Moving through spacetime

1. Jun 13, 2010

Paul77

I've been informed that when you move through spacetime:

If you move through time with the same space-time curvature, your effective "speed" through time is c.

Does anyone have a link that explains this?

Last edited: Jun 13, 2010
2. Jun 13, 2010

bcrowell

Staff Emeritus
What do you mean by "move spacetime?"

No, because it's not true.

3. Jun 13, 2010

Paul77

I meant "move through spacetime".

I think its true because its a quote from one of the main PF contributors.

4. Jun 13, 2010

Fredrik

Staff Emeritus
Brian Greene claimed that everything moves through spacetime at speed c in "The elegant universe".

For those of you who know SR already: It only means that any velocity four-vector u satisfies $$\sqrt{-u^T\eta u}=1$$. (The minus sign is needed if our convention for the metric is -+++). Since this is just the normalization convention for four-velocities, it's true by definition. It's like saying that bald guys have no hair, and making it sound like an insight of deep significance.

I posted some comments here. (Post #18. The Greene quote is in #15).

This has nothing to do with curvature.

5. Jun 13, 2010

Naty1

Paul77...if you keep Greene's "simple" explanation in mind on one hand and the fact that such analogies have their limitations on the other, you have the best of both worlds. An introduction on one hand but some subtlies on the other.

I think it's in Greene's book that there is a nice diagram....(or is it Smolin??)..anyway, two space and one time axis. An object of constant velocity moves in a straightline, an accelerating object in a curve, and a object in uniform rotational motion about a fixed point plots as a corkscrew. As soon as I saw that I had a simple "analogy" for reference; on the other hand, the diagrams of a "slice of bread" describing slices of time, relativity of simultaneity, did NOT hit a cord with me....

Part of the issue is, I think, that fact since v = c is impossible as far as we know, there is no reference frame for such motion...but that doesn't mean you can't think about the fact that as something gets arbitrarily close to v = c, it's time becomes arbitrarily slow [in its own frame] and any mass becomes arbitarily large....Thought experiments, especially of simplified situations or ones at limits can offer useful insights even if not entirely practical.

6. Jun 13, 2010

DaveC426913

Yes, that is a fine thought experiment. Notice that it does not toss aside known laws of physics.

I should clarify - it's not that you can't ignore laws of physics - nothing wrong with slicing a star in half and seeing what's inside - it's that the laws you ignore can't also be the ones you are intersted in examining. Such is the disappearing planet proposal.