# I How can the universe expand faster than light?

1. Jan 27, 2016

### A AM ARYA

According to the theory of relativity the speed of light is the cosmic speed limit which means(I think) nothing can go faster than the speed of light.Then how universe can expand faster than light itself???

2. Jan 27, 2016

### A.T.

Metric expansion and relative movement are different things.

3. Jan 27, 2016

### A AM ARYA

Still confused.Will you explain a little bit in the context of theory of relativity please...

4. Jan 27, 2016

### Orodruin

Staff Emeritus
Expansion is not about things becoming further apart due to their velocities, it is about space itself expanding. This has been discussed here countless times. I suggest you check the links to similar threads and search the forum and then ask about things you still find unclear.

5. Jan 27, 2016

### Staff: Mentor

It isn't. Take two galaxies that are far enough apart that their "recession velocity" is faster than $c$. Let each of these galaxies emit a light ray in the direction away from the other. The "velocity" of those two light rays relative to each other, defined in the same way as that for the galaxies, will be larger than that of the galaxies themselves--i.e., light itself is "moving faster than light" by this definition.

What all this really means is that this "velocity" isn't a velocity in the usual sense of special relativity, which is the only sense of the term "velocity" to which the rule that velocities can't be faster than $c$ applies. As Orodruin said, one way to interpret what is going on is that space itself is expanding. But that interpretation also has limitations. Another way to think of it is simply that, in a curved spacetime (i.e., in the presence of gravity), the concept of "relative velocity" has no well-defined meaning for spatially separated objects. The "velocity" that people are talking about when they say galaxies far enough away from us have a "recession velocity" faster than light is what is called a "coordinate velocity", and doesn't have any direct physical meaning; that's why it doesn't obey the same rules as a relative velocity in special relativity does.

6. Jan 28, 2016

### A AM ARYA

I know that space itself is expanding but can't figure out how the speed of expansion is superluminal..

7. Jan 28, 2016

### Orodruin

Staff Emeritus
This quote seems to imply that you have heard that space itself is expanding, but you have not understood the meaning of it. Please see Peter's post.

8. Jan 28, 2016

### Elliot Svensson

Would Peter be willing to provide the best available meaning of "relative velocity" in curved spacetime? Or alternately, which of the terms of v = d / t (velocity equals distance divided by time) are we more certain of, and which are we less certain of? Lastly, is this ambiguity due to an application of a theory based on measurements, or are the measurements themselves giving us the ambiguity?

9. Jan 28, 2016

### Elliot Svensson

Goodness, I have another question. I thought that general-relativity curvature due to gravity was totally different than curvature due to a cosmological constant. Are these curvatures actually the same curvature, same effect but different cause, or pretty much unrelated?

10. Jan 28, 2016

### Staff: Mentor

As I said in post #5:

11. Jan 28, 2016

### Staff: Mentor

Why would you think that? A cosmological constant produces spacetime curvature, which is the kind of curvature GR talks about.

12. Jan 28, 2016

### Elliot Svensson

Oh, that makes sense... thanks!

13. Jan 28, 2016

### Elliot Svensson

Do you agree with me that metric expansion of space, if true, is a really big departure from intuitive physics just like wave-particle duality?

14. Jan 28, 2016

### Staff: Mentor

No, because "metric expansion of space" depends on how you choose your coordinates. Wave-particle duality does not.

15. Jan 28, 2016

### A AM ARYA

Can it be put forward in the following way?
The speed of light is the cosmic speed limit only relative to the inertial frames of reference moving at constant velocities.But as the universe is not an inertial frame of reference,distant parts of universe can travel faster than light relative to each other.

16. Jan 28, 2016

### Staff: Mentor

If you say "local inertial frames" instead of just "inertial frames", this is ok. In a curved spacetime, there are no inertial frames except locally.

17. Jan 28, 2016

### A AM ARYA

OK & thanks for the correction.

18. Jan 29, 2016

### Elliot Svensson

I have another question. If there's no good definition for relative velocity for spatially separated objects, is it also true that there's no good definition for the age of one spatially separated object from the reference frame of the other spatially separated object? A subset of this question: in the "twins paradox", at the end, how old are the twins? Wouldn't the stationary twin say "my brother has aged less during his time away"? And wouldn't the traveling twin say "my brother has aged more while I was away"? And wouldn't the word "age" only have any meaning at all when taken from one or another reference frame?

19. Jan 29, 2016

### Staff: Mentor

There is no unique definition for the "age" of spatially separated objects relative to each other, yes. It's a matter of what simultaneity convention you adopt.

When the twins meet again at the end, they aren't spatially separated. They are spatially co-located, so there is a unique, invariant meaning to their relative age, and they both agree on what it is (that the traveling twin has aged less).

20. Jan 29, 2016

### Elliot Svensson

Would it be true to say that the traveling twin's age is less? Or is it only true that he or she has aged less?

21. Jan 29, 2016

### Orodruin

Staff Emeritus
What do you perceive to be the difference between the two?

Note that the comparison can only be made unambiguously when the twins are co-located.

22. Jan 29, 2016

### Elliot Svensson

If it's only true that the traveling twin has aged less, then his age is sort of ambiguous: he's the same age as the stationary twin, but we apply a correction factor to account for his travel history.

23. Jan 29, 2016

### Orodruin

Staff Emeritus
This is not very logic. If the travelling twin has aged less, he will be younger - not the same age.

24. Jan 29, 2016

### Elliot Svensson

So you agree with me that the traveling twin is younger than his stationary twin after the travel is done--- and this does not contradict the fact that they were born on the same day.

25. Jan 29, 2016

### Elliot Svensson

So when we here talk about the age of the universe, is this more precisely the age of an arbitrary object that began to exist during the Big Bang and which has existed in the reference frame which has aged most?