By Dr. John Millam1
In this short series of articles, we have explored the wonders of quantum mechanics. Our journey has proceeded by first presenting an overview of quantum mechanics (part 1), then discussing wave-particle duality (part 2), and finally describing quantum tunneling (part 3). (For a quick review, see Appendix: Overview of Quantum Mechanics.) This section will explore the strange and mysterious phenomena of quantum entanglement. Quantum entanglement was so contrary to everything known at that time that the brilliant Albert Einstein dismissed it as “spooky action at a distance.” The obvious question is, “what is it, and how do we know if it is real?”
What is Quantum Entanglement?
Quantum entanglement is a subtle but powerful quantum phenomenon. Although entanglement is impossible to directly observe, we do have abundant evidence that it is real. To help wrap our brains around this, imagine the following scenario. Take two friends, whom we will call Alice and Bob, and place them in separate rooms. Give each of them a coin and instruct them to flip it a thousand times while carefully recording the results of each toss. Once finished, compare the outcomes for each pair. For truly random coin tosses, the two coins should agree (i.e., either both heads or both tails) half the time and disagree (i.e., one heads and one tails) the other half.
What would you conclude if the coin tosses agreed every time? And what if this were true even if Alice and Bob performed the experiment in rooms located miles apart? Naturally, you might assume some form of cheating. Perhaps Alice and Bob were communicating via cell phones to synchronize their results. A reasonable person would think that there must be some explanation for this extraordinary agreement. The strange truth is scientists have been able to reproduce this type of eerie correspondence using sub-atomic particles. And after 70 years, they have not been able to explain away these results as some form of hidden mechanism. Somehow, these particles synchronize their behavior even when separated by large distances.
The essence of quantum entanglement is that a group of particles can interact in such a way that they become interdependent. That is, the particles cannot be fully described individually—even separated they represent a single composite system. Because of this interconnectedness, affecting one of the particles will instantly influence the behavior and properties of its entangled partners. This is true even if they are located very far apart.
Practical Uses for Quantum Entanglement
While quantum entanglement is still not fully understood, it does enable an amazing array of technological advances. Some specific examples summarized from “Five Practical Uses for ‘Spooky’ Quantum Mechanics:”
1 Ph.D. in Theoretical Chemistry from Rice University. Full permission is given to reproduce or distribute this document, or to rearrange/reformat it for other media, as long as credit is given, and no words are added or deleted from the text.
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- Ultra-Precise Clocks. Atomic clocks monitor the specific radiation frequency needed to make electrons jump between energy levels in a collection of atoms. The precision of these clocks can potentially be significantly enhanced by utilizing entangled atoms.
- Uncrackable Codes. Traditional cryptography works using keys: a sender uses one key to encode information, and a recipient uses another to decode the message. This strategy is susceptible to eavesdropping, but quantum cryptography protects against this vulnerability. Quantum rules dictate that “reading” the polarized photons will always change their states; therefore, any attempt at eavesdropping will alert the communicators to a security breach.
- Super-Powerful Computers. A standard computer encodes information as a string of binary digits, or bits. Quantum computers supercharge processing power because they use quantum bits, or qubits, which exist in a superposition of states—until they are measured, qubits can be both “1” and “0” simultaneously.
- Improved Microscopes. Differential interference contrast microscopy uses two beams of photons fired at a substance and measures the interference pattern created by the reflected beams—the pattern changes depending on whether they hit a flat or an uneven surface. Using entangled photons dramatically increases the amount of information the microscope can gather, because measuring one entangled photon gives information about its partner.
- Biological Compasses. Some birds, like the European robin, may use a form of quantum sensing to keep on track when they migrate. A light-sensitive protein called cryptochrome, which may contain entangled electrons, allows the animals to effectively “see” the Earth’s magnetic field and use it for navigation.
Some additional applications of quantum entanglement include quantum radar and quantum teleportation.
