B Proper time of the observer resting in CMB reference frame

[ongoer]

@PeterDonis that's not nice to pull a half of my sentence out of context and change its meaning in this way.

You don't have to communicate with anyone to know, that when you're moving with respect to the CMB and measure its dipole in your frame, then you're time dilated with respect to all the observers, who rest in their CMB reference frames even if they are separated from you by the spacelike intervals.

 

[Ibix]

You don't have to communicate with anyone to know, that when you're moving with respect to the CMB and measure its dipole in your frame, then you're time dilated with respect to all the observers, who rest in their CMB reference frames even if they are separated from you by the spacelike intervals.

That would depend on how they choose to extend their local reference frames into global coordinate systems. The obvious way to do it is using cosmological time, but then you are back to "yes everybody is the same age because I have defined it so".

 

[ongoer]

That would depend on how they choose to extend their local reference frames into global coordinate systems. The obvious way to do it is using cosmological time, but then you are back to "yes everybody is the same age because I have defined it so".

What is unreasonable in assumption that all my immortal observers are in the same age equal to the universe age, if it's homogenous on the large scale?

 

[Ibix]

What is unreasonable in assumption that all my immortal observers are in the same age equal to the universe age, if it's homogenous on the large scale?

It's a very sensible definition. However, others are possible. But as I already said, they make the maths messy.

 

[Nugatory]

What is unreasonable in assumption that all my immortal observers are in the same age equal to the universe age, if it's homogenous on the large scale?

It's tautologically and uninterestingly true that for each one their age and any given moment is equal to the proper time along their worldline (presuming these immortals have all been around from the beginning, as we have in this thread).

Now if you choose to define a surface of simultaneity as the locus of all events on those worldlines at which they are a particular age... then yes, of course they are all the same age because that's how you defined it.

 

[ongoer]

@Nugatory what's your definition of the age of the universe?

 

[PeterDonis]

@PeterDonis that's not nice to pull a half of my sentence out of context and change its meaning in this way.

Since you didn't quote anything from me, I don't know what you're referring to here.

You don't have to communicate with anyone to know, that when you're moving with respect to the CMB and measure its dipole in your frame, then you're time dilated with respect to all the observers, who rest in their CMB reference frames

No, you're not. They're time dilated with respect to you. At least that's what things look like from your rest frame. The concept of "time dilation" you're using here, due to relative motion, is frame dependent; there is no absolute sense in which either you or the comoving observers are "time dilated".

even if they are separated from you by the spacelike intervals

To even define these intervals, you have to adopt a simultaneity convention--a convention that tells you which events on different worldlines happen at the same time. And any such convention is arbitrary. Simultaneity is not a physical thing.

In any case, none of this is even relevant to the claim you are actually trying to defend, which is that there is some meaningful concept of "time dilation" between an observer now and that same observer in the distant past. Every actual example you've given has been about comparisons between different observers at events on their worldlines that are spacelike separated. But the claim you're making is about comparisons between events on the same worldline, which are timelike separated. There is simply no meaningful concept of "time dilation" that even applies to such a case.

 

[PeterDonis]

@Nugatory what's your definition of the age of the universe?

The usual definition is the proper time since the Big Bang along comoving worldlines.

 

[ongoer]

The usual definition is the proper time since the Big Bang along comoving worldlines.

It's tautologically and uninterestingly true that for each one their age and any given moment is equal to the proper time along their worldline (presuming these immortals have all been around from the beginning, as we have in this thread).

Now if you choose to define a surface of simultaneity as the locus of all events on those worldlines at which they are a particular age... then yes, of course they are all the same age because that's how you defined it.

 

[ongoer]

No, you're not. They're time dilated with respect to you. At least that's what things look like from your rest frame. The concept of "time dilation" you're using here, due to relative motion, is frame dependent; there is no absolute sense in which either you or the comoving observers are "time dilated".

You're teaching me about frame dependency even though I wrote "with respect to" every time I was talking about the different reference frames.

If they're time dilated with respect to me, then I'm also time dilated with respect to them.

 

[ongoer]

In any case, none of this is even relevant to the claim you are actually trying to defend, which is that there is some meaningful concept of "time dilation" between an observer now and that same observer in the distant past. Every actual example you've given has been about comparisons between different observers at events on their worldlines that are spacelike separated. But the claim you're making is about comparisons between events on the same worldline, which are timelike separated. There is simply no meaningful concept of "time dilation" that even applies to such a case.

Is she talking crap?

Indeed, the two things, redshift and time dilation, necessarily go together. Think about it this way, if you have a wave you could use each crest of the wave as a tick of a clock. Now if the wave shifts to the red, it stretches, and those time markers move apart. It’s a direct consequence of Einstein’s theory of general relativity. And yes, this time-dilation is the same effect that slows down time near a black hole. You see, if you are near a black hole and you want to send a signal to someone far away, then the signal needs to escape, so it has to work against the pull of gravity. But it can’t slow down because light always moves with, well, the speed of light. So rather than slowing down, the light instead loses energy, and that means that its frequency becomes smaller and the wavelength longer. It gets redshifted. The closer to the horizon you are when you send the signal, the more it gets redshifted. But as we just discussed, you can think of the crests of the wave like ticks of a clock. So this also means that the duration between the ticks becomes longer. Indeed, if you send a signal from the horizon exactly, it can’t escape at all. This means if someone is falling into a black hole, for the faraway observer it seems like their image gets increasingly redder and is moving slower an slower. It's like watching paint dry, but in space. It’s a fascinating consequence of Einstein’s theory.

