Timeline for Time dilation clock experiment: what would happen if the clock were flipped 90 degrees?
Current License: CC BY-SA 3.0
8 events
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| Oct 27 at 0:33 | comment | added | Amit | @GumbyTheGreen In case that's still relevant (to you or anyone else) here is how you do it: $$c\Delta t_0' =\ell'+ v\Delta t_0' $$ $$\ell' = c\Delta t_0' -v\Delta t_0' $$ $$ \ell' = c\Delta t_0' \left(1-\frac{v}{c}\right) $$ $$ \frac{\ell'}{1-\frac{v}{c}} = c\Delta t_0' $$ | |
| Jan 17, 2022 at 19:02 | comment | added | robphy | @MichaelSeifert I just contributed an answer using a related method that doesn't directly use the Bondi k-calculus. | |
| Jan 17, 2022 at 4:21 | comment | added | robphy | @MichaelSeifert The "longitudinal light clock" is developed in my paper "Relativity on Rotated Graph Paper" AmJPhy 84, 344 (2016); doi.org/10.1119/1.4943251 using radar measurements (Bondi) and the relativity principle. This implies the invariance of the area of a causal diamond (Mermin). This area is equal to the square interval. Written in light-cone coordinates, this is the essentially the product of radar-times formula (Geroch, Synge). Time dilation and length contraction follow as consequences. (See physicsforums.com/insights/relativity-rotated-graph-paper ) | |
| Jan 16, 2022 at 8:34 | comment | added | Gumby The Green | Lots of skipped algebra (and associated reasoning) here. It all looks technically correct but it's hard to verify certain things and see why they're being done. The last step took some effort to figure out and I still don't know how you get from ℓ′+vΔto′ to ℓ′/(1+v/c). I had to plug in numbers to verify that those two things are equal. Would you (or someone) mind adding some detail to those parts? | |
| Sep 12, 2021 at 13:02 | comment | added | Michael Seifert | In many introductory treatments of SR, one uses the time dilation formula obtained from a "perpendicular light clock" to get the length-contraction formula. Is it possible to derive the time-dilation equation for a "parallel light clock" without assuming the length-contraction formula? Or does one just have to take it on faith in this account? | |
| Aug 28, 2016 at 19:12 | history | edited | Paul T. | CC BY-SA 3.0 |
typos
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| Aug 26, 2016 at 20:15 | history | edited | Paul T. | CC BY-SA 3.0 |
add some commentary, and sectioning
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| Aug 26, 2016 at 20:05 | history | answered | Paul T. | CC BY-SA 3.0 |