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

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In the principle study of the Pioneer Anomaly, John Anderson and Slava Turyshev suggested a speculative explanation for the apparent deceleration of the spacecraft : as an acceleration of the clock rate used for telemetry back on earth. To be clear, this explanation has been discounted- although it was explored further in this paper. The Pioneer Anomaly is generally considered solved, being due to asymmetric thermal radiation from the probes.My question is, if such a universal change in clock time did exist, i.e. that every subsequent second ticked by faster or slower than the one before it, how could we detect it? Can anyone imagine an Earth-based experiment? As I understand it, the effect that Anderson was proposing would be universal, effecting all clocks equally. Such an effect would be independent of special or general relativistic time dilations, occurring without any specific circumstances of motion or gravitation (although these effects would need to be subtracted from any experiment).The magnitude of the effect if it were to explain the Pioneer Anomaly, 2.9E-18 sec^-1, would exceed the uncertainty of an ordinary cesium atomic clock in a week. I suspect the most sensible comparison would be to compare the proper time of 2 observers at 2 different cosmic times.

I'm not asking if this effect is real, I'm asking if we could make a practical experiment to detect something like it, or if it could even be logically possible for such an effect to exist. I proposed this thought experiment over at scienceforums.net, and we got as far as assuming light delay could put us in contact with a past rate of time (even of the very same clock, if a signal is bounced off something like the Pioneer probes), and so an interferometer with arms of very different lengths might register such an effect, but would require absurd precision for something on the order of magnitude of the Pioneer Anomaly.

 

[PeterDonis]

if such a universal change in clock time did exist, i.e. that every subsequent second ticked by faster or slower than the one before it, how could we detect it?

We couldn't. The idea is physically meaningless; it sounds plausible but when you try to make it rigorous, it doesn't work.

 

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We couldn't. The idea is physically meaningless; it sounds plausible but when you try to make it rigorous, it doesn't work.

I wondered if this might be the case, I get hung up on it when I think about reciprocity between 2 observers. But can you elaborate on where it fails to make sense fundamentally?

 

[PeterDonis]

can you elaborate on where it fails to make sense fundamentally?

Because there's no such thing as "universal clock time" to begin with. There is only proper time along particular worldlines, as measured by particular clocks following those worldlines. So the question isn't even well posed, since it assumes that there is a meaningful "universal" definition of time, when in fact there isn't.

 

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Because there's no such thing as "universal clock time" to begin with. There is only proper time along particular worldlines, as measured by particular clocks following those worldlines. So the question isn't even well posed, since it assumes that there is a meaningful "universal" definition of time, when in fact there isn't.

change in proper time over cosmic time. We all refer regularly to the cosmic age of co-moving observers at rest relative to the Hubble flow. Better posed?

 

[PeterDonis]

change in proper time over cosmic time.

Which is not well-defined either. See below.

We all refer regularly to the cosmic age of co-moving observers at rest relative to the Hubble flow.

Yes, and what that means is proper time elapsed along the worldlines of such observers. There is no "cosmic time" other than that.

Better posed?

No. See above.

 

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Ok, so can you imagine how Drs Anderson and Turyshev were referring to a clock acceleration in the original cited paper in my post? Were they and others involved referring to something that is physically meaningless? Or what is it that I am misrepresenting in their hypothesis?

 

[PeterDonis]

can you imagine how Drs Anderson and Turyshev were referring to a clock acceleration in the original cited paper in my post? Were they and others involved referring to something that is physically meaningless?

As far as I can tell, yes. I think the point at which they go wrong is when they talk about a time-varying "gravitational potential" throughout the universe. The concept of "gravitational potential" only makes sense in a stationary spacetime (basically, a spacetime that you can slice up into a stack of spacelike slices that all have the same geometry). But our universe is not a stationary spacetime.

 

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ok then. Anybody disagree with PeterDonis?

 

[Chronos]

Lacking an absolute clock, an idea that was ceremonially buried by Einstein, there is no grounds for disagreement.

 

[Tanelorn]

Often wondered if, during the 13.8B years since the BB, has "local Earth time" always remained exactly the same, with 1s throughout those years always lasting 1s as we experience it now? If it hasn't then I presume that the often quoted 13.8B years might not be very precise?

