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Over hundreds of years the conservation of energy and momentum in a closed System was proven. 100 years ago, Emmy Noether showed that these fundamental laws arise from the following facts and vice versa: - Homogenity in time (i.e. physical laws will be the same independent of the time where physics take place) leads to energy conservation - Homogenity in space leads to momentum conservation

Now I have heard that quantum field theory in curved spacetime does not contain energy and momentum conservation (Why?). Also in the theory of Phonons I have seen that there are existing single interactions with no momentum or energy conservation.

But almost every physical Research states that energy and momentum is conserved; even in single quantum mechanical interactions like electron + positron -> photon.

Can it be that there might be interactions on Quantum Level where energy and momentum is not conserved?

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The violation of conservation and momentum in quantum field theory is only local; globally, these quantities are still conserved.

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  • $\begingroup$ A quantum interaction is local, right? Do you mean if the theory has some non-conserving interactions then there must occur the gain-interaction with the same probability as the loss-interaction, right? Are there such theories which state local nonconservations? $\endgroup$
    – kryomaxim
    Commented Feb 5, 2015 at 17:16
  • $\begingroup$ Individual interactions are local. Conservation of energy and momentum must still occur globally; that is the correspondence principle. $\endgroup$
    – Paul
    Commented Feb 5, 2015 at 17:20

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