Understanding Entanglement
When physicists attempt to generate pairs of entangled particles, it generally involves entangling one of two different properties: spin or polarization state. All fundamental particles have a property called spin, a form of intrinsic angular momentum.2 The spin of an electron can only take on one of two distinct values: +1/2 and -1/2. These two states are commonly called “spin up” and “spin down,” respectively, for historical reasons. For photons (particles of light), scientists generally use their polarization state instead. Light can oscillate (relative to its direction of motion) in one of two perpendicular directions: vertical and horizontal. The spin of an electron and the polarization state of light are useful in studying quantum phenomena because they are limited to having two measurable outcomes. Both properties behave analogously to a flipped coin that will land either heads or tails.
Consider two electrons sharing the same orbital in an atom, such as the two electrons in a helium atom. Because of the Pauli exclusion principle, two electrons occupying the same orbital must have opposite spins. That is, one electron must be spin up, and the other spin down. This seemingly straightforward situation is complicated by the fact that electrons are indistinguishable particles. Indistinguishability means that one cannot identify which of the electrons is spin up
2 The term spin was coined by George Uhlenbeck and Samuel Goudsmit in 1925. They envisioned particles behaving like a planet rotating about its own axis. The two possible spin values would then correspond to the particle rotating either clockwise or counterclockwise. This description, however, cannot be correct because fundamental particles are point-like objects and therefore cannot rotate in the conventional sense. The label remains but scientists today understand spin in much more abstract mathematical terms.
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because that would allow you to distinguish between them. Instead, the pair of electrons are in a superposition state that preserves their indistinguishability. Labeling the electrons as A and B respectively, we can describe the entangled state as consisting of 50% of the state with A as spin up and B as spin down and 50% of the state with A as spin down and B as spin up. These electrons are entangled in the sense that neither particle has a well-defined spin. Instead, we can only know the total spin of the combined pair. However, if we were to measure the spin of one electron, it would be forced to take on a definite state—either spin up or spin down. Once the spin of one is known, the other must now possess the opposite spin.
To illustrate this, let us consider a pair of electrons entangled as previously described, but not associated with an atom (see Figure 1).3
1) Take two electrons entangled to have opposite spins.
2) Now, spatially separate them until they are far apart. They remain entangled even though they can no longer interact with each other.
3) If electron A is measured to be spin up, then electron B must be spin down. The change in B occurs instantly.
The big mystery of quantum entanglement is explaining how measuring A can instantly affect electron B despite the distance between them. If the electrons were close to each other, then one could imagine a hypothetical force transmitting the effect from one to the other. This would be like gluing the faces of two coins together, so they are forcefully constrained, such that if one lands heads, the other must be tails and vice versa. While some unknown force could potentially explain the behavior for cases when the particles are located close together, it cannot explain the case when they are far apart. Effects from quantum entanglement are instantaneous, regardless of distance, whereas known forces cannot act faster than the speed of light.
Mechanisms for Generating Entangled Particles
Just how do experimentalists generate entangled particles in the lab? Currently, there are six commonly used techniques (summarized from “How Do You Create Quantum Entanglement?):”
3 Summarized from https://cosmosmagazine.com/physics/einstein-bohr-and-the-origins-of-entanglement/
Figure 1: Effect of measurement on entanglement.
Credit: John Millam based on footnote 3.
4 - Positron-electron Annihilation. When a positron (an anti-electron) hits an electron, they annihilate each other, releasing two gamma rays whose polarization states are entangled. (Positrons are emitted by certain radioactive isotopes when they decay.)
- Cascade Transitions. Calcium atoms in a highly excited state can emit two photons. If the photons move in opposite directions, then their polarization states must be entangled.
- Spontaneous Parametric Down-Conversion. Light shown on a non-linear crystal (e.g., beta-barium borate or lithium niobate) will produce pairs of entangled photons with opposite polarization states (see Figure 2).
- Second Generation Entanglement. A pair of entangled photons are absorbed by a pair of atoms. If done correctly, the atoms will be entangled with each other even though they never interacted.
- Indirect Entanglement. Photons emitted by two widely separated ytterbium ions are combined in a beam splitter. This has the effect of entangling the ions.
- Rydberg Blockade. Two atoms are brought into extremely close contact. Each atom is excited into a Rydberg state that overlaps with the opposing atom resulting in the states of both atoms being entangled.
