• 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
5,079 questions , 2,229 unanswered
5,348 answers , 22,758 comments
1,470 users with positive rep
819 active unimported users
More ...

  When periodic solutions are combined with timelessness, do we get closed timelike curves?

+ 7 like - 0 dislike

In quantum gravity, ADM wavefunctional solutions have to satisfy the Wheeler-DeWitt equation. This leads to timelessness. What happens if we have a time periodic solution? In classical general relativity, a time periodic solution just means that and no more. But when combined with a timeless wavefunctional, if the same configuration occurs twice or more often, the coefficient of the configuration component in the wavefunctional has to be exactly the same both times around, both in magnitude and in phase. That is because we have no disambiguating clock external to the timeless wavefunctional, which is not multivalued. But this is exactly the description of a closed timelike curve.

Assume space is compact so we do not have to worry about asymptotic infinity.

This post imported from StackExchange Physics at 2014-06-13 12:31 (UCT), posted by SE-user user1902
asked Feb 15, 2011 in Theoretical Physics by user1902 (35 points) [ no revision ]

See my answer below, which has been lying dormant for quite some time now.

1 Answer

+ 2 like - 0 dislike

If there is a time periodic solution of $\hat{\mathcal{H}}\Psi=0$, then obviously there are only a finite number of solutions throughout the whole of time. A closed timelike curve is a closed worldline, i.e., the particle whose worldline is a CTC must have a repeated 4-position. If the position $\overrightarrow{x}$ has a linear dependence on time, then your argument is true and a CTC is created. If no such linear dependence exists, then the particle may end up with the same time coordinate, but not the position - and this is not a CTC.

This post imported from StackExchange Physics at 2014-06-13 12:31 (UCT), posted by SE-user Sanath Devalapurkar
answered Jan 12, 2014 by SDevalapurkar (285 points) [ no revision ]

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