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Can A Common Cause Explain Entanglement?
Abstract
Two local causal interactions inside the entanglement apparatus project the entangled particles into a spherically symmetric two-particle quantum state ΨAB that Erwin Schrödinger said cannot be represented as a simple product of two independent single-particle states ΨAΨB. As the particles travel away from the central apparatus C in opposite directions toward measurement devices at A and B the two-particle wave function is in a spherically symmetric singlet state with total spin angular momentum zero. The wave function is a linear combination or superposition of ΨA ↑ΨB ↓ + ΨA ↓ΨB ↑. The total spin zero is conserved as a constant of the motion until a local causal interaction at either A or B collapses the two-particle wave function, decohering it to a product of single-particle states, either ΨA ↑ΨB ↓ or ΨA ↓ΨB ↑ The particles are then disentangled. As long as local measurements are made at the same pre-agreed upon angle their planar symmetry will maintain total spin zero, the particles will have correlated opposite spin states, either up-down or down-up, and individual spin states will be randomly up or down. Should measurements at A and B not be made in the same plane, with angles differing by angle θ, perfect correlations will be reduced by cos2θ, as quantum mechanics predicts. We note that no information is communicated (at any speed) between A and B. The two bits of information are locally created at A and at B, distally caused by the initial entanglement at C. These bits of information did not exist as the particles were in transit to A and B. They were proximally caused by the local measurements at A and at B.We propose that simultaneous measurement outcomes at two entangled particles widely separated in space are caused to be perfectly correlated as the result of 1) local causes at initial entanglement, 2) a conservation principle as the particles travel to the measurement devices, and 3) measurements at A and B that are made in a (previously agreed upon arbitrary) single plane that replaces the spherical symmetry of the two-particle wave function with the planar symmetry that guarantees the perfectly correlated measurement outcomes. We regard this "causal chain" of events as a "common cause" in the sense of Hans Reichenbach's Common Cause Principle If an improbable coincidence has occurred, then there must have been a common cause.3In our case, if events at A and B are perfectly correlated, then either A causes B, B causes A, or there is a common cause C coming to A and B. Since A and B occur simultaneously, neither can cause the other. The initial local causes in the causal center C put the entangled particles in a spherically symmetric two-particle quantum state ΨAB that Erwin Schrödinger said cannot be represented as a simple product of two independent single-particle states ΨA ΨB. Instead it is a linear combination or superposition of ΨA ↑ΨB ↓ and ΨA ↓ΨB ↑.
ΨAB = 1/√2 (ΨA ↑ΨB ↓) - 1/√2 (ΨA ↓ΨB ↑)
Conservation of total spin zero maintains the spherical symmetry of this wave function ΨAB as the particles travel to A and B (provided no environmental interaction disturbs the symmetry).
The initial local causes are in the past light cone of the final measurement events, as is required for a common cause. They are distal causes. The proximal causes are the two local causal measurements at A and at B that create two bits of new information.
The final local causes produce perfectly correlated outcomes. But there is no faster-than-light communication or interaction between the separated measurement events at A and B.
As Einstein saw clearly, some moving inertial frames of reference exist in which A measures first, others in which B measures first. In our picture of a common cause, neither A nor B measures first.
This model opposes the standard view, developed over five decades by Albert Einstein and many others, that some kind of faster-than-light instantaneous and nonlocal interaction between a particle and its wave function, or between two particles, is needed to explain entanglement.
Instead, it is the instantaneous "collapse" of the wave function, in which nothing is actually moving, but in which values of the wave function ΨAB are instantly changed everywhere, specifically they are changed simultaneously at A and B whatever their separation in spacetime, at the moment that either of them causes the wave function to "collapse."
Einstein first saw an instantaneous (nonlocal) change across the front of a widespread light wave in his 1905 photoelectric effect work.
In his later years, Einstein famously called two-particle entanglement "spooky action at a distance" (spukhafte Fernwirkung) in a March 3, 1947 letter to Max Born.
Although our focus is on experiments and their data correlations, we will also describe the mathematical quantum theory, its wave functions, and their superpositions or linear combinations of product states that perfectly predict the puzzling correlations.
Our model of a "common cause" explaining entanglement is a causal chain of events that begins with the local causes in the entangling apparatus C that establishes the initial symmetry of the entangled particles.
