How to prove the stretching of space

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  • #1
timmdeeg
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Hi,

according to several scientists, among them

J.A.Peacock: A diatribe on expanding space
M.J.Chodorowski: The kinematic component of the cosmological redshift
E.F.Bunn&D.W.Hogg: The kinematic origin of the cosmological redshift

space doesn't expand, instead the cosmological redshift is due to a combined kinematic/gravitational effect. Peacock is author of the book "Cosmological Physics".
An interesting consequence is e.g. "Summing up, the expansion of the universe is never superluminal", Chodorowski.

The Maxwell-Equations don't have a "stretching" term, but it seems a plausible assumption that the streching of space goes along with the stretching of a photon's wavelength, though - at least to my knowledge - there is no fundamental physical explanation for that. Or am I wrong?

This leads to my question, if and how the stretching of space could in principle be proved experimentally.

One can imaging long-living physicists in the center of a large void (they don't see galaxies), which supposedly expands because of its subcritical energy density, equipped with all necessary tools like watches, metersticks, ropes, light-pulse-generators, redshift analysis, whatsoever.

With which kind of experiment could the physicists prove the stretching of space?
 

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  • #2
Chalnoth
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There are multiple ways of describing the universe that are mutually-compatible. The Bunn & Hogg paper that you cite makes this explicit:

"We show that an observed frequency shift in any spacetime can be interpreted either as a kinematic (Doppler) shift or a gravitational shift by imagining a suitable family of observers along the photon’s path."

In other words, it is perfectly-valid to talk about the redshift either as coming from the motions of galaxies, or as coming from the stretching of space. The stretching of space interpretation is, however, mathematically simpler in many respects, and doesn't have weird effects at the edge of the visible universe. But it is always useful to realize that there are other ways of describing the universe.
 
  • #3
bapowell
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The Maxwell-Equations don't have a "stretching" term, but it seems a plausible assumption that the streching of space goes along with the stretching of a photon's wavelength, though - at least to my knowledge - there is no fundamental physical explanation for that. Or am I wrong?
From general relativity (specifically, the geodesic equation), it is seen that the momentum of a particle is inversely proportional to the expansion (the scale factor, a(t)). From de Broglie, this becomes a statement about the wavelength of photons -- as space expands, the wavelength of light must increase.
 
  • #4
Chronos
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The integrated Sachs-Wolf effect is the clearest, independent [of supernova], evidence of dark energy [the strange anti-gravity effect that powers expansion]. The sloan digital sky survey [SDSS] confirmed this effect to better than 4 sigma - which is almost good enough to be considered conclusive even by particle physics standards. Photons entering a large gravitational well [like a galactic supercluster] get a gravitional energy boost upon entering the region causing a small gravitational blue shift. Upon exiting, they lose this free energy and redshift back to their original energy state upon exiting - almost. If the universe were flat and static, the net effect would be zero. In an expanding universe, the photon takes so long to pass through the gravity well that it gets to keep a small amount of the blue shift it acquired on the way in due to expansion and the resulting dilution of gravity. This extra energy shows up as a slight anisotropy in the CMB photons passing through a supercluster or supervoid [the effect is just the opposite for CMB photons passing through a supervoid]. See http://arxiv.org/abs/0805.3695 for discussion.
 
  • #5
timmdeeg
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There are multiple ways of describing the universe that are mutually-compatible. The Bunn & Hogg paper that you cite makes this explicit:

"We show that an observed frequency shift in any spacetime can be interpreted either as a kinematic (Doppler) shift or a gravitational shift by imagining a suitable family of observers along the photon’s path."

In other words, it is perfectly-valid to talk about the redshift either as coming from the motions of galaxies, or as coming from the stretching of space. The stretching of space interpretation is, however, mathematically simpler in many respects, and doesn't have weird effects at the edge of the visible universe. But it is always useful to realize that there are other ways of describing the universe.
Bunn & Hogg talk about the kinematic shift (motion of galaxies) and the gravitational shift as an alternative view and then identify the former as more natural. However none of these views coincides with the "stretching of space" notion.

In contrast, Bunn & Hogg criticize this notion (page 8):

"The common belief that the cosmological redshift can only be explained in terms of the stretching of space is based on conflating the properties of a specific coordinate system with properties of space itself. This confusion is precisely the opposite of the correct frame in mind in which to understand relativity."

Supposing that stretching belongs to the "properties of space itself", shouldn't this be measurable?
 
  • #6
timmdeeg
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From general relativity (specifically, the geodesic equation), it is seen that the momentum of a particle is inversely proportional to the expansion (the scale factor, a(t)). From de Broglie, this becomes a statement about the wavelength of photons -- as space expands, the wavelength of light must increase.
This is very interesting approach. Usually the geodesic equation deals with the momentum of particles having a rest mass. A photon has momentum, but no rest mass. Is it compulsory that this equation is valid for photons too, via de Broglie? Could you show an article? Thanks.
 
