# How to prove the stretching of space

by timmdeeg
Tags: prove, space, stretching
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P: 4,598
 Quote by azzkika If space really does expand how do we know the expansion is uniform? If space expansion is variable then redshift readings cannot be relied on as an accurate measurement of distance/recessional velocity.
The expansion is the same in every direction we look. Whether it is uniform in distance as well as direction is a bit harder to determine, but would appear in the data as a strongly-varying expansion rate with distance, which we just don't see.
P: 164
 Quote by Old Smuggler A Doppler shift in curved space-time only means that the special-relativistic Doppler formula can be used after the described procedure of parallel-transport. Any further interpretation is not included. In particular, a Doppler shift in curved space-time has nothing to do with any possible split-up into "gravitational" plus "kinematic" parts (or any other way of decomposing the redshift for that matter).
Ah, so one can say it's formally correct to use the Doppler formula in this context, but the statement "the most natural interpretation of the redshift is as a Doppler shift" (Bunn & Hogg 2009) goes too far.

In the example in #43 you mentioned "observers with fixed spatial Schwarzschild coordinates". Instead one could think of observers falling freely one after another on a radial path. Wouldn't then the similarity with FOs in curved RW models be even closer? And if yes, wouldn't they similarly wonder whether their "space" expands and how to interpret the redshift, as they recognize their moving away from each other, the faster the farther? Sorry, this may be quite silly, thanks for your patience.
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P: 4,598
 Quote by timmdeeg Ah, so one can say it's formally correct to use the Doppler formula in this context, but the statement "the most natural interpretation of the redshift is as a Doppler shift" (Bunn & Hogg 2009) goes too far.
The problem is that everybody's idea of "most natural" is different.
P: 164
 Quote by Chalnoth The problem is that everybody's idea of "most natural" is different.
Yes, hence it becomes easily a semantic discussion. But the gap beween "most natural" and "meaningless" is remarkable. It is also possible that B&H don't share the latter classification.
P: 87
 Quote by timmdeeg Ah, so one can say it's formally correct to use the Doppler formula in this context, but the statement "the most natural interpretation of the redshift is as a Doppler shift" (Bunn & Hogg 2009) goes too far.
The problem is B&H's claim that it is "most natural" to interpret the cosmic redshift as a Doppler shift in FLAT space-time for sufficiently small distances. But as I have argued in this
thread this claim is false; with a few exceptions said interpretation is in general simply inconsistent with the geometry of the RW-models.

So in my opinion the B&H paper is an extremely lousy paper; just about everything in that paper is wrong or misleading and it should never have been published (the reputation of the American Journal of Physics has been tainted by accepting it). The paper is a prime example of how bad things may turn out when trying to do physics by gut feeling. Furthermore, based on the reception of the paper, B&H have not only succeded in fooling themselves, but have apparently done a good job of fooling some other professionals as well. This is what I find the most remarkable about the paper.
 Quote by timmdeeg In the example in #43 you mentioned "observers with fixed spatial Schwarzschild coordinates". Instead one could think of observers falling freely one after another on a radial path. Wouldn't then the similarity with FOs in curved RW models be even closer? And if yes, wouldn't they similarly wonder whether their "space" expands and how to interpret the redshift, as they recognize their moving away from each other, the faster the farther? Sorry, this may be quite silly, thanks for your patience.
The similarity between the Schwarzschild metric and the RW-models I was trying to illustrate in #43 was the effect of space-time curvature on the spectral shift in the two cases, not any similarity regarding "space expansion".
P: 164
 Quote by Old Smuggler The problem is B&H's claim that it is "most natural" to interpret the cosmic redshift as a Doppler shift in FLAT space-time for sufficiently small distances. But as I have argued in this thread this claim is false; with a few exceptions said interpretation is in general simply inconsistent with the geometry of the RW-models. . Furthermore, based on the reception of the paper, B&H have not only succeded in fooling themselves, but have apparently done a good job of fooling some other professionals as well. This is what I find the most remarkable about the paper.
Chodorowski (Abstract, 2011) then seemingly has criticised B&H for false reasons by stating: "We find that the resulting relation between the transported velocity and the redshift of arriving photons is not given by a relativistic Doppler formula. Instead, for small redshifts it coincides with the well known non-relativistic decomposition of the redshift into a Doppler (kinematic) component and a gravitational one." But, as you have pointed out, such a decomposition is mathematically inconsistent.

