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Is the law of inertia compatible with quantum mechanics? If yes, how?

And if a particle is both present and absent at the same time, (the uncertainty principle: stating that when an electron is on coordinates say x1;y4;z8 then it is impossible to know what is it’s velocity at that very coordinates and if the velocity is known we can’t be sure of where it actually is in the space!), how can we apply a law to it which states that its motion, which manifests itself in the form of changing coordinates and velocity (which can only be calculated if coordinates are unknown in quantum mechanics on a particle which isn’t even there if it’s velocity is known to us?), remains constant?

Vincent Thacker
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A.M.
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  • Your question isn't clear, can you please clarify? – Ofek Gillon Sep 24 '21 at 13:01
  • This is a follow-on question from https://physics.stackexchange.com/q/667781/123208 & https://physics.stackexchange.com/q/667714/123208 – PM 2Ring Sep 24 '21 at 16:12
  • Yeah! so? Why, one can’t ask them? – A.M. Sep 24 '21 at 16:18
  • Of course you can ask follow-on questions! But you can't expect readers to have read those earlier questions, so it's a good idea to give the links. Otherwise, people may cast down votes or close votes because they think your question is unclear, &/or lacking in context. – PM 2Ring Sep 24 '21 at 18:26
  • Oh! I see, Thank you. – A.M. Sep 24 '21 at 18:42

1 Answers1

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contrary to popular belief, quantum mechanics don't state that "a particle is present and absent at the same time". It rather tells us quite clearly what we can and cannot know simultaneously of a particle, or, in different phrasing, which set of properties of the particle can be well defined simultaneously.

We can generalize the law of conservation of momentum to quantum mechanics without much difficulty. There is a quantum analog to the classical momentum (also called momentum, of course) and we can show under which conditions it is conserved. Here, "conserved" means that its observed value does not change in time. Unsurprisingly, this quantum momentum retains all the properties of the classical momentum when we take the proper classical limit. This is a requirement when we define our quantum theory, as we want it to describe the classical world as well, in the large-scale limit!

By the way: note that for photons, the Newtonian formulation of "momentum is mass times speed" is not valid, as they have no mass. We rather have to use the relativistic definition of the momentum, which for photons will be directly related to their energy. However, they to follow laws of conservation of momentum.