“Poem Number Two on Bell’s Theorem, or The New Physicality of Long Distance Love”

There is no chance that we will fall apart
There is no chance
There are no parts.

Like a quantum particle, a poem can exist in several ways depending on its reader. As we explored in “Preface to the Quantum World,” a particle may exist in a superposition of possible states (particulate, wave-like) before measurement. So too may a poem encompass several meanings and coexisting states. While this article will not attempt to offer an interpretation of “Poem Number Two,” we will try to use poetry to explain another type of poetry, using this poem as a guide for understanding the physics it describes, and by doing so, provide an entry point for deeper reading.

Before we address the most obvious question prompted by Jordan’s poem, what exactly Bell’s theorem is, we must look into a paper that preceded it. Bell’s 1964 paper, “On the Einstein-Podolsky-Rosen Paradox,” was written in response to an earlier paper by Albert Einstein, Boris Podolsky, and Nathan Rosen (otherwise known as “EPR”), which sought to demonstrate that quantum mechanics was an incomplete theory using two entangled particles, where the state of one determines the state of the other.

(A brief side note on entanglement: entangled states can occur from a variety of causes, including close interaction, a shared origin, or needing to fulfill conservation of momentum or energy; for example, an unstable atom undergoing beta decay will produce one electron and one neutrino. In this case, even though the decay is random, the available energy is shared between the electron and neutrino in a way that preserves conservation of energy and results in the entanglement of the two produced particles.)

Suppose then, as the thought-experiment did, that the entangled particles are accelerated to opposite sides of the universe. According to quantum mechanics, if a scientist somehow measures the quality of one particle, the state of the other particle will immediately be known. For example, if the initial spin state of the entangled system is 0, and the scientist measures the spin of particle A to be +1, then, following conservation laws, we know that the spin of particle B must be -1.

However, while the entangled particles abide well enough by theories of conservation, they seemingly violate another theory: namely, Einstein’s theory of relativity, which states that c, the speed of light, is the universal speed limit, which nothing can surpass. But according to quantum mechanics, which states that the particles did not have a single, definitive spin until measured (like how Schrödinger’s cat is neither dead nor alive before the box is opened), measuring one particle appears to determine the state of the pair instantaneously. In order for particle B to instantly take on the counter-quality of particle A, says EPR, particle B must receive some sort of signal from particle A, which is impossible because that would mean that this signal can travel faster than light.

In order to solve what Einstein called “spooky action at a distance [spukhafte Fernwirkung],” EPR concluded that the particles must have “hidden variables.” In this case, the hidden variables, or fundamental information embedded in each particle that would lead to a pre-determined outcome, mean that particle A always “knew” that it would end up with a spin of +1, and particle B likewise “knew” that it would have a spin of -1. In this picture, relativity is preserved because no information needs to travel between the particles after measurement—however, Einstein’s proposal challenged the probabilistic interpretation of quantum mechanics, including the role played by Heisenberg’s uncertainty principle.

So, is Einstein correct that “God does not play dice with the universe?”

In 1964, Bell published the “On the Einstein-Podolsky-Rosen Paradox,” addressing the puzzle of “spooky action at a distance” with probability. Remarkably, Bell’s solution demonstrated that any local hidden-variable theory must satisfy a mathematical constraint—Bell’s inequality—that quantum mechanics can violate. While we will not delve too deeply into the mathematical proof, we will attempt to understand the theoretical workings of Bell’s inequality.

First, Bell begins with the assumption that EPR is correct. When our scientist decides to measure particle A, they choose between two possible measurement settings (for example, two different directions along which to measure spin) from which they can measure a binary quality that was pre-possessed (a0, a1) and will either turn out to -1 or +1. A second scientist may do the same for particle B. A classical combination of the two probabilities looks like this:

If the binary quality is indeed prepossessed, then there will only be a certain number of times that the particles come out with directly opposite values (+1 and -1, respectively), strongly affecting the right-hand side of the equation as a0+a1 and a0-a1 can only ever turn out to +2 or -2. The upper bound of correlation is restricted to this value.

However, using a quantum mechanical combination, the correlation of the two particles becomes far higher than the classical combination could logically yield. In the quantum mechanical treatment, however, the predicted correlations exceed Bell’s classical bound. Later formulations using qubits and Pauli matrices make this especially clear, yielding Tsirelson’s bound of 2√(2). The higher correlation between the two particles aligns more closely with what we can observe in a lab: the instant “communication” between entangled particles that allows them to take on directly opposing forms. Quantum probability works.

