• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,064 questions , 2,215 unanswered
5,347 answers , 22,731 comments
1,470 users with positive rep
818 active unimported users
More ...

  Which geometric relations obtain between two distinct rest systems?

+ 0 like - 1 dislike

Consider, as a thought experiment, a set of participants who measure throughout the experiment having been at rest to each other; among them explicitly participants \({\mathbf A}\)\({\mathbf B}\) and \({\mathbf F}\) who determine the ratios of their (chronogeometric) distances between each other as real number values \(\frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}}\), \(\frac{{\mathbf B}{\mathbf F}}{{\mathbf A}{\mathbf F}}\)and \(\frac{{\mathbf A}{\mathbf B}}{{\mathbf B}{\mathbf F}} = \frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}} / \frac{{\mathbf B}{\mathbf F}}{{\mathbf A}{\mathbf F}}\)

Further let there be another set of participants (of which neither \({\mathbf A}\), nor \({\mathbf B}\), nor \({\mathbf F}\) are a member) who measure throughout the experiment having been at rest to each other as well; among them \({\mathbf J}\), \({\mathbf K}\) and \({\mathbf Q}\), who determine the ratios of their (chronogeometric) distances between each other as real number values \(\frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}}\)\(\frac{{\mathbf K}{\mathbf Q}}{{\mathbf J}{\mathbf Q}}\), and \(\frac{{\mathbf J}{\mathbf K}}{{\mathbf K}{\mathbf Q}} = \frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}} / \frac{{\mathbf K}{\mathbf Q}}{{\mathbf J}{\mathbf Q}}\),   

such that

  • \({\mathbf J}\) passed \({\mathbf A}\), then passed \({\mathbf B}\),

  • \({\mathbf A}\) passed \({\mathbf J}\), then passed \({\mathbf K}\),

  • \({\mathbf Q}\) passed \({\mathbf F}\), in coincidence with \({\mathbf Q}\) and \({\mathbf F}\) observing \({\mathbf J}\) and \({\mathbf A}\) having passed each other,

  • \({\mathbf B}\) and \({\mathbf F}\) determined that \({\mathbf B}\)'s indication of the passage of \({\mathbf J}\) was simultaneous to \({\mathbf F}\)'s indication of the passage of \({\mathbf Q}\), and

  • \({\mathbf K}\) and \({\mathbf Q}\) determined that K's indication of the passage of \({\mathbf A}\) was simultaneous to \({\mathbf Q}\)'s indication of the passage of \({\mathbf F}\).

Is thereby guaranteed that for these distance ratios obtains

\(\frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}} = \frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}}\)?,

and (moreover)

\(\left( \left(\frac{{\mathbf B}{\mathbf F}}{{\mathbf A}{\mathbf F}}\right)^2 + 1 - \left(\frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}}\right)^2 \right) \left( \left(\frac{{\mathbf K}{\mathbf Q}}{{\mathbf J}{\mathbf Q}}\right)^2 + 1 - \left(\frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}}\right)^2 \right) = 4 \left( 1 - \left( \frac{{\mathbf A}{\mathbf B}}{{\mathbf A}{\mathbf F}} \right) \left( \frac{{\mathbf J}{\mathbf K}}{{\mathbf J}{\mathbf Q}} \right) \right)\)?

Or otherwise:
What could be concluded if (1) and/or (2) were not found satisfied?

This question was deleted from Physics Stack Exchange and restored from an archive.  

asked Apr 24, 2014 in Experimental Physics by Frank Wappler (0 points) [ revision history ]
edited Apr 24, 2014 by dimension10

The answer to this question can be worked out in a few minutes by writing down the trajectories of all the observers (I didn't do it, but you should do it), voting to close.

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights