The Efficiency Loophole: A Local Hidden Variables Theory?

[harrylin]

But that would suggest that it's irrelevant to Bell's proof whether or not there is a spacelike separation between the two measurements or a timelike one, as long as there is a "great distance" between the two measurements. Do you really think that's the case? What about the locality loophole in Bell experiments?

Not at all: for testing theories against each other it is essential to test situations where there can be no doubt that they predict something different; if one fails to do so, one creates a loophole*. For those (like Einstein) who accept Relativity, local causality implies that no influence towards another location can occur faster than light.

However, you do make a good argument here below that Bell defined local causality slightly different from what I am used to; see next.

Also, in Bell's own paper La nouvelle cuisine, much of which can be read on google books starting on p. 216 of this book (it's also available in Speakable and Unspeakable in Quantum Mechanics), he specifically defines his notion of "local causality" in terms of the speed of light limit, and this plays an essential role in his derivation. On p. 217 he starts out connecting locality and the speed of light:

Thanks for the very useful link! There he starts out with the common meaning of local causality:

"the idea that effects are near to their causes",

and next indeed he states that he will be very much concerned with the limit of the speed of light.

Then on p. 224 he gives a definition of his "principle of local causality", saying:

"The direct causes (and effects) of events are near by, and even indirect causes (and effects) are no further away than permitted by the velocity of light."

Indeed. Note that he doesn't suggest that a theory would be necessary "non-local" if events happen close enough to each other to be within the light cone. And what you did not cite:

"Here we have preferred to see it not as a formulation of local causality but as a consequence thereof."
("It" = factorizability due to independence of A on B and vice versa).

[..] And this step is essential to his proof that QM cannot be explained by a "locally causal" theory of hidden variables.

Yes indeed - thanks for your nice summary.

I find Shimony's definition natural and linguistically pure, while I now see that indeed Bell's is subtly different; thanks for pointing that out. Note that it has no consequence for the derivation. Bell admitted that what is "very often" done (differently form his formulation), is to define that A and B do not depend on each other nor on remote polarizers. (p.228/109).Harald

*PS: Shimony calls it the "communication loophole"
- http://plato.stanford.edu/entries/bell-theorem/