peoples like the Babylonians and the Egyptians saw mathematics as a purely practical tool with which they might improve their food production and other such pressing issues. For example, the Babylonians applied fairly sophisticated mathematics to problems in administration, surveying, construction, and engineering. The Pythagoreans, though, founded the concept of pure mathematics—the study of mathematical objects for their own sake. Famously, it was they who discovered the Pythagorean theorem—that the sum of the squares of a right triangle’s shorter sides equals the square of the length of its hypotenuse. The Egyptians had some familiarity with the theorem, but only the Pythagoreans explicitly recognized it as universal for all right triangles. They also discovered irrational numbers—numbers that cannot be expressed as the ratio between two integers (see below).

The Pythagoreans’ most important mathematical innovation was that of a mathematical proof. For the Pythagoreans, a piece of mathematics should have a logical procedure behind it that takes as input some initial postulates or axioms and outputs a mathematical theorem or some other surprising piece of mathematical knowledge. Just as the predecessors to the Pythagoreans chose applied mathematics over pure mathematics, so too were they satisfied merely that a mathematical formula worked for their purposes. The Pythagoreans, on the other hand, demanded to know why a formula worked—and they regarded the proof process as the definitive means of discovery. Their emphasis on the importance of proofs would lay the groundwork for Euclid, another ancient Greek thinker whom we will meet later in this course.

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Irrational Failure

While they made great strides in mathematics, the Pythagorean school proved too cultish to survive as a long-lasting tradition of open-ended criticism (see our Civilization course). Its own discovery of irrational numbers violently contradicted their religiously held view that all of the natural world could be captured by whole numbers and their ratios. This was “a staggering blow,” writes Susan Wise Bauer in The Story of Western Science. Citing a commentator who lived not long after Pythagoras, she relays that “the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled.” While surely apocryphal, this entire episode exposes the Pythagorean school as too dogmatic in its mysticism to make continual progress in either pure mathematics or the application of mathematical tools to scientific questions.

Apparently, the decades that separated Thales from Pythagoras were not enough time for the former’s tradition of criticism to inspire the latter. Before such a tradition takes hold, it is not obvious that openness to alternative theories, willingness to admit one might be wrong, and acceptance that even our most cherished ideas may contain mistakes are not only beneficial but essential for infinite progress. The Pythagoreans failed to adopt this attitude in time, and irrational numbers ended their irrational tradition.

Our online conference, Advances in Physics, will take place on June 17th.

Register here.

What does it mean to take our best theories in physics seriously? What do they tell us about what the world is really like?

This conference gathers researchers who pursue these questions in quantum gravity, foundations of quantum mechanics, and constructor theory.

Attendees are welcome to ask questions, and those who register are free to come and go as they please.

The entire event will be recorded and uploaded to YouTube.

See you there!

Office Hours

Listen to Fellow Paul Raymond-Robichaud, Fellow Sam Kuypers, Ambassador Brett Hall, and others discuss the nature of infinity.

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Taking Children Seriously

Cofounder Aaron Stupple: “When a constraint is imposed upon a child without her understanding, she can’t apply it in novel circumstances, or know when to ignore it, or use it to acquire some new idea. Instead, it becomes fixed in time, unable to improve, a lifeless feature of her world. What’s worse, this constraint will grate against other ideas that she has, but since the parent has resorted to coercion, she is on her own to try to resolve the conflict that this grating represents.”

Physics

1. Senior Scientist Chiara Marletto: “While a Turing machine can simulate an ecosystem with cells reproducing and undergoing natural selection, it cannot itself be programmed to create a replica of itself. Von Neumann thought that we needed to treat more general programmable machines. Constructors were used to label this more general class of objects that could perform physical transformations (including self-replication), not just computations.”
   

2. Read Fellow Charles Bedard’s paper, The ABC of Deutsch-Hayden Descriptors: “...locality holds even in the face of Bell’s theorem. Today, most researchers in quantum foundations are still convinced not only that a local description of quantum systems has not yet been provided, but that it cannot exist. The main goal of this paper is to address this misconception...”
   

