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Gravitational energy is non-local which is essentially because of the equivalence principle. The equivalence principle says that you can always transform your frame so that you feel like in a Minkowski space-time locally. Mathematically, there is no tensor-like definition for gravitational energy in General Relativity. All energy-momentum tensor for gravitational energy must be pseudo-tensor, namely frame-dependent tensor. About the non-locality of gravitational energy I have a question:

How can the non-locality of gravitational energy be implemented in String theory where, for example, gravitons are simply zero modes of closed strings and strings are explicitly local (of course except for the resolution of strings which, as I see, is different from the non-locality of gravitational energy)?

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    $\begingroup$ This seems like a re-post of physics.stackexchange.com/q/240793. $\endgroup$ – CuriousOne Mar 3 '16 at 9:09
  • $\begingroup$ @CuriousOne, Qmechanic removed my second question there since there should be only one question for one post. $\endgroup$ – Wein Eld Mar 3 '16 at 9:11
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    $\begingroup$ That explains why I had the feeling to have seen the entire question before. I don't think you need the introduction part, to begin with. We know that gravitational energy is non-local. $\endgroup$ – CuriousOne Mar 3 '16 at 9:16
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    $\begingroup$ Except that it doesn't have anything to do with the question. If string theory describes gravity correctly, at least in the weak field limit, then the answer is trivial. If it doesn't do even that... then who needs string theory? I am not quite sure what you mean by "implementation" to begin with. Are you saying that this has to be forced into string theory because it's not naturally in there, already? $\endgroup$ – CuriousOne Mar 3 '16 at 9:22
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    $\begingroup$ You can experimentally localize the energy in the field of a point charge? $\endgroup$ – CuriousOne Mar 3 '16 at 9:43
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According to the abstract of a paper at https://arxiv.org/abs/hep-th/0604072,

Breakdown of local physics in string theory at distances longer than the string scale is investigated. Such nonlocality would be expected to be visible in ultrahigh-energy scattering. The results of various approaches to such scattering are collected and examined. No evidence is found for non-locality from strings whose length grows linearly with the energy. However, local quantum field theory does apparently fail at scales determined by gravitational physics, particularly strong gravitational dynamics. This amplifies locality bound arguments that such failure of locality is a fundamental aspect of physics. This kind of nonlocality could be a central element of a possible loophole in the argument for information loss in black holes.

In other words, there are three options here.

  1. It's a problem with string theory, which would make some sense, because there really is no experimental evidence for string theory, though it does have some nice dualities as shown by m-theory.
  2. This is a problem with quantum field theory and other theories as well, and so it might be a fact of life.
  3. There's something we're missing, which is fairly likely.
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