Of these, spontaneous parametric down-conversion is the most widely used method today because it is the most efficient at generating entangled photons.
Correlation as Evidence for Entanglement
To better understand the concept of correlation and what it means for entanglement, let us revisit the scenario of Alice and Bob flipping coins. Coins have two possible observed states (heads and tails). Those states are a helpful analog to an electron’s two spin states (spin up and spin down) or to the two polarization states of light (vertical and horizontal). Some details for our thought experiment: - The two coin-flippers are named Alice and Bob.
- Alice is in Washington DC and Bob is in London.
- Each person flips thousands of fair coins and records each outcome (either heads or tails).
- Alice and Bob submit their data to an auditor who records their results in the form of a correlation table. Each pair of coin tosses are tabulated according to the four possible outcomes, which are converted into percentages.
Let us now consider two different scenarios.
Case 1: Independent Coins
To begin, we will consider using simple, ordinary coins. Each coin flip is completely independent. As a result, each of the four possible resulting combinations has an equal probability of occurring. The odds work out to a 25% chance for each arrangement. The coins will match (heads-heads or
Figure 2: Diagram of Spontaneous Parametric Down-Conversion.
Credit: Wikipedia commons.
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tails-tails) half of the time and mismatch (heads-tails or tails-heads) the other half. This result
indicates a complete lack of correlation, meaning one result does not influence the other.
Correlation Table 1: Independent coins – no correlation.
Alice
Heads Tails
Bob
Heads 25% 25%
Tails 25% 25%
Case 2: “Entangled” Coins
For our second case, imagine that the coins behave equivalently to pairs of particles entangled to
have matching states. For each toss, the coins come up either both heads or both tails. This
outcome represents perfect correlation. This means that the two coins are in communication with
each other.
Correlation Table 2: “Entangled” coins – perfect correlation.
Alice
Heads Tails
Bob
Heads 50% 0%
Tails 0% 50%
The EPR Debate
Quantum mechanics was birthed in the 1920s-1930s based on efforts to fix problems in
classical (Newtonian) mechanics. In 1926, Erwin Schrödinger published an equation describing
the behavior of quantum systems:
ˆH
(r) = E (r)
n n n
, Equation 1
where Ĥ is the Hamiltonian operator, n(r) is the set of wavefunctions, En are the associated
energies, and n is an integer.
Solving Schrödinger’s equation for a given system yields a set of possible wavefunctions, n(r),
describing everything we can know about the system.
As physicists began to solve the equation for various systems, they found perplexing cases
where a group of particles were intertwined in such a way that their properties could no longer be
described independently. This was a radical departure from the previous Newtonian mechanics,
where particle properties were always clearly and independently defined.
The EPR Paradox
Despite being an early proponent of quantum mechanics, Albert Einstein was deeply
disturbed by the notion of entanglement (although the term entanglement was not coined until
later). Because quantum entanglement ran contrary to long established principles, he concluded
that quantum theory could not be entirely correct. To express his concern, Einstein and his research
students, Boris Podolsky and Nathan Rosen, published a paper in 1935.4 The EPR paper (based
4 A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality be Considered
Complete?” Phys. Rev. 47, 777-780 (May 15, 1935).
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on the author’s initials) presented a novel thought experiment designed to highlight their objections.
The paper described a situation where two particles—labeled A and B—are allowed to interact in such a way that they become entangled, with the properties of A being tied to the properties of B. The two particles are then separated by a considerable distance, such that they are no longer able to interact. According to quantum mechanics, they will remain in this entangled state even when distantly separated. Precisely measuring the position of A will reduce it to a well-defined location. This causes B to simultaneously collapse to a specific position that can be predicted based on the position of A. The curious point is that the position of B can be precisely known without measuring or disturbing it in any way. In the same way, measuring the momentum of A gives us certain knowledge of the momentum of B.
This thought experiment leads to a curious dilemma known as the EPR paradox. According to Heisenberg’s uncertainty principle, it is impossible to simultaneously measure the position and momentum of an individual particle to perfect precision. In other words, the more precisely you know one of these quantities, the greater the uncertainty in the other. The EPR setup seems to violate this by allowing us to know both the position and momentum of B with certainty in violation of the uncertainty principle.
