B Proper time of the observer resting in CMB reference frame

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Does t in a(t) in the FLRW metric correspond to the proper time of the immortal observer, who’s been resting in the CMB reference frame since its emission?
Does t in a(t) in the FLRW metric correspond to the proper time of the immortal observer, who’s been resting in the CMB reference frame since its emission?
 
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Nearly. It's the time of such an observer since the singularity, which is a couple of hundred thousand years earlier than the CMB emission.
 
Ibix said:
Nearly. It's the time of such an observer since the singularity, which is a couple of hundred thousand years earlier than the CMB emission.
Thank you. 380,000. Does the FLRW metric tell us, that this observer's time ran slower in the past due to cosmological time dilation?
 
ongoer said:
Thank you. 380,000. Does the FLRW metric tell us, that this observer's time ran slower in the past due to cosmological time dilation?
Passed more slowly than what?
 
Jaime Rudas said:
Passed more slowly than what?
Than it's passing today.
 
ongoer said:
Than it's passing today.
How would you compare that?
 
ongoer said:
Thank you. 380,000. Does the FLRW metric tell us, that this observer's time ran slower in the past due to cosmological time dilation?
No, and I think we've discussed the rather poor naming of that first paper here before, I think. It shows that the cosmological redshift is just redshift by checking that other processes are stretched out by the same factor as light is.

So despite the name, it shows that there's nothing but redshift.
 
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ongoer said:
No, cosmological time dilation doesn't mean that time in the past passed more slowly, but rather that very distant events APPEAR to pass more slowly than they do now due to the expansion of the universe. So, for example, if signal 1 is emitted when the universe was half its current size, and signal 2 is emitted one second later, then when signal 2 is emitted, signal 1 will be 300,000 km from signal 2. However, when those signals reach us, due to the expansion, the distance between the two will be 600,000 km, and therefore, we will see signal 2 two seconds after signal 1.
 
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  • #10
Jaime Rudas said:
No, cosmological time dilation doesn't mean that time in the past passed more slowly, but rather that very distant events APPEAR to pass more slowly than they do now due to the expansion of the universe. So, for example, if signal 1 is emitted when the universe was half its current size, and signal 2 is emitted one second later, then when signal 2 is emitted, signal 1 will be 300,000 km from signal 2. However, when those signals reach us, due to the expansion, the distance between the two will be 600,000 km, and therefore, we will see signal 2 two seconds after signal 1.
Shouldn't time run slower in space with higher energy density according to the Einstein field equations?

https://www.advancedsciencenews.com...he-early-universe-just-as-einstein-predicted/
 
  • #11
Jaime Rudas said:
No, cosmological time dilation doesn't mean that time in the past passed more slowly, but rather that very distant events APPEAR to pass more slowly than they do now due to the expansion of the universe.
...and (for the benefit of @ongoer) this is why the last time this paper came up we argued that "time dilation" is a bad name for what's going on here. Everything being called "time dilation" here is the same stretch factor as you get in the cosmological redshift, so it's consistent with there just being one effect: the light is stretched out so it takes us longer to receive everything, whether it's one wavelength or a days-long signal from some astronomical process.
 
  • #13
ongoer said:
Shouldn't time run slower in space with higher energy density according to the Einstein field equations?
No. It's at least arguably true in some circumstances, but not in general. The article you linked is just a popularisation of the paper you already linked, and that's just describing cosmological redshift. As I noted in the discussion I linked above they considered the possibility that something other than redshift was going on, but they found nothing.
 
  • #14
ongoer said:
Shouldn't time run slower in space with higher energy density according to the Einstein field equations?
https://www.advancedsciencenews.com...he-early-universe-just-as-einstein-predicted/
No, time always passes at the same rate, one second per second. When people talk about time speeding up or slowing down they’re being careless about what’s really going on (and that sort of carelessness is why the forum rules don't allow pop-sci sources like Advanced Science News as references - they oversimplify and mislead).

To get a sense of what is going on, go back to @Jaime Rudas post #9 above. There are four relevant events: First signal emitted, second signal emitted, first signal received, second signal received. We can use a clock at the source, ticking away at one second per second, to measure the time interval between the two emission events; and likewise a clock at the destination will measure the time between the two reception events. Say the time between the two reception events is twice the time between the two emission events. That does not mean that one clock is running slower than the other - we have two intervals between wto unrelated pairs of events and there's no more reason why tthey ought to be the same than for the distance between Moscow and Paris to be related to the distance between Singapore and Peking.

