You can probably come up with lots of systems that look approximately like they have velocity. The trouble comes when you want them to exactly satisfy the rule of “for any trajectory t, there is an equivalent trajectory t’ which is exactly the same except everything moves with some given velocity, and it still follows the laws of physics”, because if you have that property then you also have relativity because relativity is that property.
for any trajectory t, there is an equivalent trajectory t’ which is exactly the same except everything moves with some given velocity, and it still follows the laws of physics
This describes Galilean relativity. For special relativity you have to shift different objects’ velocities by different amounts, depending on what their velocity already is, so that you don’t cross the speed of light.
So the fact that velocity (and not just rapidity) is used all the time in special relativity is already a counterexample to this being required for velocity to make sense.
Sure. I’d say that property is a lot stronger than “velocity exists as a concept”, which seems like an unobjectionable statement to make about any theory with particles or waves or both.
I guess there’s “velocity exists as a description you can impose on certain things within the trajectory”, and then there’s “velocity exists as a variable that can be given any value”. When I say relativity asserts that velocity exists, I mean in the second sense.
In the former case you would probably not include velocity within causal models of the system, whereas in the latter case you probably would.
As far as I know, condensed matter physicists use velocity and momentum to describe quasiparticles in systems that lack both Galilean and Lorentzian symmetry. I would call that a causal model.
Yes, it’s exactly the same except for the lack of symmetry. In particular, any quasiparticle can have any velocity (possibly up to some upper limit like the speed of light).
You can probably come up with lots of systems that look approximately like they have velocity. The trouble comes when you want them to exactly satisfy the rule of “for any trajectory t, there is an equivalent trajectory t’ which is exactly the same except everything moves with some given velocity, and it still follows the laws of physics”, because if you have that property then you also have relativity because relativity is that property.
I just realized,
This describes Galilean relativity. For special relativity you have to shift different objects’ velocities by different amounts, depending on what their velocity already is, so that you don’t cross the speed of light.
So the fact that velocity (and not just rapidity) is used all the time in special relativity is already a counterexample to this being required for velocity to make sense.
Sure. I’d say that property is a lot stronger than “velocity exists as a concept”, which seems like an unobjectionable statement to make about any theory with particles or waves or both.
I guess there’s “velocity exists as a description you can impose on certain things within the trajectory”, and then there’s “velocity exists as a variable that can be given any value”. When I say relativity asserts that velocity exists, I mean in the second sense.
In the former case you would probably not include velocity within causal models of the system, whereas in the latter case you probably would.
As far as I know, condensed matter physicists use velocity and momentum to describe quasiparticles in systems that lack both Galilean and Lorentzian symmetry. I would call that a causal model.
Interesting point. Do the velocities for such quasiparticles act intuitively similar to velocities in ordinary physics?
Yes, it’s exactly the same except for the lack of symmetry. In particular, any quasiparticle can have any velocity (possibly up to some upper limit like the speed of light).