The authors argue, “If, without in any way disturbing a system, we can predict with certainty … the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.”5 More simply, a property is an “element of physical reality” if it has a definite value independent of measuring it. The EPR thought experiment seems to demonstrate that both position and momentum for the entangled partner are elements of reality. This conflicts with the uncertainty principle that declares the position and momentum for a single particle cannot be simultaneously known and are, therefore, not simultaneously real. The paper proposes that quantum theory must be incomplete because it fails to simultaneously describe individual particles’ position and momentum. Consequently, they argued that even though quantum theory makes accurate predictions, it cannot be a complete description of reality. They did, however, suggest that it might be possible to modify quantum theory to correct this deficiency.
Twelve days before the EPR paper was published, the New York Times got wind of the story and much to Einstein’s dismay printed a sensational article (see Figure 3).6 The article boldly proclaimed, “Einstein Attacks Quantum Theory.”
But not everyone was persuaded by the famous scientist. Niels Bohr led the defense of the orthodox interpretation of quantum mechanics. He quickly published a paper arguing the authors of the EPR paper had reasoned fallaciously.7 In it, he stated that, position and momentum are complementary in quantum theory and, therefore, cannot be simultaneously observed. An experimentalist can freely design their experiment to measure either the particle’s position or its momentum, but not both. Essentially, this inability to simultaneously know the position and momentum of the particle is not a flaw, but a fundamental feature of quantum mechanics.
5 Ibid, p. 777.
6 “Einstein Attacks Quantum Theory,” The New York Times, May 4, 1935, p. 11.
7 N. Bohr, “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?” Physical Review 48 (8): 696–702 (October 15, 1935).
Figure 3: New York Times, May 4, 1935.
Credit: Wikipedia commons.
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Lost amidst the complex theoretical argument was a far more significant and more disturbing issue. Measuring particle A causes an instantaneous change in particle B even though they are too far apart to interact. Moreover, the wavefunction of B is entirely determined by the state of A. That means that what happens to A must somehow be instantaneously communicated to B. This observation distressed Einstein because it seemed to violate his theory of relativity which dictates that forces cannot act faster than the speed of light. Erwin Schrödinger shared Einstein’s concerns about possible faster-than-light influences and wrote two papers where he introduced the term “entanglement” to describe the state of the coupled particles.8
EPR Criteria
Central to the EPR paradox is the assumption of local realism. These two ideas are summarized as follows: - Local. Actions and measurements can only influence nearby objects. Specifically, effects cannot propagate faster than the speed of light as taught by the theory of relativity.
- Realism. The properties of entities exist independent of measurement. Measurement only reveals the properties rather than determining them.
Quantum mechanics violates both assumptions. The EPR paper (written by Podolsky) focused on the issue of realism. However, Einstein later wrote that his primary concern was the issue of locality (as required by his theory of relativity).9 Bohr had defended quantum mechanics’ lack of realism but side-stepped the apparent violation of locality.
Let us consider why Einstein and other scientists were so passionate about fighting to preserve locality.10 The main reason is that locality is essential to our ability to do science and make sense of the world. The concept of locality can be divided into two main aspects. - Separability. This aspect allows you, in principle, to isolate an object from other nearby objects so that you can consider it independently of everything else.
- Local Action. Objects can only interact with other nearby objects.
Simply put, separability defines what objects are, and local action dictates what they do. Nonlocality, therefore, was perceived as evidence that quantum mechanics could not be wholly correct and there should be an improved theory that would restore locality.
Throughout history, locality was generally assumed in science. One significant violation of this principle was Isaac Newton’s formulation of gravity. His equation implied that gravity acted instantly across space. Centuries later, Einstein’s general theory of relativity corrected this by showing that gravitational forces cannot act faster than the speed of light, thus reestablishing locality. Under relativity, all known forces are limited by the speed of light. Relativity enforced locality by establishing the speed of light as the ultimate speed limit. Without this limit, objects could move at infinite speed, and distance would lose meaning. Relativity theory thereby provides a measure of isolation among separated objects and ensures their mutual distinctiveness.