3. Listen to Senior Scientist Vlatko Vedral discuss black holes and quantum gravity with Fellow Maria Violaris.

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Civilization

1. Watch Advisor David Deutsch discuss the battle of ideas and error-correction with Advisor Peter Boghossian and Reid Nicewonder.
   

2. Advisor Daniel Hannan: “Liberty for almost everyone until a blink ago was almost unimaginable. How extraordinarily privileged we are to live in a time and in a country where the government is constrained, where the people don’t just get to make up the rules as they go...”

Economics

1. Listen to Fellow Ray Scott Percival explain the importance of free entry into the market.
   

2. Read Economics, Module 1: Preference Scales, by President Logan Chipkin.

Epistemology

Watch Fellow Carlos De la Guardia’s video, Why Care about Epistemology?

Aesthetics

Listen to Fellow Tom Hyde preview his book about Wonderism: “I’m trying to beautify knowledge and knowledge-creation.”

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Philosophy

Ambassador Brett Hall: “Expertise is absolutely real. Someone who knows a lot or almost everything in a particular field, whereas a layperson knows much less. The point is that you ought never give over your critical faculties to an expert. You want to develop an explanation of how the expert error corrects and whether that meets your own standards.”

Conjecture Press

Download our first three books for free here.

Conjecture University

1. Discover our courses here.
   

2. Discover our affiliates’ original research here.

Conjecture Institute Handbook & Glossary

1. Read our Handbook to learn more about our mission, people, values, and worldview.
   

2. Peruse our Glossary to learn more about the concepts that make up our worldview.

If you want to keep up with everything we’re doing at Conjecture Institute, follow us on social media: X, LinkedIn, Facebook.

Every book, research paper, documentary, and event that we’ve delivered is because of donations from you and people like you. We have concrete plans for other projects that we want to deliver, but we can’t do it without your help. In addition to the perks we offer, know that we are eternally grateful for your support and will continue to grow Conjecture Institute in size, scope, and influence.

Donate here.

The fact that all knowledge is creatively guessed immediately rules out any and all deterministic models of economic activity. The ‘physics envy’ that plagues so many economics departments is misplaced - unlike a collection of particles or planets, the economy cannot be captured by a set of algebraic equations. There can be no equation that quantitatively predicts how a given good’s price changes following a change in the supply of or demand for that good. Nor can a relationship between algebraic symbols ever correspond to the relationship between, say, interest rates and purchasing power.

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Those economists who insist that algebraic, deterministic models must play a role in explaining the regularities that constitute an economy are implicitly insisting on a false epistemology - namely that people are predictable, uncreative automata.

So much for econophysics and similar ways of trying to understand economics.

Values are ideas - fallible, theoretical, and improvable. This is one reason that the labor theory of value is impossible - the economic value of a good is not derived from the work required to produce a good. Individuals conjecture the value of a good in light of their moral theories (including what they want), the tradeoffs they’re willing and unwilling to make, and their knowledge of what they could and could not do with the good in question.

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Finally, economic theories that implicitly assume the necessity of a particular institution do not make sense, since institutions are primarily constituted by the conjectured ideas of the individuals who operate them. If institutions are characterized by ideas, and if people can criticize those ideas and replace them with better ones, then no particular institution is necessary for an economy to exist. Therefore, any economic theory that assumes the existence of money, or a State, or even trade is at best incomplete.

So any fundamental theory of economics cannot be deterministic, it cannot assume the existence of any particular institution, and it must be consistent with critical rationalism. Econophysics and models that assume the necessity of the State are at best approximative, and the labor theory of value is ruled out from the start.

Taking Children Seriously

Watch Cofounder Aaron Stupple explain to Stephan Livera why ‘Where should parents draw the line?’ is not the best question when it comes to parenting.

Physics

Read Fellow Sam Kuypers explain why general relativity is not just Newtonian mechanics with a small correction.

Civilization

Read Fellow Arjun Khemani discuss a common theme across history that help to explain successful subcultures.

Philosophy

Watch Fellow Paul Raymond-Robichaud how there can be free will in a deterministic universe.

Epistemology

Read Fellow Carlos De la Guardia discuss knowledge-creation and the nature of progress.

