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mokeejoe5
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Does the relativity of simultaneity imply the impossibility of non local conservation laws?
jtbell said:Such as?
(I'm just trying to clarify what exactly you're asking about, and what your "sticking points" are in your understanding, so people don't go shooting off in a half-dozen different directions, none of which may be the one you want.)
This just implies that all global conservation laws need local equivalents.mokeejoe5 said:Thanks for the reply.
My current understanding is that all quantities that are conserved must be conserved locally. If for example you had charge appearing in one place and disappearing 'instantaneously' in another place then depending on your frame of reference you would be able to see the conservation of charge violated and be able to establish whether or not you were moving.
I heard Feynman say this in one of his messenger lectures and I'm just tying to confirm whether my understanding of what he said corresponds to what he was trying to say.
mfb said:This just implies that all global conservation laws need local equivalents.
Local conservation laws exist, and they can lead to global conservation laws - at least in special relativity, where you can still consider "the universe at this moment in my reference frame". It becomes tricky in general relativity because that concept stops being meaningful.
Why do you want charge appearing and disappearing to have a conservation law?mokeejoe5 said:Sorry to repeat myself but all I'm asking is is it possible in principle for a conservation law to be non local (to have charge disappearing at one point and appearing at another point) in other words is that what Feynman said outdated.
mfb said:Why do you want charge appearing and disappearing to have a conservation law?
A global conservation law and special relativity imply a local conservation law.
mokeejoe5 said:I don't want one I'm asking is it theoretically impossible for one to exist, as Feynman said in the video above.
edit: by one I mean a conservation law that does not apply locally.
bcrowell said:Feynman is correct.
bcrowell said:Sorry, what I originally thought you were talking about was something different than what you actually meant. The possibility that Feynman is talking about isn't one that people normally consider.
mokeejoe5 said:Does the relativity of simultaneity imply the impossibility of non local conservation laws?
martinbn said:So if a cat disappears here now and appears in Greece now (Feynman's example), for a moving observer it will disappear at some instant and appear at a later instant (for example).
vanhees71 said:can I start from the integral ##Q^{\nu \rho \ldots}## and the assumption that it is a constant in time to prove that ##Q^{\nu \rho\ldots}## is a tensor
vanhees71 said:Do you have a reference, where this is really done? That's then a really strong theorem, making non-local theories even less likely to work than it's apparent so far only by the absence of any working example.
vanhees71 said:Do you have a reference, where this is really done? That's then a really strong theorem, making non-local theories even less likely to work than it's apparent so far only by the absence of any working example.
vanhees71 said:I don't think that this is "pretty trivial".
atyy said:"To dramatize the question, imagine two parties Alice and Bob, many light years apart, who share a “superluminal charge transport line” (SCTL). Alice places a single electrically charged particle, an electron, at her end of the SCTL (the point y); then her charge mysteriously disappears, and in an instant reappears at Bob’s end of the SCTL (the point x). The electron has been transmitted through the SCTL far more rapidly than Alice could send a light signal to Bob. Is such a device physically possible?
Yes."
In my original reply I talked only about classical field theory, and also there it's not trivial!PeterDonis said:What you describe isn't trivial, yes, but what you describe is a lot more than just the simple claim that the principle of relativity requires that all conservation laws be local conservation laws. You don't need all the machinery of relativistic QFT to evaluate that claim.
vanhees71 said:In my original reply I talked only about classical field theory
vanhees71 said:also there it's not trivial!
PeterDonis said:What they're describing is not a nonlocal process; there is no actual superluminal transport of charge, and charge is locally conserved in the process. If you look at Fig. 7(a), which describes the process (Fig. 7(b) is the non-Abelian version, which doesn't work the same), you will see an unbroken line of charge all the way through the diagram, indicating that local charge conservation is not violated. What is going on is just a prearranged process that produces apparent superluminal "motion", while in fact everything is local and causal. (It's something like the way apparent superluminal "motion" could be produced by having a very long line of LEDs, each prearranged to light up for an instant in such a way as to make it appear that a light flash is moving superluminally, when in fact everything is local and causal.)
PeterDonis said:What you describe isn't trivial, yes, but what you describe is a lot more than just the simple claim that the principle of relativity requires that all conservation laws be local conservation laws. You don't need all the machinery of relativistic QFT to evaluate that claim.
atyy said:can it be shown that QFT doesn't change anything?
atyy said:Also, the OP asked whether considering gravitation changes anything.
PeterDonis said:I haven't had a chance to look at the paper bcrowell referenced. But I don't see how QFT would affect the basic argument; the only possible subtlety would be carefully distinguishing between underlying fields and observables, with the basic argument applying to observables.
atyy said:For a gauge theory, the gauge invariant observable is a Wilson loop or something nonlocal. Experimentally, I think these lead to things like Aharonov-Bohm effects.
atyy said:Wave function collapse in quantum mechanics shows that some nonlocality is compatible with relativity.
PeterDonis said:Yes, this is true, but these effects are not "nonlocal" in the sense of breaking local conservation laws. That's part of the point of the paper we were discussing earlier; yes, some effects can "appear" nonlocal, but no local conservation laws are ever violated, and no information is ever transmitted faster than light.
PeterDonis said:Wave function collapse is a very "fuzzy" concept--for one thing, not all interpretations of QM even have it (the MWI being the most obvious example of one that doesn't). Part of the reason it's a "fuzzy" concept is precisely the apparent incompatibility with relativistic invariance; in QFT (as opposed to non-relativistic QM), as I understand it, collapse doesn't really appear (Weinberg's classic text, for example, IIRC never brings it up or uses it), because it just doesn't work once you require your theory to be relativistically invariant. IMO collapse is best viewed as a heuristic, a way of extracting practical predictions from the theory even though we don't really understand how things work underneath.
PeterDonis said:Yes, but you did bring up the whole QFT thing in the post I was responding to.
Once again, I agree that the details of how local conservation laws work in specific cases are not trivial. But you don't need all that detail to evaluate the simple claim that the principle of relativity requires that all conservation laws be local conservation laws.
I don't want to discuss quantum collapse assumptions here. If at all, one should discuss this in the quantum mechanics subforum, where it belongs (if at all, because I consider collapse a flawed und fortunately unnecessary concept, as you know from our earlier discussions).atyy said:The CJS paper? I guess I don't quite understand what "local" means if there are not even gauge-invariant local observables. Also, you describe "local" as no information is ever transmitted faster than light, which is indeed a requirement of relativity. But as wave function collapse shows, one can have nonlocality without violating the restriction on faster than light transmission of information.
vanhees71 said:Ok, so what's the specific argument that all conservation laws must be local? Is Feynman's claim available in a scientific paper?
vanhees71 said:The apparently "nonlocal observable" is, as you stated, the interference pattern in the Aharonov-Bohm effect. But this is just the manifestation of a non-integrable phase factor, which is gauge invariant and expressible in a local form via the electromagnetic four-potential. So there is no violation of locality in the usual sense in the AB effect.