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> Momentum is mass x velocity.

Only for objects with nonzero rest mass traveling at speeds much slower than the speed of light. Which obviously doesn't apply to light itself. When you are talking about light (or about massive particles like electrons traveling at speeds close to the speed of light), you have to use the correct relativistic equations. When you do that, you find that energy and momentum are conserved for light just like anything else.

> Maybe with light, only energy conservation matters and momentum can be changed via redshift/blueshift relative to the container.

Not according to our best current theories, no. See above.



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