A ← C → B
As the particles travel away from the central apparatus C in opposite directions toward measurement devices at A and B the two-particle wave function ΨAB is in a spherically symmetric singlet state with total spin angular momentum zero. This total spin zero is conserved as a constant of the motion.
Emmy Noether's theorem on the fundamental relationship between symmetry and conservation principles is extremely simple:
For any property of a physical system that is symmetric, there is a corresponding conservation law.Conservation is thus not a causal process in the sense of a causal interaction. Indeed, it demands the lack of any causal interaction with the environment which might decohere the two-particle wave function. But we might say that the conserved property of total electron spin zero is also "local" in the sense that it is traveling along with each particle just as David Bohm's "hidden variables" or David Mermin's "instruction sets" were thought to do. Galileo's law of Inertia, which became Newton's first law of motion, is a conservation principle. If a particle experiences no causal interactions it will maintain its state of motion, including remaining at rest. The final causal interactions in our "causal chain" of events are the two measurements at A and B, which create two bits of digital information. As long as local measurements are made at the same pre-agreed upon angle their planar symmetry will maintain total spin zero, the particles will have correlated opposite spin states up-down or down-up, and individual spin states will be randomly up or down. Should measurements at A and B differ by angle θ, perfect correlations will be reduced by cos2θ, as predicted by quantum mechanics. There is no physical mechanism or interactions between the particles that maintains the total angular momentum from moment to moment as they travel from initial state preparation to final measurements, just as quantum mechanics cannot explain many "motions," e.g., the "jumps" of electrons in and between different shells or orbitals in atoms and molecules or their passage through the slits in the two-slit experiment. As Richard Feynman told us, we can't find any "machinery" that explains what he called this one and only mystery in quantum mechanics. We criticize the claim by David Bohm1 that the three components of spin angular momentum must exist and be defined in all spatial directions, x, y, and z (which is impossible), in order for experiments to find the spins perfectly correlated and in opposite directions when measured. Similar is the claim by David Mermin2 that photon polarizations must exist in all directions!. The correct requirement is that there be no preferred spin direction at all (spherical symmetry) in initial entanglement and as the particles travel to A and B. It is the arbitrary but agreed upon angle chosen for the two final measurements that introduces the preferred direction. The planar symmetry of the measurement devices maintains the spin symmetry. Each final spin measurement creates a single bit of information. No information is communicated from A to B as Einstein feared.
Summary of Three Steps to Explain Entanglement
In our explanation of two-particle entanglement the first step is the formation of the spherical symmetric singlet state.
The second step is the conservation of the total spin angular momentum (and its spherical symmetry), which is a constant of the motion as the entangled particles fly apart.
The third step is the conserved spherical symmetry. As long as the two measurement devices are set at a (pre-agreed upon) same angle, they will have planar symmetry which bisects the spherical symmetry. Their measurement angle can then be arbitrary and the interactions will still produce perfectly correlated results.
Measurements made at different angles would destroy that symmetry, causing correlations to be reduced by cos2θ, where θ is the angle difference. This is the well-known "law of Malus."
We shall critically examine the details of entanglement state preparations and the experimental data from particle measurements in six different kinds of entanglement experiments. The first three (from the 1930's to 1960's) were thought ("gedanken") experiments (really hypothetical theories) involving material particles, atoms and electrons. The first was Einstein's theoretical work starting in 1905 and culminating in the 1935 EPR paradox paper, his most cited work and the touchstone for all subsequent research on entanglement. David Bohm's proposal in the 1950's that hidden variables could explain entanglement is the second kind of thought experiment. The third is the great work of John Stewart Bell in the 1960's, including his Bell Theorem and his claim that if hidden variables exist they must be non-local. The fourth and the sixth kind of experiments were actual physical experiments done in laboratories with light particles (photons) entangled by atomic cascades in calcium atoms. In the 1970's John Clauser and Stuart Freedman did the first experiments that violated Bell's inequality. They confirmed the correctness of quantum physics and showed that any "hidden variable" must be non-local. In the 1980's Alain Aspect used fast switching to ensure the particles were already in flight when the choice of measurment angle is made. In the 1990's Anton Zeilinger and his colleagues in Vienna developed spontaneous parametric down conversion(SPDC) techniques to generate entangled photons that are now used in most entanglement experiments. Clauser, Aspect, and Zeilinger received the 2022 Nobel Prize in Physics for their work. Our fifth kind of entanglement study was the very popular thought experiment of David Mermin in the 1980's.
