How to prove the stretching of space

timmdeeg

Does it mean that in curved space-time a given cosmological redshift may be interpreted as a non-kinematic Doppler shift or equivalently as a gravitational shift as well? To me 'non-kinematic Doppler shift' sounds a bit contradictory.

Okay, this clarifies that the notion of a 'climbing photon' is avoidable, which is very helpful, thanks.

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). A "non-kinematic" Doppler shift is meaningless in this context.

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.

Chalnoth

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.

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.

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.

Chalnoth

The problem is that everybody's idea of "most natural" is different.

timmdeeg

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.

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.

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.
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".

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.

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.

Old Smuggler

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.

George Jones

Chodorowski writes
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.

Naty1

Two issues of interest:

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

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: 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


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?

timmdeeg

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.

Naty1

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

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.

This gets a LOT closer, but the overall quote I posted is more complete

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.

timmdeeg

Naty1,
I welcome you criticism.
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.

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.

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]

timmdeeg

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.