 

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Thanks Guys.

This should perhaps split into another post, but if it is meaningless to refer to a background gravitational potential in relation to the flow of time, why do we expect the overall density of mass to influence the expansion of space?

 

[PeterDonis]

if it is meaningless to refer to a background gravitational potential in relation to the flow of time, why do we expect the overall density of mass to influence the expansion of space?

Because "gravitational potential" is not the only effect that density of mass (more precisely, stress-energy, which includes mass/energy density but also pressure, etc.) can have. "Gravitational potential" is just a way of describing one portion of that effect in a particular set of spacetimes (the stationary ones).

 

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Because "gravitational potential" is not the only effect that density of mass (more precisely, stress-energy, which includes mass/energy density but also pressure, etc.) can have. "Gravitational potential" is just a way of describing one portion of that effect in a particular set of spacetimes (the stationary ones).

Thanks Peter. In my mind, the stress energy tensor was roughly synonymous with gravitational potential, but I imagine this just betrays that I can't do the math of GR. Thanks for reviewing my question.

 

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Often wondered if, during the 13.8B years since the BB, has "local Earth time" always remained exactly the same, with 1s throughout those years always lasting 1s as we experience it now? If it hasn't then I presume that the often quoted 13.8B years might not be very precise?

I should probably stick to the question asking rather than answering, but I'll make an attempt here, and hopefully someone can back it up or refute it. The 13.8billion years is a cosmic time coordinate, extrapolated from our observations of the dynamics of spatial expansion. Because expansion has been close to constant over history, this age is pretty close to 1/H_o. It's the time it would take the universe to grow to it's present size at this observed rate. Any object on Earth, say a primordial proton, would have an age less than that if you could date it, because it has spent it's lifetime in various gravitational fields, which have an attendant time dilation.

 

[rootone]

Measuring a rate for flow of perceived time; would that not need a second dimension of time to compare it with?
Time apparently only has one dimension, and it's not easy to argue that there could be more.
Occam's razor and all that.

 

[PeterDonis]

Often wondered if, during the 13.8B years since the BB, has "local Earth time" always remained exactly the same, with 1s throughout those years always lasting 1s as we experience it now?

Since the definition of "1 second" is based on an atomic process, which hasn't changed, then the second hasn't changed either. In other words, the 13.8B years is equivalent to a definite number of cycles of the atomic process on which the definition of the second is based.

The 13.8billion years is a cosmic time coordinate, extrapolated from our observations of the dynamics of spatial expansion.

This is correct, but it doesn't quite address Tanelorn's question. He's asking (possibly without quite realizing it) whether it's possible that coordinate time in the standard coordinates used in cosmology could have been different from proper time along a comoving worldline in the early universe, even though the two are the same now. The answer to that is, first, that this is not possible if our current cosmological model is correct (or even approximately correct), and second, we have evidence that the physical constants governing the processes we use to measure proper time, such as atomic clocks, have not changed from then to now.

 

[Garth]

ok then. Anybody disagree with PeterDonis?

I would like to make a few observations.

In order to measure a clock drift you need two different types of clock that run on different physical principles.

If part of the Pioneer anomaly is caused by a clock drift then there would be a discrepancy between the 'atomic clock' (the period of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom) behind the apparatus transmitting and receiver the radio pulses and the 'gravitational clock' (the period of the orbit of a test particle) used in Newtonian (and GR) gravitation determining the position of the spacecraft in its trajectory.

In standard physics these two clock systems remain synchronised over cosmological time scales.

However the frequency of the radiation emitted by a caesium 133 atom (and any other atomic process) is proportional to atomic particle mass, so standard theory assumes that these masses are constant, and the period of an orbiting test particle depends of GM being constant. A clock drift explanation of the PA (or part of it) would indicate that either particle masses or GM are actually varying.

The nature of science is not to dogmatically insist on standard theory discovered so far but to constantly test it.

Perhaps the PA is such a test.