1) Einstein and the EPR paradox.
Einstein first described two particles exhibiting nonlocal behavior in a conversation with Leon Rosenfeld at a meeting in Berlin in 1933. Before this, nonlocality was between a single light quantum and its light wave.
In 1933, shortly before he left Germany to emigrate to America,
Einstein attended a lecture on quantum electrodynamics by Léon
Rosenfeld. Keep in mind that Rosenfeld was perhaps the most
dogged defender of the Copenhagen Interpretation. After the talk,
Einstein asked Rosenfeld,
“What do you think of this situation?” Suppose two particles are set in motion towards each other with the same, very large, momentum, and they interact with each other for a very short time when they pass at known positions. Consider now an observer who gets hold of one of the particles, far away from the region of interaction, and measures its momentum: then, from the conditions of the experiment, he will obviously be able to deduce the momentum of the other particle. If, however, he chooses to measure the position of the first particle, he will be able tell where the other particle is. It is most unfortunate that Einstein did not explain that measuring the momentum of the first particle allows us to deduce the momentum of the second particle because of the conservation of linear momentum. The same conservation principle explains, as Einstein says, "If, however, he chooses to measure the position of the first particle, he will be able to tell where the other particle is." If Einstein had called this ability "knowledge (information) at a distance," instead of "spooky action at a distance," entanglement might never have been thought "spooky". It would be just a correlation of physical properties resulting from a common cause and a conservation law. Einstein and colleagues Boris Podolsky and Nathan Rosen, proposed in 1935 a paradox (known by their initials as EPR or as the Einstein-Podolsy-Rosen paradox) to exhibit internal contradictions in the new quantum physics. They hoped to show that quantum theory could not describe certain intuitive "elements of reality" and thus was incomplete. They said that, as far as it goes, quantum mechanics is correct, just not "complete." Einstein was correct that quantum theory is "incomplete" relative to classical physics, which has twice as many dynamical variables that can be known with arbitrary precision. But half of this information is missing in quantum physics, due to the indeterminacy principle which allows only one of each pair of non-commuting observables (for example momentum or position) to be known with arbitrary accuracy. Even more important, an individual particle, cannot be said to have a known position before a measurement, since evolution described by the unitary and deterministic Schrödinger equation provides us only probabilities. The most that can be said is that the particle can be found anywhere the probability amplitude is non-zero. This was the core idea of Einstein's claim of "incompleteness." For Bohr to deny this and call quantum mechanics "complete" was just to play word games, which infuriated Einstein. Einstein was also correct that indeterminacy makes quantum theory an irreducibly discontinuous and statistical theory. Its predictions and highly accurate experimental results are statistical in that they depend on an ensemble of identical experiments, not on any individual experiment. Einstein wanted physics to be a continuous field theory, in which all physical variables are completely and locally determined by the four-dimensional field of space-time in his theory of relativity. Einstein and his colleagues Erwin Schrödinger, Max Planck, (later David Bohm), and others hoped for a return to deterministic physics, and the elimination of mysterious quantum phenomena like the superposition of states, the mysterious "collapse" of the wave function, and Schrödinger's famous cat. EPR continues to fascinate determinist philosophers of science who hope to prove that quantum indeterminacy does not exist.
What happens according to the information interpretation of quantum mechanics is an instantaneous change in the information about probabilities (actually complex probability amplitudes). Nothing physical (matter or energy) is moving anywhere.
As we've seen, Einstein had been bothered by "nonlocal" phenomena between a light quantum and its light wave (function) since his 1905 photoelectric paper. But this phenomenon was even more clearly exhibited in EPR experiments as the apparent transfer of something physical, an "action," from one particle to another particle faster than the speed of light.
The 1935 paper was based on Einstein's 1933 question to Leon Rosenfeld about two material particles fired in opposite directions from a central source with equal velocities. He imagined them starting at t0 some distance apart and approaching one another with high velocities. Then for a short time interval from t1 to t1 + Δt the particles are in contact with one another.
After the particles are measured and become entangled at t1, quantum mechanics describes them with a single two-particle wave function Ψ12 that is not the simple product of two one-particle wave functions Ψ1 and Ψ2.
