Is the Universe's age 13.7B years in a particular frame?

Is the universe aged 13.7B years in a particular frame? In other words would it be a different age for an observer at relativistic speed?

Devin-M said:

Is the universe aged 13.7B years in a particular frame? In other words would it be a different age for an observer at relativistic speed?

Yes, our frame. And yes, it may be different with respect to another.

Note, one convenient frame is stationary with respect to the CMB and we're close enough to stationary with respect to it (368 km/s).

Yes and no. The usually quoted age is the proper time of a comoving observer, one who sees the cosmic microwave background as isotropic. Observers moving with respect to comoving observers will have experienced less time since the beginning of the universe, but may have trouble defining a unique "age of the universe" that is consistent with that.

There is another interesting fact about the comoving age, which is that it is also the age of most of the matter in the universe. That is the same as saying that most of the matter in the universe is highly nonrelativistic, so there is not a wide range of time dilation in the ages of the matter we encounter. This is a consequence of the extreme amount of expansion the universe has undergone, such that even if most matter is created under conditions that make it mildly relativistic (i.e., if matter tends to be created with kinetic energy similar to its rest energy), expansion quickly causes the kinetic energy to drop and go nonrelativistic. So that's why we don't have to worry about different ages for all the stuff we encounter, it was not only created at very close to the same time but it has also aged by almost the same amount, aspects of the situation that go beyond the existence of a comoving frame (in contrast to a static or contracting universe, for example).

(I think that post got removed.)

Ken G said:

There is another interesting fact about the comoving age, which is that it is also the age of most of the matter in the universe. That is the same as saying that most of the matter in the universe is highly nonrelativistic, so there is not a wide range of time dilation in the ages of the matter we encounter. This is a consequence of the extreme amount of expansion the universe has undergone, such that even if most matter is created under conditions that make it mildly relativistic (i.e., if matter tends to be created with kinetic energy similar to its rest energy), expansion quickly causes the kinetic energy to drop and go nonrelativistic. So that's why we don't have to worry about different ages for all the stuff we encounter, it was not only created at very close to the same time but it has also aged by almost the same amount, aspects of the situation that go beyond the existence of a comoving frame (in contrast to a static or contracting universe, for example).

In terms of motion, relativistic and non-relativistic are relative terms!

... so from the perspective of a neutrino the universe is still quite young, isn't it?

timmdeeg said:

... so from the perspective of a neutrino the universe is still quite young, isn't it?

Depends very much what you mean by "the universe is still quite young". Certainly a neutrino emitted at the last scattering surface and being absorbed today will have experienced far less than 14bn years by its own clocks. However, the only coordinate systems that provide a unique age for the universe are ones that use cosmological time - planes of simultaneity that are not parallel to these define some regions of the universe to be older than others. So a neutrino-riding observer must either adopt cosmological time and acknowledge that their own experience is not consistent with that (the universe is much older than their own elapsed time would imply), or accept that they cannot define a unique age of the universe.

Moderator's note: Thread moved to cosmology forum.

PeroK said:

In terms of motion, relativistic and non-relativistic are relative terms!

Yes, but they don't require a choice of global reference frame. The core of a massive star will collapse because the degenerate electrons within it are "relativistic", and that core will collapse in any global reference frame, so the electrons are relativistic in any global reference frame. That is the same sense as the fact that matter in the universe is, by and large, "highly nonrelativistic" (and that is due to the expansion).

Ken G said:

The core of a massive star will collapse because the degenerate electrons within it are "relativistic", and that core will collapse in any global reference frame, so the electrons are relativistic in any global reference frame.

I don't think this is a good way of stating it.

If we treat the massive star as an isolated system in an asymptotically flat spacetime, then we can assign the star as a whole a 4-momentum in the asymptotic flat background. The electrons in the core during a core collapse are relativistic in this frame. That does not mean that they are relativistic in every frame, nor do they have to be.