Note although the PA can be explained by 'normal' physics it has only just been so resolved by taking every possible source of acceleration on the spacecraft and vector summing the maximum values within their error bars together as if they were all were at these maximum values and acting in the same direction. IMHO a more reasonable assumption would be that they are not all at these maximum values and do not all act in the same direction so the sunwards component of the vector addition explains only part of the PA. The remaining acceleration seems interestingly close to cH: Hubble acceleration.

We can define two physically significant ‘clocks’ as follows:

Sample two photons, one emitted by a caesium atom the other sampled from the CMB radiation.

The first definition of an ‘atomic’ second, is defined as the duration of exactly 9.19263177x10⁹ periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. This is the standard physical definition of a second.

The second, a ‘photonic’ second, can be defined as the duration of exactly 1.604x10¹¹ periods of the radiation corresponding to the peak of the CMB black body spectrum.

Both systems of time measurement are physically significant and agree with each other in the present time, although they will diverge from each other at other times.

If gravitational time actually follows the 'photonic second' then the clock drift between the two time systems would be cH.

Just a thought...

Garth

 

[Jonathan Scott]

Surely if the rate of time were changing that is in principle detectable, because as we look into the distance we are looking back in time, so we can compare the time rate now with the past. The effect of a gradually increasing time rate would be similar to cosmological redshift, but in theory it would be possible to distinguish the effect because an object at a fixed distance would still show the redshift.

 

[PeterDonis]

The first definition of an ‘atomic’ second, is defined as the duration of exactly 9.19263177x10^9 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. This is the standard physical definition of a second.

The second, a ‘photonic’ second, can be defined as the duration of exactly 1.604x10¹¹ periods of the radiation corresponding to the peak of the CMB black body spectrum.

Only the first of these definitions corresponds to proper time as it appears in the mathematical model. So only the first corresponds to the time we use to define the "age of the universe". And our standard physics does predict that these two "seconds" will diverge as we look further into the past; so this "definition" is not in any way a change in standard physics.

If gravitational time actually follows the 'photonic second'

What is "gravitational time"? Meaning, what actual math are you referring to by this term? It has no meaning in standard physics.

 

[PeterDonis]

if the rate of time were changing

What is "the rate of time"? What actual math are you referring to by this term?

 

[Jonathan Scott]

What is "the rate of time"? What actual math are you referring to by this term?

Whatever is shown by a standard clock, such as one which counts the frequency of some atomic transition. If today's clocks ran a tiny bit faster than yesterday's, then if we observed a clock at sufficient distance it would appear to be running a little slow, in a similar way to the effect of cosmological redshift, but at a constant distance (which of course we would need some other way of measuring). Of course, one could shuffle around definitions to model the effect in other ways, but the result would be the same.

 

[PeterDonis]

Whatever is shown by a standard clock, such as one which counts the frequency of some atomic transition.

In other words, you're using Garth's definition #1. Then the way to spot changes in this "rate of time" is to look for changes in the dimensionless physical constants that govern the process--in the case of our current standard definition of the second, this would be the fine structure constant $\alpha$. We have found no evidence of such changes between the early universe and now.

If today's clocks ran a tiny bit faster than yesterday's, then if we observed a clock at sufficient distance it would appear to be running a little slow, in a similar way to the effect of cosmological redshift, but at a constant distance (which of course we would need some other way of measuring).

Yes, looking for anomalies in the relationship between redshift and, for example, luminosity (which is one way of independently estimating distance), is one way of looking for changes in the fine structure constant. As I said above, we have found no evidence of any such changes.

 

[Garth]

Only the first of these definitions corresponds to proper time as it appears in the mathematical model. So only the first corresponds to the time we use to define the "age of the universe". And our standard physics does predict that these two "seconds" will diverge as we look further into the past; so this "definition" is not in any way a change in standard physics.

I agree, I was not introducing any new physics here, just defining a second by two different methods, using two different physical processes to define two different clocks, but ones that would not remain synchronised.

What is "gravitational time"? Meaning, what actual math are you referring to by this term? It has no meaning in standard physics.

I mean that as measured by a gravitational clock, that defined in my post as being measured by the orbital period of a test particle, i.e the time that is used in Newtonian gravity and General Relativity.