(If you’re interested in the full proof, I highly recommend reading Bell’s original paper. It is remarkably short and concise.)

Let us remember, now, what brought us here: June Jordan’s “Poem Number Two on Bell’s Theorem, or The New Physicality of Long Distance Love,” which illustrates the remarkable connection between physics and poetry: In developing a language for scientific reality, we enrich the language we have access to for human expression. In asking the question, “What is Bell’s theorem?” we might also ask, “What is love?” In the distant and theoretically dense, we come ever so much closer to understanding ourselves.

Now understanding Bell’s theorem, feel free to reread Jordan’s poem. What does it say to you now? Perhaps between physics and poetry, a new Theory of Everything will emerge.

Until next time.

The world around you is filled with objects. As homo sapiens, we are the most object-dependent creatures on Earth. As social as we are in the 21st century, we require an endless list of physical items to get us through the day, from toothbrushes to cars to satellites. Our poets thrive in this world; after all, to write poetry is to see deeper truths through the medium of objects and solid surfaces—Tennyson’s subjects of beauty are crowned with moss and lit by silver-backed poplars; Lucille Clifton re-envisions an entire history through vegetables in “cutting greens.” However, the turmoil, frenzy, and restlessness of their words only truly manifests when we zoom into the matter itself (bad pun unintended).

A gentle reminder. The field of quantum physics is one that is both extraordinarily fascinating and difficult to comprehend. The basis of quantum physics, quantum mechanics, is a whole lot of mathematics describing the world in the gorgeous detail that classical mechanics failed to capture in the 20th century. Even Einstein refused to accept much of quantum logic toward the end of his life. As poets, we’ll do our best to approach the subject through concept, perception, and imagination. Remember that much of the why gets lost in translation from the language of numbers and symbols to letters.

The first thing that pops to mind when you think of the word quantum might be science’s most famous cat: Schrödinger’s cat. At its simplest: a cat is placed in a closed box with a radioactive atom, which shatters a vial of poison if the atom decays. As long as the box isn’t opened and the state of the atom (and of the vial of poison) is never observed, the cat can be both dead and alive at the same time.

There is a single principle that allows the cat to be both dead and alive: Heisenberg’s Uncertainty Principle.

At the most rudimentary level, matter is made of atoms. You might remember from high school chemistry Bohr’s or Rutherford’s model of the atom, composed of a proton and neutron core, with electrons orbiting in standardized positions around the nucleus. However, neither Bohr’s nor Rutherford’s model quite passes the requirements of quantum existence.

In Newtonian physics, and even in Einstein’s theory of general relativity (which we explored in “On the Make of Time, Part II”) physical phenomena tend to exist as they are—that is to say, the Sun is a yellow dwarf of hot plasma (at least our Sun is), and a baseball going at 60mph is a leather sphere going at 60mph. It’s very possible to find the momentum (mass times velocity, mv) and position (s) of the Sun or a baseball at a given point in time, because they will always made of atoms, no matter when you measure their momentum or position.

However, in both special relativity (which we explored in “On the Make of Time, Part I”) and quantum physics, this type of certainty becomes fallible. At the atomic level, we can observe the wild disjunction between a classical reality and a quantum one, where the particles forming matter no longer exist in a singular, unchanging state. Quantum systems reject classical logic by existing in a superposition of several states at once. This phenomenon is known as wave-particle duality, where a particle exists both in a particulate state, composed fundamentally of quarks, and in a wave state.

This way of thinking—through probability rather than classical mechanics—revolutionizes the atom, replacing electron orbitals with electron clouds, and replacing position with possible paths. If relativity tells us that every observation is relative to your person, quantum physics tells us that everything is unobservable in its original state.

But how can this be, since particles make up solid matter? If the atoms making up your electronic screen are both particles and waves, how is it possible that you’re able to touch and scroll, when you certainly can’t touch and scroll something like sound, which travels in waves?

When the top of Schrödinger’s cat box is opened, the atom will have either decayed or remained stable by the time a measurement or observation of its state is made. By using a macroscopic instrument on a quantum system, the quantum wave function is forced to yield to the particulate state of the macroscopic instrument. By simply interacting with an object, the quantum system becomes inextricably tied to it through a process called entanglement. In other words, the particles making your phone screen interact with the macroscopic objects around them (like your fingers).

Introduced as a theory in 1935, quantum entanglement stunned the scientific community. Einstein famously said that entanglement was “spooky action at a distance,” and for good reason; it seemed to contradict every breakthrough made up until then. Suddenly, there could be travel that surpassed the speed of light, teleportation seemed possible, and particles that were light years apart could communicate with each other instantly. If all these things were impossible, how was it that entanglement could be possible?

