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How to prove the stretching of space 
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#37
Jan213, 02:06 PM

P: 231

To me this statement And how about this thought experiment: Supposed the universe doesn't expand at the time of emission and absorption but expands during the photon's travelling. What kind of shift if any will be measured? 


#38
Jan213, 02:11 PM

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#39
Jan213, 05:23 PM

P: 87

Sorry for the late reply (no internet connection for the last week).
In RWmodels with flat or spherical space sections, the redshift is entirely due to the nonflat connection and thus indirectly to spacetime curvature (i.e., "gravitational"). (See, e.g., arXiv:0911.1205.) For RWmodels with hyperbolic space sections things are more complicated, and some part of the redshift is "kinematic" (meaning that some part of the redshift survives even if one replaces the curved spacetime metric with a flat one). To decide how much of the redshift is "kinematic", a recipe for spectral shift splitup into "kinematic" and "gravitational" parts is necessary (this can be done unambiguously, at least for small distances). 


#40
Jan313, 08:25 AM

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#41
Jan313, 09:34 AM

P: 231




#42
Jan313, 11:18 AM

P: 231

"Hence, ironically in the context of the recent debate, paralleltransport of fourvelocities along photons path can allow cosmological redshifts to be interpretet as a relativistic Doppler effect without the contradiction presented here, provided that the concept of expanding space is added to the Minkowski spacetime ... and provided that the velocity is thought of as being tied to a path and not as a global concept." But irrespective of such an ambiguous debate I have a problem to understand the cosmological redshift in the sense of a purely gravitational shift. It is quite clear that a photon looses energy und thus becomes redshifted as it climbs out of a gravitational field or in other words as it moves away from a mass (i). In contrast the photon traveling through homogeneous space doesn't move away from a gravitational center, but undergoes a redshift (= looses energy) as well. How shall I understand this (obvious?) discrepancy? You mentioned already the dependence on spatial geometrie ... . Is there any explanation besides the stretched wavelenght picture as simpel as (i)? 


#43
Jan313, 12:37 PM

P: 87

For example, in the Schwarzschild metric, the chosen observers defining gravitational spectral shifts are observers with fixed spatial Schwarzschild coordinates. The flat spacetime limit of this metric is obtained by setting the mass M=0. Now it is rather obvious that there is no spectral shift between the chosen observers in the Schwarzscild metric with M=0, so the spectral shift obtained when M is nonzero must be purely gravitational. A similar situation to that of the Schwarzschild metric occurs for RWmodels with flat or spherical space sections, so the spectral shifts obtained between the FOs in these models must also be purely gravitational. 


#44
Jan313, 01:51 PM

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P: 4,782

Either way, though, our spacetime does have a definite degree of overall curvature, as it must due to the fact that our universe is not empty (more pedanticallystated, the average energy density of our universe is nonzero). Regardless of the overall curvature, however, the amount of the redshift that is attributed to gravitation and the amount attribute to motion of the emitter or observer is still arbitrary. Some choices may seem more or less natural to some people, but many choices are possible in any event. 


