I 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"?

 

[Elliot Svensson]

I would expect this of something that was ever in a strong gravity field, right?

 

[phinds]

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 possible difference can there be in those two concepts?

 

[bahamagreen]

...age is less? Or has aged less?

This is a fine question... it looks to me like the difference between the two concepts is this:

Age is less is based on a calculation of traveler age which is going to be different for the stay at home folks and the traveler. The stay at home folks will figure the traveler's age by subtracting their birth date from the present date (arrival date). The traveler will append their elapsed travel clock time to their age at time of departure (departure date minus birth date plus elapsed travel clock time).
Aged less is going to be the same conclusion and magnitude for both the traveler and the stay at home folks - both will notice that the traveler's clock (and the traveler) have experienced less time during the trip than the stay at home folks...

As an example...

Of the twins, Bob and Alice both 55 years old, Bob stays home and Alice travels out and back. Before she goes they match their clocks.

When she returns, Bob looks at his clock and notes that 10 years has past; he is now 65 years old, no longer eligible to hold a spacecraft operator license but eligible to begin Social Security benefits.

Alice notes that her clock shows only 5 years elapsed time and figures she is 60 years old. Alice attempts to renew her spacecraft operator license but they subtract her birth date from the present application date and refuse her renewal because they figure she is 65 years old... but the SS administration mails her instructions for benefits figuring she is 65 years old.

Both Bob and Alice agree that there is a five year difference between their clocks, Alice's being 5 years behind Bob's...

 

[Orodruin]

The stay at home folks will figure the traveler's age by subtracting their birth date from the present date (arrival date).

No they wont. There is a precise definition of proper time in special relativity. Please use it.

 

[bahamagreen]

I understand somewhat the definition; maybe you could clarify or correct how I'm thinking, which is about under what circumstances who will use proper time, and why (I mean Bob and Alice after the fact).

Looks to me like Bob's proper time and coordinate time are the same and both are "direct" to him in the sense that both of these are measurable by him without resorting to "indirect" transformation calculations. Alice's proper time looks direct only to her, not Bob; and likewise, Alice's coordinate time is direct for Bob, not for Alice for whom it is indirect. When Alice is returned, both Bob and Alice are in the same coordinate and proper time... why would Bob invoke Alice's past proper travel time to figure her age when he knows her date of birth and the present date? His figuring of her age must be in years of his (and now her) coordinate same proper time; to do otherwise makes no sense because he would have to include her proper time years as longer unit years than her years before traveling (her age would be comprised of two different sized year units).

 

[andrewkirk]

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.

I find the following explanation entirely satisfying and dispels the potential confusion around recession rates vs 'peculiar velocities'. I made it up a while ago and have not seen it written elsewhere. But it seems so natural and satisfying to me that I find it hard to believe that some textbook doesn't take this approach:

The cosmic speed limit is actually a rule that no particle can have a spacelike velocity, and if the particle has mass, it can't have a lightlike velocity either.

The properties 'spacelike' and 'lightlike' are properties of the velocity vector, and are independent of reference frame. A velocity vector is 'Spacelike' if its magnitude is positive, and 'Lightlike' if its magnitude is zero. It is called 'timelike' if its magnitude is negative.

The magnitude of a velocity vector $\vec v$ is $-(v_t{}^2) +v_1{}^2 +v_2{}^2 +v_3{}^2$ where $v_1$ to $v_3$ are the spatial components in a given reference frame and $v_t$ is the time component in that reference frame. The magnitude is independent of the choice of reference frame.

It is possible for far-separated parts of the universe to be receding from one another at a superluminal rate, even though both have timelike velocities, and in fact that is what's happening in this universe.

 

[Adam al-Girraweeni]

[QUOTE="andrewkirk, post: 5361568, member: 265790I made it up a while ago and have not seen it written elsewhere. But it seems so natural and satisfying to me ...
The magnitude of a velocity vector $\vec v$ is $-v_t{}^2 +v_1{}^2 +v_2{}^2 +v_3{}^2$ where $v_1$ to $v_3$ are the spatial components in a given reference frame and $v_t$ is the time component in that reference frame. ...[/QUOTE]

I like this, although I don't understand it (yet).