Conjecture Studios

1. Watch or listen to the entire conversation between Ambassador Brett Hall and Fellow Jaber Hassoun, who is bringing a deeper understanding of epistemology to both the Anglosphere and the Arabic world.

2. Watch Fellow Dimitri Vallein’s original short film, New Specimen.

Conjecture Forum

Our first online conference, Advances in Physics, takes place on June 17th. Talk titles and descriptions are coming soon. Learn more.

Conjecture Institute Handbook & Glossary

1. Read our Handbook to learn more about our mission, people, values, and worldview.
   

2. Peruse our Glossary to learn more about the concepts that make up our worldview.

If you want to keep up with everything we’re doing at Conjecture Institute, follow us on social media: X, LinkedIn, Facebook.

Every book, research paper, documentary, and event that we’ve delivered is because of donations from you and people like you. We have concrete plans for other projects that we want to deliver, but we can’t do it without your help. In addition to the perks we offer, know that we are eternally grateful for your support and will continue to grow Conjecture Institute in size, scope, and influence.

Donate here.

Ancient Greeks: Thales of Miletus

In our post-Enlightenment age, it’s easy to take progress for granted. Our scientific theories become ever deeper, our technology ever more empowering, our moral ideas ever more sophisticated. Not many generations ago, our ancestors thought that the Sun revolved around the Earth, rightly considered a full belly and robust shelter to be luxury items, and held attitudes towards their fellow man that we now regard as cruel and irrational.

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That progress occurs at all is not guaranteed—and indeed, humanity made little or no progress for most of its time on Earth. Why did people begin to make progress? More generally, what ideas, institutions, and processes are required for progress to take place at all?

Our story begins in the seventh century BCE in the Greek city-state of Miletus, where philosopher Thales was set to discover several of the ingredients humanity required to make progress henceforth.

Although he left no writings of his own, subsequent Greek philosophers—such as Plato and Aristotle, both of whom we’ll encounter again—routinely referred to Thales’ ideas. The so-called Pre-Socratic philosopher’s intellectual contributions ranged from mathematical theorems to calculating the dynamics of the equinoxes to predicting eclipses. All of these discoveries were ontological—that is, they improved our knowledge about what the world is like.

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But none of Thales’ ontological contributions hold a candle to his epistemological contributions—how and why knowledge grows in the first place (see our People, Reason, and Reality Course). Because of the intimate connection between the growth of knowledge and the possibility of progress, Thales’ epistemological discoveries empowered subsequent thinkers themselves to make progress that would otherwise not have been possible.

In Thales’ time, dogmatic adherence to the prevailing wisdom was the informal law of the land. One dared not question the explanations of how the world worked—it was simply so. With respect to inhibiting progress, that these explanations were mythological was less significant than the fact that they were dogmatically held.

One of Thales’ great epistemological discoveries was that progress requires a tradition of criticism, which he concretized in the founding of his famous Milesian School. The culture of his school was an epistemological achievement in its own right, as pupils regularly criticized the ideas of their masters in an effort to improve them. Thales’ own student, Anaximander, rejected some of his teacher’s ideas in favor of his own. It may well be that the Milesian School was the first institution built precisely for the purpose of argument in pursuit of the truth.

No singular ontological discovery could have done such a thing. If all Thales did was create a novel mathematical theorem, then it may well have spread across ancient Greece. But the theorem would have lent itself to progress only in problem-situations to which the theorem applied. Like the fruit of a tree, the theorem would have been eaten and done with.

But Thales’ epistemological discovery of a tradition of criticism was the creation of an entire—and potentially immortal—fruit tree.

As Patricia F. O’Grady writes in Thales of Miletus, “Something extraordinary, astonishing and momentous was happening, and its birthplace was Miletus. It is an historical fact that the hypotheses of the Milesians were soon followed by a plethora of bold, creative theories from men of originality, courage, outstanding perception and, sometimes, of astonishing absurdity.”

(As an aside, it’s entirely plausible that Thales made this discovery unintentionally. He may have never been conscious of the fact that he’d established a tradition of criticism in creating his school, nor of its significance in allowing for unending progress. Understanding the importance of a tradition of criticism is not the same as ‘merely’ creating one.)

