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In the comment in What are the reasons to expect that gravity should be quantized? by Ron Maimon, it is mentioned that taking analogy from classical electromagnetic wave to classical grvational wave, one can notice that conservation of energy is violated.

However, general relativity does not really have conservation of momentum as fundamental concept, and thus it is unclear what this would mean. Can anyone explain this?

Can Bohr-Kramers-Slater (BKS) theory really serve as an example refuting possible validity of classical gravity?

Qmechanic
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Matsu Takama
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However, general relativity does not really have conservation of momentum as a fundamental concept, and thus it is unclear what this would mean. Can anyone explain this?

GR does have conservation of momentum as a fundamental concept. Specifically, the structure of GR requires that the stress-energy tensor have zero divergence, which is a statement of local conservation of the energy-momentum four-vector. What GR doesn't have is a generic global conservation law for energy-momentum, but I don't think that has any logical consequences for the argument you refer to, because we do have such conservation laws for special cases like asymptotically flat spacetimes, and one can in principle detect gravitons, and falsify a classical theory of gravity, in an asymptotically flat spacetime.

In any case, the argument about the nonconservation of energy in BKS is really more about the nonconservation of probability, i.e., it's about unitarity. It's just that in 1927, people described it in terms of having only statistical conservation of energy and momentum.

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