Timeline for Is the Euclidean metric a necessary accessory of Lorentzian spacetime?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 7, 2022 at 8:25 | answer | added | Moonraker | timeline score: 0 | |
| Oct 6, 2022 at 16:58 | comment | added | Moonraker | @A.V.S. - Very good comment in the heart of my question: On one hand there is no "god-given" metric, on the other hand it seems hard to get rid of the Euclidean metric. If I have a .csv file spacetime manifold with two points 1;1;1;1 and 6;4;1;1, this corresponds approximately to the diagram I sketched. Any person who reads and interprets the file will choose automatically the Euclidean diagram for the description, and the Euclidean metric appears. | |
| Oct 6, 2022 at 16:04 | comment | added | A.V.S. | I am beginning to understand. You seem to believe that collection of points that could be labelled by four real numbers carry an inherent euclidean metric. But this is not true, we only have an inherent manifold topology of $\mathbb{R}^4$, but there is no “god-given” euclidean metric that goes with it, and there could be other topologies on a spacetime. See wiki, | |
| Oct 6, 2022 at 14:06 | comment | added | Moonraker | @A.V.S. - Interesting idea, but I would say that this is rather representing R3 space (in time slices). The animation provides the 4th dimension of time, and in your brain (or in the data base of a computer, e.g. in the form of a .csv file) there are formed Euclidean fourdimensional manifolds. The meaningless Euclidean metric is still dominating the hidden Lorentzian metric. | |
| Oct 6, 2022 at 10:50 | comment | added | A.V.S. | What kind of animations? I am thinking about something like this (and other gifs from the same page), with the screen representing space and animation frames corresponding to evolution w.r.t. time. How are light rays and light cones… on this kind of animation one could do instantaneous snapshots of wavefronts corresponding to signal emission at particular events. | |
| Oct 5, 2022 at 8:14 | comment | added | Moonraker | @A.V.S. - What kind of animations? How are light rays and light cones represented (with null Lorentzian spacetime interval zero)? | |
| Oct 4, 2022 at 6:59 | comment | added | A.V.S. | Is there a way to get rid of this superfluous Euclidean metric… I don't get it. Do not draw spacetime diagrams and you are set. There are ways to visualize spacetime other than spacetime diagrams (e.g. animations). | |
| Oct 3, 2022 at 11:44 | comment | added | Moonraker | @John Rennie - Thank you for your answer which helps! I understand it in the sense that currently it is not tried to "get rid" of this superfluous Euclidean metric, and that it is just not taken into account. | |
| Oct 3, 2022 at 10:33 | comment | added | Qmechanic♦ | Possible duplicates: physics.stackexchange.com/q/129187/2451 , physics.stackexchange.com/q/729771/2451 and links therein. | |
| Oct 3, 2022 at 10:21 | comment | added | John Rennie | You are drawing the diagram on a piece of paper that has two spacelike dimensions i.e. you are drawing a timelike axis on a spacelike dimension. But unless you have access to Lorentzian paper I don't see how you can get around this. You just have to remember not to take distances on the paper literally. | |
| Oct 3, 2022 at 9:15 | comment | added | FlatterMann | Are you aware of the derivation of Lorentz transformations from a metric background and relativity? | |
| Oct 3, 2022 at 9:10 | history | asked | Moonraker | CC BY-SA 4.0 |
