# Is the expansion of the universe affecting time or just space?

• I
• exander
In summary: There is no influence of a(t) on lifetime of muon. All the people in differt era of a(t) get the same value of 2.197034(21)×10−6 second with their own watch showing t.Yes, I am perfectly aware of this, but I am unsure how does this relate to expanding time dimension. As I mentioned above, the length of second is still the same (similar to the length of a meter).
exander
And I am confused by the responses.

When I consider time dimension expansion, I perceive it the same way as space dimension expansion.

The expansion doesn't change the unit size. The meter is still meter and the second is still second when dimension undergoes expansion.

What happens is that events are further apart after expansion. If you expand space between galaxies than galaxies are further apart in space. If you expand the time dimension then events are further apart in time. Basically more units can be fit between them in both cases.

For example, you have events A and B that are watched by a first observer 100 light years away and a second observer 200 light years away. If the time dimension is expanding then events A and B will seem further apart for the second observer.

Am I missing something?

$$ds^2=c^2dt^2-dL^2$$
Say our universe is closed and homogeneous, it is 3d shere of radius a in 4d Euclid space. So the space is scaled with a
$$ds^2=c^2dt^2-a^2dl^2$$
where dl refers 3d unit sphere of a=1. a, radius of universe, can be function of time a(t). Time has have nothing to do with it, but if we introduce a trick of
$$d\eta=\frac{c}{a(t)}dt$$
$$ds^2=a(t)^2[d\eta^2-dl^2]$$
It is simple and convenient to handle which physicists love. Scaled time ##\eta## is introduced for this purpose. Usual time or proper time is still t. We experience no expansion of time as you may suspect. In younger universe of smaller a and in older universe of larger a, there is no change of physics, e.g. life time of muon changes in ##\eta## but same in t .

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anuttarasammyak said:
It is simple and convenient to handle which physicists love. Scaled time ##\eta## is introduced for this purpose. Usual time or proper time is still t. We experience no expansion of time as you may suspect. In younger universe of smaller a and in older universe of larger a, there is no change of physics, e.g. life time of muon is same in t not in ##\eta##.
I am confused with this part, which goes exactly against to what I wrote. How would expansion of time dimension influence the lifetime of muon? The unit of measurement - second - has the same length regardless of expanding time dimension. In all time periods the lifetime was the same.

exander said:
I am confused with this part, which goes exactly against to what I wrote. How would expansion of time dimension influence the lifetime of muon? The unit of measurement - second - has the same length regardless of expanding time dimension. In all time periods the lifetime was the same.
There is no influence of a(t) on lifetime of muon. All the people in differt era of a(t) get the same value of 2.197034(21)×10−6 second with their own watch showing t.

anuttarasammyak said:
There is no influence of a(t) on lifetime of muon. All the people in differt era of a(t) get the same value of 2.197034(21)×10−6 second with their own watch showing t.
Yes, I am perfectly aware of this, but I am unsure how does this relate to expanding time dimension. As I mentioned above, the length of second is still the same (similar to the length of a meter).

Say there is a ring of radius 1 and and a point is moving on it with 1 turn/second.
The radius of ring increase with time and the speed of the poin is same so the rate changes e.g. to 0.5 turn/second for radius 2. If we introduce a new measure of time so that the rate is 1 turn/new secod always.
1 new second = 2 traditional second for radius 2 in this case.
New measure of time is introduced so that angular velocity shows always same value with this new time measure. It is introduced just for simple description of mathetatics.

exander said:
For example, you have events A and B that are watched by a first observer 100 light years away and a second observer 200 light years away. If the time dimension is expanding then events A and B will seem further apart for the second observer.
But they'll seem further apart if the spatial dimensions are expanding too, because the light speed delay would increase so the time between the arrival times of light from the events (which I assume are one after the other, timelike separated) increases. So you're back to "how do you tell".

anuttarasammyak said:
Say there is a ring of radius 1 and and a point is moving on it with 1 turn/second.
The radius of ring increase with time and the speed of the poin is same so the rate changes e.g. to 0.5 turn/second for radius 2. If we introduce a new measure of time so that the rate is 1 turn/new secod always.
1 new second = 2 traditional second for radius 2 in this case.
New measure of time is introduced so that angular velocity shows always same value with this new time measure. It is introduced just for simple description of mathetatics.
I am not sure how any of it is relevant. I already specified in the opening post that the measuring unit second is not changing. Furthermore, I am in no way changing the pace of the time, measuring of the time or length of the unit of the time.

