How to prove the stretching of space

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In summary: If you measure the frequency of a light signal as it travels through space, you'll find that the frequency of the signal has shifted. This shift is called the cosmological redshift. According to several scientists, among them J.A.Peacock of the University of Portsmouth in the United Kingdom, the cosmological redshift is not a sign that space is expanding, but is instead the result of a combined kinematic/gravitational effect. Peacock is author of the book "Cosmological Physics".
  • #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
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
timmdeeg said:
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
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 gravitational 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
Chalnoth said:
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
bapowell said:
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
timmdeeg said:
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
Chronos said:
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
bapowell said:
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
timmdeeg said:
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
Thank you for answering, Chalnoth,

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

Chalnoth said:
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 traveling 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
timmdeeg said:
The result - the photon's stretched wavelength - is the same. But the physical reasons, climbing in a gravitational field versus traveling 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
Chalnoth said:
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
timmdeeg said:
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
Chalnoth said:
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
timmdeeg said:
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.

timmdeeg said:
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.

timmdeeg said:
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
Chalnoth said:
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
Chalnoth said:
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
Old Smuggler said:
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
Chalnoth said:
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
Old Smuggler said:
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
Old Smuggler said:
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
timmdeeg said:
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
Chalnoth said:
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
Old Smuggler said:
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.
 
  • #26
timmdeeg said:
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.
The Milne model is equivalent to an empty RW-manifold and is mathematically a subset of Minkowski space-time. The FOs are those observers moving orthogonally to the "preferred" hypersurfaces (with hyperbolic geometry) foliating this RW-manifold. There is no alternative set of observers involved here. Since this RW-manifold is flat, the corresponding cosmological redshifts must of course be interpreted as Doppler shifts in flat space-time. This has nothing to do with transformations of coordinates.
timmdeeg said:
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.
What alternative set of observers do you have in mind? Perhaps you are thinking of the set of (non-expanding) observers moving orthogonally to some foliation of Minkowski space-time into flat hypersurfaces? If so, yes, these observers are irrelevant for interpretations of cosmological redshifts in the empty RW-model.
(Note that the empty RW-manifold is only a SUBSET of Minkowski space-time, so the FOs and these alternative observers do not really describe "the same universe".)
 
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  • #27
Old Smuggler said:
The Milne model is equivalent to an empty RW-manifold and is mathematically a subset of Minkowski space-time. The FOs are those observers moving orthogonally to the "preferred" hypersurfaces (with hyperbolic geometry) foliating this RW-manifold. There is no alternative set of observers involved here. Since this RW-manifold is flat, the corresponding cosmological redshifts must of course be interpreted as Doppler shifts in flat space-time. This has nothing to do with transformations of coordinates.
On the other side the recession velocities depend on the choosen coordinates. In RW coordinates they are a function of the Hubble Constant, whereas in Minkowskian coordinates they are distance/time (Special Relativity). So, according to that the cosmological redshift depends on H, or can be described by the special relativistic Doppler formula, respectively. Hereby I take reference to the thesis of Tamara Davis, Chapter 4 - The empty universe, http://www.dark-cosmology.dk/~tamarad/papers/thesis_complete.pdf.

But as you say, both models (Milne and empty RW) are equivalent, so, the redshifts should not depend on coordinates and are Doppler shifts for both models therefore. Somewhere my reasoning must be wrong. I appreciate any help.

Another point. The empty RW model is negatively curved (and therefore expands?). This curvature means the geometry of space, right? The spacetime is flat, which is common to both models.
 