Next time, we’ll learn about the reality of entanglement, the Einstein-Rosen-Podolsky paradox, and Bell’s theorem. Then, we’ll make our way to reconciling (or failing to reconcile) “On the Make of Time” and the make of matter.

In the meantime, let me know if you come up with the next theory of everything. See you later.

Before we begin, please note that all of the theories we will discuss are theories. The only physical law that can is incontestable is that there are no laws that are incontestable. Everything is constantly developing, and, like literature, science is only our way of attempting to explain our experiences, and, as with any form of expression, artistic or otherwise, there is no objective scientific standard. The best scientist is one who is most open to change. (Of course, some theories have more ground than others, but I hope this goes without saying.)

Welcome to the second part of our deep-dive into the substance of spacetime. In the last part, we discussed how Einstein’s Theory of Special Relativity (governing light, mass, energy, and time) and entropy could create a “timeless space.” In this part, we’ll focus on why this is a tricky phrase, general relativity (a theory of gravity and spacetime), the two types of time, and fluidity.

First, the trick question. Previously, we achieved the impossible by removing all sense of relativeness (distinct from relativity) from our isolated system, a vacuum at zero Kelvin with nothing in motion and zero entropy. Past, present, and future blur into one unified state. However, so long as we continue to include space in our system, time must exist. This is not to say that time passes—but, like stillness implicates movement, or silence implicates sound, space implicates time.

Previous to Einstein’s Theory of General Relativity, it was thought that gravity was a Newtonian force, possessing direction and a magnitude measured in newtons and having the same effect as pushing on a box. For two centuries, gravity was the force exerted by a larger mass on a smaller mass, such as the Earth and an apple, dropping on Newton’s head, or the Sun and the Earth.

However, Newton’s description of gravity was just that—only a description. He had no explanation for the mechanisms underlying gravity, and thus failed to account for gravitational extremities, including how light, a massless agent, was affected by gravity. It was only in 1915 that Einstein proposed a solution, a decade after the publication of his theory of special relativity.

In our endeavor to undertake the conceptual and poetic approaches to the big questions of physics, we can use a metaphor for the nature of space and the spacetime fabric. You may have heard of the idea that time is some kind of “fourth dimension.” However, this is a bit misleading. It is true that time has dimension (insofar as any conceptual object may have dimension), but it isn’t a dimension of space. Rather, consider time and space as being infinitely woven of fine threads, crossing over one another to create a spacetime fabric that possesses all the qualities and stretch factor of a given textile. From here, we can posit two kinds of time: one that is observed as an effect of change, detailed in Part I, and one that is measured as an effect of spacetime warping (producing curvature).

But what does it even mean to have dimension?

Mathematically, increasing dimensions is the act of doubling all given points, corners, vertices, etc. of a given object. A point is considered “zero” dimensional due to its lack of length, width, height, or otherwise, lacking any definition but its location, but if you double it and connect the two points with a line, the line is now one-dimensional, and you can move backwards or forwards on that line. By doubling the line and connecting the endpoints to each other, you produce a two-dimensional square, with length and height. Double the square, connect the corners, you get a three-dimensional cube. Double the cube, connect the vertices, you get a four-dimensional hypercube—so on, and so forth.

Side-note: it’s impossible for humans to truly visualize more than two dimensions due to our being three-dimensional beings. We only ever see the front of things, like our hands, and our brains fill in the width with graduation, shadows, hues, and optical tricks. If we were to see in three dimensions, we’d see the back and front of our hand simultaneously, as well as everything inside. You can imagine, then, how difficult it is to even conceive what four dimensions is, much less what it looks like.

When physicists have to represent spacetime visually, this is usually the graphic that comes up, where three-dimensional bodies with various masses produce depressions as though sunk in two-dimensional fabric:

In Figure 2, orbiting bodies come about as they enter the curved area, “falling” toward the more massive body in three-dimensional ellipses.

However, a more accurate representation of spacetime curvature looks like Figure 3—

—where, as our three-dimensional body of mass moves, the three-dimensional grid around it contracts accordingly. If we were to be even more accurate, we’d double more and more (to whatever amount of dimensions is appropriate for the theory of spacetime that you subscribe to).

In this model, orbits are better represented not as three-dimensional ellipses but as four-dimensional circles:

Geometrically, when the circles are “flattened” into a three-dimensional space, they become elliptical. You can test this out for yourself by cutting out a strip of paper, connecting the ends to create a circle, and trying to flatten your three-dimensional circle onto a two-dimensional surface.