In 1905, Einstein’s theory of relativity had just enshrined locality as a bedrock principle of modern science. Not surprisingly, he was dismayed when quantum entanglement seemed to undermine his revolution by reintroducing the specter of nonlocality.
8 E. Schrödinger, “Discussion of probability relations between separated systems,” Mathematical Proceedings of the Cambridge Philosophical Society 31 (4): 555–563 (1935). E. Schrödinger, “Probability relations between separated systems,” Mathematical Proceedings of the Cambridge Philosophical Society 32 (3): 446–452 (1936).
9 Source: Einstein–Podolsky–Rosen paradox, Wikipedia.
10 George Musser, Spooky Action at a Distance. See also excerpt George Musser, “Weighing the Importance of Locality, Science Friday, April 28, 2016, https://www.sciencefriday.com/articles/weighing-the-importance-of-locality/.
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Local Hidden Variables
The EPR paper hinted it might be possible to modify quantum theory to make it consistent with local realism. This adjustment would involve supplementing the quantum wavefunction with additional information referred to as “local hidden variables.” In this context, “local” means that it only includes nearby interactions, so there are no faster-than-light influences. “Hidden” describes unobserved quantities. The net effect of including these hypothetical new variables would be that all the particle’s properties, such as position and momentum, would always be fully defined, thus enforcing realism. In the case of entangled particles, this alteration would avoid the need for the measured particle to instantly affect its entangled partner because both would already be in a definite state. This change would restore locality.
Local hidden variables can be viewed as a classical alternative to quantum entanglement that avoids any need for faster-than-light influences between the particles. Quantum entanglement and local hidden variables are mutually exclusive models—they cannot both be true. Physicists, however, needed a way to determine which model was correct.
Testing Entanglement
When the EPR debate was raging in 1935, quantum entanglement was just an abstract theoretical question. The status of the debate changed in 1950 when Chien-Shiung Wu and Irving Shaknov demonstrated a correlation between entangled photons generated by positron-electron annihilation. Quantum entanglement was now a testable reality. The debate then shifted to determining which of the two models best explained the observed behavior. Were the photons truly entangled as described by quantum mechanics? Or were they governed by local hidden variables, as Einstein, Podolsky, and Rosen implied? Both models made similar predictions, so how to distinguish between them?
The first challenge was that the EPR paradox, as initially proposed, was ill-suited for experimental testing. The problem was that it would be extremely difficult to measure the positions and momentums of pairs of particles to sufficiently high precision. In 1951, David Bohm suggested a useful alternative: spin.11 Using the spin of an electron would greatly simplify the analysis because there are only two possible spin states to consider: up and down. In a 1957 paper with Yakir Aharonov, he revisited this idea in the context of the EPR paradox.12 They recognized that testing the EPR paradox using spin was not technically feasible at the time but could be performed using the two polarization states of light.
Despite Bohm’s suggestion, progress was stymied for another decade by an even more significant challenge—there were no known experimental testing criteria capable of distinguishing between genuine entanglement and local hidden variables. One factor that made this especially difficult was that local hidden variables was just a theoretical idea rather than a clearly defined model. It was, therefore, essential to create a test general enough to apply to all possible local hidden variable models.
11 D. Bohm, Quantum Theory, Prentice-Hall, Englewood Cliffs, 1951, pp. 611-623.
12 D. Bohm, Y. Aharonov, “Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky,” Physical Review 108 (4), p. 1070–1076 (November 15, 1957).
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The big breakthrough came in 1964 when John Stewart Bell (see Figure 4) developed a mathematical criterion for testing the validity of local hidden variables.13 Bell’s theorem was a mathematical inequality that placed an upper limit on the degree of correlation that local hidden variables could produce. If the measured correlation exceeded this limit, then local hidden variables could not explain the result and would be ruled out. Unfortunately, he published his theorem in a relatively obscure journal. It would be another five years before scientists recognized it as the long-awaited tool they needed to resolve the EPR paradox. In the end, Bell’s theorem would be considered one of the most influential theorems in quantum mechanics.
