bcrowell said:
As in #24, I think you're confusing an assumption of a theorem with the result of a theorem. This may also be relevant:
http://en.wikipedia.org/wiki/No-communication_theorem
I read the linked article and several other related articles.
The notion of causality that we're discussing here really doesn't require any notion that A causes B. The laws of physics, e.g., Newton's laws or the Einstein field equations, are just differential equations. Differential equations don't make statements like "A causes B." The notion of causality that is relevant here only really requires that if A comes earlier in time than B according to one observer, then this is also true for all other observers.
The causality I have in mind is the notion that the act of measuring one particle determines the state of that particle and the state of a distant particle. The measurement is thus the cause; the effect is the combination of states [spin up and spin down, e.g.] taken on by the two particles.
There is a sticky at the top of this forum, titled "FAQ: Experimental Basis of Special Relativity." Every experiment in that sticky constitutes empirical evidence that causality is satisfied, as predicted by SR.
I read through the full page. I don't think there were any experiments in the list which dealt with entangled particles. If one accepts the premise that the measurement of a particle is a cause and the state of a distant (non-local) particle is an effect of that cause, then it seems true on the face of it that the effect of the cause has propagated at a speed faster than c.
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That said, I read this statement in an article about the De Broglie-Bohm theory:
The de Broglie–Bohm theory describes the physics in the Bell test experiments as follows: to understand the evolution of the particles, we need to set up a wave equation for both particles; the orientation of the apparatus affects the wavefunction. The particles in the experiment follow the guidance of the wavefunction. It is the wavefunction that carries the faster-than-light effect of changing the orientation of the apparatus. An analysis of exactly what kind of nonlocality is present and how it is compatible with relativity can be found in Maudlin.[18] Note that in Bell's work, and in more detail in Maudlin's work, it is shown that the nonlocality does not allow for signaling at speeds faster than light.
I don't doubt the truth of the two fragments in bold--but neither can I make sense of them with my current knowledge of quantum mechanics [which is even more limited than my knowledge of relativity--draw your own conclusions :)]
Your interpretation of Wald assumes that such a relative velocity is uniquely defined, which it isn't.
I'm not sure what you are getting at here. If you mean that I cannot identify two Lorentz inertial frames which have a relative velocity greater than c, I agree. But as I understand Wald, that failure is a consequence of the fact that GR is a manifold onto a Lorentz space. (I'm sure I'm not speaking the technical language with precise correctness, but I believe I have sufficient gist of the math for the purposes of this discussion.) That is, inertial frames are inherently local ['nearby'] in GR, while the two objects which have a relative velocity greater than c are necessarily not local ['nearby']. Born asserts that "if gravitational fields are present the velocity either of material bodies or of light can assume any numerical value". ("Einstein's Theory of Relativity", VII-11)
But there is no logical connection between the given information you start with and the conclusion you claim
I believe the logical connection is clarified in the above.
and there is a century's worth of experimental evidence against your conclusion.
As noted, the listed experiments do not deal with entangled particles.
As DaleSpam has pointed out, you haven't provided a definition of "reality."
I don't believe that a comprehensive definition of reality is a precondition for this discussion. Einstein, Born, Taylor-Wheeler, Schumm ("Deep Down Things"), Ford ("The Quantum World") all address the issue of reality as distinct from measurement; none of them presents a comprehensive definition of reality (in the books I have read).
I would argue that the assertion of fundamental probability in quantum theory is itself a statement about the nature of reality, as distinct from the measurements we make in the lab. Yet so far as I know neither the standard model nor the Copenhagen model presents a formal definition of reality.
Here's Treiman on the subject of quantum mechanics and classical reality (in "The Odd Quantum"): "Within quantum mechanics itself, there seems to be an unbridgeable divide between the future and the present instant. The future is intrinsically statistical, with probabilities governed by the equations of quantum mechanics. The trouble is that this way of looking at the situation seems something of a cop-out. In effect, it abandons the idea of explaining how facts come about, taking as the main function of science merely to correlate them. When a fact in fact happens, the quantum mechanical wave function is simply declared to have collapsed; after all, it's only a correlational tool! And that's that."
Treiman is no doubter of quantum mechanics--for that matter neither am I insofar as the measurements are concerned--yet he expresses dissatisfaction with its approach to reality. He makes these comments without attempting a formal definition of reality.
Which brings us back to the question in the original post: The WHY vs. the FACT of c.
I agree with Treiman that science is intimately concerned with the WHY, because scientists, as human beings, are motivated to understand what they observe in nature, not merely to organize the facts.