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Fundamentally why require causality?

  1. Feb 24, 2015 #1
    I have been wondering for some time now why causality is a prerequisite for every "good theory" all the way from classical mechanics, to QM, even in QFT the correlators for spacelike separated interactions cancel out.
    Now, since we usually take make a general theory and then usually simplify, consider special cases, etc, why not assume a general theory at the quantum level of which causality is just a special case ?
    To clarify my thoughts, my question arises from debates with colleagues who said it might just be axiomatic since we have not seen any evidence to the contrary. However, the same holds for tunneling, so why not assume a more general theory in which non-causal interactions are simply exponentially suppressed as we approach macroscopic scales and build a theory from that ?
    What is the fundamental argument for insisting on causality ?
     
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  3. Feb 24, 2015 #2

    jedishrfu

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  4. Feb 24, 2015 #3

    Vanadium 50

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    Because an acausal theory is not predictive.
     
  5. Feb 24, 2015 #4

    mfb

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    Tunneling has been observed in many experiments.

    A general acausal theory does not allow to make clear predictions, at least not beyond self-consistency.
     
  6. Feb 24, 2015 #5
    First of all, many thanks for your answers.
    Based on your answers, I would like to recycle my question to why would an acausal theory be incapable of predictions ?
    The way I see it, we could build a theory of which (in set theory language) subset A is causal, and subset B acausal. Therefore in A we look at causes and predict effects while in B we look at effects and predict causes. Both are predictive and "effect" and "cause" seem to be somewhat arbitrary definitions.
    Also, this seems to respect the conditions of the Novikov self-consistency, or in the worst case, simply act as an advocate for the many-worlds interpretation.
     
  7. Feb 24, 2015 #6

    PeterDonis

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    How are you defining "causality"? In QFT, the definition of "causality" is not "nothing can travel faster than light"; it is "field operators must commute at spacelike separations" (which is basically what you are referring to when you say the "correlators cancel out" at spacelike separations). So QFT itself is the "general theory at the quantum level", of which classical "causality", i.e., the "nothing can travel faster than light" sense of "causality", is a special case.

    Once again, how are you defining an "acausal theory"? It seems like you are defining it as "effects predict causes" as opposed to "causes predict effects", but that's not correct. In a completely deterministic theory (which classical SR and GR are), you can use effects to "predict" causes, in the sense that you can run solutions backwards in time just as easily as forwards. That doesn't make the theory "acausal"; SR and GR are both theories with causality (in the classical "nothing can travel faster than light" sense).

    In a completely deterministic theory, they are, yes; see above.
     
  8. Feb 24, 2015 #7

    mfb

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    Where do you get the effects in B from?
    If A and B are completely separated, then you could "invert the timeline" in B (as a mathematical trick) and get something with (mathematically) "inverted causality", but that would still be causal. The problem arises from closed circles of influence (closed timelike curves in the context of general relativity), where you cannot work step by step.
     
  9. Feb 24, 2015 #8

    atyy

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    If by "the correlators for spacelike separated interactions cancel out" you mean that observables at spacelike separation commute (ie. classical information cannot be transmitted faster than light), then that is not a requirement in quantum theory, only in relativistic quantum theory. In non-relativistic quantum theory, there are things like the "Lieb-Robinson bounds" which in some sense say that non-causal interactions are exponentially suppressed. In such a quantum theory, it is possible in principle to transmit information faster than light.

    Another line of thinking is to use the Bell inequalities, which rule out quantum mechanics as a theory obeying local causality. Relativistic quantum theory is not locally causal, but is "signal local" in that faster than light signalling is not permitted. Is quantum theory the most general theory that is not locally causal, but still signal local? As Popescu and Rohrlich showed in http://arxiv.org/abs/quant-ph/9508009v1, it is not. So why doesn't quantun theory violate local causality even more strongly within the bounds of signal locality? Some thoughts are given in http://arxiv.org/abs/1112.1142v1 and http://arxiv.org/abs/1208.3744.

    Can quantum mechanics be consistent in the presence of closed timelike curves? There is discussion and pointers to the literature in http://arxiv.org/abs/1309.4751.
     
    Last edited: Feb 24, 2015
  10. Feb 25, 2015 #9
    Wow, I will need some time to go through the literature, thank you all very much for your thoughts.
     
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