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If it can accelerate forever, thats proof enough for everyone. However violating the conservation of momentum is a Big Deal. Mathematically that shouldn't be possible due to Noether's. The bar to proof is therefore very high.


General relativity doesn't conserve energy in some spacetimes, so it's not unheard of.


I'm fairly certain GR conserves momentum, even if it doesn't conserve energy.


I thought so too until recently, but in GR energy and momentum are unified in an energy-momentum metric which is only locally conserved [1].

[1] https://en.wikipedia.org/wiki/Physical_theories_modified_by_...




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