This seems too strong. Can’t you write down a linear field theory with no (Galilean or Lorentzian) boost symmetry, but where waves still propagate at constant velocity? Just with a weird dispersion relation?
(Not confident in this, I haven’t actually tried it and have spent very little time thinking about systems without boost symmetry.)
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).
I had to look up “boost symmetry”, so for posterity, here’s the results of the lookup. From text-davinci-003:
Boost symmetry is a property of quantum field theory [note: actually, relativity] which states that the laws of physics remain unchanged under a Lorentz boost, or change in the relative velocity of two frames of reference. This means that the same equations of motion will be true regardless of the observer’s velocity relative to the system, and that the laws of nature do not depend on the frame of reference in which they are measured.
Very first I tried google, which gave results that seemed to mostly assume I wanted a math reference rather than a first visual explanation; it did link to wikipedia:LorentzTransformation, which does give a nice summary of the math, but I wasn’t yet sure it was the right thing. So then I asked text-davinci-003 (because chatgpt is an insufferable teenager and I’m tired of talking to it whereas td3 is a … somewhat less insufferable teenager). td3 gave the above explanation.
I was still pretty sure I didn’t quite understand, so I popped the explanation into metaphor.systems which gave me a bunch of vaguely relevant links, probably because it’s not quantum, it’s relativity, but I hadn’t noticed the error yet.
Then I sighed and tried a youtube search for “boost symmetry”. that gave one result, the video I linked above, which did explain to my satisfaction, and I stopped looking. I don’t think I could pass many tests on it at the moment, but my visual math system seems to have a solid enough grasp on it for now.
Yeah, sorry for the jargon. “System with a boost symmetry” = “relativistic system” as tailcalled was using it above.
Quoting tailcalled:
Stuff like relativity is fundamentally about symmetry. You want to say that if you have some trajectory τ which satisfies the laws of physics, and some symmetry σ (such as “have everything move in → direction at a speed of 5 m/s”), then στ must also satisfy the laws of physics.
A “boost” is a transformation of a physical trajectory (“trajectory” = complete history of things happening in the universe) that changes it by adding a fixed offset to everything’s velocity; or equivalently, by making everything in the universe move in some direction while keeping all their relative velocities the same.
This seems too strong. Can’t you write down a linear field theory with no (Galilean or Lorentzian) boost symmetry, but where waves still propagate at constant velocity? Just with a weird dispersion relation?
(Not confident in this, I haven’t actually tried it and have spent very little time thinking about systems without boost symmetry.)
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).
I had to look up “boost symmetry”, so for posterity, here’s the results of the lookup. From text-davinci-003:
I found this video on Lorentz transformations by minutephysics to be the best explanation I found, and I now feel I understand well enough to understand the point being made in context.
Here’s a lookup trace:
Very first I tried google, which gave results that seemed to mostly assume I wanted a math reference rather than a first visual explanation; it did link to wikipedia:LorentzTransformation, which does give a nice summary of the math, but I wasn’t yet sure it was the right thing. So then I asked text-davinci-003 (
because chatgpt is an insufferable teenager and I’m tired of talking to it whereas td3 is a … somewhat less insufferable teenager). td3 gave the above explanation.I was still pretty sure I didn’t quite understand, so I popped the explanation into metaphor.systems which gave me a bunch of vaguely relevant links, probably because it’s not quantum, it’s relativity, but I hadn’t noticed the error yet.
Then I sighed and tried a youtube search for “boost symmetry”. that gave one result, the video I linked above, which did explain to my satisfaction, and I stopped looking. I don’t think I could pass many tests on it at the moment, but my visual math system seems to have a solid enough grasp on it for now.
(I enjoyed this style of “log of how I looked something up” comment.)
I have a series of search case studies if you want to read more like that.
curious if you’ve tried metaphor.
Yeah, sorry for the jargon. “System with a boost symmetry” = “relativistic system” as tailcalled was using it above.
Quoting tailcalled:
A “boost” is a transformation of a physical trajectory (“trajectory” = complete history of things happening in the universe) that changes it by adding a fixed offset to everything’s velocity; or equivalently, by making everything in the universe move in some direction while keeping all their relative velocities the same.