Since the spacetime of the universe as a whole is curved, in a global reference frame, i.e., a frame that covers the universe as a whole, it doesn't even make sense to speak of electrons at a particular location (the location of the collapsing star) as relativistic or not, because in a curved spacetime you can't assign relative speeds to spatially separated objects. You can still assign the collapsing star a 4-momentum in the global (entire universe) frame and analyze its internal dynamics in a local inertial frame in which that 4-momentum is at rest (which basically amounts to doing the same analysis I described above). But in the global frame, you are modeling the star as a single object with a single 4-momentum, and its internal dynamics, including the internal motion of electrons in its core, are not included in the model. The core will of course still collapse in this frame, since the core collapse is an invariant and must happen in every frame; but nobody would try to analyze the details of the core collapse in a global reference frame. You would use the local frame described above.

Ken G said:

That is the same sense as the fact that matter in the universe is, by and large, "highly nonrelativistic" (and that is due to the expansion).

I would say that the matter in the universe is highly nonrelativistic with respect to comoving observers, i.e., observers who always see the universe as homogeneous and isotropic. That statement has the advantage of being independent of any choice of frame. But it also illustrates that, as@PeroK said, "relativistic" and "non-relativistic" are relative terms; you have to pick some state of motion that is treated as being "at rest" for such terms to be meaningful. Here that is the state of motion of comoving observers; above it was the state of motion of the center of mass of the collapsing star.

PeterDonis said:

I don't think this is a good way of stating it.

If we treat the massive star as an isolated system in an asymptotically flat spacetime, then we can assign the star as a whole a 4-momentum in the asymptotic flat background. The electrons in the core during a core collapse are relativistic in this frame. That does not mean that they are relativistic in every frame, nor do they have to be.

The point is, the phrase "the electrons are highly relativistic" is a quite important, and physically correct, way to talk about the matter in a collapsing core, without the need (or any advantage to) specifying any reference frame at all. Thus, we should not confuse readers that whether or not some collection of matter "is relativistic" should be considered to be a matter of choice of reference frame, when we talk about what it means for particles to be considered "relativistic" as a population. That is the situation similar to our universe, except the opposite situation: it is very important that most of the matter in the universe is highly nonrelativistic, that is why it can form stars and planets and so forth. It is also important to understand why this is true: because of the expansion of the universe. A static universe is either too cool to create matter, or if hot enough to create it, it is too hot to do anything useful with it (because it will be too relativistic, in any single chosen frame). Hence the importance of our universe's expansion, and the nonrelativistic nature of the matter in our universe, without specifying any reference frame at all.

PeterDonis said:

Since the spacetime of the universe as a whole is curved, in a global reference frame, i.e., a frame that covers the universe as a whole, it doesn't even make sense to speak of electrons at a particular location (the location of the collapsing star) as relativistic or not, because in a curved spacetime you can't assign relative speeds to spatially separated objects.

The physical "truth" to the fact that the matter in our universe is "highly nonrelativistic" has to do with a frame independent element of their motion-- their relative motion when they meet. This is the entire point here-- we should not think of the nonrelativistic nature of the particles as being individual properties they carry around with them, we should think of it is a property they possess when they encounter each other. That's where the physics happens.

PeterDonis said:

You can still assign the collapsing star a 4-momentum in the global (entire universe) frame and analyze its internal dynamics in a local inertial frame in which that 4-momentum is at rest (which basically amounts to doing the same analysis I described above).

But the 4-momentum of the star as a whole, just by itself, is of no interest or physical importance to what the star is doing, since that is a matter of sheer reference frame. Nor does that relate to why we say the electrons in a collapsing core are "relativistic." Similarly, we do not care about the 4-momentum of some individual particle in the Big Bang, we care about their interaction kinetic energy when two such particles meet. That is frame independent, and that is the only time we are going to care if the particles are "relativistic" or not.

