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Continued from post #763



[1] Einstein constructed his static model in such a way as to have no cosmological redshift. The [imath]g_{00}=-1[/imath] for a metric signature of ' [imath]-+++[/imath] ' ensures that there is no redshift.

[2] As I have been proving in my posts above, Ernst Fischer has shown no such thing. He has not presented a case for a universe of constant positive Gaussian/Riemannian curvature. But he at least recognizes that the Einstein static model does not involve a cosmological redshift.

[3] Since Einstein's model involved a "cosmological fluid" that was homogeneous, and a space that was isotropic at every point, and no redshift, then, given Hubble's results, his model was obviously wrong. So his rejection of it can hardly be called premature.


Again, I am not advocating a return to the original 1917 Einstein model as described by Einstein and the field equations of the time. The metric signature and the interpretation of the time element, amongst other components, are open to re-evaluation.




[1] GR makes no claim that there is an inherent inability to distinguish gravitational redshift from doppler redshift. It cannot be interpreted as making such a claim.


Once the spacetime metric is known, the equivalence principle determines how matter and fields respond to it. “From this correspondence follows that it is impossible to discover by experiment whether a given system of coordinates is accelerated, or whether its motion is straight and uniform and the observed effects are due to a gravitational field” (Einstein 1940, 1954, p.330)


The equivalence principle guided the development of general relativity. It is not a founding principle of relativity but rather a simple consequence of the geometrical nature of GR.


It's one small step the extrapolation of the Einstein equivalence principle to cosmology, but it may represent one giant leap in our understanding of the physical universe and its evolution in time. Even if the curved spacetime interpretation for resdhift z turns out to be untenable, it is still a step worth taking.


The benefit-to-risk ratio remains uncertain. However, the uncertainty can (and should) be addressed.




[2] Previously:
  • in post #748 on 29 March 2011 - 02:23 AM, you said:

    "Therefor, in cosmology, there is an inability to distinguish between a Doppler effect, the expansion of space, and gravitational redshift. "

  • in post #751 on 30 March 2011 - 04:02 AM, you said:

    "Galaxies are not seen to move. The interpretation of radial motion comes from redshift, which can be interpreted as either a Doppler effect, expansion or stretching of space, or a curved spacetime effect."

  • in post #757 on 06 May 2011 - 08:15 PM, you said:

    "Sufficient observation time needed to distinguish between the two effects (e.g., to actually 'see' galaxies move radially via an increase in redshift) would be on the order of millions of years. So yes, it is in principle possible, but in all practical purposes impossible."


Theoretical physics is concerned with what is in principle possible, it is not constrained by the dictates of practical puposes. If something of relevance to a theory is in principle possible then the formulator of the theory would be quite remiss in neglecting to include considerations of that something-of-relevance.


You've missed the point. If the aim is to show empirically that galaxies are being displaced radially your proposition is useless, since the only way to test it would be to wait millions of years, in the hopes of seeing a change in redshift. So, even though in principle it would be possible to distinguish between cosmological zgrav and Doppler interpretations, practically, waiting millions of years is out of the question. We must for the present and near future resort to other means which are now available or will soon be.




Such a topic as GR cannot be approached from a perspective that limits itself to what is humanly possible at this time. Although the existence of observational procedures of several millions of years duration, or observers with lifespans of millions of years, may seem very unlikely, nevertheless the possiblity of such observation times must be entertained in order to determine the validity of some hypotheses.

If cosmological redshift was only a Doppler effect or was due to a cosmological "time-dilation with distance" then it would not be expected to increase with time, but if it was due to expansion of space in such a way as to contradict Hogg and Bunn then it would increase over time. However If the cosmological redshift was due to a cosmological time-dilation then the angular width, as seen from earth, of far distant galaxies would not be expected to decrease, but if the redshift was either Doppler or space-stretch then the angular width would be expected to decrease.

So the hypothesis, that "in cosmology there is an inability to distinguish between a Doppler effect, the expansion of space, and gravitational redshift", is false.


Once again, in order to determine of the validity or invalidity of the Doppler shift via your hypotheses we would have to wait millions of years. It serves no purpose, even in principle, for the present discussion.


It's pure entertainment.