  • #7
bapowell
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Usually the geodesic equation deals with the momentum of particles having a rest mass.
Why do you say this? The geodesic equation describes massless particles as well.
 
  • #8
timmdeeg
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The integrated Sachs-Wolf effect is the clearest, independent [of supernova], evidence of dark energy [the strange anti-gravity effect that powers expansion]. ...
Yes, the discovery of accelerated expansion seems to support the stretching of space view.
But I suspect the authors I named would argue that during the parallel transport of the velocity four-vectors along the path of the photon any changes of the rate of the expansion of the universe are included. Thus, it seems still possible to argue that the cosmological redshift is due to kinematic/gravitational effects. However I am not sure myself at all.
 
  • #9
timmdeeg
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Why do you say this? The geodesic equation describes massless particles as well.
Yes, sorry I was wrong (forgot the null geodesic:redface:). So, your explanation why λ goes with a(t) is very convincing and new to me, thanks.
 
  • #10
Chalnoth
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Bunn & Hogg talk about the kinematic shift (motion of galaxies) and the gravitational shift as an alternative view and then identify the former as more natural. However none of these views coincides with the "stretching of space" notion.

In contrast, Bunn & Hogg criticize this notion (page 8):

"The common belief that the cosmological redshift can only be explained in terms of the stretching of space is based on conflating the properties of a specific coordinate system with properties of space itself. This confusion is precisely the opposite of the correct frame in mind in which to understand relativity."
The "stretching of space" picture is precisely the picture under which the redshift is a gravitational phenomenon. What they are saying is that this is simply an interpretation, and there are other ways of understanding the redshift. They claim that their way is somehow more natural (this is open to debate: which is more natural is more about personal preference than it is about the universe).

My main point is that the "stretching of space" picture is mathematically simple for many calculations, and so most people working in the field will naturally default to this view out of simple pragmatism.

The Bunn & Hogg paper is, to me, mostly useful in terms of showing that we should be careful as to whether some apparent fact of the universe is a real fact, or simply a result of a particular interpretation that disappears if we look at the universe a bit differently. The recession velocity of galaxies is one such fact: what the recession velocity of a given galaxy is depends entirely upon your coordinate choice. You'll get very different answers for the "stretching of space" and "things moving apart" views.
 
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  • #11
timmdeeg
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Thank you for answering, Chalnoth,

I agree with most of that, but have still a problen with your statement:

The "stretching of space" picture is precisely the picture under which the redshift is a gravitational phenomenon.
Why do I have this choice? With regard to the Pound-Rebka experiment we talk about a fixed distance.

The result - the photon's stretched wavelength - is the same. But the physical reasons, climbing in a gravitational field versus travelling through stretching space is much different and hence not subject of personal preference.

I must have missed something, where am I wrong?
 
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  • #12
Chalnoth
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The result - the photon's stretched wavelength - is the same. But the physical reasons, climbing in a gravitational field versus travelling through stretching space is much different and hence not subject of personal preference.
Except it is the subject of personal preference, because the ultimate cause of the redshift is entirely a result of the coordinate system you choose to use. That's the entire point: whether the redshift is a result of gravitation or velocity is not a physical question at all, as the answer depends upon your coordinates. The redshift itself is physical, but the distinction between the doppler effect and gravitational redshift is not.
 
  • #13
timmdeeg
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That's the entire point: whether the redshift is a result of gravitation or velocity is not a physical question at all, as the answer depends upon your coordinates. The redshift itself is physical, but the distinction between the doppler effect and gravitational redshift is not.
And presumably the distinction between the doppler effect and the stretching of space is not a physical question as well. Here I would like to mention, that both, Peacock and Chodorowski don't interpret the cosmological redshift as purely kinematic (in contrast to B&H). Chodorowski, page 9: "in a non-empty Universe there is a gravitational field, inducing a gravitational shift. Therefore, with an exception of the empty model, the origin of the cosmological redshift must be partly gravitational." To my understanding Chodorowski thus distinguishes very well different physical reasons of the redshift. Also Peacock's Equation (16) shows the combined effect of velocity and gravity.

All this in mind I still miss the meaning of your remark "whether the redshift is a result of gravitation or velocity is not a physical question at all, as the answer depends upon your coordinates." You seem to say that the physical result, the stretched wavelength, originates from mathematics, not from physics. :confused:
 
  • #14
Chalnoth
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And presumably the distinction between the doppler effect and the stretching of space is not a physical question as well. Here I would like to mention, that both, Peacock and Chodorowski don't interpret the cosmological redshift as purely kinematic (in contrast to B&H). Chodorowski, page 9: "in a non-empty Universe there is a gravitational field, inducing a gravitational shift. Therefore, with an exception of the empty model, the origin of the cosmological redshift must be partly gravitational." To my understanding Chodorowski thus distinguishes very well different physical reasons of the redshift. Also Peacock's Equation (16) shows the combined effect of velocity and gravity.