 Quote by Old Smuggler The similarity between the Schwarzschild metric and the RW-models I was trying to illustrate in #43 was the effect of space-time curvature on the spectral shift in the two cases, not any similarity regarding "space expansion".
That was just the perhaps crazy idea to compare the cosmological tidal stretching with that happening to freely falling observers towards a mass. Things move away from each other with increasing acceleration in either case. The freely falling observers (not knowing about the mass) develop models just as the FOs do too. I wonder whether the phenomenon tidal stretching should be subject of interpretation, e.g. as expansion of space (not truely physical, meaning not measurable) in both cases.
P: 87
 Quote by timmdeeg Chodorowski (Abstract, 2011) then seemingly has criticised B&H for false reasons by stating: "We find that the resulting relation between the transported velocity and the redshift of arriving photons is not given by a relativistic Doppler formula. Instead, for small redshifts it coincides with the well known non-relativistic decomposition of the redshift into a Doppler (kinematic) component and a gravitational one." But, as you have pointed out, such a decomposition is mathematically inconsistent.
This non-relativistic decomposition is arrived at by using a Newtonian approximation to calculate the "gravitational" contribution. But this approach is misguided, and inconsistent with a relativistic approach.

The cited statement should not be taken as a criticism of B&H, since the parallel-transport procedure Chodorowski performs is different from that referred to in B&H. That is, Chodorowski defines a "recession velocity" as the 3-velocity obtained by parallel-transporting the 4-velocity of the emitting FO along a space-like geodesic rather than along a null geodesic. This is a perfectly valid procedure to do mathematically. But then he defines the redshift obtained from this "recession velocity" as the "kinematic" part of the redshift and the remainder part of the redshift is defined as "gravitational". These definitions are very misleading, since (for small distances) the definition of "kinematic redshift" does not correspond to the redshift obtained by using SR, and the definition of "gravitational redshift" does not correspond to the effects of space-time curvature. Chodorowski should have named his spectral shift split-up in some other way, reflecting the procedure on which it is based.
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P: 5,902
 Quote by Old Smuggler That is, Chodorowski defines a "recession velocity" as the 3-velocity obtained by parallel-transporting the 4-velocity of the emitting FO along a space-like geodesic rather than along a null geodesic.

Chodorowski writes
 In practice, however, as a 'preferred' path one can choose a geodesic connecting the galaxy an the observer.
Some care is need with the terminology. The path chosen is spacelike, but it is not a spacetime geodesic, it is spatial geodesic.

Consider an analogy: a portion of a great circle is geodesic on the 2-dimensional surface of the Earth, but it is not geodesic in 3-dimensional space.

Similarly, the path chosen is a geodesic for the 3-dimensional spatial hypersurface that represents all of space for one instant of cosmic time, but it is not a geodesic for 4-dimensional spacetime.
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P: 5,501
Two issues of interest:

I just came across the following in my notes..and had forgotten about the concept:

 http://www.astro.ucla.edu/~wright/cosmo_02.htm To say the Universe is homogeneous means that any measurable property of the Universe is the same everywhere. This is only approximately true, but it appears to be an excellent approximation when one averages over large regions…. The homogeneity of the Universe must be defined on a surface of constant proper time since the Big Bang. [Because the density of the universe was different a billion years ago than today.]
So it seems we may not have such as widely varied choice of space-times as is often implied??. Some do seem 'natural' given this criteria as a starting point!

GeorgeJones:
 Consider an analogy: a portion of a great circle is geodesic on the 2-dimensional surface of the Earth, but it is not geodesic in 3-dimensional space.
This seems really interesting....sometime ago there was a discussion about weaknesses in the balloon analogy....I think it may have been when phinds was developing an explanation of how far the balloon analogy should be taken.
I suggested the great circle on a balloon was not the same path as that used in coordinate and proper distance measurements....and consequently there were severe weakness in the balloon analogy regarding cosmological distances....

