Comment by fnordpiglet
10 months ago
Except there is no absolute coordinate system. Position is relative to something, and it’s not space. Likewise movement is only meaningful if defined with respect to something else.
Momentum is simply established movement with respect to something else. Acceleration is the only really meaningful thing, as it involves force and a transfer of energy. Momentum is a measure of how much acceleration it would require to change relative speeds with respect to something else. If you removed the something else from the system or substituted it for something with the same “momentum,” everything would cease to have momentum and would not be moving.
The insight that there is no global coordinate system in space is a key insight of relativity. Momentum is a measurement of the state of a system in an inertial frame and can be seen as a measure of the energy required to effectively get all the mass to have that velocity, or the energy required to bring the entire frame to relative rest. It’s a conserved measure, and a bunch of other useful things - but it itself isn’t “a thing,” it’s a measure.
"Except there is no absolute coordinate system. Position is relative to something"
Yes, just pick something. I think I get what you're saying, but I'm unclear why its not straightforward. I must be missing something.
Well because in relativity accelerating frames of reference are pretty complex, space isn’t flat, neither is time, and the position of something is a fairly complex concept as is causality etc. Momentum changes depending on what frame of reference you use, and space itself can’t be a frame of reference. That’s because momentum isn’t actually a thing but a measure of things within a frame of reference with respect to each other. Energy, mass, etc these are things - but momentum itself isn’t other than as a way to describe the needed energy to align the frame of reference into a different configuration of relative motion, mass, and energy. Its conservational nature is derived from the fact those things are conserved.
Now of course Newton and most people before and after him through to Einstein did just fine ignoring all these things and just “picking something” worked for everything they needed to do. But it was at its most fundamental nature wrongs and position is not simple. In fact due to relativity even ignoring quantum, you can’t even know your relative position with any certainty - just your relative position as of some distance in time proportional to the relative distance you observe.