Garth

 

[Jonathan Scott]

In other words, you're using Garth's definition #1. Then the way to spot changes in this "rate of time" is to look for changes in the dimensionless physical constants that govern the process--in the case of our current standard definition of the second, this would be the fine structure constant αα\alpha. We have found no evidence of such changes between the early universe and now.

I'm not convinced that it is necessarily the case that we would see any changing physics.

Suppose for example that we were in a region where the gravitational potential was slowly increasing (which could for example be artificially constructed by moving a ring of material away from us). Our clocks would be gradually getting faster relative to distant objects, but we would observe standard physics everywhere. If the same effect as an increasing gravitational potential could happen due to some unknown physics, this would be similar to a changing time rate.

 

[PeterDonis]

I mean that as measured by a gravitational clock, that defined in my post as being measured by the orbital period of a test particle

Ah, ok. So here the comparison will be between an atomic process governed by $\alpha$ and a gravitational process governed by the spacetime geometry. But that still leaves a question: orbital period around what?

If you just have an ordinary gravitationally bound system, like a star and a planet, whose center of mass is moving on a comoving worldline in FRW spacetime, then the "gravitational time" defined by this system will not change relative to $\alpha$ between the early universe and how, because bound systems are unaffected by the expansion of the universe.

If you are imagining some kind of "orbiting test particle" whose period is affected by the expansion of the universe, can you describe such a system in more detail?

i.e the time that is used in Newtonian gravity and General Relativity.

I don't understand what you mean by this; "time" in these theories is not defined by the orbital periods of test particles. Those orbital periods are derived quantities which assume that you have a particular solution of the appropriate equations already in hand, and such a solution will already have a definition of time included in it. (In Newtonian gravity, time is absolute so the definition is the same for all solutions; in GR we have coordinate time, which is defined by your choice of coordinates, and proper time, which is defined by the metric. All of those things are logically prior to any computation of the orbital periods of test particles.)

 

[PeterDonis]

Suppose for example that we were in a region where the gravitational potential was slowly increasing (which could for example be artificially constructed by moving a ring of material away from us). Our clocks would be gradually getting faster relative to distant objects, but we would observe standard physics everywhere.

We would observe the same $\alpha$ everywhere (by hypothesis); but if we made observations of objects outside the ring of material, we would definitely see the difference in "rate of time flow". However, that would be because the two "clocks" in question (ours and the one outside the ring of material) would be separated by the ring of material, i.e., by a large concentration of stress-energy that would affect the spacetime geometry. So we could correlate the difference in "rate of time flow" to the difference in spacetime geometry, and once we had factored that in, we could then run independent tests of whether $\alpha$ had changed.

That is the sort of thing I mean when I say we have no evidence of $\alpha$ changing from the early universe to now: I mean that we first account for all the effects of the spacetime geometry of the universe between then and now, based on our best current models, and then we look for effects that cannot be explained by that.

 

[Garth]

Ah, ok. So here the comparison will be between an atomic process governed by $\alpha$ and a gravitational process governed by the spacetime geometry. But that still leaves a question: orbital period around what?

If you just have an ordinary gravitationally bound system, like a star and a planet, whose center of mass is moving on a comoving worldline in FRW spacetime, then the "gravitational time" defined by this system will not change relative to $\alpha$ between the early universe and how, because bound systems are unaffected by the expansion of the universe.

If you are imagining some kind of "orbiting test particle" whose period is affected by the expansion of the universe, can you describe such a system in more detail?

I am imagining theories in which G may vary - such as in the Brans Dicke theory or in which atomic/particle masses may vary such as in Hoyle's http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1975ApJ...196..661H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

Garth said: ↑i.e the time that is used in Newtonian gravity and General Relativity.

I don't understand what you mean by this; "time" in these theories is not defined by the orbital periods of test particles. Those orbital periods are derived quantities which assume that you have a particular solution of the appropriate equations already in hand, and such a solution will already have a definition of time included in it. (In Newtonian gravity, time is absolute so the definition is the same for all solutions; in GR we have coordinate time, which is defined by your choice of coordinates, and proper time, which is defined by the metric. All of those things are logically prior to any computation of the orbital periods of test particles.)

