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I know that conservation of momentum is what einstein used to derive e=mc². But, it's said that momentum is relative. I'm getting confused here. Please note that I'm not having a science degree, just a curious guy. Can you explain it in a way i could understand it?

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    $\begingroup$ Note that "momentum is relative" is true of Galilean relativity (i.e. non-relativistic physics) as well. $\endgroup$ Jan 21, 2018 at 15:38
  • $\begingroup$ I meant, if it's relative, then how momentum is conserved? $\endgroup$ Jan 21, 2018 at 15:46
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    $\begingroup$ And I mean that the exact same issue comes up before Einstein and the resolution is exactly the same before and after Einstein. "How or why can we use conservation of momentum when the speed of objects depends on the coordinate system you use?" is just as good a question in Newtonian physics as it is in Einsteinian physics., but you may find it easier to suss out the answer in the classical case because you won't confuse yourself by worrying about the strange features of relativity. $\endgroup$ Jan 21, 2018 at 15:52
  • $\begingroup$ Okay, I think now I understand. Also, the difference between Newtonian and Einsteinian momentum is trivial on slower speed, but on the speed close to the speed light, momentum approaches infinity, whereas newtonian does not. Also, p=mv, is the gamma coming from the fact that the m(mass) is relative? $\endgroup$ Jan 21, 2018 at 16:27
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    $\begingroup$ See, that's why I suggested you think about the classical system. This has nothing to do with the Lorentz factor. As an aside I am firmly in the camp that never groups $\gamma$ with $m$ and calls the result "relativistic mass"—you can do physics that way but it doesn't help and does breed confusion and mistakes. $\endgroup$ Jan 21, 2018 at 16:35

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The phrase "momentum is relative" means that observers using different coordinate systems may not agree on the value of momentum for a particular object. In particular observers whose coordinate systems are in relative motion will not agree. This is true in classical physics as well as in relativity.

By contrast the principle of conservation of momentum, which tells us that

For system subject to zero net external impulse the total momentum of the system is constant in time.

implicitly assumes that you are using the same coordinate system for the all your measurements.

The interesting thing is that thought two observer might not agree on the value of the total momentum for an isolated system, they can agree that the total momentum is staying the same as time passes.

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  • $\begingroup$ "The interesting thing is that thought two observer might not agree on the value of the total momentum for an isolated system, they can agree that the total momentum is staying the same as time passes." - That really gives me insight!! $\endgroup$ Jan 21, 2018 at 17:09

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