I like to use the Wikipedia illustration to 'picture' this for myself:

http://en.wikipedia.org/wiki/Metric_...s_expanding.3F

 ....we can single out two distances which appear to be physically meaningful: the distance between the Earth and the quasar when the light was emitted [red curve], and the distance between them in the present era [orange curve] (taking a slice of the cone along the dimension that we've declared to be the spatial dimension). The former distance is about 4 billion light years, much smaller than ct because the universe expanded as the light traveled the distance, the light had to "run against the treadmill" and therefore went farther than the initial separation between the Earth and the quasar. The latter distance (shown by the orange line) is about 28 billion light years, much larger than ct. If expansion could be instantaneously stopped today, it would take 28 billion years for light to travel between the Earth and the quasar while if the expansion had stopped at the earlier time, it would have taken only 4 billion years.
Anyway, how do we describe the 'curve' in space at a constant coordinate time...[this is the 'path' of parallel-transport of four-velocities along which the FLRW metric is calculated].

I've heard it described as a 'straight line...as when laying rulers end to end' [for a proper distance 'measure' ] and I believe also as a space-like geodesic and a space-time geodesic....

Seems like the proper description is 'a geodesic in three dimensional space'......

edit: Found this in my notes:
Wallace: {commenting on weakness in balloon and raisin bread analogy}
The rate of expansion [velocity] is unimportant; It is the rate of acceleration of the expansion [a’[t] that tells you what happens. So in a contracting universe a distant particle could move away, or in an expanding universe a distant particle could come toward you. You don't intuitively expect this behavior if you think of the universe as the model loaf of rising bread filled with raisins! [or the balloon analogy]

Source not recorded:

A curve of constant cosmological time [along which we would like to measure a proper distance’ ] connecting two points in a FRW [model] universe is not a "straight line", i.e. it is not a geodesic.

But it IS the Hubble ‘distance’ calculated distance.

So what, then is the 'Hubble curve' over which distance is calculated called?
P: 164
 Quote by Old Smuggler The cited statement should not be taken as a criticism of B&H, since the parallel-transport procedure Chodorowski performs is different from that referred to in B&H. That is, Chodorowski defines a "recession velocity" as the 3-velocity obtained by parallel-transporting the 4-velocity of the emitting FO along a space-like geodesic rather than along a null geodesic. This is a perfectly valid procedure to do mathematically. But then he defines the redshift obtained from this "recession velocity" as the "kinematic" part of the redshift and the remainder part of the redshift is defined as "gravitational". These definitions are very misleading, since (for small distances) the definition of "kinematic redshift" does not correspond to the redshift obtained by using SR, and the definition of "gravitational redshift" does not correspond to the effects of space-time curvature. Chodorowski should have named his spectral shift split-up in some other way, reflecting the procedure on which it is based.
Okay, thanks, you gave me a better understanding of Chodorowski's paper.

And I want to thank all participants of this thread for helpful comments.

So, in simple words, one should use the notion of 'expanding space' with some care, as the 'stretching or the creation of space' is not measurable, or perhaps better per se is physically not meaningful.
Then the demystfied version could be the conclusion, "that the expansion of space is neither more or less than the increase over time of the distance between observers at rest with respect to the cosmic fluid", refering to the author's of the paper Expanding Space: The Root of all Evil?. The knowledge of the increasing distances results from the cosmological redshifts, which depend only on the space-time curvature. I hope, that's correct so far.
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timmdeeg

This issue is not one easy to describe in a few sentences. And summarizing long discussions about this issue as understandings and explanations evolve is also not so easy.

Timmdeeg

 So, in simple words, one should use the notion of 'expanding space' with some care, as the 'stretching or the creation of space' is not measurable, or perhaps better per se is physically not meaningful.
I heartily disagree! It is, in principle observable, as post #2 shows clearly.

The issue is what does the observation [measurement] mean? How do we interpret observed redshift, exactly as posted by Chalnoth, post #2.

Further,if you conclude the effect is 'physically not meaningful', how do you explain that CMBR radiation emitted at almost 3,000 K is today observed at about 2.7K? If this loss of energy had NOT occurred, there would have been no evolution of the universe as we observe it....no stars, no galaxies, no us....also recall I quoted Chalnoth in post #33 integrated Sachs=Wolf effect as experimental evidence.

 ..."that the expansion of space is neither more or less than the increase over time of the distance between observers at rest with respect to the cosmic fluid",
This gets a LOT closer, but the overall quote I posted is more complete

 ...the expansion of space is neither more nor less than the increase over time of the distance between observers at rest with respect to the cosmic fluid in terms of the FRW metric. With this metric..... the density and pressures of cosmological fluids must change over cosmic time, and it is this change that represents the basic property of an expanding (or contracting) universe.
The rest of this is important because the explanations discussed here are based on the assumptions and conventions in the FLRW cosmological model.....and are unique to that model.....assumptions like an isotropic and homogeneous universe, conventions like co-moving observers [at rest wrsp to the CMBR].....