#45
Jan313, 02:02 PM

P: 5,632

Chalnoth:
[Note, especially the change in scale factor and,in Schwarzschild coordinates, the change in velocity, comments.] http://www.physicsforums.com/showthr...nt+flow&page=4 edit: oops, that link no longer works??? [In the great 2007 thread Wallace, Chronos and Oldman take a different view than expressed here [and there] by Marcus...you can read the posts from the 40's thru 50's and see the pros and cons.] I do think it is better to think of (photons) as being redshifted by being observed in a different frame ......Now as t ticks along, the scale factor a(t) increases. Therefore two observers who are both at rest wrt to the CMB, but who have different times t will therefore be in different frames (have different metrics). This is what leads to photons being redshifted when observed and emitted at different times. I tend to agree, photons are not redshifted by traveling through the universe, they are redshifted only because they are observed in a different frame from which they were emitted. Marcus: # 48] I am not comfortable with that because among other things I see cosmologists doing inventories of the energy density which are implicitly estimated IN A CMB FRAME.... These 'conflicting' viewpoints stem from this as explained by Chalnoth elsewhere: " … You get some total redshift for faraway objects due to cosmological expansion. How much of that redshift is due to the Doppler shift# and how much is due to the expansion between us and the far away object is completely arbitrary." # Doppler shift is based on [relative velocity] frame based differences, not expansion, Hence photon frequency and wavelength can be viewed as fixed just like in a static Spacetime.. Doppler shift is a particular explanation of redshift, with a particular formula. Marcus: Don’t think of the redshift as a Doppler [relative velocity] effect. It is not the result of some particular speed. The formula involves the entire [varying] factor by which distances have been expanded during the whole time the light has been traveling. PeterDonis: The law governing the relationship of emitted to observed photon energies (or frequencies) is general and applies in any spacetime. The 4momentum of the photon gets determined at the emitter; then it gets parallel transported along the photon's worldline from emitter to observer; then you contract that 4momentum with the observer's 4velocity to get the observed energy (or frequency if you throw in a factor of Planck's constant). That "parallel transport" process is actually where the "redshift" occurs in an expanding universe; the expansion alters the 4momentum of the photon as it travels (or at least that's one way of looking at it), whereas in a static universe the photon's 4momentum would "stay the same" as it traveled. There's another complication here, btw; what about the gravitational redshift of photons in Schwarzschild spacetime? Here the "change" with changing radius is actually in the 4velocity of the observer; the photon's 4momentum stays the same, but the 4velocities of "hovering" observers are different at different radii, so they contract differently with the constant photon 4momentum. PAllen: Redshift is a measured shift in received frequency versus emitted frequency. Doppler [shift] refers to one of two formulas (prerelativistic; relativistic) for relating redshift to velocity. Doppler shift is a particular explanation of redshift, with a particular formula. It is not a measure of redshift. Where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the classical Doppler shift formula; in cosmology, where we deal with lightspeed 'c' and recessional 'velocities' greater than 'c' we need the relativistic version of the formula. [Doppler is like a radar speed trap: The radar signal goes out and returns and keeps the same 'color', but we record the difference in wavelength as a speed measure.] Cosmological redshift is typically considered distinct from Doppler redshift because it is a relation between distance and redshift rather than speed and redshift, under the assumption that both source and target are motionless relative to center of mass of the local matter (here, local is quite large  galaxy or galaxy cluster). 


#46
Jan313, 02:39 PM

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#47
Jan313, 02:39 PM

P: 87

The empty RWmodel is an exceptional case since the spacetime geometry is flat, so in this case, the observed redshift would be purely kinematic. But this does not apply to a general RWmodel where the spacetime geometry is not flat. The interpretation of the redshift in a general RWmodel depends on the spatial geometry. (Only if the spatial geometry is hyperbolic there will be a nonzero "kinematic" contribution to the redshift.) 


#48
Jan313, 02:55 PM

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#49
Jan313, 03:24 PM

P: 87

(For sufficiently small distances the effects of geodesic deviation can be neglected, so the world lines of the FOs are still geodesics and the null curves are still null when replacing the curved spacetime metric with a flat spacetime metric.) Since the redshift is obtained by paralleltransporting the 4velocity of the emitter along a null curve to the observer, this shows that the redshift obtained using the procedure described in #43 is unambiguous, only depending on the spacetime geometry. Thus, changing the spacetime geometry from curved to flat will in general change the redshift, so it cannot be interpreted as purely kinematic. Any concept of "relative velocity of two objects separated by some distance" is not part of the procedure; this is irrelevant since the coordinatefree concept of paralleltransport makes it unnecessary. 


#50
Jan313, 04:54 PM

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#51
Jan413, 08:16 AM

P: 33

I enjoyed this tread and thank the diligence of all contributors. What I found the most stimulating was Naty1’s inclusion of the link to Expanding Space: the Root of all Evil?
In this article it mentions that space might not be stretching but that additional space is being created. The author implies that stretching and creating are equivalent. I find it more satisfying to consider the processes different. We are still back to square one – what is space? However, now attention is focused on how space is created rather than just assuming that it is there. 


#52
Jan513, 11:44 AM

P: 231




#53
Jan613, 10:14 PM

P: 87




#54
Jan813, 06:25 AM

P: 68

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.



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