One quick question, though. Why "$-v_t{}^2$" ? Why the negative? And doesn't squaring it make this not matter anyway?

 

[Orodruin]

One quick question, though. Why "−vt2−vt2-v_t{}^2" ? Why the negative?

These are the components of the 4-velocity, not of velocity. The sign comes from the metric.

And doesn't squaring it make this not matter anyway?

It is $-v_t^2$, not $(-v_t)^2$.

 

[Adam al-Girraweeni]

...

thanks

 

[Elliot Svensson]

I understand somewhat the definition; maybe you could clarify or correct how I'm thinking, which is about under what circumstances who will use proper time, and why (I mean Bob and Alice after the fact).

Because there's normally no reason at all to imagine that proper time might be different from what you measure, it's important to take a step back when something might be happening relativistically.

Suppose that I found two meteorites and used uranium-lead dating to determine that one was liquid just 1,000 years ago and the other, 4.5 billion years ago, but the alloy mix is otherwise remarkably similar. Would you be skeptical if I told you that based on the dates alone they have got to be from totally different sources?

And to continue the example, if we had some way of proving that they were of the same spatio-temporal origin, and that origin was the same as the earth, have we proven that the Earth is only 1,000 years old?

 

[PeterDonis]

maybe you could clarify or correct how I'm thinking

You are attributing some physical meaning to coordinate time, when it doesn't have any. Coordinate time is just a convention; it has no physical meaning. Proper time has a direct physical meaning.

For example, consider your scenario where Alice comes back from her trip having aged only 5 years, while Bob has aged 10 years (as has everyone else on Earth). Alice claims she is only 60 years old so she can get her spaceship operator's license renewed, but the government says no. Who is right? It depends on what the actual rule is. If the actual rule is that eligibility depends on how much time has passed on Earth since her birth, then 65 years has passed on Earth and she is not eligible. But if the actual rule is that eligibility depends on her physiological age, i.e., how much her body has actually aged (which would be reasonable since that's what actually determines her ability to pilot a spacecraft ), then she has only aged 60 years and is still eligible. But note that neither of these rules depend on "coordinate time"; they just depend on two different proper times (proper time elapsed on Earth in once case, proper time elapsed for Alice in the other).

 

[PeterDonis]

Because there's normally no reason at all to imagine that proper time might be different from what you measure

Proper time is what you measure. See below.

Suppose that I found two meteorites and used uranium-lead dating to determine that one was liquid just 1,000 years ago and the other, 4.5 billion years ago

Note that "years ago" means proper time elapsed for the meteorites. It does not mean proper time elapsed for you, who were not spatially co-located with the meteorites for their entire existence.

Would you be skeptical if I told you that based on the dates alone they have got to be from totally different sources?

Not if I had information to suggest that one (the 1000 year old one) had been traveling at ultrarelativistic velocity while the other had been more or less stationary.

if we had some way of proving that they were of the same spatio-temporal origin, and that origin was the same as the earth, have we proven that the Earth is only 1,000 years old?

Again, not if we have information to suggest that the 1000 year old one had been traveling at ultrarelativistic velocity. (Of course in the real world, that would be extremely unlikely, first because something would have had to accelerate it to that velocity relative to the Earth, second because something would then have had to turn it around somehow to return to Earth, and third because at that velocity the meteorite would have been destroyed on impact, not to mention a large area around the impact point--it would have been about a million times more destructive than a one megaton nuclear explosion.)

 

[Elliot Svensson]

...not if we have information to suggest that the 1000 year old one had been traveling at ultrarelativistic velocity.

Would ultrarelativistic velocity be greater than C or more like between 0.1C and 0.9C?

 

[PeterDonis]

Would ultrarelativistic velocity be greater than C or more like between 0.1C and 0.9C?

Neither. "Ultrarelativistic" just means that the $gamma$ factor is extremely large. In your case, the meteorite that is only 1000 years old by radioactive dating must have had a $\gamma$ factor on the order of 4.5 million relative to Earth, since it aged only 1000 years while 4.5 billion years passed on Earth. You can easily calculate what velocity this corresponds to; you will find that it is very, very, very close to c.

 

[Elliot Svensson]

...not if we have information to suggest that the 1000 year old one had been traveling at ultrarelativistic velocity.

Or if it experienced gravity time dilation, right?