Yes indeed, time as measured by a clock is always a derived quantity, derived from the theory describing the internal workings of that particular clock. I also agree that relativity theory introduces the added complication of different time rates as observed when compared between different observers on different world-lines. In the case of the PA though, and in my musings on a possible time drift, we are considering two different types of clock used by the same observer.

Garth

 

[Jonathan Scott]

That is the sort of thing I mean when I say we have no evidence of $\alpha$ changing from the early universe to now: I mean that we first account for all the effects of the spacetime geometry of the universe between then and now, based on our best current models, and then we look for effects that cannot be explained by that.

If for example due to some unknown physics there was an effect as if the whole observable universe were at a steadily increasing gravitational potential, increasing the rate of all clocks, then I do not think that would produce any observable physical effect that would be easily distinguishable from cosmological redshift unless it were sufficiently strong that we could detect it at a distance close enough to be measurable via some other means.

Of course, I'm unaware of any evidence of such a thing, and I think the Pioneer Anomaly is sufficiently well explained (by radiation pressure) that any remaining doubts are not strong enough to provide much evidence for any non-standard physics.

 

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I have a strong intuition that this makes sense, as you say,

Surely if the rate of time were changing that is in principle detectable, because as we look into the distance we are looking back in time, so we can compare the time rate now with the past.

but doesn't this test

The effect of a gradually increasing time rate would be similar to cosmological redshift, but in theory it would be possible to distinguish the effect because an object at a fixed distance would still show the redshift.

lead to paradoxical lack of reciprocity? Two observers at a fixed distance to one another would both observe each other's clocks falling gradually behind. What happens if they accelerate equally to come together? Non-reciprocity is solved in relativity by accelerating (or gravitational) frames of reference, but here the observers can be in identical gravitational wells with identical histories of acceleration, so it doesn't work. I think the clock drift only makes sense as an an error in distance measurement between 2 observers at rest relative to one another, maybe based on an intrinsic drift in photon frequency. To see the clocks losing time, the 2 observers would have to be moving apart.

If this conjecture were true, would there be any meaningful difference between a clock drift and a redshift?

If for example due to some unknown physics there was an effect as if the whole observable universe were at a steadily increasing gravitational potential, increasing the rate of all clocks, then I do not think that would produce any observable physical effect that would be easily distinguishable from cosmological redshift unless it were sufficiently strong that we could detect it at a distance close enough to be measurable via some other means.

 

[PeterDonis]

I am imagining theories in which G may vary

This adds further complications, since $G$ is not a dimensionless constant.

such as in the Brans Dicke theory or in which atomic/particle masses may vary such as in Hoyle's http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1975ApJ...196..661H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

AFAIK both of these, at least in any regime where they would make predictions significantly different from standard GR, are ruled out by observation.

If for example due to some unknown physics there was an effect as if the whole observable universe were at a steadily increasing gravitational potential

As I've already pointed out in this thread (and in plenty of previous discussions with you), the concept of "gravitational potential" makes no sense in a non-stationary spacetime. (Note that in the paper the OP cited where this concept is used, the term "gravitational potential" is never defined; it's just hand-waved into existence.) Please bear in mind the PF rules about speculative or personal theories. If you can give a mainstream reference that defines the concept of "gravitational potential" in a non-stationary spacetime, then we can discuss it. Otherwise it's off topic here.

I have a strong intuition that this makes sense

Your intuition is incorrect, as I've already pointed out. See above.

 

[Jonathan Scott]

As I've already pointed out in this thread (and in plenty of previous discussions with you), the concept of "gravitational potential" makes no sense in a non-stationary spacetime. (Note that in the paper the OP cited where this concept is used, the term "gravitational potential" is never defined; it's just hand-waved into existence.) Please bear in mind the PF rules about speculative or personal theories. If you can give a mainstream reference that defines the concept of "gravitational potential" in a non-stationary spacetime, then we can discuss it. Otherwise it's off topic here.