When we talk about the age of the universe, there it is interesting to think about the role that is being played by our chosen reference frame. If we were flying around in a relativistic rocket from the start of the Big Bang, we would not think our universe is 13.8 billion years old now, but we would recognize that most of the matter is 13.8 billion years old, so we'd have to regard our own reference frame as being problematic. But that's my point, thinking matter, like us, isn't in a relativistic rocket, it's nonrelativistic matter, so the problem does not appear. This is not about the existence of a reference frame, it is about the absence of relativistic thinking matter, and the fact that most of the matter we consider is also nonrelativistic. It's special to our universe, whereas there is nothing special about defining a comoving frame.

PeterDonis said:

I would say that the matter in the universe is highly nonrelativistic with respect to comoving observers, i.e., observers who always see the universe as homogeneous and isotropic.

And I would say the problem with bringing in the frame of the observers is that it implies this somehow matters. It doesn't, the physics of the universe is the same for someone in a relativistic spaceship, they will still conclude the matter is "nonrelativistic" in terms of the physics it is obeying, and they will discount any importance of their own frame of reference.

PeterDonis said:

That statement has the advantage of being independent of any choice of frame. But it also illustrates that, as@PeroK said, "relativistic" and "non-relativistic" are relative terms; you have to pick some state of motion that is treated as being "at rest" for such terms to be meaningful. Here that is the state of motion of comoving observers; above it was the state of motion of the center of mass of the collapsing star.

The emphasis I'm giving is on freeing our perspective from the need to identify any frame at all. The physics of the particles is what matters, not the frame we choose to talk about it. The physics is the physics of nonrelativistic interactions, so there is no need to even mention a "comoving frame", as such a frame plays no role in that physics. The "particles are nonrelativistic" because their interactions are nonrelativistic, not because we are observing them from any particular frame. If we were in a relativistic spaceship, we would not think the physics of the Sun is relativistic physics, even if the Sun seemed length contracted and time dilated to us, we would regard that as an artifact.

Ken G said:

"the electrons are highly relativistic" is a quite important, and physically correct, way to talk about the matter in a collapsing core

Yes.

Ken G said:

without the need (or any advantage to) specifying any reference frame at all.

That depends on what you mean by "specifying a reference frame". You do have to specify that the electrons are relativistic relative to the object's center of mass. You can, if you're careful, formulate that statement in such a way that it only involves invariants and is therefore true regardless of what frame you choose. But many people would just take the simpler route of saying that the electrons are relativistic in the object's center of mass frame, and leave implicit the fact that the center of mass frame can be defined in terms of invariants. If you're arguing that the latter approach is sloppy, yes, that's true strictly speaking, but this is only a "B" level thread.

Ken G said:

The physical "truth" to the fact that the matter in our universe is "highly nonrelativistic" has to do with a frame independent element of their motion-- their relative motion when they meet.

This is fine, but then you would be saying, in the core collapse case, that the electrons are highly relativistic when they meet each other and when they meet the ions in the core (the latter would more or less correspond to the center of mass specification I gave earlier). You still have to specify what they are meeting; you can't just leave "relativistic" hanging there with no specification. I agree that the specification does not have to include any choice of frame; but the specification still has to be there.

Ken G said:

the 4-momentum of the star as a whole, just by itself, is of no interest or physical importance to what the star is doing,

I disagree. The 4-momentum of the star is a good proxy for the average 4-momentum of its ions, and that is in turn the average state of motion relative to which the electrons are relativistic.

What is not relevant for the internal dynamics of core collapse is the relationship between the star's total 4-momentum and the 4-momenta of any other external objects.

Ken G said:

I would say that's the same thing, except it makes it seem like the frame of the observers matters.

I don't see why. I explicitly specified the comoving condition in terms of invariants (homogeneity and isotropy), not in terms of any choice of frame.

timmdeeg said:

... so from the perspective of a neutrino the universe is still quite young, isn't it?