Ibix said:
But they'll seem further apart if the spatial dimensions are expanding too, because the light speed delay would increase so the time between the arrival times of light from the events (which I assume are one after the other, timelike separated) increases. So you're back to "how do you tell".
I fully agree with what you wrote, but "how do you tell" is my own question. Why do We assume it is just space expanding? I can very well say that it is both time and space that is expanding. If you can't distinguish if space or time is expanding then until proven otherwise We should assume that both space and time are expanding.

We already know that space is expanding the same rate in all spacial dimensions, so why shouldn't it expand in time as well?

exander said:
Why do We assume it is just space expanding?
Because rescaling your coordinate system so "time is expanding" is just a unit change and makes no difference to anything real. That's the point. It's more convenient to have your co-moving clocks match your global notion of time.

Ibix said:
Because rescaling your coordinate system so "time is expanding" is just a unit change and makes no difference to anything real. That's the point. It's more convenient to have your co-moving clocks match your global notion of time.
How do you know that it makes no difference to anything real?

If time is expanding as well, and We assume it is just space, don't We calculate badly the rate of the expansion of space? If time expansion is indeed happening then space is not expanding that fast, because the part of the perceived expansion is caused by the expansion of time.

exander said:
How do you know that it makes no difference to anything real?
Because it's just a coordinate system. You can change a coordinate system by rotating or zooming the map on your phone. Does that change anything about the world?

Dale
Ibix said:
Because it's just a coordinate system. You can change a coordinate system by rotating or zooming the map on your phone. Does that change anything about the world?
I think it would be pretty influential if space expanded only in x, y and not z.

If space expanded 1m/s/km (1m per second per km) in each of the spacial dimension (x, y, z) then after 1s the volume of space of 1km2 becomes cca 1.003 km2 after 1s. If you assumed it expanded only in x and y then you would deduce the speed of expansion is cca 1.5m/s/km. I haven't really thought it through, but wouldn't this cause perception of accelerating expansion as well?

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exander said:
I think it would be pretty influential if space expanded only in x, y and not z.
Sure. You'd have removed the rotational symmetry of spacetime, so you'd be describing some other universe. So there's a direct way to detect such a thing: point telescopes in different directions and see if you get no redshifts in one direction.

On the other hand, there's no physical consequence to "time is expanding". There's no way to take a clock now and compare it to a clock in the past except to look at a clock in the past, but the light rays carrying the information are subject to expansion as well, so you know that the time you actually see is redshifted. So you can just define "time" to be whatever co-moving clocks are ticking off and ascribe the apparent changes in perceived rate to the expansion of space. Or you can say that clocks in the past were ticking slow (or fast) compared to coordinate time and your expansion rate changes (because you changed your definition of "rate", not because anything has actually changed) and some of the redshift is due to that.

The underlying point here is that the best statement of the physics is that the congruence of co-moving worldlines has a positive expansion scalar. Translating that as "space is expanding" is not a complete translation because you have to inject assumptions about what you mean by "space" - in other words, you have to pick a coordinate system (or at least a foliation, for the pedantic). You can pick a different assumption, a different coordinate system, and get a different ordinary language translation where (for example) time is expanding as well.

The simple "space is expanding" description is probably the easiest one because co-moving clocks tick coordinate time. There's no point to making life more complicated.
exander said:
I haven't really thought it trough
Indeed. Perhaps you should study some GR (the proper maths) so that you can think these things through correctly?

Ibix said:
Sure. You'd have removed the rotational symmetry of spacetime, so you'd be describing some other universe. So there's a direct way to detect such a thing: point telescopes in different directions and see if you get no redshifts in one direction.
Doesn't rotational symmetry of spacetime include time? At least in SR via Lorentzian transformations? But in GR the rotational symmetry only holds locally, isn't it?

To your suggested experiment, the objects move and light carries angular momentum, it's path is curved by gravity etc., you can't assume the light would go to you along the same dimension over large distance, I am pretty sure that passage through all spacial dimensions would average out over such large distances.
Ibix said:
On the other hand, there's no physical consequence to "time is expanding".
Haven't We already established that perception of expanding time is the same as expanding space?

