Quantum Entanglement

by Jed Brody

  The two-dimensional scientists wonder if the appearance of one blob causes the three other blobs to appear, some distance away. Is this spooky action at a distance? The two-dimensional scientists are scratching their two-dimensional heads. Eventually, an idea forms in their two-dimensional brains. Perhaps the isolation of the blobs is an illusion; perhaps, in an unimaginable higher-dimensional space, the four blobs are part of a unified whole. The properties of one blob don’t influence the properties of any other blob. Instead, the relationships among the blobs exist all along in a higher-dimensional space, which only occasionally intersects the familiar, two-dimensional reality.

  This is how some physicists explain entanglement: We live in a cross-section of a higher-dimensional reality. Much like the two-dimensional scientists, we cannot intuitively understand causality in the higher dimension. Nicolas Gisin writes, “In a certain sense then, reality is something that happens in another space than our own, and what we perceive of it are just shadows, rather as in Plato’s cave analogy used centuries ago to explain the difficulty in knowing the ‘true reality.’”16 This is an extraordinary statement. Scientists are stereotyped to equate reality with empirical data, but evidently some scientists equate reality with an invisible higher realm.

  Let’s review, once more, the assumptions of locality and realism. We’ve seen that the assumption of local realism imposes constraints on measurable quantities, and measurement violates those constraints. Thus, unless we embrace an exotic viewpoint like superdeterminism, we must abandon locality, realism, or both. As we’ve seen, locality and realism are both very reasonable:

  •Locality means that the measurement of one object can’t affect a distant object.

  •Realism means that objects have properties that exist prior to measurement; measurement merely reveals properties that the objects had all along.

  If physics forces us to abandon at least one of these common-sense notions, what’s left, other than a higher-dimensional reality? Here are some possibilities.

  Scientists are stereotyped to equate reality with empirical data, but evidently some scientists equate reality with an invisible higher realm.

  Abandon Both Locality and Realism

  As I mentioned earlier, I find it expedient and straightforward to suppose that measurement creates objectively real states. If a photon passes through one vertical polarizer, it will pass through any number of vertical polarizers lined up in a row. The vertical polarization of the photon seems to be an objective fact, once it’s measured in the first place.

  A pair of entangled photons shares a single state, and the initial state is noncommittal. The photons do not have properties that predetermine their behavior at polarizers; they’re not predestined to pass through polarizers or get blocked by polarizers. Let’s suppose both polarizers are set to the same angle. If we first measure one photon in the pair, the measurement instantly creates a definite state for both photons. If we believe that the state is objectively real, then the measurement of one photon physically alters the distant photon. This is the spooky action at a distance that Einstein decried (and that many physicists continue to reject). We can’t prove that the measurement of one photon changes the other because we can’t watch the change take place; we can’t make an observation prior to the first observation on either photon. But for exactly this reason, we can’t prove that the measurement of one photon doesn’t affect the other. For all practical purposes—predictions of outcomes—the measurement of one photon indeed affects both. Both photons transform from a noncommittal state to a known state. As Tim Maudlin writes, “Going from not having a physical state to having a physical state is some sort of change, call it what you will!”17

  Even if spooky action at a distance is real, is it any spookier than other influences, like gravity? If you lived a thousand years ago and someone told you, “The only thing stopping Earth from floating off into the endless midnight of black space is a wrenching attractive force from the distant sun,” wouldn’t you think that was spooky? The only reason gravity doesn’t seem spooky is that we’re so familiar with it; we’ve absorbed it into our intuition about how the world works.

  To me, spooky action at a distance is disappointingly unalarming. The real mystery resides in the measurement problem: Exactly what were the photons like before they were measured? How does a measurement transform their polarization from something essentially undefinable to something definite? And when does this transformation take place: What physical process functions as a measurement? And why don’t we observe quantum effects on a large scale? Why can’t we be in two places at once, or dead and alive at the same time?

  Some physicists believe these questions have been partially answered by quantum decoherence: when objects are jostled by the surrounding air molecules and photons, they lose the ability to be in two mutually exclusive states at the same time. One state survives, and the other state dissipates. This process is explained through quantum equations. What’s not explained is how the surviving state is chosen: the selection of the state remains a purely random process.

  Can We Save Realism by Rejecting Locality?

  There have been attempts to formulate nonlocal, realistic theories. David Bohm’s theory is the most famous example. If we accept nonlocality, we have a chance of preserving realism. We’ve assumed all along that each photon is unaffected by the other photon’s polarizer. Why, indeed, would a photon be affected by a distant sheet of plastic that it never even approaches? If your polarizer affects my photon, it must be indirect, through your polarizer’s effect on your photon (which is entangled with mine).

  In 2003, Anthony Leggett derived a generalized Bell inequality. We recall that ordinary Bell inequalities are based on two assumptions: realism and locality. Leggett retained the assumption of realism, but permitted a restricted form of nonlocality.18 Quantum mechanics and measurements violate Leggett’s inequality, but physicists dispute the significance of this result.19

  Can We Save Locality By Rejecting Realism?

  We need to identify just a single false assumption to explain why Bell’s constraints do not apply to real particles. Could the false assumption be realism, such that locality may be valid? If we reject realism, then particles are not predestined to behave any particular way when they are eventually measured. Thus one photon in an entangled pair is not predestined to be vertically polarized, even if that’s what the measurement ultimately shows. But when both polarizers are vertical, the two photons always do the same thing: they both pass through, or they’re both blocked. If the photons are in a fundamentally undecided state before measurement, how can they possibly arrange to always behave identically when the polarizer angles are identical? Nonlocality is much more obviously necessary when realism is rejected. Indeed, Einstein’s objection to quantum mechanics was that its lack of realism necessitates nonlocality.

  But we can insist (boldly? shrilly? petulantly?) that direct observation is the only scientific reality. This assertion has been made in a variety of forms, starting with Niels Bohr’s Copenhagen interpretation. An extreme version of this idea is called genuine fortuitousness, which denies the existence of microscopic particles! In this view, there are probabilities of responses from our detectors, but we shouldn’t say that the detectors are actually detecting anything.20

  “Direct observation is the only scientific reality” takes a less extreme, though still brazen, form, in a recent interpretation of quantum mechanics called QBism (pronounced “cubism” to deliberately create a sense of radical departure from established norms).21 QBism is the abbreviation of “quantum Bayesianism.” In Bayesian statistics, probabilities are updated as new information comes in.

  For example, one time I was visiting Chicago. Coming out of a train I noticed that my wallet was gone. The departing train receded before my saddened eyes. I asked the transit staff if there was a lost and found. They gave me the phone number, but they told me that there was no point because I had been pickpocketed. I called the los
t and found, but it was closed for the day. I spent the whole harrowing night believing that Chicago was a city of villains. Even if I got a new wallet, I would surely be robbed again.

  The next morning, I called the lost and found, and learned that someone had turned in my wallet, with all $136 in it! I immediately reversed my judgment of Chicago. Chicago was a city of good Samaritans, and I could expect nothing but kindness from strangers.

  The daily risk of crime in Chicago at no point actually changed over that 12-hour period. My subjective judgment of the risk, however, underwent two drastic updates.

  In QBism, quantum mechanical probabilities are subjective judgments. There’s no such thing as an absolutely accurate, objective probability “out there.” Quantum mechanics is a tool for making our subjective judgments as accurate as possible. Different people will assign different probabilities to the same event if they have different information about it. Before a photon’s polarization is measured, you and I may agree that the probability of vertical polarization is 50 percent. If you do the measurement and the photon is found to be vertically polarized, you update the probability to 100 percent. If I’m out of the room, I still think it’s 50 percent until you give me the news. Until then, 50 percent and 100 percent are equally legitimate probabilities in the sense that they’re both based on the best information available to the person.

  Thus, according to QBists, there is absolutely no action at a distance. If I measure the polarization of one entangled photon and find it to be horizontally polarized, I immediately believe with 100 percent certainty that the other photon will also be horizontally polarized. If the other photon is traveling to you, a full light-year away, I have no way of communicating my knowledge to you before the other photon arrives; your photon had too much of a head start, even if I send you the news at the speed of light. For the whole year, you’ll continue to believe that the probability of horizontal polarization is 50 percent, while I know it’s really 100 percent. According to QBism, we’re both right! We’re both applying quantum mechanics as accurately as possible with the information we have.

  QBists refuse (humbly? peevishly?) to assign a cause to the observed correlations between entangled photons. The correlations are a fact of nature, and quantum mechanics gives us the math to accurately predict them. Any speculation as to how the correlations come about is outside the scope of physical science. (This approach is sometimes called “shut up and calculate.”) Since QBist physicists don’t speculate about underlying causality, the speculation and discussion must therefore come from ... philosophers ... or from theologians, poets, or science-fiction writers?

  I don’t permanently encamp with the QBists. But on occasion, QBism feels like an invigorating breeze that clears away a cloying miasma of confusion. QBism fends off the questions of what a particle’s like before measurement, what constitutes a measurement, and what is the underlying deep reality. QBism ejects these questions from the realm of science because they all inquire about something that can never be scientifically determined: the state of an object before it’s observed. It’s not wrong to speculate about what a particle’s like before it’s measured, or to wonder what invisible mechanism enables one photon to always behave like its twin; it’s just that we step outside of QBist science when we speculate about things that can never be directly observed.

