Tim Maudlin's book Quantum Non-Locality and Relativity
is a critical analysis of Bell's Theorem
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)
- 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
- 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 hae interacted with each other in the past seem to retain this power of private communication.
- 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.
Maudlin does not discuss the possibility that there is a "common cause" for these distant but perfect correlations, coming along with the particles from the past light cone, so not violating relativity. Nor does he mention David Bohm
's claim that no such common cause is possible.
Bohm suggested that "local hidden variables" traveling with the particles might explain the perfect correlations (which John Bell
said seemed "pre-determined
"), but it could not explain the apparent randomness (indeterminism
) of the sequence of measurement outcomes of each particle (critically needed for the random bit strings of quantum cryptography).
Maudlin's method is a logical analysis of the "questions" and "answers" in a game that reproduces the results of a sequence of Bell-test experiments, similar to that in David Mermin
's 1985 "contraption."
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
After all, this is what the photons manage to do. (Non-Locality, p.14)
- 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.
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 at the same angle (by pre-agreement), their spins are always perfectly correlated. When their measurement angles differ by angle θ, their correlations are diminished by the square of the angle's cosine - cos2
θ, as Maudlin explains.
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, is not discussed.