Even in the simplest case of special relativity time dilation (commonly misdescribed as "times slows down for fast moving objects") if you look carefully you will see that we are considering time intervals between two different pairs of events. It is only when we introduce additional assumptions about some of these events happening "at the same time" that we can compare them. But there is no way "at the same time" going on anywhere in the cosmological case that we're considering in this thread, so no meaningful way of making the comparison.
 
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  • #15
Nugatory said:
No, time always passes at the same rate, one second per second.
How about gravitational time dilation?
 
  • #16
ongoer said:
How about gravitational time dilation?
Just another example of what Nugatory said:
Nugatory said:
if you look carefully you will see that we are considering time intervals between two different pairs of events. It is only when we introduce additional assumptions about some of these events happening "at the same time" that we can compare them
 
  • #17
@Ibix what are the additional assumptions, that allow us to compare the flow of time on the planet's surface and on the planet's orbit?
 
  • #18
ongoer said:
@Ibix what are the additional assumptions, that allow us to compare the flow of time on the planet's surface and on the planet's orbit?
We can each see each others' clocks and compare rates. Clocks in the past can't see clocks in the present, so "time dilation between the future and the past" doesn't make sense.
 
  • #19
Ibix said:
We can each see each others' clocks and compare rates. Clocks in the past can't see clocks in the present, so "time dilation between the future and the past" doesn't make sense.
That's why I have the immortal observer in my question. His clock's tick is equal to the observed CMBR's wave period, and during his whole 13.8 billion years life he has observed, that this period has been extending.
 
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  • #20
ongoer said:
That's why I have the immortal observer in my question. His clock's tick is equal to the observed CMBR's wave period, and during his whole 13.8 billion light years life he has observed, that this period has been extending.
No, he just sees his clock ticking at one second per second. He can't compare rates at different times - what would he actually measure?
 
  • #21
ongoer said:
How about gravitational time dilation?
Two ways of thinking about gravitational time dilation:
1) We compare the elapsed time between he emission from within the gravity well of two consecutive light signals with the elapsed time between the reception of the two signals outside the gravity well. This is essentially the same situation as the cosmological one we've been discussing in this thread; we observe redshift but can't make any sensible statement about clock rates.
2) We make an additional assumption, namely that the signal the outside observe receives when their clock reads ##T## was emitted at the same time that their clock read ##T-\frac{H}{c}## where ##H## is the height of the outside observer. This assumption (more like a definition of "at the same time") is equivalent to being able to watch the other clock and allows the upper observer to claim that "at the same my clock read ##T_2## the lower clock read ##t_2##; earlier when my clock read ##T_1## the lower clock read ##t_1##; ##t_2-t_1\lt T_2-T_1##; therefore time is passing for slowly for the lower clock".

#2 is what's going on whenever people are talking about time dilation and clocks running faster or slower, and i makes sense only in the context of a given (and more or less arbitrarily chosen) definition of "at the same time".
 
  • #22
Ibix said:
No, he just sees his clock ticking at one second per second. He can't compare rates at different times - what would he actually measure?
His own time dilation with respect to his own past. If he had a mechanical watch with the tick equal to the CMBR's wave period at the moment of its emission, then this tick would extend just like the observed wave's period. If it didn't, then he wouldn't measure a constant c=λ0(z+1)/(T0(z+1)).
 
  • #23
ongoer said:
then this tick would extend just like the observed wave's period. I
What exact measurement would he be doing? How would you compare your watch's tick rate yesterday to its tick rate today?
 
  • #24
Ibix said:
What exact measurement would he be doing? How would you compare your watch's tick rate yesterday to its tick rate today?
Being immortal - by comparing the CMB's redshift from my own past to its value today.
 
  • #25
ongoer said:
Beeing immortal - by comparing the CMB's redshift from your own past to its value today.
Comparing what exactly? What will you measure? Just saying "I'll compare rates" doesn't help you.

I repeat: how would you confirm that your watch ticked at the same rate yesterday as it does today?
 
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  • #26
Ibix said:
Comparing what exactly? What will you measure? Just saying "I'll compare rates" doesn't help you.

I repeat: how would you confirm that your watch ticked at the same rate yesterday as it does today?
I repeat: I would measure my own time dilation with respect to my own past.