In both models depicted in Figure 2 and 3, the key detail is that gravity, rather than acting as an independent force determined by mass and acceleration, is an effect of massive objects warping spacetime fabric around it.

There is a fantastic tie to bring us full circle. The second type of time, not the measurement of change but the intriguing and evasive threads of spacetime fabric, behaves as both the cause of and an effect of gravity—the cause of an effect of an effect. The substance of time, what is measured by our clocks and watches rather than our sundials that measure time as change and entropy, is moulded through spacetime curvature, slowing down as the fabric warps near objects of mass, and speeding up in a vacuum. General relativity gives us the gift of time dilation.

Physics is a ripple effect. A series. A scattering of wind into cloud into rain and space. By understanding the mechanisms that underlie the universe, we better understand our own existence and significance. Thank you for reading, you massful, phenomenal cause of an effect of an effect.

“To respond is to offer again. An object is not an object. It is the witness to a relationship. In complementary union, two opposites collide to create new forms. Seeing and naming creates the space for the beauty of the exchange to unfold.”

—Uji: The Time-Being by Eihei Dogen

We will tackle this problem in two parts and attempt to deconstruct the two theories of relativity in modern physics while at it. Let’s begin.

In traditional philosophical thought (often what governs poetry), poets usually tend to agree that time is an abstraction. In day to day life, time is more so a tool to live and conduct the tasks which living things conduct rather than something that is lived in. Life meaning not its scientific self, but the type that revives Anne Carson’s heroes retold, Frank O’Hara’s traffic lights, the tide, wet stones shining on shores, what-have-you.

To think about time is to think about chronology, progression, chaos, and order: change. At zero kelvin, absolute zero, in a vacuum with absolute atomic stillness, does time pass? How do you separate past from present from future when nothing, not even the vacuum itself, changes? Here, we confront time as the product of mass and cosmic fields, effects of distorting spacetime fabric; time as a field or dimension itself; time as what we measure our days with; time as what we have left; time as abstraction of human intuition; time as the sum of its effects.

Before delving into this perspective more, let’s discuss relativity, a theory of gravitation and thus time.

Relativity is divided into two theories by Albert Einstein: special and general relativity. Special relativity can be called a theory of light because it is the exemption. Such as we learn about the human condition through its extremes, so too do we learn about science (which is why black holes are such a fascinating and important topic—more to come on that). According to special relativity, there is no definite speed, only relative speed that depends on a frame of reference. For example, if you’re sitting on a bus moving at 20 m/s in one direction from an inertial (unmoving) frame of reference, a child running at 5 m/s in the same direction from an inertial FoR would really have a speed of -15m/s (or 15 m/s in the opposite direction).

Light, however, moves at the same rate no matter what your FoR is. It would travel and appear to travel at the speed of light c (299,792,458 m/s) regardless of whether you were on a rocket traveling at 200,000,000 m/s or running at 10 m/s. The speed of light is also the universal speed limit: everything within our universe must remain within a light cone. We cannot go where light does not reach. Note that the graphical map of a light cone, the “space” axes are condensed to two dimensions, when in reality the cone would really be four dimensions (three of space, one of time) with cross-sectionals of 3D cones. More on the multi-dimensional aspect of relativity to come.

For now, we reach the most famous equation in science: Einstein’s E=mc² (where E is energy, m is mass, and c is the speed of light). To simplify things, let’s rearrange the equation to be m=E/c². This is also how the equation appeared in Einstein’s original paper. In other words, energy divided by the speed of light must equal mass, also called “mass-energy equivalence.”

This is exactly what it sounds like. All things with mass are partially weighed with the additional mass of energy. Energy itself is massless, but can be described as inhabiting mass. All this means for the sake of our discussion on time is that the speed of light allows us to relate mass and energy with time.

Entry point into the conversation: time is movement. Speed is quintessentially reliant on time (measured in meters per second). It is the extreme, nearly three-hundred million meters per one second, that lets us quantify the minute; in the beginning, we described a scenario at absolute zero in a vacuum and asked if time passes. In the framework we have established, the answer is no, because there is nothing to be relative to, and no boundary between past, present, and future. We have created a timeless space.

By ruling out where time cannot be, we learn what is necessary for time to exist, and get closer to what it is made of.

Caveat: time is not to be confused with spacetime. Spacetime cannot be separated into components of time and space.

This, we will explore in the next part. Try not to evaporate into photons in the meanwhile.

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