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Less significant than Thales’ discovery of a tradition of criticism but still a crucial ingredient for progress was his rejection of supernatural explanations in favor of naturalistic alternatives. While his Greek contemporaries were satisfied in attributing the caprices of the world around them to the actions of the gods, Thales found these wanting (though he may not have been able to articulate why supernatural explanations were inferior to naturalistic ones). Thales’ view that the world could be explained naturalistically—so-called materialism—is one that most modern scientists now take for granted.

As O’Grady writes, “Thales made a distinct break from the mythical ways of describing the universe to a scientific explanation. It was the beginning of science.”

For instance, the Greeks attributed earthquakes to the mood swings of Poseidon, god of the sea. Thales conjectured that the Earth floated on a body of water, and that earthquakes were caused by the Earth’s swishing and bobbing around, much as a ship does at sea.

We now know that the content of Thales’ hypothesis was mistaken. Our planet does not float on water but rather travels across empty space. And earthquakes aren’t caused by the Earth’s movements relative to some external frame of reference at all, but rather by the internal dynamics of subterranean plates and fault lines.

Yet in proposing this false idea, Thales inched towards a true aspect of reality, a crucial ingredient for scientific progress, namely that all phenomena can be explained without reference to the supernatural.

Nor did Thales restrict his materialism to earthquakes. He universalized the idea to all phenomena via the principle that ‘water is the source of all things’. Thales conjectured that the regularities around us were not caused by supernatural, alien entities, but rather by a fluid that could itself be studied, probed, and understood. Once again, the explicit content of the principle is wrong, but the implicit assumption that the universe is materialistic underlies the whole of modern science.

Finally, the very notion of a principle was a bold innovation (see our Constructor Theory Course). In taking seriously that seemingly disparate phenomena could be accounted for via the same universal explanation, Thales must have taken for granted that reality was a unified, comprehensible whole. Nowadays, this is obvious to most Westerners—for instance, the principles of general relativity apply to all massive objects, and those of economics apply to all purposeful action (see our Economics Course). Once again, Thales may not have even explicitly appreciated the role that principled thinking necessarily plays in fundamental science (in fact, our own understanding of the role that principles play in science has evolved). Nevertheless, it was Thales who brought the notion of principles to the fore of philosophy.

With his advent of a tradition of criticism, materialism, and the notion of universal principles, Thales gave every subsequent philosopher and scientist indispensable tools of reason that have lasted for thousands of years. From everyday life to scientific research, these tools are so baked into the modern mind that we rarely appreciate them for the revolutionary discoveries that they are. It is thanks to Thales that we deploy them as easily as we draw breath.

Thanks to Edwin de Wit for valuable feedback.

Fellow Ray Scott Percival’s work applies optimism to thinking itself. The logic and epistemology of the transmission of ideas, whether good or bad, is central to his work. In both his documentary, Liberty Loves Reason, and his book, The Myth of the Closed Mind, he refutes the pessimistic tropes that people are unpersuadable, that minds are indelibly tainted by irrational biases. On the contrary, individuals have been changing their minds since humanity began, and especially since the Enlightenment. And biases are simply conjectures—they may fail, at which point the individual may criticize his own biases and replace them with something better. Or they might foster the discovery of a solution, in which case the biases were not banes to thinking but rather facilitators of it.

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Clearing the mind of all biases is not necessarily the right thing to do, since the contents of one’s mind must always be understood in light of the problem-situation in which it finds itself. Blind insistence on removing particular errors in one’s worldview without intrinsic reason for doing so is a recipe for adopting ideas uncritically. Moreover, not all errors impinge on every problem-situation, so insisting on removing as many errors as you can before trying to solve the problem in front of you is itself an error (and, since errors are inevitable, there is no such thing as an error-free mind).

Typically, your first conjecture will fail, and you will either discard it completely or modify it, and try to solve the problem again. Had your initial conjecture been reliant on some bias, then maybe it was this bias that was the reason for the conjecture’s failure. But maybe not. Modifying conjectures is always a creative process, and one must be opportunistic when thinking about how to improve them. In short—there is no guarantee that any cognitive error or bias is the reason why a given idea isn’t working.

