• 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.


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

203 submissions , 161 unreviewed
5,007 questions , 2,163 unanswered
5,342 answers , 22,657 comments
1,470 users with positive rep
815 active unimported users
More ...

  How to determine whether two participants in the same event had been momentarily co-moving at this event?

+ 0 like - 0 dislike

Consider two participants (a.k.a. "material points"), $P$ and $Q$, who had been coincident ("meeting, in passing") at exactly and only one event, $\varepsilon_{P Q}$.

Further, for all events in which $P$ had taken part, i.e. the (ordered) set of events
$\{ ... \, \varepsilon_{B P} \, ... \, \varepsilon_{K P} \, ... \, \varepsilon_{P Q} \, ... \, \varepsilon_{P V} \, ... \, \varepsilon_{P Y} \, ... \}$,
along with all events in which $Q$ had taken part, i.e. the (ordered) set of events
$\{ ... \, \varepsilon_{A Q} \, ... \, \varepsilon_{J Q} \, ... \, \varepsilon_{P Q} \, ... \, \varepsilon_{U Q} \, ... \, \varepsilon_{X Q} \, ... \}$,
the values of Lorentzian distance $\ell$ between any pairs of events shall be given.

Under exactly which condition, expressed in terms of the given values $\ell$, are participants $P$ and $Q$ said to have been "momentarily co-moving" at event $\varepsilon_{P Q}$ ?


Notes concerning terminology:

(1) While in 2015 the notion of Lorentzian distance $\ell$ was denounced as "a mathematical function that isn't used in physics", its use in physics appears suitably reputable since 2016.

(2) Apparently, Lorentzian distance $\ell$ is also referred to as "time-separation function (or time function) $\tau$", e.g. here and elsewhere. For the purposes of my question above, I'd like to ask that the terms "time-separation function" (or "time-function") are not used where "Lorentzian distance" could be used equivalently instead, and that the symbol $\tau$ remains reserved to denote durations (a.k.a. "arc lengths of timelike paths", a.k.a. "proper time"), if need be.

asked Jun 10, 2017 in Theoretical Physics by Frank Wappler (0 points) [ revision history ]
edited Jun 10, 2017 by Frank Wappler

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).
To avoid this verification in future, please log in or register.

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

Your rights