  What happens to objects that no one’s looking at? Does the seemingly solid world dissolve into the phantasms and mirages of our own assumptions and mental images? The visible universe does not completely blink out of QBist existence when we close our eyes; the lapse in observation is filled in by the subjective judgment that the world is still there. QBism preserves our common sense. Quantum mechanics is classified as a prediction tool, not a gateway to ultimate reality.

  QBism sweeps the cobwebby spookiness out of quantum physics (and into someone else’s discipline). There’s no action at a distance, and there’s no speculation (within physics) about what particles are doing when we’re not looking at them. But we can push this idea in a direction unintended by QBism’s inventors. If we really believe that direct observation is the only reality, then, looking at the night sky is a single truth; observer and observed cannot be logically separated. And the quest to preserve locality leads to unification with everything we see.

  Glossary

  Bell inequality

  A constraint imposed on a measurable quantity by local realism, with the added assumption that the experimenter can freely choose detector settings.

  Coincidence

  In the context of quantum optics, simultaneous detection of two photons.

  Copenhagen interpretation

  A family of interpretations that reject realism. Quantum mechanics is a tool for predicting measurement outcomes, not a description of what particles are doing when we’re not looking at them.

  Counterfactual definiteness

  The assumption that we can state what the result of a measurement would be under conditions different from actual conditions. Counterfactual definiteness is assumed implicitly in the derivation of Bell inequalities. Bell inequalities can be derived assuming that particles have properties that predetermine the results of all possible measurements.

  Detection loophole

  A consequence of limited efficiencies of particle detectors. Unless efficiency is sufficiently high, we must assume that all incoming particles have an equal probability of detection; the detector does not preferentially detect particles that violate Bell inequalities.

  Freedom-of-choice loophole

  A consideration of the possibility that particles somehow affect detector settings, or that an unknown influence affects both the particles and the detector settings.

  Hidden variables

  Unknown properties or influences that determine the outcomes of all possible measurements.

  Length contraction

  The shortening of lengths of objects moving at relativistic speeds.

  Locality

  The assumption that the measurement of a particle is unaffected by the measurement of a distant particle.

  Locality loophole

  A consequence of hypothetical communication between measuring equipment and entangled particles. The locality loophole is closed if the measuring equipment makes unpredictable changes so rapidly that no communication (up to the speed of light) can enable the entangled particles to violate a Bell inequality.

  Local realism

  The combination of two assumptions: objects have properties that exist regardless of whether anyone is observing them or knows what they are, and the measurement of one object is unaffected by the measurement of a distant object. Local realism is common sense, and yet it is rigorously contradicted by measurements of entangled particles.

  Many-worlds interpretation

  The view that the deep reality is the sum of all possible states of particles. Mutually exclusive results occur in parallel universes, which are branches of the one deep reality.

  Photon

  A particle of light.

  Polarizer

  A material that transmits light whose electric field is restricted to a single plane.

  QBism

  A relatively recent interpretation of quantum mechanics, which emphasizes that all probabilities are subjective judgments.

  Realism

  The assumption that objects have properties that exist regardless of whether anyone is observing them or knows what they are. Measurement reveals properties that objects already had.

  Relativistic speed

  A speed close to the speed of light.

  Superdeterminism

  The view that everything in the universe, down to the smallest detail, was predetermined from the moment of the Big Bang.

  Time dilation

  The slow elapsing of time of anything moving at relativistic speeds.

  Wormhole

  A hypothetical shortcut through space and time.

  Notes

  Preface

&n
bsp; 1. A. Einstein, M. Born, and H. Born (1971), The Born-Einstein Letters (Macmillan).

  Introduction

  2. G. Orwell (1949), 1984 (Secker & Warburg).

  Chapter 1

  1. This statement may be controversial, as we’ll see in chapter 6. It’s certainly true that measuring one particle helps us predict the outcome of measuring the other particle—with 100% certainty in some cases. It’s also certainly true that something changes as a result of the measurement of the first particle; the measurement does not merely reveal properties that the particle had all along. Combining these facts, we are tempted to say that the measurement of one particle instantly affects both particles, but not all physicists would agree.

  2. To be fair, we must recognize that geocentrism was supported by legitimate arguments based on observation. For example, we don’t feel the motion of the earth, in contrast to the fact that we feel the motion of a ship. Also, with the unaided eye, we can’t observe stellar parallax: apparent motion of stars relative to one another due to the motion of the earth around the sun.