Perhaps it would be better to say the neutrino is quite young, with respect to the universe. Remember there is not one time, but many times, every clock has different elapsed time. What is remarkable about our universe, because of its expansion, is that most of the clocks we care about (clocks attached to planets and stars, for example) read pretty much the same time (they don't experience time dilation effects relative to each other). That's because our universe is mostly so "nonrelativistic." This is an important irony-- the first step in learning any Big Bang model is going to be to learn relativity, so you can understand what a metric is. The second step will be learning why there is actually so little relativity going on! A truly relativistic universe is not much good at anything, the matter collides at too high an energy to be able to build anything useful (by which I mean, relativity allows particles to have kinetic energy that exceeds their rest energy, but the matter around us has kinetic energy that is thousands or millions times less than that), and the curvature of the space is too unstable to maintain consistent behavior for long (by which I mean, general relativity allows space to curve on any scale you can name, yet on the largest scales it doesn't curve hardly at all). Our universe is so nonrelativistic that it is very special indeed, and that's what lets so many interesting things happen.

Ken G said:

Our universe is so nonrelativistic ...

... except neutrinos. Leaving out "quite young" we can say assuming neutrino and comoving observer are passing by closely they both see each other's clock running very slow. This can be combined with the knowledge that their clocks show the elapsed time in their frame since the big bang.

PeterDonis said:

That depends on what you mean by "specifying a reference frame". You do have to specify that the electrons are relativistic relative to the object's center of mass.

It's that they are relativistic with respect to what they are colliding with, in binary collisions. It doesn't really matter about the center of mass frame, though that is certainly the frame we are going to use to conceptualize the situation. Since the electrons don't need to conceptualize, they don't care about that frame, they only need to know what phenomena will happen to them in a binary interaction. This is why I mentioned physicists flying by in a relativistic rocket-- it's not a convenient frame, but it would work, no need to have anything expressed in the stellar center of mass frame. That's the point-- the relativisticness of the electrons comes from the phenomena of their interactions, not any reference frame.

PeterDonis said:

You can, if you're careful, formulate that statement in such a way that it only involves invariants and is therefore true regardless of what frame you choose. But many people would just take the simpler route of saying that the electrons are relativistic in the object's center of mass frame, and leave implicit the fact that the center of mass frame can be defined in terms of invariants. If you're arguing that the latter approach is sloppy, yes, that's true strictly speaking, but this is only a "B" level thread.

I agree that the simplest frame is the center of mass frame, but what does still belong in a "B" thread is the concept of where the "relativisticness" comes from. It's not the center of mass frame of the star, and it's not the frame of any observers, and its not the comoving frame of the CMB, it's just the interactions of the particles. We live in a nonrelativistic universe because most of the matter in it does not undergo relativistic kinds of interactions, their interactions involve kinetic energies way smaller than their rest energies (from their mass). That's a perfectly "B" statement, without mention of any reference frame, so we should not give the impression that the reference frame is essential.

PeterDonis said:

This is fine, but then you would be saying, in the core collapse case, that the electrons are highly relativistic when they meet each other and when they meet the ions in the core (the latter would more or less correspond to the center of mass specification I gave earlier). You still have to specify what they are meeting; you can't just leave "relativistic" hanging there with no specification. I agree that the specification does not have to include any choice of frame; but the specification still has to be there.

That's why I explained what I meant by the electrons being "relativistic," and why our universe is so largely "nonrelativistic." Those aren't affected by what frame you use.

PeterDonis said:

I disagree. The 4-momentum of the star is a good proxy for the average 4-momentum of its ions, and that is in turn the average state of motion relative to which the electrons are relativistic.

If we were physicists in relativistic rockets, then the 4-momentum of the star would be an awful proxy for the 4-momentums relevant to the interactions its particles would be undergoing. That's why the 4-momentum of the star has no place in the description of whether the particles in the star are undergoing relativistic or nonrelativistic phenomena.

PeterDonis said:

What is not relevant for the internal dynamics of core collapse is the relationship between the star's total 4-momentum and the 4-momenta of any other external objects.