Ray is now writing another book that will offer prescriptions about how to reignite the Enlightenment in the modern age. He will argue that Enlightenment values, rooted in autonomy, reason, and fallibilism, remain our best hope for human flourishing. Drawing on the ideas of Bartley, Miller, Popper, Deutsch, and Polanyi, the book will critique scientism, defend liberal institutions, and offer a vision of progress grounded in critical rationalism, individual responsibility, and poetic insight.

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Taking Children Seriously

Watch Cofounder Aaron Stupple explain to Advisor Peter Boghossian why education and learning should be subordinate children’s interests.

Physics

1. Watch Senior Scientist Chiara Marletto’s paper explain to Ambassador Brett Hall why constructor theory may shed light on the fine-tuning problem.
   

2. Read Fellow Maria Violaris’ paper, A physics lab inside your head: Quantum thought experiments as an educational tool.
   

3. Get Senior Scientist Vlatko Vedral’s book, Portals to a New Reality: Five Pathways to the Future of Physics.
   

4. Read Fellow Paul Raymond-Robichaud’s paper, Can Free Will Emerge from Determinism in Quantum Theory? (with Gilles Brassard).

Civilization

1. Fellow Arjun Khemani: “Creativity is the source of all that is new and good in the world. Privacy is a precondition for creativity. Total surveillance is civilizational suicide.”
   

2. Fellow Maxime Desalle: “We should embrace exceptional human beings, not hate them. Scientists and entrepreneurs are those who move humanity forward, and we should have much more respect for them.”
   

3. Watch Advisor Daniel Hannan explain how the American Revolutionary War was, in fact, a civil war within the Anglosphere.

Economics

Read Economics, Module 1: Preference Scales, by President Logan Chipkin.

Epistemology

1. Read Fellow Ray Scott Percival explain why irrationality is no insuperable obstacle to persuasion.
   

2. Listen to Ambassador Brett Hall explain the folly of IQ tests.

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Aesthetics

Fellow Tom Hyde: “Beauty is rare and non-fungible. The meagre abundance we do enjoy is hard-won by unique genius...Artistic optimism, like all optimism, does not mean that progress is easy. It means that it is possible despite being hard.”

Philosophy

1. Advisor David Deutsch: “Turing and Godel were replying to one of the questions that David Hilbert had asked in 1900. Turing and Godel both addressed the problem and got the right answer. Turing was focused on what could be done by a physical object...Godel was focused on what can’t be done by any physical object.”
   

2. Watch Chiara explain why there can never be a final theory of everything.
   

3. Advisor Judea Pearl: “Why don’t philosophers define [or explain] counterfactuals in terms of causes rather than the other way around? Are counterfactuals less problematic than causes?”

Conjecture Press

Download our first three books for free here.

Conjecture University

1. We now have fifteen modules on our Course page on subjects such as economics, quantum mechanics, the principle of locality, epistemology, civilization, and constructor theory.

   We will continue to build out our courses throughout the year.

   Discover our courses here.
   

2. Discover our affiliates’ original research here.

Conjecture Forum

1. Join us in Philadelphia the weekend of September 25th-27th for our flagship in-person event, Conjecture Con. Get tickets here.
   

2. Conjecture Con Europe takes place the weekend of May 15th in Oxford. Discover the schedule here.
   

3. Our first online conference, Advances in Physics, takes place on June 15th. Schedule, talk titles, and talk descriptions coming soon. Learn more.

Conjecture Institute Handbook & Glossary

1. Read our Handbook to learn more about our mission, people, values, and worldview.
   

2. Peruse our Glossary to learn more about the concepts that make up our worldview.

If you want to keep up with everything we’re doing at Conjecture Institute, follow us on social media: X, LinkedIn, Facebook.

Every book, research paper, documentary, and event that we’ve delivered is because of donations from you and people like you. We have concrete plans for other projects that we want to deliver, but we can’t do it without your help. In addition to the perks we offer, know that we are eternally grateful for your support and will continue to grow Conjecture Institute in size, scope, and influence.

Donate here.

We are thrilled to welcome our newest Fellow, Jaber Hassoun!

Jaber is a computer science graduate and educational YouTuber focused on science and philosophy communication.

