Timeline for answer to A reference frame is any coordinate system or just a set of Cartesian axes? by zzz
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| Apr 3, 2015 at 1:36 | comment | added | zzz | Let us continue this discussion in chat. | |
| Apr 2, 2015 at 21:49 | comment | added | user12262 |
bechira: "[...] why you think this is inconsistent with [...]" -- Well, to repeat the obvious: we compare "one frame" being described either as "an infinite set of point particles" (possibly with additional requirements); i.e. using terminology you suggested yourself above: as a set of (infinitely many) "timelike curves (assuming Lorentzian metric)"; or whatever you've been describing in your answer in detail, "at one single point $p$ in $M$".
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| Apr 2, 2015 at 20:53 | comment | added | zzz | @user12262 if you explain more clearly why you think this is inconsistent with the usual definition of frames in SR it will help me address your question better. | |
| Apr 2, 2015 at 20:20 | comment | added | user12262 | bechira: "Ah I see [...]" -- Fine. Now: did I understand correctly that what you described as "frame" in your answer is quite different from (and even inconsistent with) the understanding of "frame" based on W. Rindler's explicit description of "inertial frame" (in distinction to "inertial coordinate system")? | |
| Apr 2, 2015 at 19:37 | comment | added | zzz | Ah I see, the more clear statement would be elements in a fibre of the frame bundle over some fixed point $p$ are related by the lorentz group, which is well known - that the frame bundle is a principle bundle whose fibre and structure group are the rotation group (and lorentz group for lorentzian signatures) | |
| Apr 2, 2015 at 19:06 | comment | added | user12262 | bechira: "why would local frames at the same point on a general spacetime be related by a translation?" -- I didn't mean to suggest that; but the phrase "these frames are related by" in the final sentence of your answer could be (mis?-)interpreted as including such "frames at" various distinct points. "take a point particle to be a timelike curve $\mathbb R\rightarrow M$ (assuming Lorentzian metric)." -- Indeed. And consequently, in Rindler's sense, take "frame" to mean "timelike congruence" | |
| Apr 2, 2015 at 18:23 | comment | added | zzz | But looking at the diagrams it looks like the usual introduction to special relativity - I would take a point particle to be a timelike curve $\mathbb{R} \rightarrow M$ (assuming Lorentzian metric). The point $p$ I'm referring to above is a single point in $M$. | |
| Apr 2, 2015 at 18:19 | comment | added | zzz | Not sure what you're getting at, why would local frames at the same point on a general spacetime be related by a translation? Also didn't read that article by Rindler yet, so really not sure what notion of a point particle you're using, I can post a reply later. | |
| Apr 2, 2015 at 17:26 | comment | added | user12262 | bechira: "$p$ is a point in spacetime [...]" -- Well, then your answer is all the harder to relate to W. Rindler's notion; because, surely, any one of Rindler's "point particles" would be characterized by a (suitable) set of several "points in spacetime". Also: Shouldn't your answer therefore have referred to "Poincaré transformations", or some suitable generalization(s) of those, instead of "Lorentz transformations, as expected." ?? | |
| Apr 2, 2015 at 17:13 | comment | added | zzz | $p$ is a point in spacetime (or slightly more confusingly, some people call it an event). | |
| Apr 2, 2015 at 16:56 | comment | added | user12262 | bechira: I find it very difficult to reconcile your answer with W. Rindler's dictum: "We should, strictly speaking, differentiate between an inertial frame and an inertial coordinate system {...} An inertial frame is simply an infinite set of point particles sitting still in space relative to each other.". Does "point $p$" in your answer mean "point particle $p$" (as for Rindler), or does it instead mean "element $p$ of the manifold" ?? | |
| Mar 30, 2015 at 15:59 | history | edited | zzz | CC BY-SA 3.0 |
typo
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| Mar 30, 2015 at 1:44 | vote | accept | Gold | ||
| Mar 30, 2015 at 0:17 | history | answered | zzz | CC BY-SA 3.0 |