Theoretically we would be able to observe space expansion. Today we attach retractable measure from galaxy A to galaxy B. Next day we will find that the measure is pulled out further like a tall measurement of growing child. How do we observe time expansion? We observe light speed c every day and if we find c(t) is increasing, we may deduce that time is expanding.

anuttarasammyak said:
Theoretically we would be able to observe space expansion. Today we attach retractable measure from galaxy A to galaxy B. Next day we will find that the measure is pulled out further like a tall measurement of growing child. How do we observe time expansion? We observe light speed c every day and if we find c(t) is increasing, we may deduce that time is expanding.
What the hell man? I already told you like five times that time unit is not changing with time expansion. No matter how you shrink or expand the time dimension a second is still second. Same as 1 meter is still 1 meter even if space expands. On the contrary, if meter extended with expansion of space, We would not perceive any expansion. If you had two objects A and B, I and you extend space between them, they are further apart, the number of meters between them increased. If the meter extended, they would have the same distance after expansion.

It is like saying the space is not expanding because the speed of light is still the same. Makes no sense.

Hornbein
As an example of time space expansion, we may see rotating frame of reference in GR. As rotation speed increase in time, SR says that the periphery length increase so the bricks making a periphery will be torn and broken by space expansion. Also SR says that clocks pace down, "time expansion".
For universe of our interest here, space expansion is similar but there is no corresponding time expansion.

I think this has crossed a line between "asking a question" an d "promoting a personal theory".

I think this has crossed a line between "asking a question" an d "promoting a personal theory".
What?

anuttarasammyak said:
As an example of time space expansion, we may see rotating frame of reference in GR. As rotation speed increase in time, SR says that the periphery length increase so the bricks making a periphery will be torn and broken by space expansion. Also SR says that clocks pace down, "time expansion".
For universe of our interest here, space expansion is similar but there is no corresponding time expansion.
Doesn't periphery length contracts? It moves faster. Speed contracts lengths.

Also, this mixes SR and GR. An observer on the edge of a rotating disk would measure distances along the disk to be larger than an observer at the center would predict based on the non-rotating radius and the angle subtended. This is often referred to as the Ehrenfest paradox. This doesn't result in physical tearing of the disk. The rotating observer's space is not Euclidean, so their geometry is different from the non-rotating observer's.

exander said:
For example, you have events A and B that are watched by a first observer 100 light years away and a second observer 200 light years away. If the time dimension is expanding then events A and B will seem further apart for the second observer.
exander said:
What the hell man? I already told you like five times that time unit is not changing with time expansion. No matter how you shrink or expand the time dimension a second is still second.
The problem is that you have two mutually-contradictory assertions. You cannot have both “the time unit is not changing” and “events A and B will seem further apart for the second observer”. The spacetime interval between two nearby events is invariant. So the only way for the two observers to disagree is for them to use different units.

Since this is based on a contradiction and has become a bit heated when respondents must logically contradict one part or the other, we will go ahead and close this thread.

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exander said:
I fully agree with what you wrote, but "how do you tell" is my own question. Why do We assume it is just space expanding?
Our choice of how to slice spacetime into "space" and "time" is pretty much arbitrary and the most mathematically convenient way doing this is to slice spacetime up in such a way that all the expansion is along the space axes. So the answer to your "Why do we assume?" question is that that's how we generally choose our coordinates.
I can very well say that it is both time and space that is expanding. If you can't distinguish if space or time is expanding then until proven otherwise We should assume that both space and time are expanding.
The observational fact is that light from distant galaxies is red-shifted. We can explain this fact by choosing time and space axes in such a way that the distant galaxies are moving away from us (space is expanding) or in such a way that the distant galaxies are subject to time dilation (time is also expanding).

But.... If you choose the latter formulation, it's on you to do the calculations using your preferred time-expanding coordinates and show that this calculation matches the observed results. And even then you haven't produced any new physics, you've just produced a different mathematical treatment of the same physics. It's analogous to how the equation of the parabola ##y=x^2## looks way more complicated if we rotate the x and y axes by 16.3 degrees - but that more complicated equation is still describing the same parabola.

Ibix

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