 

[Nugatory]

Is she talking crap?

She is providing a compelling example of why the forum has its rule about acceptable sources: peer-reviewed publication and standard textbooks only.

We reminded you of this rule back in post #14 of this thread. Don’t violate it again.

And be aware that your reliance on these sources is getting in the way of your understanding.

 

[ongoer]

She is providing a compelling example of why the forum has its rule about acceptable sources: peer-reviewed publication and standard textbooks only.

We reminded you of this rule back in post #14 of this thread. Don’t violate it again.

And be aware that your reliance on these sources is getting in the way of your understanding.

Doesn't it bother you, that she has a PhD?

 

[Nugatory]

Doesn't it bother you, that she has a PhD?

Writing good popularizations and doing good science are different skills.
And do remember that a popularization is by definition going to simplify and cut corners; it is never a substitute for a real textbook or peer-reviewed paper.

 

[ongoer]

Writing good popularizations and doing good science are different skills.
And do remember that a popularization is by definition going to simplify and cut corners; it is never a substitute for a real textbook or peer-reviewed paper.

Like those two on arxiv, which thoughtlessly use the "cosmological time dilation" expression in their titles and don't clarify it.

What does g00 element of the Schwarzschild metric tensor tell us?

 

[Jaime Rudas]

Like those two on arxiv, which thoughtlessly use the "cosmological time dilation" expression in their titles and don't clarify it.

That's false: both articles you cited clarify in the same abstract what they specifically mean by "cosmological time dilation". Note:

https://arxiv.org/abs/2306.04053
"We present a precise measurement of cosmological time dilation using the light curves of 1504 type Ia supernovae from the Dark Energy Survey spanning a redshift range 0.1≤z≤1.2. We find that the width of supernova light curves is proportional to(1+z), as expected for time dilation due to the expansion of the Universe."

https://arxiv.org/abs/2406.05050
"A fundamental prediction of relativistic cosmologies is that, due to the expansion of space, observations of the distant cosmos should be time dilated and appear to run slower than events in the local universe."

 

[ongoer]

That's false: both articles you cited clarify in the same abstract what they specifically mean by "cosmological time dilation". Note:

https://arxiv.org/abs/2306.04053
"We present a precise measurement of cosmological time dilation using the light curves of 1504 type Ia supernovae from the Dark Energy Survey spanning a redshift range 0.1≤z≤1.2. We find that the width of supernova light curves is proportional to(1+z), as expected for time dilation due to the expansion of the Universe."

https://arxiv.org/abs/2406.05050
"A fundamental prediction of relativistic cosmologies is that, due to the expansion of space, observations of the distant cosmos should be time dilated and appear to run slower than events in the local universe."

1. It doesn't tell you, that time didn't run slower in the past.
2. "Appear" - that's your argument.

The same question which I asked @Nugatory:
What does g00 element of the Schwarzschild metric tensor tell us?

 

[ongoer]

@Jaime Rudas I don't have a problem with "cosmological time dilation" expression used in these papers. You all have it.

Like those two on arxiv, which thoughtlessly use the "cosmological time dilation" expression in their titles and don't clarify it.

That was irony.

 

[Nugatory]

Like those two on arxiv, which thoughtlessly use the "cosmological time dilation" expression in their titles and don't clarify it.

You will have noticed that no one has objected to either of these papers as references, and @Ibix even linked the earlier discussion here of one of them. They aren't popularizations.

Both are clear that they are comparing the proper time between two emission events with the proper time between two reception events, analogous to the first case I considered in post #21 above. It's an open question whether that should be called "cosmological time dilation" because that phrase invites confusion (as witness this thread).... but whatever they call it, it is clear what they mean by the term and that it does not support what you're trying to do in post #3 and following.

What does g00 element of the Schwarzschild metric tensor tell us?

It tells us that Schwarzschild coordinate time corresponds to proper time only at infinite distance from the center of mass.

 

[Nugatory]

The question in the thread title has been answered - in post #2! - and the subsequent discussion has been informative but is reaching the point of diminishing returns so this thread is closed.

As with all such thread closures, we can reopen it on request for additional comments if there is more to say... but not to repeat points that have already been made.

 

[PeterDonis]

Doesn't it bother you, that she has a PhD?

As an additional note: this is an argument from authority and should not carry any weight in an actual scientific discussion. Here at PF, in any case, we look at the actual substance of what is being said, not the credentials of who is saying it.

For an example of me pointing out an error in a popular book written by one of the most famous physicists of the 20th century, see here:

https://www.physicsforums.com/insights/block-universe-refuting-common-argument/