  • #28
timmdeeg said:
On the other side the recession velocities depend on the choosen coordinates. In RW coordinates they are a function of the Hubble Constant, whereas in Minkowskian coordinates they are distance/time (Special Relativity). So, according to that the cosmological redshift depends on H, or can be described by the special relativistic Doppler formula, respectively. Hereby I take reference to the thesis of Tamara Davis, Chapter 4 - The empty universe, http://www.dark-cosmology.dk/~tamarad/papers/thesis_complete.pdf.
It is not a good idea to introduce coordinate-dependent quantities if they are not directly related to coordinate-free objects. That is, the proper objects to consider are the 4-velocities of the FOs and not some independently defined "recession velocities". The question of what speed to use in the SR Doppler formula is then answered by performing the following procedure (see J.V. Narlikar, American Journal of Physics 62, 903-907 (1994) for the mathematical details). Parallell-transporting the 4-velocity of the emitting FO along a null geodesic to the receiving FO and projecting the resulted parallell-transported 4-velocity into the local rest frame of the receiving FO yields a 3-velocity that can be put into the SR Doppler formula to give the desired redshift. This procedure is independent of any choice of coordinates; it depends only on the 4-velocities of the emitting and receiving FOs and on the space-time geometry.
timmdeeg:4205749 said:
But as you say, both models (Milne and empty RW) are equivalent, so, the redshifts should not depend on coordinates and are Doppler shifts for both models therefore. Somewhere my reasoning must be wrong. I appreciate any help.
The reason for the confusion is that the defined "recession velocities" are not components of any coordinate-free space-time objects. Therfore, any reference to such "recession velocities" is fraught with danger and should be avoided.
timmdeeg:4205749 said:
Another point. The empty RW model is negatively curved (and therefore expands?). This curvature means the geometry of space, right? The spacetime is flat, which is common to both models.
Right.
 
  • #29
Old Smuggler said:
The reason for the confusion is that the defined "recession velocities" are not components of any coordinate-free space-time objects. Therfore, any reference to such "recession velocities" is fraught with danger and should be avoided.

Right.
Thanks.

If I understood you correctly, the redshift observed between FOs depends in the non-empty RW model on whether these are closed, flat, or open and on the space-time curvature and thus not on the choice of coordinates (i). Would you please specify in which cases the redshift is purely gravitational and gravitational/kinematic respectively, including the Lambda-CDM model, the universe in which we live.

(i)
Old Smuggler said:
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.
In the sense, that there is no other choice, so my understanding.
 
  • #30
Thanks to everybody for your explanations.

Chalnoth said:
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.

The increase in measured distances is real. But whether you interpret this increase in distances as a velocity is, well, up to your interpretation.
Perhaps it is legitimate to overcome the problems in the void by imagining a gedanken experiment. But I guess, even then your final statement would be the same. I am free to interpret any increase in distance in this or that way.

So,
Chalnoth said:
The "stretching of space" picture is precisely the picture under which the redshift is a gravitational phenomenon.
we talke about a picture. And therefore the answer is: The stretching of space being not something truly physical can not be measured.

Nevertheless there is
bapowell said:
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.
some physical support for this "picture". It's still a bit confusing, "as space expands, the wavelength of light must increase." You didn't say, "as space is stretched ...", but I wonder, if this was meant. Perhaps one should careful distinguish between expansion and stretching. The universe expands according to a(t), but the expansion isn't necessarily a true stretching of space effect.

Please don't hesitate to correct if I said something wrong.
 
  • #31
timmdeeg said:
So,we talke about a picture. And therefore the answer is: The stretching of space being not something truly physical can not be measured.
That's not an accurate take-away.

The correct statement is that there is a real physical phenomenon here, and one correct description of that phenomenon is that it is a stretching of space. There are other seemingly-different but nevertheless also completely correct descriptions of the exact same physical phenomenon.

This is one of the weird things about physics: it is sometimes possible to describe the exact same thing in seemingly completely different ways, while actually describing the same system. And sometimes the difference is so different that it is hard to believe that it's actually the same system being described (e.g. sometimes you can describe a system using different numbers of spatial dimensions and still be describing the same system).
 
  • #32
If I understood you correctly, the redshift observed between FOs depends in the non-empty RW model on whether these are closed, flat, or open and on the space-time curvature and thus not on the choice of coordinates (i).

Choice of coordinates also DOES affect the outcome. The standard cosmological measure involved comoving coordinates, an observer at rest with respect to the CMBR.

The description of curved 4D spacetime as 'expanding' or 'increasing distances' over time depends on a choice of 3+1D split. We use one that is convenient but not unique.)
 