Einstein said that at a later time t2, a measurement of one particle's position would instantly establish the position of the other particle - without measuring it explicitly. And this is correct, just as after the collision of two billiard balls, measurement of one ball tells us exactly where the other one is due to conservation of momentum. But this is not "action at a distance." It is more nearly "knowledge at a distance."
Note that Einstein is implicitly using conservation of linear momentum to know the position of the second particle. Although conservation laws are rarely cited as the explanation, they may be the physical reason that entangled particles always produce correlated results. If the results were not always correlated, the implied violation of a fundamental conservation law would be a much bigger story than mysterious entanglement itself, as interesting and important as that is.
This idea of something measured in one place "influencing" measurements far away challenged what Einstein thought of as "local reality." Einstein thought that when the particles moved far enough apart they could be treated as separated, with independent wave functions Ψ1 and Ψ2.
But Erwin Schrödinger quickly replied to the EPR paper, telling Einstein that his "separation principle" (Trennungsprinzip) was not correct. Today this is known as nonseparability.
The particles can not be separated into a product of independent wave functions, for example, particle A definitely in state 1, particle B in state 2,
Ψ12 ≠ Ψ1A Ψ2B
Instead, particles A and B are each randomly found in state 1 or 2. But Particle B is certain to be in state 2 if particle A is measured in state 1, and vice versa.
Ψ12 = 1/√2 (Ψ1A Ψ2B) + 1/√2 (Ψ2A Ψ1B)
Quantum mechanics says that the particles are not in "pure" quantum states, but a "mixture" of two states, which maintain the coherent phase relations that allow them to interfere with one another.
Schrödinger used Paul Dirac's 1926 principle of superposition and John von Neumann's 1932 motion of "mixed states" in the "density matrix" to create two of the most popular and controversial ideas in quantum mechanics.
First, Schrödinger described the two particles as "entangled" at their first encounter. He called it verschränkt in German. Verschränkt means something like cross-linked. It describes someone standing with arms crossed, where each arm reaches out to touch the other. Today EPR is the classic example of entanglement.
Second, Schrödinger introduced his famous cat, claiming it is in a mixed state or a superposition of live and dead cats!
It was at this point in quantum history that the most controversial two-particle equation above appeared. It combines the ontological chance that Einstein discovered in 1916 with the idea that one quantum state can be described as in a linear combination or superposition of two other states that Dirac introduced in his 1927 "transformation theory" of quantum mechanics.
In Dirac's theory, the coefficients of the two states (1/√2) when squared (1/2) give us the 50% probabilities of finding the particles in the one or the other state.
The equation combines quantum randomness with quantum interference. Interference was made famous in the two-slit experiment, which Richard Feynman almost thirty years after EPR called the “one mystery,” the only mystery at the heart of all quantum mechanics.
Note that the equation does not describe two material particles interacting with one another but their abstract immaterial wave functions Ψ1 and Ψ2 interfering with one another.
These quantum mechanical wave functions, solutions to Schrödinger’s equations of motion (which replace Newton's equations of motion in classical mechanics), were thought by Schrödinger to be describing matter or energy, photons for light waves, mass and perhaps electric charge for electrons.
But in the quantum mechanics of Heisenberg, Jordan, Born, and Dirac the wave functions became “probability amplitudes,” whose absolute squares predict the probability of finding the values of observable quantum properties. And those predictions have been confirmed with extraordinary accuracy by countless experiments.
Let’s look at the equation in its simplest form that describes the superposition state of Schrödinger’s cat.
| Cat > = ( 1/√2) | Live > + ( 1/√2) | Dead >
Although this equation predicts interference between the cat states, such interference is never seen in cats, though it has been measured in surprisingly large macroscopic objects.
Nevertheless, squaring the coefficients 1/√2 tells us that there is 50% chance of finding such a cat in either the live or dead state, i.e., which is confirmed in principle.
Cats = (1/2) Live + (1/2) Dead.
Let's see how this simple equation also describes the two-slit experiment.
Ψ = ( 1/√2) | Left > + ( 1/√2) | Right >
The wave function beyond the two slits is a linear combination or superposition of the wave function passing the left slit | Left > with the wave function passing the right slit | Right >.
Note that whichever slit the particle passes through (and it must go through just one, because a quantum particle cannot become two (violating conservation of mass and/or energy), the probabilities of finding it on the screen are determined by the two-slit superposition. If a particle was detected passing through the left slit, or if the right slit were closed, the interference pattern would depend on a wave function passing through only that slit | Left >.