For example as bapowell posted in #3 with the FLRW model the wavelength of a cosmological photon [or a mass particle] λ(t) varies according to the scale factor a[t]. In this model, they go together.

I don't even prefer the wording of the quote I posted.....

"... the density and pressures of cosmological fluids must change over cosmic time, and it is this change that represents the basic property of an expanding (or contracting) universe...."

I would have said something like

"...it is this change [from general relativity] that causes [or 'powers' or 'determines']...the basic expanding universe....that is, Einstein's equations relate the evolution the scale factor to the changes in pressure and energy density of the matter in the universe.
P: 164
Naty1,
I welcome you criticism.
Quote by Naty1
This issue is not one easy to describe in a few sentences. And summarizing long discussions about this issue as understandings and explanations evolve is also not so easy.

 So, in simple words, one should use the notion of 'expanding space' with some care, as the 'stretching or the creation of space' is not measurable, or perhaps better per se is physically not meaningful.
I heartily disagree! It is, in principle observable, as post #2 shows clearly.

The issue is what does the observation [measurement] mean? How do we interpret observed redshift, exactly as posted by Chalnoth, post #2.
.
Further,if you conclude the effect is 'physically not meaningful', how do you explain that CMBR radiation emitted at almost 3,000 K is today observed at about 2.7K?
I think, it might be helpful to distinguish between 'truely physical', 'measurable', 'interpretation', 'not measurable' and 'correct description' in order to better clarfy the issue.

Would you agree with that:

Truely physical: the cosmological redshift, increasing distances between FOs.

Measurable: The redshift. It yields information about the increase of the scale-factor between emission and absorption and thus about increasing distances.

Interpretation : the redshift can be interpreted as due to the stretching of space or as due to the motion of galaxies, #2. Furthermore, the interpretation of the redshift depends "on the spatial geometrie", #39.

Stretching of space not measurable: a thought experiment may result in increasing distances, but these again can be interptreted in this or that way, #16.
So, the experiment doesn't prove the stretching of space (or the creation of space, resp.). If I claim that I have measured the stretching of space, you could say, no, you have measured just motion.
Especially here I ask for any differing opinions.

Correct description: the interpretations are "correct descriptions" of a "real physical phenomenon", #31. And "as space expands, the wavelenth must increase", #3, is to my understanding also covered under correct description.
So, "correct description" and "real phenomenon" don't have the same meaning.

