Tim Maudlin's 2011 book Quantum Non-Locality and Relativity is a critical analysis of Bell's Theorem and his "Inequalities" which are "violated" by experiments, confirming standard quantum mechanics and denying the existence of"local" hidden variables."

Maudlin says that the "interaction among distantly separated particles presents profound interpretive difficulties." (p.20). He cites three features of this "quantum connection" between particles as surprising, even "weird." (pp.22-23)

1. The quantum connection is unattenuated.

   It appears to be unaffected by distance. Quantum theory predicts that exactly the same correlations will continue unchanged no matter how far apart the two wings of the experiment are

2. The quantum connection is discriminating.

   It is a private arrangement between two particles. When one is measured, its twin is affected, but no other particle need be. Only particles which have interacted with each other in the past seem to retain this power of private communication.

3. The quantum connection is faster than light (Instantaneous).

   [N]o relativistic theory can permit instantaneous effects or causal processes. We must therefore regard with grave suspicion anything thought to outpace light.

While Maudlin's three features accurately describe what many philosophers and scientists mistakenly think is going on with non-locality and entanglement, there is in fact no "quantum connection," especially in the sense of a communication or "unattenuated, discriminating, and instantaneous interaction" between the "distantly separated particles" at the "two wings" A and B of a Bell experiment.

The only "communication" or "interaction" is the two-particle wave function Ψ₁₂ that travels out (at light speed) from the initial entanglement setup in the center C between the two distant measurement experiments at points A and B.

Measurements at A and B are perfectly correlated. An observer at A (Alice) may mistakenly think her measurement has caused the measurement by Bob (at B), since it appears to her after the light travel time between them. Bob has the opposite impression. Neither of their measurements are interacting or communicating with the other, as most popular descriptions of entanglement mistakenly claim.

The only interaction/communication is from the center to Alice and to Bob. There is no instantaneous communication between A to B as they are simultaneous events. Such a communication would violate special relativity, as everyone knows and Maudlin's third "feature" says clearly!

The physical properties created in the initial entanglement, together with conservation laws for the properties mass, energy, linear and angular momentum (spin) are a "common cause" traveling from the center C to A and B.

Maudlin clearly states that there cannot be such a "common cause."

[O]utcomes on one side are not statistically independent of those on the other and, as Bell showed, this dependency cannot be accounted for by common causes which lie in the past light cone of the measurement events.

[W]e get a counterfactual-supporting causal connection between the photons which cannot be explained by a common cause.

Quantum Non-Locality and Relativity, p.114 and p,134

But without the initial entanglement at the center between the separate measurements at A and B there can be no entanglement of A and B!.

The experimental equipment at A and B are indeed "distantly separated," but the two-particle wave function Ψ₁₂ can not be separated into two single-particle wave functions Ψ₁ and Ψ₂. According to Erwin Schrödinger, the creator of wave mechanics and the wave equation, Ψ₁₂ is non-separable until there is a measurement (or a random interaction with the environment).

As Einstein first saw in his photoelectric effect paper of 1905, twenty years before there was a wave function, the light wave goes out in all directions, but the photon ejection of an electron at a spot on the metal surface instantly changes the possibility of that photon being anywhere else. The wave appears to "collapse" everywhere, faster than light speed. But nothing material is moving, only abstract informationis changing!

Richard Feynman said that the wave-function collapse in the two-slit experiment is the one and only mystery in quantum mechanics. Entanglement is the same mystery.

Maudlin writes...

Over a long run of this game you are aiming to reproduce the behavior of the photons in similar circumstances, That is, after a long series of plays, you want to ensure that

• Fact 1: When you and your friend happen to be asked the same question you always give the same answer.
• Fact 2: When your questions differ by 30, that is, when one is asked "0?" and the other "30?" or one is asked "30?" and the other "60?", you and your friend agree 3/4 of the time
• Fact 3: When your questions differ by 60, that is, when one of you is asked "0?" and the other "60?", your answers agree 1/4 of the time.

After all, this is what the photons manage to do. (Non-Locality, p.14)

Quantum Non-Locality and Relativity, p.14

The "questions" in Maudlin's logical game correspond to the physical angle settings of the particle detectors at positions A and B. The "answers" correspond to the spin directions ("up" or "down") found as outcomes of the measurements. When A and B measure by pre-agreement at the same angle (ask the same "questions"), their spins are always perfectly correlated in opposite directions. This is Maudlin's fact 1.

When their "questions" (the measurement angles) differ by angle θ, their correlations are diminished by the square of the angle's cosine - cos²θ, as Maudlin explains.

The mathematics of quantum theory predicts precisely the observed experimental results.

The Dirac/Schrödinger "superposition" equation for Schrödinger's two-particle wave function is

The coefficients 1/√2, when squared, tell us that there is a 50/50 chance that the particles will be found in the state + - or in the state - +.

When measurements by A and B (the "questions") are made at angles differing by angle 30°, since the cosine of 30° is 1/2, the "answers" agree cos²30° = 1/4 of the time. This is Maudlin's fact 2.

When measurements by A and B (the "questions") are made at angles differing by angle 60°, since the cosine of 60° is √3/2, the "answers" agree cos²60° = 3/4 of the time. This is Maudlin's fact 3.

Now when measurements differ by 30°, the "answers" disagree sin²30° = 1/4 of the time.

Instead of the state + - or the state - +, the outcomes that disagree are found randomly in states + + or - -. Either of these outcomes appears to violate the conservation of total spin angular momentum zero.

We call the conserved total spin zero a "hidden constant of the motion". The initial entangled state is a "singlet" state that is spherically symmetric. The rotational symmetry means it has spin angular momentum zero in any and all directions. Measurements will find the spins opposite as long as the measurements are made in perfectly parallel or perfectly opposite directions.

Conservation ensures that this shared property of the two particles is true at all times up to and including the moment of (simultaneous) measurements. (If measurements are not made symmetrically, the measurement apparatus imparts additional spin angular momentum to the particles, and its loss of that spin balances the particles' gain, so the particles plus the apparatus continue to conserve the total spin angular momentum zero.)

The conservation law is the implicit reason why David Bohm, John Bell, and many others say that when one particle is measured spin-up, we instantly know the other must be spin-down.

Exactly how the bit strings of data at A and at B are indeterministically random, even as the combined A and B results appear to be deterministically correlated, Maudlin does not really discuss.

But the Dirac/Schrödinger "superposition" equation cited by Maudlin explains this perfectly. The fact there is a 50/50 chance that the particles will be found in the state + - or in the state - +, just as observed, means that the bit strings at A and B can be used as quantum keys that have been distributed to A and B in a way that cannot be intercepted by an eavesdropper.

Quantum key distribution (QKD) does not require impossible faster-than-light instantaneous actions at a distance between Alice and Bob. The "keys" are perfectly correlated random bit strings that are generated from the entangling apparatus at the center. Nothing is communicated between Alice and Bob

No "hidden variables" are needed. The "hidden constant of the motion" will suffice as a "common cause" emanating from the past light cone of Alice and Bob's measurements.

Richard Feynman famously said in 1964 "Nobody understands quantum mechanics." He said it's because there is no "machinery" that can explain the deterministic evolution of the wave function in the two-slit experiment. The same can be said about entanglement and John Bell's theorem, published the same year.