B Proper time of the observer resting in CMB reference frame

[ongoer]

TL;DR

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?

 

[Ibix]

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.

 

[ongoer]

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?

 

[Jaime Rudas]

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?

 

[ongoer]

Passed more slowly than what?

Than it's passing today.

 

[Jaime Rudas]

Than it's passing today.

How would you compare that?

 

[ongoer]

How would you compare that?

https://arxiv.org/abs/2306.04053

https://arxiv.org/abs/2406.05050

https://www.youtube.com/watch?v=RuSbqFL6VcY

 

[Ibix]

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.

 

[Jaime Rudas]

https://arxiv.org/abs/2306.04053

https://arxiv.org/abs/2406.05050

https://www.youtube.com/watch?v=RuSbqFL6VcY

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.

 

[ongoer]

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/

 

[Ibix]

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.

 

[Ibix]

Previous discussion:
https://www.physicsforums.com/threads/cosmological-time-dilation-of-high-redshift-quasars.1053780/

 

[Ibix]

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.

 

[Nugatory]

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.

 

[ongoer]

No, time always passes at the same rate, one second per second.

How about gravitational time dilation?

 

[Ibix]

How about gravitational time dilation?

Just another example of what 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

 

[ongoer]

@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?

 

[Ibix]

@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.

 

[ongoer]

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.

 

[Ibix]

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?

 

[Nugatory]

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".

 

[ongoer]

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)).

 

[Ibix]

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?

 

[ongoer]

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.

 

[Ibix]

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?

 

[ongoer]

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.

 

[Nugatory]

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.

 

[Ibix]

I would measure my own time dilation with respect to my own past.

How? What would you compare?

 

[ongoer]

How? What would you compare?

Redshift.

 

[Ibix]

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.