His videos and interviews are dedicated to promoting Enlightenment values, progress, philosophical optimism, open society, and a critical rational attitude.

His is one of the only Arabic-speaking channels that offers deep dives into Conjecture Institute Advisor David Deutsch’s second book, The Beginning of Infinity, and Popperian epistemology in general.

Jaber will play an integral role in creating (English) video content for Conjecture Studios, our film, documentary, and general media arm.

Discover more of Jaber’s work: YouTube, Instagram, and X.

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Taking Children Seriously

Read from Cofounder Aaron Stupple: “How do kids acquire knowledge? They don’t, they build it, they construct it. They create ideas in their minds and try them out in the world. To learn about things like teeth brushing or being polite, they need to be free to see the problem that teeth brushing and politeness solve. Forcing behaviors can produce the intended actions, but not the intended understanding. In fact, it will contaminate understanding in some way.”

Physics

1. Watch Fellow Maria Violaris’ Intro to Quantum Computing video series.

2. Read about a novel way to test whether or not biological systems exploit quantum mechanics in a paper by Conjecture Institute Senior Scientists Vlatko Vedral and Chiara Marletto and Fellow Giuseppe Di Pietra.

3. Listen to Fellow Sam Kuypers discuss quantum gravity and the physics of time.

4. Read Fellow Maxime Desalle explain one of the problems with the Copenhagen interpretation of quantum mechanics.

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Civilization

1. Watch Advisor Daniel Hannan discuss civilization as a hard-won achievement.

2. Watch Fellow Arjun Khemani and President Logan Chipkin explain why the growth of wealth and knowledge is necessary for unbounded progress.

3. Read from Fellow Paul Raymond-Robichaud: “An open, problem-solving society thrives on a pluralism of interests. A society that dictates the “correct” things to be happy about is authoritarian.”

Economics

Read our first two Economics course modules by Logan.

Epistemology

1. Watch Fellow Eric Denton explain why Bayesian epistemology is false with founding publisher of Skeptic Magazine, Michael Shermer.

2. Read from Fellow Ray Scott Percival: “We can decide not to read or listen to an argument, but we can’t decide to remain untouched by a telling argument that we have heard or read.”

Artificial General Intelligence

1. Watch Fellow Carlos De la Guardia explain how universality is relevant to both coming up with new ideas and distinguishing good ideas from bad ones.

2. Watch the latest episode of AGI with Carlos: Universality = System + Relationship + Set.

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Conjecture Press

1. Read Fellow Tom Hyde’s explanation and outline of his book about Wonderism, which he is currently working on.

2. Download our first three books for free here and buy our fourth, The Farthest Reaches by Ambassador Brett Hall.

Conjecture University

1. We now have fifteen modules on our Course page on subjects such as economics, quantum mechanics, the principle of locality, epistemology, civilization, and constructor theory.
   
   We will continue to build out our courses throughout the year.
   
   Discover our courses here.
   
   Our latest module by Logan is Civilization, Module Four: Knowledge, Wealth, and Institutions Read here.
   

2. Discover our affiliates’ original research here.

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YouTube & Podcast

We’ve uploaded the audio versions of a few Conjecture University Course modules, as well as a few companion interviews for our next compendium, to our YouTube channel and podcast. More to come.

Conjecture Con Europe 2026

We hope everyone has a wonderful time at Conjecture Con Europe in a couple of weeks! Some of our Fellows will be in attendance: Ray Scott Percival, Maxime Desalle, Sam Kuypers, Maria Violaris, Arjun Khemani, and Tom Hyde. Advisor David Deutsch will also participate in a live Q&A session.

Learn more about the event here.

Conjecture Con 2026

Join us in Philadelphia the weekend of September 25th-27th for our flagship in-person event. Get tickets here.

If you want to keep up with everything we’re doing at Conjecture Institute, follow us on social media: X, LinkedIn, Facebook.

Every book, research paper, documentary, and event that we’ve delivered is because of donations from you and people like you. We have concrete plans for other projects that we want to deliver, but we can’t do it without your help. In addition to the perks we offer, know that we are eternally grateful for your support and will continue to grow Conjecture Institute in size, scope, and influence.

Donate here.