All this in mind I still miss the meaning of your remark "whether the redshift is a result of gravitation or velocity is not a physical question at all, as the answer depends upon your coordinates." You seem to say that the physical result, the stretched wavelength, originates from mathematics, not from physics. :confused:
What I am saying is that it is only coordinate-invariant quantities that are truly physical. Anything else depends upon the numbers we use to describe the space-time, and thus must be at least partly due to our choice of those numbers. As it turns out, neither the strength of the gravitational field nor the velocity of far-away objects is a coordinate-invariant quantities.
 
  • #15
timmdeeg
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What I am saying is that it is only coordinate-invariant quantities that are truly physical.
Like mass. And the redshift itself, as you mentioned. If I understand you correctly energy then is not truly physical. But I am free to measure energy in a given coordinate-system.

At least in that sense, the stretching of space should be measurable. When a gravitational wave passes by, the change of spacing of two testmasses relative to coordinates provided by meter-sticks is measurable using interferometry techniqes. An analogue measurement should be possible in a void. What happens to two testmasses, which initially are at rest relative to each other and then are allowed to move freely. They don't get a kick. Will their distance measured with meter-sticks increase over time?
In the case of a receding galaxie we have nothing but a redshift which we can interpret. In the void we have distances additionally. Is the moving apart from each other (provided that happens) still a matter of interpretation?

Thanks for your valuable comments.
 
  • #16
Chalnoth
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Like mass. And the redshift itself, as you mentioned. If I understand you correctly energy then is not truly physical. But I am free to measure energy in a given coordinate-system.
Well, energy is at least a coordinate covariant quantity, meaning that if you measure energy in your coordinate system, I can figure out what it is in my coordinate system just fine.

At least in that sense, the stretching of space should be measurable. When a gravitational wave passes by, the change of spacing of two testmasses relative to coordinates provided by meter-sticks is measurable using interferometry techniqes. An analogue measurement should be possible in a void. What happens to two testmasses, which initially are at rest relative to each other and then are allowed to move freely. They don't get a kick. Will their distance measured with meter-sticks increase over time?
The problem with doing the measurement in a void is you'd need to do it in an expanding void, which means having the test masses extremely far apart and far away from any other matter in the universe, which makes it an undoable experiment (at least for the forseeable future). This is because the local space-time around massive objects is not expanding.

In the case of a receding galaxie we have nothing but a redshift which we can interpret. In the void we have distances additionally. Is the moving apart from each other (provided that happens) still a matter of interpretation?
The increase in measured distances is real. But whether you interpret this increase in distances as a velocity is, well, up to your interpretation.
 
  • #17
timmdeeg
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The increase in measured distances is real. But whether you interpret this increase in distances as a velocity is, well, up to your interpretation.
Ok, thanks for clarifying my questions.
 
  • #18
Except it is the subject of personal preference, because the ultimate cause of the redshift is entirely a result of the coordinate system you choose to use. That's the entire point: whether the redshift is a result of gravitation or velocity is not a physical question at all, as the answer depends upon your coordinates. The redshift itself is physical, but the distinction between the doppler effect and gravitational redshift is not.
The question of interpretations of the cosmic redshift in Robertson-Walker (RW) models is not a
question about a choice of coordinates. The reason for this is simple: in the RW-models there is a
set of "preferred" observers (the so-called "fundamental observers" (FOs)) defining the cosmic redshift; i.e., the high symmetry of the RW-manifolds implies that they can be foliated in a "preferred" way such that the spatial hypersurfaces are homogeneous and isotropic. The FOs are those observers always moving orthogonally to the "preferred" hypersurfaces. The cosmic redshift is then defined as that obtained by exchanging pulses of electromagnetic radiation between the FOs.
This means that the cosmic redshift is in principle an observational result defined via specific observers, and that cannot be dependent on a choice of coordinates.

Moreover, it is possible (at least for sufficiently small regions) to change the geometry of the RW-models from curved to flat but holding the world lines of the FOs and the coordinate system fixed. One may then compare the cosmic redshift calculated in the two cases, and in general the two results will differ (these calculated results are of course independent of the choice of coordinate system). In particular, it is possible that the redshift may vanish in the flat space-time case (this happens for all RW-models with flat or spherical space sections). In these cases it is obvious that the cosmic redshift is entirely due to space-time curvature so that any interpretation in terms of a Doppler shift in flat space-time is mathematically inconsistent with the RW-model.

In sum, the question of interpretations of cosmic redshifts as described by the RW-models is not a subject of personal preference, but rather depends on the geometrical properties of the particular RW-manifold under consideration. This is a mathematical fact, and no arguments based on personal gut-feelings can change that.
 