Given that the double-slit interference appears even if only one particle at a time is incident on the two slits, we see why many say that the particle interferes with itself. But it is the wave function alone that is interfering with itself. Whichever slit the particle goes through, it is the probability amplitude ψ, whose squared modulus |ψ|2 gives us the probability of finding a particle somewhere, the interference pattern. It is what it is because the two slits are open.
Why interference patterns show up when both slits are open, even when particles go through just one slit, though we cannot know which slit or we lose the interference.
2) David Bohm and "hidden variables."
In our second kind of "thought experiment," David Bohm replaced Einstein's separating particles with a hydrogen molecule disassociating into two hydrogen atoms, each with ℏ/2 of spin angular momentum.
Instead of measuring linear momentum, Bohm proposed using two hydrogen atoms that are prepared in an initial state of known total spin angular momentum zero (the H2 molecule). Momentum and position are continuous variables. Spin is discrete. Bohm argued that measurements of discrete variables would be more precise. Bohm also proposed local "hidden variables" might be needed to explain the correlations. Here is his description. Note that it includes the two-particle wave function describing the superposition of mixed states.
We consider a molecule of total spin zero consisting of two atoms, each of spin one-half. The wave function of the system is thereforeNote that when Bohm says "because the total spin is still zero, it can immediately be concluded that the same component of the spin of the other particle (B) is opposite to that of A," he is implicitly using the conservation of total spin angular momentum. Note also that our superposition equation for the two particles predicts a 50% chance that the first particle will be spin up (ψ+ (1)) and the second down (ψ- (2)) and a 50% chance of the reverse, that the first particle will be spin down (ψ- (1)) and the second will be up (ψ+ (2)). In either case the total spin is always certain to be conserved as zero. Next note that while the total spin is certain to be zero, the outcome for each particle is completely random, half the outcomes are found up and the other half outcomes down. Finally note that these amazing predictions of outcomes individually random but together perfectly correlated, as confirmed by numerous experiments, provide us with no mechanisms, no interactions between the particles that produce these perfectly correlated outcomes. It is simply that as Bohm says, "because the total spin is still zero, it can immediately be concluded that the same component of the spin of the other particle (B) is opposite to that of A." We can ask ourselves whether the first thought experiment (EPR) really needed some mechanism, some interaction, an "action-at-a-distance," as Einstein called it, to keep the particles moving symmetrically away from their center? In the absence of an external asymmetric force, all motions are mirror images, preserving their original symmetry and their perfect conservation of total linear momentum, as well as spin angular momentum. If linear momentum is conserved (by symmetry) without continuing interactions between particles, isn't conservation of spin angular momentum a much more plausible explanation than impossible faster-than-light interactions? In 1964, John Bell made a study of EPR and David Bohm's suggestion that local hidden variables could provide a mechanism that would explain entanglement. Instead of electrons, Bell proposed an experiment using photons and polarizers that measures the angular dependence of the falloff in perfect correlations when experimenters at A and B (usually called Alice and Bob) don't set their polarizers at the same angle (which we argue is needed to preserve the symmetry of the initial entanglement and the conservation of critical properties like spin angular momentum). Correlations are perfect when they measure at the same (pre-agreed-upon) angle. When their polarizer angles differ by ninety degrees, all correlations are lost. At intermediate angle differences θ, correlations diminish proportional to the square of the cosine of their angle difference - cos2θ, and not in a straight line as John Bell's theorem about inequalities mistakenly assumed.
Arguments Against a Common Cause
David Bohm gave the best known (but mistaken) criticism of a common cause explanation. He said that the electron spins would need to have pre-determined values in all three x, y, z directions at initial entanglement, but that this is impossible.
Only one spin component can have a definite value, say sz. When sz has the value ℏ, the other two components sy and sx are indeterminate.
Bohm and his colleague Yakir Aharonov wrote in 1957 that in classical mechanics, the molecule could have all three components of the spin well-defined, but this is impossible for quantum mechanics, since at most one component of the spin can be well-defined...