In 1967, Carl Kocher developed the atomic cascade method to generate pairs of entangled photons using highly excited calcium atoms. Using Kocher’s method, Stuart Freedman and John Clauser (1972) and later Alain Aspect (1982) performed experiments demonstrating a violation of Bell’s theorem. These measurements provided solid experimental support for quantum entanglement by ruling out local hidden variables. Clauser and Aspect shared the 2022 Nobel Prize in Physics for their pioneering work demonstrating quantum entanglement.
Bell’s Theorem Experiments
Just how did Freedman, Clauser, and Aspect demonstrate quantum entanglement? Let us examine their methodology and results. For the sake of simplicity, we will assume these experiments used photons entangled to have the same polarization state, rather than the opposite. In the experimental setup, pairs of entangled photons are generated and directed toward two widely-separated, highly-sensitive photon detectors labeled A and B (see Figure 5a). A polarization filter is placed in front of each sensor. Both polarization filters can be adjusted independently, although only the relative difference in angle is relevant. A coincidence detector counts whether the photons pass through one, both, or neither sensor to give the measure of correlation.
13 J. S. Bell, “On the Einstein Podolsky Rosen Paradox” Physics 1 (3), p. 195–200 (1964). The derivation of Bell’s theorem and its application to quantum entanglement is beyond the scope of this paper, however, an excellent discussion of this topic can be found in A. Montwill and A. Breslin, Quantum Adventure, pp. 224-229.
a) b)
Figure 5: Bell’s theorem test using entangled photons.
Credit: a) Alex Montwill and Ann Breslin, The Quantum Adventure, p 218 and b) Quora (shading added).
Figure 4: John Stewart Bell.
Credit: Wikipedia commons.
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The polarization filters only allow photons to pass through if their polarization state matches the filter’s orientation. In this way, the polarization filters serve to measure the state of the photons by forcing them to have a definite polarization state. Perfect correlation corresponds to the photons having matching polarization states and, therefore, either both photons reaching the detector or neither. Zero correlation represents photons with perfectly mismatched states, so only one of the two photons reaches the detector. This degree of correlation is plotted on a graph as a function of the angle between the polarization filters, with Figure 5b showing the results. The red line represents Bell’s theorem inequality. Any results less than or equal to the value (red shaded area) can potentially be explained with local hidden variables. The blue line is the actual result and exceeds Bell’s theorem inequality, ruling out local hidden variables. Quantum entanglement really does demonstrate “spooky action at a distance.”
To better understand what is going on in these experiments, let us anthropomorphize the particles so they can explain events from their perspective. According to local hidden variables, the polarization states of the entangled photons must be established while they are still interacting. So, imagine the two photons agreeing to a randomly selected orientation. With that settled, they do a quick fist-bump before flying off to their respective detectors. For true quantum entanglement, the photons refuse to resolve their polarization state, preferring to remain undecided. Instead, they decide to stay in touch by exchanging cell phone numbers. They speed off to their respective destinations until one of them encounters a polarization filter. When interacting with the filter, the measured photon is forced to take on a definite polarization state. He then calls up his partner and tells him to take on the matching orientation.
The difference is now clear. For the local hidden variables, the resolution of their polarization state happens before reaching the polarization filters. This fundamentally limits the degree of correlation they can possess, as quantified by Bell’s theorem. For quantum entanglement, the polarization state is determined when one of the photons encounters a polarization filter. This gives both photons information about the orientation of one of the polarization filters. Because of this, the entangled photons can achieve a greater degree of correlation than allowed by Bell’s theorem.
One last point. When Wu and Shaknov performed their experiments demonstrating quantum entanglement in 1950, they only tested the cases where the polarization filters had the same (angle = 0°) and the opposite (angle = 90°) orientation. For these two cases, local hidden variables and quantum entanglement make identical predictions (see Figure 5b). Part of the insight from Bell’s theorem was recognizing the need to explore angles intermediate between these two cases because only under these circumstances is it possible to distinguish between the two models.
Closing the Loopholes
Because Bell’s inequality was extremely difficult to test, there were lingering doubts. Some scientists proposed loopholes that could save local hidden variables from falsification. Two primary issues: - Detection Loophole. Photon detectors at the time did not always register all the incoming photons, which could skew the resulting statistics.