Yes, exactly, and the star's total 4-momentum cannot be described in any other way, it has no other meaning. That's why it doesn't matter.

PeterDonis said:

I don't see why. I explicitly specified the comoving condition in terms of invariants (homogeneity and isotropy), not in terms of any choice of frame.

This is circling back to the essential point of the thread, which is a little hard to say exactly because it kind of depends on what question is really being asked. As often happens, a simple question opens up into a wide variety of less simple ones, and it's never clear exactly what insight is the one being sought! The OP asked if it is necessary to choose a frame to define the age of the universe. I'm saying that it is not, because the real reason the universe can be said to have a fixed age is that the universe is so highly nonrelativistic, that clocks attached to the matter we care about (i.e., not neutrinos, and of course not photons) would all read very close to the same age. If that were not true, then the universe would not have a fixed age, because you could have a star that formed early on that is only 1 billion years old, and another star that formed much later that is 10 billion years old. All that could happen even though such a universe would still have comoving frames, so it's not about the existence of a comoving frame that lets us use age a unique quantity.

timmdeeg said:

... except neutrinos. Leaving out "quite young" we can say assuming neutrino and comoving observer are passing by closely they both see each other's clock running very slow. This can be combined with the knowledge that their clocks show the elapsed time in their frame since the big bang.

Yes, neutrinos are the exception. And black holes, who knows how to talk about their age. Clocks attached to neutrinos that formed in the Big Bang would read times much less than 13.8 billion years, yet they would, as you say, think that clocks attached to Earth were running very slow, even though our clocks would read 13.8 billion years (if they were attached to the matter the Earth formed from). So it's the twin paradox, the universe does not appear to have originated at the same time everywhere to a neutrino, but they could notice there is a comoving frame that does originate at the same time everywhere. So they could come up with a concept of universal time, but it would not be their time, so it wouldn't have much value for them. What good would it do neutrino physicists to say that they were born at the start of a universe that is 13.8 billion years old, but they are only 1 billion years old?

Ken G said:

It's that they are relativistic with respect to what they are colliding with, in binary collisions.

By which you mean, I assume, the dominant interactions that are causing the electrons to radiate energy away into space, and thus cause the core to keep shrinking? Would those be electron-electron or electron-ion collisions? (Both would be relativistic, but the electrons are more relativistic relative to each other than relative to the ions, correct?)

PeterDonis said:

By which you mean, I assume, the dominant interactions that are causing the electrons to radiate energy away into space, and thus cause the core to keep shrinking?

Yes, that's part of it, though the main thing is the relativistic stress-energy tensor. That relates to how the electrons respond to the heat loss, and how easily gravity can pull in the ions that attract the electrons via their electric fields. That's the kind of thing we would always treat in the comoving frame of the star for simplicity (no doubt the gravity of a relativistically moving star would be a real pain), but the gas pressure associated with the stress-energy tensor would work the same way if the star appeared to be moving at half the speed of light. So the usual reference frame works to be able to say whether the electrons are "acting relativistic" or not, but it is not a required viewpoint, we would still be able to tell (in principle) if the stress-energy tensor was acting relativistic in a star moving at half the speed of light (not saying it would be a wise approach to the calculation).

PeterDonis said:

Would those be electron-electron or electron-ion collisions? (Both would be relativistic, but the electrons are more relativistic relative to each other than relative to the ions, correct?)

Light usually comes more from electron-ion collisions due to the contrast between the center of mass (which won't be accelerated by the interaction) and the center of charge (the dipole moment, strongly accelerated by the interaction), due to the opposite charges. That changes a bit in the relativistic case, where you can have more light creation from electron-electron interactions and pair production. But those aren't really the main issue, it's more just the response of the electron stress-energy tensor to heat loss.

Ken G said:

What good would it do neutrino physicists to say that they were born at the start of a universe that is 13.8 billion years old, but they are only 1 billion years old?

Being good physicists they would have fun to calculate their speed relative to their comoving colleagues.