  • #33
The stretching of space being not something truly physical can not be measured.

Chalnoth posed a wonderfully insightful physical explanation in another discussion:

The integrated Sachs-Wolf effect is the clearest, independent [of supernova], evidence of dark energy [the strange anti-gravity effect that powers expansion]… Photons entering a large gravitational well [like a galactic supercluster] get a gravitational 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]. Seehttp://arxiv.org/abs/0805.3695 for discussion.
 
  • #34
Chalnoth said:
This is one of the weird things about physics: it is sometimes possible to describe the exact same thing in seemingly completely different ways, while actually describing the same system.
Yes, I will have to accept this truth, though being weird. But your remark reminds me strongly of an article of R.L.Jaffe, wherein he shows that the measurable Casimir force can not only be described by vacuum fluctuations (as usual), but without taking reference to the vacuum as a van der Waals force as well.
 
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  • #35
Naty1 said:
If I understood you correctly, the redshift observed between FOs depends in the non-empty RW model on whether these are closed, flat, or open and on the space-time curvature and thus not on the choice of coordinates (i).
Choice of coordinates also DOES affect the outcome. The standard cosmological measure involved comoving coordinates, an observer at rest with respect to the CMBR.
My remark refers to explanations of Old Smuggler. From his perspective "Coordinates are irrelevant for interpretations of redshifts in the RW-models".

Naty1 said:
Chalnoth posed a wonderfully insightful physical explanation in another discussion:
Thanks, I wasn't aware of that but read the paper meanwhile. The independent confirmation of the dark energy is very surprising and confirms the Lambda CMB model. Also, the ISW-effect is in accordance with the stretching of space description.
 
<h2>1. How do we know that space is stretching?</h2><p>Scientists have observed the phenomenon of redshift in light from distant galaxies, which is a result of the stretching of space. This is known as the cosmological redshift and is one of the key pieces of evidence for the expansion of the universe.</p><h2>2. What is the evidence for the stretching of space?</h2><p>In addition to the cosmological redshift, scientists also use the cosmic microwave background radiation and the observed distribution of galaxies to support the theory of the stretching of space. These observations show a uniform expansion of the universe in all directions.</p><h2>3. How does the stretching of space affect the objects within it?</h2><p>The stretching of space does not have a noticeable effect on objects within our own galaxy, as the force of gravity is strong enough to hold them together. However, on a larger scale, the stretching of space can cause the distances between galaxies to increase over time.</p><h2>4. Can we measure the stretching of space?</h2><p>Yes, scientists use a unit called the Hubble constant to measure the rate of expansion of the universe. This constant is determined by measuring the redshift of light from distant galaxies and comparing it to their known distances.</p><h2>5. What does the stretching of space mean for the future of the universe?</h2><p>Based on current observations, it is believed that the stretching of space will continue and eventually lead to the "heat death" of the universe, where all matter and energy will be evenly spread out and the universe will reach a state of maximum entropy.</p>

1. How do we know that space is stretching?

Scientists have observed the phenomenon of redshift in light from distant galaxies, which is a result of the stretching of space. This is known as the cosmological redshift and is one of the key pieces of evidence for the expansion of the universe.

2. What is the evidence for the stretching of space?

In addition to the cosmological redshift, scientists also use the cosmic microwave background radiation and the observed distribution of galaxies to support the theory of the stretching of space. These observations show a uniform expansion of the universe in all directions.

3. How does the stretching of space affect the objects within it?

The stretching of space does not have a noticeable effect on objects within our own galaxy, as the force of gravity is strong enough to hold them together. However, on a larger scale, the stretching of space can cause the distances between galaxies to increase over time.

4. Can we measure the stretching of space?

Yes, scientists use a unit called the Hubble constant to measure the rate of expansion of the universe. This constant is determined by measuring the redshift of light from distant galaxies and comparing it to their known distances.

5. What does the stretching of space mean for the future of the universe?

Based on current observations, it is believed that the stretching of space will continue and eventually lead to the "heat death" of the universe, where all matter and energy will be evenly spread out and the universe will reach a state of maximum entropy.

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