- Locality Loophole. The time between the setting of the polarization filters and the measurement must be small enough to prevent possible light speed influences.
A “loophole-free” version of the experiment was performed in 2015, simultaneously closing both the detection and locality loopholes. Scientists are now firmly convinced that quantum entanglement is genuine.
Despite the strong evidence for entanglement, one rather extreme version of the locality loophole remains open. In 1977, Bell pointed out that his famous inequality assumes that scientists
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are free to set the polarization filters independently of each other and independently of any local hidden variables. Based on this, he proposed a radical new interpretation of quantum mechanics called superdeterminism. According to this interpretation, there is a correlation between the hidden variables and the polarization filters. The particle would essentially know in advance what the polarization filter settings are, thus avoiding the need for faster-than-light signaling. This would allow for local hidden variables to produce the observed correlations because the scientist’s choice of polarization filter angles would be predetermined.
Philosophically, this interpretation opens a whole can of worms. For example, if everything in the quantum world is determined, we, as aggregates of quantum particles, would be determined. Physical laws would control all our actions and choices. Scientists would lack free will to choose measurement settings. One enormous problem is that this model is that it is effectively unfalsifiable. Even in theory, no experiment could ever disprove superdeterminism.
Three Particle Entanglement
In 1989, Daniel Greenberger, Michael Horne and Anton Zeilinger (GHZ) demonstrated three-photon entanglement. If two pairs of entangled photons are brought into a particular experimental arrangement that makes one member indistinguishable from one member of the other pair, and if one of the two newly indistinguishable photons is captured, then the remaining three photons are entangled. The correlation data from the GHZ experiment is impossible to explain using local hidden variables and therefore provides robust support for quantum entanglement. Moreover, this evidence is entirely independent of Bell’s theorem.
For his work on quantum entanglement, Zeilinger shared the 2022 Nobel Prize in Physics with Clauser and Aspect.
Bohm’s Interpretation of QM: Nonlocal Hidden Variables
In 1952, David Bohm proposed a new interpretation of quantum mechanics. According to Bohm’s interpretation, a particle is guided by a pilot wave (its wavefunction) like a surfer riding a wave. The wavefunction serves the role of hidden variables, but this does not violate Bell’s theorem experimental results because this model is explicitly nonlocal. Bohm’s interpretation makes explicit the ability of one particle to influence its entangled partner even at great distance.
Does Entanglement Allow Instantaneous Communication?
Science fiction shows like Star Trek regularly assume faster-than-light communication. Could quantum entanglement serve as the basis for this?
No. It cannot because one cannot control the state of the measured particle—the results are random. The only way to detect correlations in the measurements is by comparing both sets of results. This comparison requires both sets of data to be communicated to a common location, and this step requires classical communication that is limited by the speed of light.
Does Entanglement Violate the Theory of Relativity?
Quantum entanglement involves instantaneous action—measuring one particle alters its entangled partners instantly, regardless of distance. Does this violate general relativity’s prohibition against faster than light communication?
No. Quantum entanglement does not violate relativity because no actual information is communicated faster than light. Basically, it is impossible to use the measurement of one of the entangled particles to transmit a message to the observer of the other particle.
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Quantum Entanglement: The Movie
To close this discussion, I recommend a delightful 9-minute-long video: Quantum Entanglement: The Movie produced by Scientific American. It provides a quick and entertaining dramatization of the key concepts presented in this paper.
Appendix: Resources on Quantum Mechanics
Robert Gilmore, Alice in Quantumland: An Allegory of Quantum Physics.
Erica W. Carlson, The Great Courses: Understanding the Quantum World.
James Kakalios, The Amazing Story of Quantum Mechanics.
Alex Montwill and Ann Breslin, The Quantum Adventure: Does God Play Dice?
Brian Clegg, The Quantum Physics Bible: The Definitive Guide to 200 Years of Subatomic Science.
Banesh Hoffmann, The Strange Story of the Quantum.
Amir D. Aczel, Entanglement: The Greatest Mystery in Physics.
George Musser, Spooky Action at a Distance.