Understanding Conformal Time & Lorentzian Manifolds: A Layman's Guide

[palmer eldtrich]

Can anyone give a laymans explanation of conformal time in relativity? I tried to read Roger Penrose's book but I found it hard to grasp.Thanks in advance .
Also is a Lorentzian manifold different to a conformal manifold? A laymans explanation would also be much apprecitaed.

 

[Simon Bridge]

Have you seen:
http://cosmoquest.org/forum/showthread.php?109683-quot-Conformal-Time-quot-definition-for-a-layperson

 

[palmer eldtrich]

wow that's a very clear explanation, thanks. The chess board analogy is very helpful. Interestingly the previous questioner was But I am still trying to get my head round how there is a before or after in conformal time if there are no clocks due o no massive particles. IF i stick with the chessboard analogy, imagine I watch he game of chess sped up or slowed down, the moves of the game still happen in a certian order, no mater what speed the game is played at. If partciles are massless hey see the game sped up to infintley fast speeds but he sequence doesn't change? Is that right or I have muddled this?

 

[PeterDonis]

If partciles are massless hey see the game sped up to infintley fast speeds but he sequence doesn't change?

"Infinitely fast speed" is not correct; what is correct is that the concept of "speed" has no meaning for photons. But the concept of "sequence of events" still does. For example, consider a light ray A moving in the positive $x$ direction, and two light rays B and C moving in the negative $x$ direction. Even though, if all we look at is the light rays, we have no way of defining "time" or "speed", the order in which A crosses B and C (B first, then C, or C first, then B) is still well-defined (only one of the two possible orders can be true).

 

[palmer eldtrich]

Hi Peter, thansk for that. So to stick with the chess board analogy, you can still record the chess game as a definite sequence of moves even if you can't specify how long each event was? Should we think of conformal time as something like that? So if there are only massless particles, there is still conformal time ( the sequence of moves , but not poper time , how much time has elapsed between the moves).

 

[PeterDonis]

So to stick with the chess board analogy, you can still record the chess game as a definite sequence of moves even if you can't specify how long each event was? Should we think of conformal time as something like that?

Yes.

So if there are only massless particles, there is still conformal time ( the sequence of moves , but not poper time , how much time has elapsed between the moves).

Not quite. In order to even define a sequence of moves with only massless particles, you need massless particles that are moving in different directions, so that they intersect; the intersections are the "moves". (You can see that in the example I gave.) But it turns out that, if you have a network of massless particles moving in different directions, you can construct timelike intervals out of them, which means you can construct a notion of proper time out of them.

For example, in the scenario I described in my previous post, if we add a second light ray, D, moving in the positive $x$ direction, then we have four intersections ("moves" or events): AB, AC, DB, DC. We assume that the orderings are "AB then AC", and "DB then DC". Then the pair of events "AB, DC" defines a timelike interval, and the pair of events "DB, AC" defines a spacelike interval.

I haven't read enough about Penrose's model, the one discussed in the linked post, to know how all this affects it, if at all.