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How to prove the stretching of space 
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#19
Dec2112, 04:12 AM

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#20
Dec2112, 04:22 AM

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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. 


#21
Dec2112, 08:34 AM

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#22
Dec2112, 08:37 AM

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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
Dec2112, 08:49 AM

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#24
Dec2112, 09:28 PM

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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 RWmodel 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 spacetime 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 spacetime approximation for RWmodels with flat space sections.) This means that one gets something else than the Hubble law if one uses these alternative observers in the curved RWmanifold one started out with. So said procedure is indeed irrelevant for interpretations of the cosmological redshift found from the given RWmodel, and choosing other observers than the FOs to define "cosmological redshifts" does not yield consistent results. 


#25
Dec2112, 09:34 PM

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#26
Dec2112, 09:55 PM

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(Note that the empty RWmanifold is only a SUBSET of Minkowski spacetime, so the FOs and these alternative observers do not really describe "the same universe".) 


#27
Dec2212, 11:59 AM

P: 231

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
Dec2212, 11:04 PM

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#29
Dec2512, 12:55 PM

P: 231

If I understood you correctly, the redshift observed between FOs depends in the nonempty RW model on whether these are closed, flat, or open and on the spacetime 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 LambdaCDM model, the universe in which we live. (i) 


#30
Dec3012, 11:08 AM

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Thanks to everybody for your explanations.
So, Nevertheless there is Please don't hesitate to correct if I said something wrong. 


#31
Dec3012, 02:47 PM

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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 seeminglydifferent 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
Dec3012, 03:18 PM

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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
Dec3012, 03:24 PM

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#34
Dec3112, 04:25 AM

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#35
Dec3112, 05:40 AM

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#36
Dec3112, 09:52 AM

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Here is an interesting 8 page paper I stumbled across in my notes:
Expanding Space: the Root of all Evil? http://arxiv.org/PS_cache/arxiv/pdf/...707.0380v1.pdf Several of these 'issues' have been discussed in other threads......I found these are insightful: ...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 proper time for …..privileged observers at rest with regards to the cosmic fluid ticks at the same rate as cosmic time and hence the watches of all privileged observers are synchronised. In an expanding universe, the change of the metric implies that the physical distance between any two privileged [comoving] observers increases with time... The Hubble flow is then viewed as a purely kinematical phenomenon — objects recede because they have been given an initial velocity proportional to distance. the velocity of [a] particle due its motion relative to the Hubble flow (or equivalently the homogeneous fluid defining the FRW metric) must be less than the speed of light; its velocity due to the increase of the scale factor is not restricted in this way….. cosmological redshift is not, as is often implied, a gradual process caused by the stretching of the space a photon is traveling through. Rather cosmological redshift is caused by the photon being observed in a different frame to that which it is emitted. 


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