Timeline for Is my friend right about omitting $c^2$ in world famous tiny equation?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 27, 2020 at 7:07 | vote | accept | RK James | ||
| May 27, 2020 at 1:30 | comment | added | user87745 | Yes, I was assuming principle of relativity, homogeneity, and isotropy (none of which are trivial, of course). However, even given all those, both Galilean and Einsteinean relativity can work. By saying "finite" I was making the distinction that nature chooses Einsteinean relativity over Galilean relativity. But yes, I agree that to even arrive at a single parameter whose value (finite or infinite) determines Galilean/Einsteinean, we need non-trivial physical assumptions, so they're baked into a notion of $c$ in the sense in which we talk about it. | |
| May 27, 2020 at 1:25 | comment | added | tparker | 2. Eh, I mostly agree with you, but it depends on exactly what you're assuming. I personally would say the core fact underlying special relativity is that spacetime is invariant under the Poincare group. This implies some more facts - like the fact that the speed of light is spatially isotropic and does not change over time - which may or may be implicit in the statement "the speed of light is finite", depending on your exact assumptions. | |
| May 27, 2020 at 1:25 | comment | added | tparker | @DvijD.C. 1. Yes, I agree with you. But you do need to realize that in order to fully appreciate what it means to set $c = 1$, and to me the friend's explanation that the $c$ is just an "artifact" seems to incorrectly imply that the $c$ is as unphysical and conventional as Boltzmann's constant. | |
| May 26, 2020 at 23:21 | comment | added | user87745 | 1. Well, the non-trivial physical fact that the speed of light is invariant gives us an invariant/unambiguous way to measure space and time in the same units. Once we realize that, writing $c$ in a dimensionful manner seems like writing the distances along the north and those along the east in different units, to steal the analogy due to Wheeler. 2. The "physical value" of $c$ reflects everything about the history of the units we chose to measure lengths and time, etc., but not much about physics IMO. The only physically meaningful information is that $c$ is finite, no? | |
| May 26, 2020 at 23:06 | history | answered | tparker | CC BY-SA 4.0 |