The Bell Theorems, together with a collection of experimental results (such as those of Aspect et al.), provide good statistical evidence that quantum theory is “non-local.” Roughly, this means that the interaction between two bodies in quantum theory doesn’t necessarily get weaker as those bodies become spatially separated.
Is this a problem for Special Relativity? That depends on what you think Special Relativity means. Here’s a simple flow-chart illustrating some of what’s at stake.
For a very accessible view on how we should navigate many of these options, I highly recommend Tim Maudlin’s excellent book on the subject. But here are a few thoughts on each of the steps.
Bell-inequality violation. There is a sect of conspiracy theorists who aren’t convinced that the Bell-inequalities are violated by experiment. If that’s you, then there’s no reason to worry about Special Relativity.
- Minkowski Geometry. If Special Relativity requires only that the background spacetime be Minkowski spacetime, then there is no problem for non-local quantum effects. After all, we have plenty of matter theories (quantum field theories) that take place on such a background, and even respect its symmetries to a certain extent. Non-locality is not a problem here.
- Upper limit on the speed of mass-energy transfer. We would normally like to add that matter-energy cannot be transferred faster than the speed of light. But this is not a problem for quantum non-locality, either — unless you adopt a pretty unusual view of matter-energy transfer. Then what matters is statistical correlation — see below.
- Signal/Information Transfer. These terms are a bit vague, and people disagree about how to explicate them. However, as the chart suggests, I think that what’s really important is whether or not you think there are consequences for the statistical behavior of distant regions.
- Statistical Correlation. This seems to be the heart of the problem. If you think that Special Relativity implies an upper limit on the “speed” at which statistical correlation can occur, then you’ll think the Bell-type results violate this. What I mean by that is: interactions in one region can have near-immediate consequences for the statistical behavior of another region, no matter how far apart the two regions are.
But why would someone answer “yes” to the last choice in the chart? Why should we think that Special Relativity implies anything at all about the statistical behavior of matter?
There is no probability measure in SR. Of course, matter satisfying the assumption of local realism appears consistent with Special Relativity, and the Bell inequalities hold for such matter. But I see no reason to think that such matter is required by Special Relativity. If it isn’t, then Special Relativity isn’t enough to derive the Bell inequalities, and doesn’t contradict non-locality.
And that’s exactly how we all like it. Right?
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