"Potential" is just the conventional Newtonian terminology for the relative fractional difference in the time component of the metric at different locations in a frame where the sources are approximately at rest, which seems quite clear to me. This can be as stationary as you like; we are not talking about strong fields or relativistic source velocities.

All I've been trying to say is that I think we do have a way in theory to detect an intrinsic change in the flow of time, but it wouldn't necessarily show up in any changed physics at a distance, as we are already familiar with slightly different rates of time due to gravity. Instead, it would look for most purposes like a form of redshift.

To improve my earlier example, consider a large region surrounded by a slowly expanding shell of masses, as mapped in a distant coordinate system. The time rate within that region would be increasing with the potential. It seems that it might be theoretically possible for an observer somewhere in that region to detect by a light-speed delay that the time rate elsewhere in the region was a tiny bit slower earlier, although that would also require being able to measure distance to the same accuracy to ensure that the effect was not due to Doppler shift.

 

[GeorgeDishman]

the way to spot changes in this "rate of time" is to look for changes in the dimensionless physical constants that govern the process--in the case of our current standard definition of the second, this would be the fine structure constant α\alpha. We have found no evidence of such changes between the early universe and now

I'm not convinced that it is necessarily the case that we would see any changing physics.

You wouldn't see any difference in the physics in the sense that the same equations would characterise the same processes, but the value of the constant could be different. A direct comparison at first seems tricky because a change in alpha affecting all spectral lines would have the same effect as redshift, they appear degenerate. However, while some lines depend on $\alpha$, others depend on its square. The ratio of the redshift of such lines can therefore be used to determine any change in $\alpha$ independently of redshift. Webb et al did that and also used VLT/UVES and Pinho and Martins have repeated the analysis with a slightly larger dataset going back to a redshift around 4.2 (>12 billion years). They show a possible dependence on a dipole spatial term but found no evidence for a change as a function of time. The effects are at the level of less than 10 parts per million.

The possibility of systematics between telescopes and between different classes of targets raise concerns in my mind. It is also noticeable that Pinho and Martins provide tables for spatial-only and spatial-plus-redshift variations but not for a redshift-only correlation. I suspect these are the result to which PeterDonis is referring and would like to hear his opinion on them.

[edit]

it wouldn't necessarily show up in any changed physics at a distance, as we are already familiar with slightly different rates of time due to gravity. Instead, it would look for most purposes like a form of redshift.

I posted at nearly the same time as Jonathan. Any change should show up in the frequency of atomic transitions, i.e. spectral lines, and while a simple dependence cannot be distinguished from cosmological redshift, the quadratic dependence of some lines breaks the degeneracy.

 

[Jonathan Scott]

You wouldn't see any difference in the physics in the sense that the same equations would characterise the same processes, but the value of the constant could be different.

I know that we could see effects at a distance that would allow us to detect a change in the fine structure constant, but I don't think that's relevant here.

I was just trying to answer the original question:

I'm asking if we could make a practical experiment to detect something like it, or if it could even be logically possible for such an effect to exist.

I believe it's logically possible for such an effect to exist, as I think gravity can cause similar effects. For an effect of similar magnitude to the Pioneer Anomaly, it would obviously not be easy to confirm or refute it experimentally, but without a clear model of exactly how this scheme would vary from standard theory I can't be specific.

 

[PeterDonis]

"Potential" is just the conventional Newtonian terminology for the relative fractional difference in the time component of the metric at different locations in a frame where the sources are approximately at rest, which seems quite clear to me. This can be as stationary as you like; we are not talking about strong fields or relativistic source velocities.

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.

All I've been trying to say is that I think we do have a way in theory to detect an intrinsic change in the flow of time

What you are calling "an intrinsic change in the flow of time" is just a difference in "rate of time flow" along different worldlines due to the spacetime geometry. This is predicted by standard GR. In a stationary scenario, you can describe these effects in terms of a "potential"; but not in a scenario which is not even close to stationary, which is what we are talking about in this thread.

I know that we could see effects at a distance that would allow us to detect a change in the fine structure constant, but I don't think that's relevant here.

It isn't what the OP was originally asking about, but it is relevant to the additional considerations that Garth raised.

 

[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.