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  • #19
Chalnoth
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The question of interpretations of the cosmic redshift in Robertson-Walker (RW) models is not a
question about a choice of coordinates. The reason for this is simple: in the RW-models there is a
set of "preferred" observers (the so-called "fundamental observers" (FOs)) defining the cosmic redshift;
Just because one choice of observers makes the universe more symmetric doesn't mean you can't choose some other set of observers instead. The math may not be quite as nice if you do that, but it is an equally-valid thing to do.
 
  • #20
Just because one choice of observers makes the universe more symmetric doesn't mean you can't choose some other set of observers instead. The math may not be quite as nice if you do that, but it is an equally-valid thing to do.
But the fact is that the cosmological redshift in the RW-models is DEFINED in terms of a set of particular
observers (the FOs). This means that choosing some other set of observers is simply irrelevant and confuses the issue. That is, in principle the redshifts defined by these alternative observers have nothing to do with cosmological redshifts.
 
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  • #21
Chalnoth
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But the fact is that the cosmological redshift in the RW-models is DEFINED in terms of a set of particular
observers (the FOs). This means that choosing some other set of observers is simply irrelevant and confuses the issue. That is, in principle the redshifts defined by these alternative observers have nothing to do with cosmological redshifts.
Only the observer who is actually measuring the redshift and the rest frame of the emitting matter. But the coordinates do not matter, and the coordinates determine whether we think of that redshift as being gravitational or doppler (or some mixture of the two).
 
  • #22
timmdeeg
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But the fact is that the cosmological redshift in the RW-models is DEFINED in terms of a set of particular
observers (the FOs). This means that choosing some other set of observers is simply irrelevant and confuses the issue. That is, in principle the redshifts defined by these alternative observers have nothing to do with cosmological redshifts.
To my understanding the cosmological redshift in the Milne Cosmos is a Dopplershift, but is due to expansion in the empty FRW Universe. Comoving observers can be defined for both cases. If that is correct, the choice of the interpretation of the redshift depends on a transformation of coordinates, not on physics.

In this view (I might be wrong) I don't understand your remark, that the other set of observers (Milne, e.g.) is irrelevant. Arn't there just interchangeable discriptions for the same universe? Why then have a preference for one of these? If it contains mass, I guess these discriptions are more complicated which however shouldn't influence in principle the reasoning.
 
  • #23
Chalnoth
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To my understanding the cosmological redshift in the Milne Cosmos is a Dopplershift, but is due to expansion in the empty FRW Universe. Comoving observers can be defined for both cases. If that is correct, the choice of the interpretation of the redshift depends on a transformation of coordinates, not on physics.
Milne is actually a change in the geometry, and does lead to real changes in redshifts. Those changes are small out to some pretty impressive differences, but they are there.
 
  • #24
Only the observer who is actually measuring the redshift and the rest frame of the emitting matter. But the coordinates do not matter, and the coordinates determine whether we think of that redshift as being gravitational or doppler (or some mixture of the two).
Coordinates are irrelevant for interpretations of redshifts in the RW-models. What matters is the choice of observers emitting and receiving electromagnetic radiation being redshifted (but these observers are not chosen arbitrary since they are specific observers determined from the symmetry of the RW-manifolds), plus the space-time geometry of the RW-manifold under consideration. Nothing else matters and only confuses the issue.

In particular, it does not make sense to choose some other observers and define the redshifts measured by those as "cosmological redshifts". For example, given a RW-model with flat space sections, one may choose some arbitrary FO and approximate the scale factor with a Taylor series truncated after the linear term in a small region around the chosen FO. This yields a velocity field mimicking the Hubble law in flat space-time in the small region. But the observers defining this velocity field cannot be identified with the FOs since their world lines are different from those of the FOs. (The FOs yield no cosmological redshift in the flat space-time approximation for RW-models with flat space sections.) This means that one gets something else than the Hubble law if one uses these alternative observers in the curved RW-manifold one started out with. So said procedure is indeed irrelevant for interpretations of the cosmological redshift found from the given RW-model, and choosing other observers than the FOs to define "cosmological redshifts" does not yield consistent results.
 
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  • #25
Chalnoth
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Coordinates are irrelevant for interpretations of redshifts in the RW-models. What matters is the
choice of observers emitting and receiving electromagnetic radiation being redshifted (but these
observers are not chosen arbitrary since they are specific observers determined from the symmetry of the RW-manifolds), plus the space-time geometry of the RW-manifold under consideration. Nothing else matters and only confuses the issue.
There is only one emitter and one receiver for a given redshift observation. And you don't actually have to make a coordinate choice that is stationary with regard to either one, let alone stationary with regard to hypothetical observers along the path of the light ray.
 

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