How can the universe expand faster than light?

[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?

 

[A.T.]

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?

Metric expansion and relative movement are different things.

 

[A AM ARYA]

Metric expansion and relative movement are different things.

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

 

[Orodruin]

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.

 

[PeterDonis]

how universe can expand faster than light itself?

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.

 

[A AM ARYA]

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.

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

 

[Orodruin]

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

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.

 

[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?

 

[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?

 

[PeterDonis]

Would Peter be willing to provide the best available meaning of "relative velocity" in curved spacetime?

As I said in post #5:

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.

 

[PeterDonis]

I thought that general-relativity curvature due to gravity was totally different than curvature due to a cosmological constant.

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

 

[Elliot Svensson]

Oh, that makes sense... thanks!

 

[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?

 

[PeterDonis]

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?

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

 

[A AM ARYA]

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.

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.

 

[PeterDonis]

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.

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.

 

[A AM ARYA]

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.

OK & thanks for the correction.

 

[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?

 

[PeterDonis]

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?

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.

in the "twins paradox", at the end, how old are the twins? ... And wouldn't the word "age" only have any meaning at all when taken from one or another reference frame?

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).

 

[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?

 

[Orodruin]

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?

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.

 

[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.

 

[Orodruin]

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.

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

 

[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.

 

[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?

 

[Orodruin]

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.

Right.

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?

You are now trying to generalise things from special relativity to general relativity. There is a particular frame (by frame here we mean a set of coordinates) which we usually refer to when talking about the age of the universe.

Your last sentence shows a fundamental misunderstanding of even special relativity. Events do not exist or "belong" to a particular frame. All events occur in all frames, what changes are the space-time coordinates we assign to them.

 

[Elliot Svensson]

Would it be better to say that the age of the universe is the age of an arbitrary object that began to exist during the Big Bang, when that age is measured from the particular reference frame that is centered and inertial relative to our visible universe?

 

[Orodruin]

Would it be better to say that the age of the universe is the age of an arbitrary object that began to exist during the Big Bang, when that age is measured from the particular reference frame that is centered and inertial relative to our visible universe?

It does not matter what frame you use to measure the age of an object. As long as you measure it at the same event you will get the same result.

How we use age in cosmology is by referring to the time experienced by an observer at rest in comoving coordinates.

 

[Elliot Svensson]

Is the word "age" used differently in cosmology?

 

[Orodruin]

Is the word "age" used differently in cosmology?

No, but there would be an ambiguity in the definition if we did not define which observer we refer to when we say "age of the universe".

 

[Elliot Svensson]

It does not matter what frame you use to measure the age of an object. As long as you measure it at the same event you will get the same result.

So do you agree with me that when I measure an object's age I have not necessarily learned anything about my own age?

 

[Orodruin]

So do you agree with me that when I measure an object's age I have not necessarily learned anything about my own age?

Of course not, to do that you need to measure your age (or the age of an object colocated with you - like your watch).

 

[Elliot Svensson]

Does the age of the universe, when measured by an observer at rest in comoving coordinates, have a unique value? Is this the observer who would measure it greatest?

 

[Elliot Svensson]

Does the age of the universe, when measured by an observer at rest in comoving coordinates, have a unique value? Is this the observer who would measure it greatest?

Or to put my question a different way, can you please specify what would be ambiguous if we did not define which observer we refer to when we say "age of the universe"?

 

[Elliot Svensson]

Is it false to suppose that some things that are as old as the universe aren't 14 billion years old, they're younger--- as long as by "as old as" we mean, "originated at the same time and place"?