Could we detect an intrinsic change in the flow of time?

[Jonathan Scott]

We are talking about the early universe as compared to now. This situation is not even close to stationary, and there is no frame in which "the sources are approximately at rest" is even close to being true.

What I was talking about when using "potential" was an illustrative example set in the present era to show that the idea of a difference in a rate of time flow can occur and is detectable in standard gravity theory, and can be extended to a slowly changing rate of time, which I think should also be theoretically detectable by light speed delay.

And I also think that if a difference in rate of local time flow due to gravity were theoretically detectable, and we call that a change in "potential", then it would be reasonable to extend that conventional terminology back a long way, although I can't say how "early" that would go. It may be imprecise, but the intention seems clear. Of course, I very much doubt that it applies to the actual universe.

 

[PeterDonis]

What I was talking about when using "potential" was an illustrative example set in the present era to show that the idea of a difference in a rate of time flow can occur and is detectable in standard gravity theory

But what you are describing can occur in highly non-stationary situations, where there is no meaningful "potential". So it doesn't seem to me like a good way of describing what standard GR predicts in such situations.

and can be extended to a slowly changing rate of time

Only, at best, in an approximate sense, and even then you have given no actual math or references to back up your claim, either here or in previous discussions on similar topics. Once again, please bear in mind the PF rules about personal speculations.

And even putting all that aside, describing our expanding universe is not a situation where "a slowly changing rate of time" is applicable even as an approximation.

It may be imprecise, but the intention seems clear.

To me all that seems clear is that you are trying to extend a concept well beyond its domain of validity without adequate support for such a notion. Please see my comment on the PF rules above.

 

[Jonathan Scott]

I'm only trying to address the original point, not defend the referenced idea.

I'm sure that it's possible to contrive a temporarily changing flow of time (relative to some larger scale reference frame) with gravity and equally sure that observations made in that situation would not imply non-standard physics.

I also think it's probably possible in theory to detect that time is changing by using light-speed delays within the region where it is changing, although it might not be practical. I think that could be investigated by considering the weak field Newtonian limit for an expanding spherical shell and how gradual changes in the metric would propagate through the interior. If that is possible at least in theory, then one could integrate the local "rate of change" to determine a local relative time rate between a current time and a time in the past.

 

[PeterDonis]

I also think it's probably possible in theory to detect that time is changing by using light-speed delays within the region where it is changing

Standard GR predicts with certainty that this will happen, yes.

I think that could be investigated by considering the weak field Newtonian limit for an expanding spherical shell and how gradual changes in the metric would propagate through the interior.

In the interior the metric is not changing; it's Minkowski. The only "propagation" involved is that the Minkowski interior region is expanding with the shell, since it starts at the shell's interior surface.

If that is possible at least in theory, then one could integrate the local "rate of change" to determine a local relative time rate between a current time and a time in the past.

Along a single worldline, the only "change in time rate" in the spherical shell case would happen when the shell passed the worldline; and the change is entirely attributable to the effect of the stress-energy in the shell.

More technically, what is going on is that, before the shell passes the worldline, it is an integral curve of the timelike KVF in the exterior region; and after the shell passes the worldline, it is an integral curve of the timelike KVF in the interior region. But in between, there is a portion of the worldline which is not an integral curve of any timelike KVF, and that is what allows the "local rate of time" to change.

But this "change" is only definable because there is a "before" and "after" timelike KVF. In a spacetime where there are no timelike KVFs at all, i.e., a non-stationary spacetime, this reasoning can't even get started.

 

[Jonathan Scott]

In the interior the metric is not changing; it's Minkowski. The only "propagation" involved is that the Minkowski interior region is expanding with the shell, since it starts at the shell's interior surface.

That makes a lot of sense from the GR point of view, but I'm having some trouble getting my head round it. It seems that there's a scale factor involved as well, in that if you consider a spherical shell of the same mass but larger radius, the Newtonian potential inside the larger sphere is higher, and the corresponding time factor in the metric is higher too. So if you observe a standard clock within each sphere from outside, the one inside the larger sphere will run fractionally faster. That means that if you gradually change the radius with time and watch a standard clock inside it from outside, you would expect the rate of the clock to change. One would therefore also expect to be able to observe some rate change when inside the sphere watching a clock at the far side, but this clearly cannot happen in a Minkowski metric. Is the "explanation" from that point of view effectively that the relative effect of the metric on space exactly hides the effect on time?

 

[PeterDonis]

if you consider a spherical shell of the same mass but larger radius

Then the spacetime geometry is different, yes--the boundary between the exterior region (Schwarzschild) and the interior region (Minkowski) occurs at a larger radius, so the norm of the timelike KVF in the exterior region at the boundary, which is what determines the "potential" inside the shell, is larger (closer to its value at infinity).

That means that if you gradually change the radius with time and watch a standard clock inside it from outside, you would expect the rate of the clock to change.

More precisely, you would expect the ratio of clock ticks elapsed during a round trip of a light signal to change. Yes, that's correct.

One would therefore also expect to be able to observe some rate change when inside the sphere watching a clock at the far side

Sure: the ratio of clock ticks elapsed during a round trip of a light signal is an invariant.

this clearly cannot happen in a Minkowski metric

The metric as a whole is not the Minkowski metric. There is a Minkowski region, but any measurement that enables one to see the difference in "rate of time", such as the round-trip light signal measurement I described above, cannot be limited to the Minkowski region alone. Measurements that are limited to the Minkowski region alone will not see any change in "rate of time"; for example, a pair of clocks both within the Minkowski region that exchange light signals will obtain a "clock tick ratio" of 1 between them--both will show the same number of ticks elapsed during a round trip light signal's travel.

 

[Jonathan Scott]

Measurements that are limited to the Minkowski region alone will not see any change in "rate of time"; for example, a pair of clocks both within the Minkowski region that exchange light signals will obtain a "clock tick ratio" of 1 between them--both will show the same number of ticks elapsed during a round trip light signal's travel.

Although I'm fairly sure I agree with this, I'm still having some trouble with understanding this from the point of view of an observer outside the region. According to that observer's coordinates, if one clock within the region emits a stream of ticks and they are received and compared with another clock, the stream of ticks can be gradually getting faster, but the properties of the Minkowski region mean that received ticks still match the receiving clock, which is as if the ticks sped up in transit to match the new time rate. I think this can probably be understood in terms of what happens to the coordinate space factor and the coordinate speed of light, but it seems somewhat counter-intuitive.

 

[PeterDonis]

According to that observer's coordinates, if one clock within the region emits a stream of ticks and they are received and compared with another clock, the stream of ticks can be gradually getting faster, but the properties of the Minkowski region mean...

The effect you are describing has nothing to do with the properties of the Minkowski region. It has to do with the fact that the shell is moving towards the outside observer. That means the distance over which the Schwarzschild metric outside the shell is redshifting the light signal coming from inside the shell is decreasing, which means less redshift, which means faster ticks seen by the observer.

I think this can probably be understood in terms of what happens to the coordinate space factor and the coordinate speed of light

I think you are relying too much on trying to interpret things in terms of coordinates.