Can Speed Exceed the Speed of Light in General Relativity?

[Quarlep]

I read somewhere that speed can be higher then c in General Relativity.Can you show me a website

 

[Nugatory]

I read somewhere that speed can be higher then c in General Relativity.Can you show me a website

Here's a link to my favorite website for this sort of question. If you search it for "recession velocity" you'll find some good stuff.

 

[stevendaryl]

I read somewhere that speed can be higher then c in General Relativity.Can you show me a website

That depends on what you mean. In GR, in any small region of space, and for small periods of time, it is always possible to set up a coordinate system in which light has speed $c$. What's not possible, in general, is to set up a coordinate system for the whole universe so that light has the same speed everywhere.

The problem is that speed is a coordinate-dependent quantity.

 

[Quarlep]

I remember something like this.I saw it on wikipedia I guess.

 

[PeterDonis]

I remember something like this

This makes no sense without more context. What is this supposed to be a diagram of?

As a general rule, if you find yourself saying "I read somewhere" or "I guess" about where you found some piece of information, and you can't give a link or a reference, that's a sign that your question is too vague to get a meaningful answer. That seems to be the case here. You need to give more specific information.

 

[bcrowell]

That depends on what you mean. In GR, in any small region of space, and for small periods of time, it is always possible to set up a coordinate system in which light has speed $c$. What's not possible, in general, is to set up a coordinate system for the whole universe so that light has the same speed everywhere.

I wouldn't put it quite this way. This makes it sound like SR's speed limit occurs only because we choose a certain type of coordinate system (a type that we don't have the luxury of choosing in GR). That's not true.

The problem is that speed is a coordinate-dependent quantity.

I also disagree with this statement. If my detector gets hit by an electron, and I measure the electron's energy, then I can infer that the electron's speed is, say, 0.4c, relative to the detector. I didn't need any coordinate system for that. I only need a coordinate system if I want to be able to talk about the speeds of *distant* objects.

To understand this properly, I think it's necessary to start by examining carefully what we mean when we say that SR prohibits superluminal motion, and what all of this means in terms of measurement processes. It's actually not even true that SR has a blanket prohibition on superluminal motion. I've written up a presentation of this topic in section 4.7 of my SR book: http://www.lightandmatter.com/sr/ . In that treatment, I give a list of four logically independent constraints that SR puts on superluminal motion. Constraints #2 and #3 can be verified at one point, without discussing the speeds of distant objects. Since they apply at a point, they don't tell us anything about distant objects, and therefore they don't provide any constraint on, say, the speeds of distant galaxies relative to us. Constraints #1 and #4 implicitly assume Minkowski coordinates, and therefore the measurement process to which they implicitly refer is Einstein synchronization (or some other, equivalent, procedure). But we can't carry out Einstein synchronization at cosmological distances.

GR should also make us suspicious of some of the arguments that have traditionally been used to argue that superluminal motion is impossible in SR. The most popular argument is that it would violate causality, but the structure of GR is such that there is no reason to believe in causality as a general principle. For example, we can have CTCs in GR.

 

[Quarlep]

I don't remember anything about it

 

[PeterDonis]

I don't remember anything about it

Then we can close the thread.