One simple problem is physics is to determine the mechanical energy difference after an explosion. To do this, you must assume that momentum is conserved because in a explosion you have internal forces, so, using Newton's third law, you get that the total momentum is conserved.
How true is that? I mean, when a explosion happens you have LIGHT and SOUND being propagated. And they carry energy and momentum. It's clear to me that if you only consider the momentum of the parts of the body + the momentum of the sound wave + the momentum of the light wave this should be equal to zero. However, it's not so clear if the momentum of the body should be equal of the sum of the momentum of its fragments. I have some conjectures, but I didn't find nothing related to that: I) The waves propagate symmetrically, so, because momentum is a vector, it should be zero. However, the explosion may not be total symmetric, so I don't know if this argument is valid. II) The momentum is not conserved for the body, but the momentum of the wave is negligible.
These are the two possibilities I considered, so I don't know if they are valid.
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