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?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.
Passed more slowly than what?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?
Than it's passing today.Jaime Rudas said:Passed more slowly than what?
How would you compare that?ongoer said:Than it's passing today.
https://arxiv.org/abs/2306.04053Jaime Rudas said:How would you compare that?
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.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, 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 said:
Shouldn't time run slower in space with higher energy density according to the Einstein field equations?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.
...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.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.
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.ongoer said:Shouldn't time run slower in space with higher energy density according to the Einstein field equations?
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).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/
How about gravitational time dilation?Nugatory said:No, time always passes at the same rate, one second per second.
Just another example of what Nugatory said:ongoer said:How about gravitational time dilation?
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
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 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?
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 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.
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?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.
Two ways of thinking about gravitational time dilation:ongoer said:How about gravitational time dilation?
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 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?
What exact measurement would he be doing? How would you compare your watch's tick rate yesterday to its tick rate today?ongoer said:then this tick would extend just like the observed wave's period. I
Being immortal - by comparing the CMB's redshift from my own past to its value today.Ibix said:What exact measurement would he be doing? How would you compare your watch's tick rate yesterday to its tick rate today?
Comparing what exactly? What will you measure? Just saying "I'll compare rates" doesn't help you.ongoer said:Beeing immortal - by comparing the CMB's redshift from your own past to its value today.
I repeat: I would measure my own time dilation with respect to my own past.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?
If their mechanical watch does not agree with a light clock that they are also carrying along... then the mechanical watch is broken.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)).
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.His own time dilation with respect to his own past.
How? What would you compare?ongoer said:I would measure my own time dilation with respect to my own past.
Redshift.Ibix said:How? What would you compare?
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.ongoer said:Redshift.
And the measure of this redshift is also a measure of cosmological time dilation.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.
Assume that it's Swiss.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.
Cosmological time dilation is defined as the observed redshift, and the immortal observer could have seen it changing.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.
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).ongoer said:Cosmological time dilation is defined as the observed redshift, and the immortal observer could have seen it changing.
Sure, if you define the term "cosmological time dilation" to mean "redshift". But that's not physics. That's just playing with words.ongoer said:And the measure of this redshift is also a measure of cosmological time dilation.
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.ongoer said:Assume that it's Swiss.
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.Nugatory said:and a light clock is idealized and theoretically perfect device for measuring proper time.
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.ongoer said:Does this mean, that the time dilation between us and Bob makes no physical sense anymore?
Yes, that is what it means.ongoer said:Does this mean, that the time dilation between us and Bob makes no physical sense anymore?
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?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.
“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”.ongoer said:is at the same age…
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.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”.
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.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
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.ongoer said:@Ibix you skipped the lack of possibility to communicate :)
Yes.ongoer said:Does this mean, that the time dilation between us and Bob makes no physical sense 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.ongoer said:we can't communicate anymore
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".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
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.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.