My mechanical watch time dilation goes hand in hand with the extending period of the observed light.
 
  • #27
ongoer said:
If he had a mechanical watch with the tick equal to the CMBR's wave period at the moment of its emission, then this tick would extend just like the observed wave's period. If it didn't, then he wouldn't measure a constant c=λ0(z+1)/(T0(z+1)).
If their mechanical watch does not agree with a light clock that they are also carrying along... then the mechanical watch is broken.
His own time dilation with respect to his own past.
There is no such thing. "Time dilation" is defined (see my post about gravitational time dilation above) to be the ratio of the proper times between two different pairs of events that have the same coordinate time (that is, have been defined to happen "at the same time"). There's no way of doing that between someone's past and present.
 
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  • #28
ongoer said:
I would measure my own time dilation with respect to my own past.
How? What would you compare?
 
  • #29
Ibix said:
How? What would you compare?
Redshift.
 
  • #30
ongoer said:
Redshift.
So you're measuring the redshifted appearance of the old clock rate to the current rate. That's just a measure of redshift, as we have been saying since post #4.
 
  • #31
Ibix said:
So you're measuring the redshifted appearance of the old clock rate to the current rate. That's just a measure of redshift, as we have been saying since post #4.
And the measure of this redshift is also a measure of cosmological time dilation.
 
  • #32
Nugatory said:
If their mechanical watch does not agree with a light clock that they are also carrying along... then the mechanical watch is broken.
Assume that it's Swiss.
 
  • #33
Nugatory said:
There is no such thing. "Time dilation" is defined (see my post about gravitational time dilation above) to be the ratio of the proper times between two different pairs of events that have the same coordinate time (that is, have been defined to happen "at the same time"). There's no way of doing that between someone's past and present.
Cosmological time dilation is defined as the observed redshift, and the immortal observer could have seen it changing.
 
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  • #34
ongoer said:
Cosmological time dilation is defined as the observed redshift, and the immortal observer could have seen it changing.
If he has sufficiently good and also co-moving mirrors, yes. He can also see no redshift if he deploys his mirrors differently (rigidly attached to him, I think).

What he's seeing is a product of the light path he uses to observe his past watch image, which isn't the case with either kinematic or gravitational time dilation. That's why simply relabelling redshift "time dilation" seems nonsensical and misleading to me.
 
  • #35
ongoer said:
And the measure of this redshift is also a measure of cosmological time dilation.
Sure, if you define the term "cosmological time dilation" to mean "redshift". But that's not physics. That's just playing with words.

The key point you are missing is at the end of post #27 by @Nugatory. Please read that again and again until it sinks in. There is simply no way to make the comparison you would need to make to support the claim that "cosmological time dilation" refers to something "real", as opposed to just an appearance. For another quick way of stating the point: a "real" time dilation, such as gravitational time dilation between two observers at different altitudes in a gravitational field, requires round-trip light signals to measure it. But you obviously can't exchange round trip light signals with the past.
 
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  • #36
ongoer said:
Assume that it's Swiss.
The better designed and built it is, the more closely it will agree with an idealized and infinitesimal light clock. It has to be that way, because the Swiss wristwatch is measuring proper time - the difference between two readings of the watch is, to limits of accuracy of the mechanism, the proper time along the wristwatch’s worldline between the readings - and a light clock is idealized and theoretically perfect device for measuring proper time.
 
  • #37
Nugatory said:
and a light clock is idealized and theoretically perfect device for measuring proper time.
Note that it's also just a pair of mirrors. You could actually look into it and see a reflection (of a reflection of a reflection...) of your mechanical watch 14bn years ago ticking at 1s/s. In fact, all of the reflections you could see would tick in synchrony.
 
  • #38
@PeterDonis Alice is falling on the event horizon of a BH and Bob is watching her. Let's fall with Alice in her reference frame. After we cross the event horizon with her, we can't compare our time dilation with Bob using a light signal. All we've got is maths. Does this mean, that the time dilation between us and Bob makes no physical sense anymore?
 
  • #39
ongoer said:
Does this mean, that the time dilation between us and Bob makes no physical sense anymore?
Yes. The spacetime inside a black hole isn't a stationary spacetime, so you can't establish a definition of "only moving in space" and hence there's no way to define "correcting for movement". You can measure a redshift in one direction but not the other. You are free to define simultaneity between Alice and Bob in any way you wish, so time dilation between the two is anything you want. So it's not meaningful - it's just your choice of coordinates.
 
