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Causality coupled with special relativity states that no particle can travel faster than light.

Interpreting in terms of quantum mechanics, it means that dirac delta wave-function at x=a, can't convert to dirac delta wave function at x=b faster than a speed of evolution i.e. of a dirac delta function travelling x=a from x=b.

Isn't this the way we should interpret special relativity now? Thinking of the older results in terms of a newer framework, where the physical world we perceive is a shadow of the quantum mechanical wave-functions.

This can allow seemingly strange effects like entanglement to make more sense in a newer framework. We've constantly done this in the past when theories like SR & GR came out. Looking at the world through a new lens.

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    $\begingroup$ It's not really clear to me what your question here is. $\endgroup$ – ACuriousMind Nov 1 '15 at 21:08
  • $\begingroup$ This is how we interpret special relativity now, its synthesis with quantum theory is called quantum field theory, and the Standard Model is an example of that. Synthesis with general relativity is still an open problem. $\endgroup$ – Conifold Nov 1 '15 at 21:32
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Causality in special relativity implies that no signal can travel faster than light. In quantum mechanics, that does not translate in bounds on the speed of Dirac-delta wave-packets, not least because that would be in general an ill-defined condition (a localised wave-packet typically spreads out when evolving in time, so a delta at x=a would never evolve to a delta at x=b).

The way relativistic causality is currently incorporated in quantum mechanics is in the framework of quantum field theory. The axiom of microcausality states that space-like separated field operators commute, which means that space-like separated observables can be measured independently. The general understanding is that this condition implies that no signal can travel faster than the speed of light, although the meaning of this statement is sometimes debated, see for example http://arxiv.org/abs/0908.3144.

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