I How can the universe expand faster than light?

[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?

 

[PeterDonis]

Or if it experienced gravity time dilation, right?

In principle, yes. But the sequence of events that would have had to happen in that case is far more improbable even than it getting to ultrarelativistic velocity.

 

[Elliot Svensson]

During the early moments of Big Bang cosmology, the universe was denser than it is now. Is 13.8 billion years the proper time of the gravity-dilated objects or the proper time of an arbitrary clock living in a normal gravitational state?

 

[PeterDonis]

During the early moments of Big Bang cosmology, the universe was denser than it is now. Is 13.8 billion years the proper time of the gravity-dilated objects or the proper time of an arbitrary clock living in a normal gravitational state?

The concept of gravitational time dilation does not apply to the universe as a whole, because the universe as a whole is not static, and the concept of gravitational time dilation only applies to a static system.

 

[Elliot Svensson]

Do you agree with me that it is very strange to say that one of Einstein's predictions of the theory of relativity does not apply in Cosmology's most popular measurement, the age of the universe?

 

[PeterDonis]

Do you agree with me that it is very strange to say that one of Einstein's predictions of the theory of relativity does not apply in Cosmology's most popular measurement, the age of the universe?

No, because Einstein's prediction was not what you apparently believe it is. Einstein's prediction of gravitational time dilation was for a very specific situation: as I said, for an object that is static in a static gravitational field. Both "static" terms are essential. Neither one applies to the universe as a whole: the universe is not static--it's expanding--and comoving objects in the universe, which are what provide the standard of time used to define the age of the universe, are not static, because they are not "holding position" in any physical sense. They are in free fall, going wherever the geometry of spacetime takes them. (Notice that a static object in a static gravitational field cannot be in free fall; it must be accelerated. Einstein's original argument for gravitational time dilation makes essential use of this fact.)

Your issue here is that you are not reasoning from fundamentals. "Gravitational time dilation" is not a fundamental of GR; it is a derived consequence of GR when applied in a particular scenario, which has properties that the scenario you are trying to apply it to, the expanding universe, does not have. The fundamentals of GR are spacetime geometry and proper time along worldlines. When we say the age of the universe is 13.7 billion years, we mean that the spacetime geometry is such that the proper time elapsed along a particular family of worldlines--the comoving ones, the worldlines of observers who always see the universe as homogeneous and isotropic--since the Big Bang is 13.7 billion years. That's all we mean.

 

[Elliot Svensson]

That's very helpful--- thanks!

 

[tgarcia39]

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

I think expansion depends on its cause. E.g., if the cause is based on the force provided for the expansion, it may be then the force is mitigating the expansion. If so, it seems the fact it is still increasing could mean the force has yet to reach its apex, or that it never will. The Inflationary Period (IP), if it occurred, did abate somewhat, but now it seems a moot point in view of Hubble's revelation. I think the IP is no longer needed to explain the homogeneity of the elements since we now know the U. has been expanding all along, likely since the BB. The bits and pieces of scientific reseach will provide us with the so-called theory of everything, I believe.

 

[Drakkith]

I think the IP is no longer needed to explain the homogeneity of the elements since we now know the U. has been expanding all along, likely since the BB.

Inflation was developed well after we already knew the universe had been expanding. Decades after in fact. The idea of inflation isn't going anywhere anytime soon.

The bits and pieces of scientific reseach will provide us with the so-called theory of everything, I believe.

Which could very easily require inflation.

 

[tgarcia39]

Inflation was developed well after we already knew the universe had been expanding. Decades after in fact. The idea of inflation isn't going anywhere anytime soon.

Which could very easily require inflation.

The IP theory seems to have been created solely for the purpose of explaining the isotropic feature of the universe, thus to me, it is not the only possible explanation. It is a very weak idea offering no reason nor cause for it, although in my opinion, if it was the impetus given to the contents of the singularity that is causing the expansion of the U., then I wonder if that does not explain the homogeneous effect previously offered as the IP to explain the effect, thus rendering the IP unnecessary. If the force that caused the BB gave impetus to the contents of the singularity, that seems to me a more easily acceptable theory since such impetus should be expected from such a force, explaining therefore the cause of the isotropic U. Do you not agree?

 

[Drakkith]

I do not agree. Regular expansion doesn't work fast enough to create the level of homogeneity and isotropy we see today as far as I know.

The IP theory seems to have been created solely for the purpose of explaining the isotropic feature of the universe, thus to me, it is not the only possible explanation.

You can see at least part of the motivation behind it on wikipedia's article: https://en.wikipedia.org/wiki/Inflation_(cosmology)#Motivations

And remember that just because science has a predominant theory for something does not mean it is the only possibility. It's usually the simplest, most accurate one though, and inflation is no different. Nothing else explains isotropy, homogeneity, and various other things as well as inflation does.