If this were a classical system, there would be no difficulty in interpreting the above results, because all components of the spin of each particle are well defined at each instant of time. Thus, in the molecule, each component of the spin of particle A has, from the very beginning, a value opposite to that of the same component of B; and this relationship does not change when the atom disintegrates. In other words, the two spin vectors are correlated. Hence, the measurement of any component of the spin of A permits us to conclude also that the same component of B is opposite in value. The possibility of obtaining knowledge of the spin of particle B in this way evidently does not imply any interaction of the apparatus with particle B or any interaction between A and B. In quantum theory, a difficulty arises, in the interpretation of the above experiment, because only one component of the spin of each particle can have a definite value at a given time. Thus, if the x component is definite, then the y and z components are indeterminate and we may regard them more or less as in a kind of random fluctuation.N David Mermin made a similar argument in 1988, claiming that in the absence of spooky actions, it appears that both photons must have definite polarizations along every conceivable direction... Both photons must have had definite polarizations along α. Furthermore, since the conclusion that one photon has a definite polarization along the direction α does not require an actual measurement of the polarization of the other along that direction (again, in the absence of spooky connections), and since not measuring polarization along a direction α is the same as not measuring it along any other direction, we are led to conclude that both photons must have definite polarizations along every conceivable direction.Finally, John Clauser and Abner Shimony repeated Bohm's criticisms of a common cause. Suppose that one measures the spin of particle 1 along the x axis. The outcome is not predetermined by the description [wave function] Ψ12. But from it, one can predict that if particle 1 is found to have its spin parallel to the x axis, then particle 2 will be found to have its spin antiparallel to the x axis if the x component of its spin is also measured. Thus, an experimenter can arrange the apparatus in such a way that he can predict the value of the x component of spin of particle 2 presumably without interacting with it (if there is no action-at-a-distance). Likewise, he can arrange the apparatus so that he can predict any other component of the spin of particle 2. The conclusion of the argument is that all components of spin of each particle are definite, which of course is not so in the quantum-mechanical description. Hence, a hidden-variables theory seems to be required.In our analysis we show how a hidden constant of the motion (the conserved spin angular momentum) can carry common causes of entanglement to the "separated" particles. It is not that atoms and electrons must have spins along all three directions (Bohm, Clauser, Shimony) or that photons must have definite polarizations along every conceivable direction (Mermin) . It is that the two-particle wave function is spherically symmetric with no definite spins in any direction, that is, until the measurements at A and B, which each create one bit of information. The perfectly correlated spins appear in the pre-agreed upon direction of measurement. This direction was not present at the initial entanglement, which needs only to create a spherically symmetric state like the singlet state of the hydrogen molecule or the helium atom. Similarly, the two bits of information created by the final measurements did not exist as the particles traveled to points A and B. The final measurement outcomes were not determined by the local causes at the initial entanglement. Nor were the outcomes known as the particles travelled to A and B. The outcomes were the indeterministic results of the final local causes. They did not exist before the final measurements.
What Then About the Nonlocality of Entanglement?
Ever since Albert Einstein in 1905 thought a light wave had collapsed instantaneously everywhere when a part of it ejected a photo-electron somewhere, the quantum wave function has appeared to be producing "nonlocal" phenomena. All his life he thought these nonlocal "influences" were a "spooky action at a distance."
The wave function that goes through both slits, even as the particle must go through just one slit (by conservation of mass), can be seen as acting nonlocally. But this nonlocality, the one and only mystery of quantum mechanics, cannot be explained as a "causal chain" of multiple local causes as we have done for entanglement. As Feynman says, "there is no machinery."
Our proposal has identified "machinery" in the initial entanglement and in the final measurements which produces the appearance of Alice's measurement "influencing" Bob's measurement. No machinery is needed for the conserved constant of the motion.
Is There a Preferred Reference Frame?
There is no preferred reference frame in the sense of special relativity, which sees all inertial frames as equivalent (the relativity principle). But there clearly are inertial frames which provide different "points of view," some clarifying, some confusing the order of events.
The architect of special relativity himself chose to look at nonlocality from A's inertial frame and point of view. Both Einstein's first two-particle version of nonlocal events in 1933 speaking with Léon Rosenfeld and his second two-particle version in the 1935 EPR paradox paper, Einstein starts with measurement A, suggesting (falsely) that the (simultaneous) measurements at B must be acted upon at a distance to be correlated with A.
If there is what we might call a special frame to analyze entanglement it is surely the frame in which the entanglement apparatus at the causal center C is at rest along with measurement devices at A and B. The causal order of events is clear. The causal center is the physical and temporal origin of the "causal chain" of events.
References
Reichenbach, H. (1991). The Direction of Time. U. California Press. p.157
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