Timeline for Why do clocks measure arc-length?
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Oct 23, 2019 at 5:19 | answer | added | Sean E. Lake | timeline score: 0 | |
| Oct 23, 2019 at 4:30 | answer | added | benrg | timeline score: 1 | |
| Feb 8, 2013 at 15:52 | vote | accept | joshphysics | ||
| Mar 20, 2021 at 22:51 | |||||
| Feb 8, 2013 at 7:09 | history | tweeted | twitter.com/#!/StackPhysics/status/299776886412816384 | ||
| Feb 8, 2013 at 3:58 | answer | added | Eduardo Guerras Valera | timeline score: 2 | |
| Feb 7, 2013 at 21:50 | answer | added | Retarded Potential | timeline score: 4 | |
| Feb 7, 2013 at 21:33 | answer | added | Nikolaj-K | timeline score: 12 | |
| Feb 7, 2013 at 20:52 | history | edited | joshphysics | CC BY-SA 3.0 |
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| Feb 7, 2013 at 20:52 | comment | added | joshphysics | Good point; I'll remove that part since what I'm actually asking is for arguments making that assumption plausible. Let me add that I'm completely comfortable simply taking this fact as an axiom of relativity that is ultimately justified by experiment. What bothers me is that people rarely state the assumption in such terms, and it seems to me that they often even suggest that it's some obvious/trivial consequence of how events transform between inertial frames. For example, the resolution of the twin paradox ultimately rests on this assumption (as far as I can tell). | |
| Feb 7, 2013 at 20:46 | comment | added | Retarded Potential | You ask for "an example of an accelerating worldline ... calculated explicitly", but how can we calculate this without the assumption? I.e. just what assumptions are we allowed to make about an accelerating observer, if none, then it seems there is no argument that can be made. | |
| Feb 7, 2013 at 20:39 | comment | added | joshphysics | Yes I definitely agree that the result is immediate given that assumption. In fact, most of my post is an attempt to justify that assumption by approximating an arbitrary worldline by a piecewise non-accelerating (inertial) worldline. The problem I have with the assumption is that it certainly holds for inertial observers since Minkowski arc-length is Poincare invariant; but it's not clear to me why it should hold for accelerating observers without some sort of argument like the one I'm attempting to make. | |
| Feb 7, 2013 at 20:26 | comment | added | Retarded Potential | Let $\lambda=t$, the time according to inertial $O$, and let $\vec{x'}$ be the spatial position of $O'$ according to $O$, while $t'$ is the time measured by $O'$. If we are allowed the assumption $c^2(dt'/dt)^2 = c^2 - (d\vec{x'}/dt)^2$ then isn't the result immediate? And if we are not allowed the assumption how could we calculate the example of an accelerating worldline in Minkowski space? | |
| Feb 7, 2013 at 19:40 | history | edited | joshphysics | CC BY-SA 3.0 |
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| Feb 7, 2013 at 19:23 | history | edited | joshphysics | CC BY-SA 3.0 |
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| Feb 7, 2013 at 18:55 | history | edited | joshphysics | CC BY-SA 3.0 |
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| Feb 7, 2013 at 18:19 | history | asked | joshphysics | CC BY-SA 3.0 |