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  • #40
ongoer said:
Does this mean, that the time dilation between us and Bob makes no physical sense anymore?
Yes, that is what it means.
 
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  • #41
Ibix said:
Yes. The spacetime inside a black hole isn't a stationary spacetime, so you can't establish a definition of "only moving in space" and hence there's no way to define "correcting for movement". You can measure a redshift in one direction but not the other. You are free to define simultaneity between Alice and Bob in any way you wish, so time dilation between the two is anything you want. So it's not meaningful - it's just your choice of coordinates.
This also means, that you can't assume, that the other immortal observer separated from us by the spacelike interval as a result of the expansion is at the same age as we (assuming our immortality) equal to the universe age, since we can't communicate anymore and compare our proper times. Do you agree?
 
  • #42
ongoer said:
is at the same age…
“Is at the same age” is another way of saying “has experienced the same amount of proper time between birth and now” so is meaningful only if we have a definition of “now”. And if they are not colocated, there is no common definition of “now”.
 
  • #43
Nugatory said:
“Is at the same age” is another way of saying “has experienced the same amount of proper time between birth and now” so is meaningful only if we have a definition of “now”. And if they are not colocated, there is no common definition of “now”.
Yes, there is. It's called the cosmological time and it's equal to the proper time of all the immortal observers resting in their cmb reference frames and the same for all of them, because it's also the age of the universe.
 
  • #44
ongoer said:
This also means, that you can't assume, that the other immortal observer separated from us by the spacelike interval as a result of the expansion is at the same age as we (assuming our immortality) equal to the universe age
Well, since the universe age is defined to be the time measured by comoving observers since the big bang singularity, yes they are the same age by definition. So I don't have to assume it - you did it for me in your formulation of the question.

You could pick a different simultaneity criterion if you want, yes, but nobody ever does because the maths is much nastier.
 
  • #45
@Ibix you skipped the lack of possibility to communicate :) Also, tell it to @Nugatory please :)
 
  • #46
ongoer said:
@Ibix you skipped the lack of possibility to communicate :)
It doesn't matter. You constrained the answer by the way you asked the question. Other answers are possible (and the lack of ability to communicate is a part of that), but not given the definition of "at the same time" that you used.

As I said - I don't have to assume it because you did it for me. If you want to relax that assumption then we can do so.
 
  • #47
ongoer said:
Does this mean, that the time dilation between us and Bob makes no physical sense anymore?
Yes.
 
  • #48
ongoer said:
we can't communicate anymore
Sure you can. You can communicate with other comoving observers in the universe--just wait long enough for the round trip light signal. You might have to wait a long time, but a round trip light signal is still possible.

The reason you can't do that if you're inside a black hole and someone else has remained outside is that it is impossible for a light signal to make a round trip. That makes a big difference.
 
  • #49
ongoer said:
you can't assume, that the other immortal observer separated from us by the spacelike interval as a result of the expansion is at the same age as we (assuming our immortality) equal to the universe age
At the particular spacelike separated events along your worldlines that you refer to, you both have experienced the same proper time since the Big Bang. In that sense you are "the same age". But of course that is not the only possible sense of the word "age".

As for "assuming" that, well, it's not an assumption we just pulled out of thin air, it's an implication of our best current model of the universe. To confirm it, of course, you would have to exchange round trip light signals with the other comoving observer, which, as I noted in my previous post just now, might take time. But it can be done. There is nothing in principle preventing you and other comoving observers from exchanging round trip light signals and confirming whatever predictions of our best current model of the universe you are interested in.

Whereas, if you fall into a black hole and I stay outside, there is no way, even in principle, for you to ever send me a light signal telling me what things are like inside the hole. Again, that makes a big difference.
 
  • #50
ongoer said:
Yes, there is. It's called the cosmological time and it's equal to the proper time of all the immortal observers resting in their cmb reference frames and the same for all of them, because it's also the age of the universe.
Nonetheless, that definition of "now" is an arbitrary choice, albeit one that we often make because it simplifies the math. We could define "now" some other way and no physics would change, no observations would come out differently, the spacetime interval and proper times between pairs of events remains the same.

And none of that is helpful for defining time dilation along our own worldline, which seems to be what you were trying to do above.
 
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