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Daniel_Burfoot comments on Open Thread, Jul. 27 - Aug 02, 2015 - Less Wrong Discussion
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Apparently, NASA is testing an EM Drive, a reactionless drive which to work would have to falsify the law of conservation of momentum. As good Bayesians I know that we should have a strong prior belief that the law of conservation of momentum is correct so that even if EM Drive supporters get substantial evidence we should still think that they are almost certainly wrong, especially given how common errors and fraud are in science. But, my question is how confident should we be that the law of conservation of momentum is correct? Is it, say, closer to .9999 or 1-1/10^20?
I would give at least .00001 probability to the following: momentum per se is not conserved, but instead some related quantity, call it zomentum, is conserved, and momentum is almost exactly equal to zomentum under the vast majority of normal conditions.
In general, since we can only do experiments in the vicinity of Earth, we should always be wondering if our laws of physics are just good linearized approximations, highly accurate in our zone of spacetime, of real physics.
This is not a very meaningful claim since in modern physics momentum is not "mv" or any such simple formula. Momentum is the Noether charge associated with spatial translation symmetry which for field theory typically means the integral over space of some expression involving the fields and their derivatives. In general relativity things are even more complicated. Strictly speaking momentum conservation only holds for spacetime asymptotics which have spatial translation symmetry. There is no good analogue of momentum conservation for e.g. compact space.
Nonetheless, the EmDrive drive still shouldn't work (and probably doesn't work).