Quantcast
  • 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.

News

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

Attributions

(propose a free ad)

Site Statistics

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,851 answers , 20,616 comments
1,470 users with positive rep
501 active unimported users
More ...

Does the general-relativistic attraction between two optical cavities depend on the relative phase between the two oscillations?

+ 4 like - 0 dislike
98 views

My understanding is that parallel beams of light do not attract but anti-parallel beams do attract (see, for example here). But if this is true, then consider a device in which a laser is bounced between two mirrors arranged along the Z axis. Such a device should attract another similarly oriented device *only* if the two laser trajectories are out of phase (if they are in phase, then the two beams are always parallel and never anti-parallel). It is interesting to consider that if the period of oscillation of the two devices is not the same, then there will be a beat frequency between 'parallel' and 'anti-parallel' beams, and the attraction between the two devices will oscillate. How is this behavior reconciled with the fact that in both cases the stress energy is the same for each system, and therefore the general-relativistic attraction should be independent of the relative phase?  

asked Jun 30, 2015 in Theoretical Physics by user1247 (530 points) [ no revision ]

1 Answer

+ 4 like - 0 dislike

I like how this topic is treated in Tolman, Ehrenfest and Podolsky in PhysRev. To understand how gravity and null-matter works I always try to think about it as of pure gravitomagnetism. The parallel-inert and antiparallel-attracting behaviour of two rays of light is then analogous to magnetism between two wires (with the caveat that gravity can only be attractive). Another way to think about this is to ask: What else than a photon, a maximum-speed rest-mass-zero particle should exhibit pure dragging?

When you take a look in the article or think about it, you will realize that the stress-energy tensor is not equal in both the mirror-boxes you mention. Unless you are considering counter-moving streams of photons, the direction of the ray-pencil will always be reflected in the off-diagonal components (such as say $T^{tx}$ for rays moving in the $x$ direction). 


I.e., yes, the attraction will depend on the relative phase between the pulses being reflected there and back again. However, consider that the situation cannot be most certainly thought of as stationary. The very variation of the attraction between the mirror boxes will be then associated with gravitational radiation and there might lurk something very unintuitive in the gravitational radiation from light rays (I don't know about any reference on this). 

answered Jul 1, 2015 by Void (1,505 points) [ revision history ]
edited Jul 2, 2015 by Void

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:
p$\hbar$ysicsO$\varnothing$erflow
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
...