I agree, without further explanation the wording "physically not meaningful" gives rise to misunderstanding. Perhaps "not truely physical" or "not a real physical phenomenon", would make more sense.
 P: 39 I appreciate the contributions that have been made to this thread. I found it helpful and stimulating, especially in confirming my view that a large percentage of cosmologists misconceive the concept of expanding space, space stretching, etc. One question I do have, which I believe is subsumed within the subject matter of this thread, (and perhaps many others), is the following: What is the experimental basis for the assumption that the frequency/wavelength of light remains constant when traveling over cosmologically relevant distances? Are there any plans for conducting an experiment to verify the behavior of light at such distances? My sense is that there really is no experimental data on this issue and that astronomers, astrophysicists and cosmologists all rely on evidence produced from local experiments for the interpretation of data obtained from light received from distant sources. It just seems to me that until such an experiment is conducted, much of the interpretation of what we observe from sources throughout the universe remains open to controversy. Is there any reason why the scientific community would not be interested in the results of such an experiment? [if this deserves its own thread, I trust someone will pursue that]
P: 164
 Quote by ConformalGrpOp What is the experimental basis for the assumption that the frequency/wavelength of light remains constant when traveling over cosmologically relevant distances? Are there any plans for conducting an experiment to verify the behavior of light at such distances?
There is perhaps a misunderstanding.
Nobody assumes that. Since Hubble we know about the redshift (i.e. the non constancy of the wavelength) of distant galaxies.
 P: 39 Tim, I believe it is assumed that a fundamental property of EM is that the wavelength of light emitted from a distant source propagating along an unobstructed, field free path of fixed distance to an observer with no relative motion with respect to the source will exhibit no spectral shift. In other words, it is assumed that the "doppler" and "cosmological" red shifts are not the result of the "non constancy of the wavelength", but a result of the relative motion of the observer with respect to the source (doppler), and the additional distance the light traveled from the time it was emitted to the time it was observed due to the expansion of the universe (cosmological), which looks like the same thing insofar as the expansion imparts a de facto relative motion between the source and the observer. In both cases, it is assumed that the wavelength of the light remains unchanged from the point of emission to the point of observation, and it is only the relative motion of the observer with respect to the source that results in the observer detecting a shift in the wavelength. At least, that is my understanding of the current state of knowledge with respect to the behavior of light. [Note: Some theorists contend that "space stretching", a term I believe is a misnomer, imparts a stretching of the wavelength analogous to the stretching of a dot on the surface of an inflating balloon. But, most knowledgeable scientists would view this conception as little more than a second rate, and certainly misleading pedagogical device. The more accurate explanation is that as the universe expands, the successive photons being emitted from the source travel further than the preceding ones, and this, like the doppler effect, accounts for the observed spectral shift.] I am inclined to view the problem slightly differently; that Maxwell's equations admit a solution that permits light to "travel" within a metric that is not locally Minkowskian. Therefore, not inconsistent with Milne's view, the observed spectral shift, or perhaps a component of it, is quite likely to be the result of an intrinsic characteristic of light which is not velocity dependent, but rather is time/distance dependent. Verification of the behavior of light over distances where Hubble's law becomes relevant is within our ability to ascertain by experiment, a circumstance wasnt even a fathomable possibility at the time when Eddington and others announced that the relation between red shift and distance codified in Hubble's law provided compelling evidence that the universe was expanding as predicted by the de Sitter and LaMaitre models. I don't know of any experiments such as those hypothesized by Poincare, Milne and Whitrow (doing away with rigid rods and synched clocks, and using calibrated light signals), that have been proposed or carried out to specifically test the behavior of light over cosmologically relevant distances. One might ponder the idea of a massively scaled up version of the Michelson-Morley experiment, (or its modern analog), and wonder would the experiment still yield a null result? From a historical standpoint, its a bit intriguing to think about what might have happened if the late 19th Century experimentalists had access to the technology necessary to perform such a scaled up version of the M-M experiment and the experiment had yielded a positive result! Would Einstein have been able to successfully convince all those who were held to the theory that light could only propagate if there existed an omnipresent aether that: "NO! The positive results demonstrate a previously unknown property of EM allowed by Maxwell's equations, not proof of our motion through the aether!" ? (Rendering the theory of aether obsolete is, in my view, one of the most significant advances resulting from Einstein's theory of Special Relativity; which is a bit ironic for Einstein's SR was developed out of, and informed by the work of Lorentz and Poincare in attempting to explain the results of the M-M experiment with respect to the aether). Anyway, just a thought. Thanks for taking the time to respond.
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 Interpretation : the redshift can be interpreted as due to the stretching of space or as due to the motion of galaxies, #2. Furthermore, the interpretation of the redshift depends "on the spatial geometrie", #39.
That captures the alternative perspectives for me....
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 Quote by ConformalGrpOp I appreciate the contributions that have been made to this thread. I found it helpful and stimulating, especially in confirming my view that a large percentage of cosmologists misconceive the concept of expanding space, space stretching, etc.
I would say this is completely wrong. Most cosmologists use an entirely accurate picture of the expanding universe. That there are other, equally-accurate pictures is irrelevant to this fact, and doesn't mean most cosmologists are misunderstanding something.
 P: 39 Hi Chalnoth, I'm not one to quibble about such things, and certainly not with the attribution of my comment to " a large percentage" cosmologists (as opposed to "most"). The comment might have been better taken if I made no such particular attribution and simple noted that the misconception is prominent in the field. But, here too, I was speaking to the idea that empty space has physical properties (a new "force-like" characteristic), which is implied in the notion that "space" stretches. This is distinct from the concept of an "expanding" universe, which is perfectly consistent with the physical implications of the standard model. In this regard, I would simply quote Weinberg on this subject: "[H]ow is it possible for space, which is utterly empty, to expand? How can nothing expand? The answer is: space does not expand. Cosmologists sometimes talk about expanding space, but they should know better." But then again, I could be "completely wrong." Cheers!

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