So the substance of the claim in cosmology [judging by redshift alone] there is an inability to distinguish between a Doppler effect, the expansion of space, and gravitational redshift, is true.




You have conceded such changes are in principle detectable but dismiss them on the grounds of impracticability. Dismissing the need to consider such in-principle-detectable changes merely because humans cannot detect them, is displaying a fundamental lack of understanding of the nature of theoretical physics.



I am concerned with what can be investigated empirically now and in the near future. Waiting millions of years is not an option. Even for an object in our local vicinity, such as the Andromeda Galaxy (also known as Messier 31, M31, or NGC 224) it would take several hundred years before we could detect a change in the blueshift. And this still won't answer your question, since the shift in spectral lines of Andromeda have nothing to do with cosmological reshift.


Fortunately, there are tests that can be performed that will help distinguish between various models.


Certainly, a general relativistic model that interprets redshift z as a curved spacetime phenomenon should be tested against the standard model, since it offers a compelling world-view consistent with at least with preliminary observations (perhaps more so than 'tired light' scenarios, chronometric cosmology, quasi-steady state cosmology, or intrinsic redshift interpretations a la Arp).




[3] I did not "belittle" you "in order to invalidate" your "argument". I invalidated your statement, and then made a value judgment of your comprehension of science. In your previous posts you had already indulged in derision of my comprehension of and capabilities in mathematics, logic and GR, in what appeared to be attempts to invalidate my arguments. And you showed no reticence in posting Ernst Fischer's belittling comments. If you don't like it then don't deal in it.

If you agree to be more careful with your language in future then I will have no difficulty in matching your politeness.


:) The statement has not been invalidated, since: [1] General relativity, both fortunately and unfortunately, can be interpreted in a variety of ways. [2] In cosmology there are very few facts (if any) to deal with; only evidence, that often can be interpreted is a variety of ways. [3] Theoretical validity of the type you mentioned above is contingent on, in principle and in practice, millions of years of human observation time. So your "value judgment" was indeed excessively premature.


Note: Ernst Fischer is free to respond to your posts as he pleases. The tone of his posts have been on par with your criticisms, which if I am correct began with your first post at ScienceForums.com:

[...] Since no role is played by 'global curvature' in the geodesic equation for null-geodesics, but the scale factor of the Friedmann equations does play a role, then it seems that the above quote displays a lack of comprehension of the relevant physics.


Bold added.


Up until now, I have not taken the liberty to sensor his posts, and doubt I will do so in future posts.


That doesn't imply that politeness should be vacated at the detriment of constructive criticism.






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After a leave of absence I'd like to take this opportunity to remark on the above exchange between Ernst Fischer and cruel2Bkind. It was an interesting discussion, on both sides of the issue. Cruel2Bkind made several attempts to refute the curved spacetime interpretation of redshift z proposed by both Fischer and coldcreation, as modest and others had attempted earlier in this thread.


The exchange was constructive in that it revealed a sign error that Ernst Fischer has since been fixed. That change ultimately made no difference to the final conclusion regarding the general relativistic curved spacetime interpretation of redshift z.


In re-reading the above posts I can only conclude that Ernst Fischer did a superb job during the weeks of intense debate, stimulating and thought-provoking discussions.



I'd like also to take this opportunity to post a new schematic diagram. This is a modification and improvement (I hope) of another schematic diagram that can be found here; see Figure LCDM: A General Relativistic Stationary Universe. Figure LCDM can be found on a wide variety of astronomy-based websites at this time.





Lambda Cold-dark matter universe. This is an artists interpretation of the standard model of big bang cosmology model: Concordance model, ΛCDM or Lambda-CDM. The time-line extends from the big bang/inflation era,13.7 Gyr ago to the present cosmological time. This schematic diagram attempts to illustrate the accelerated expansion in two-dimensional spherically symmetric form. Both HUDF and COBE images are used, albeit transformed.




The goal of releasing this image (first here at Scienceforums.com) is to help the general public understand what is meant by the standard cosmological model along with the concept of the expanding universe and its acceleration over time.



PS. Actually I just wanted to have a little fun with photoshop. :)




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Continuing the pedagogic exposition, and having a little more fun with photoshop, here is another version of the Lambda-cold dark matter model:




Lambda Cold-dark matter universe. This is an artists interpretation of the standard model of big bang cosmology model: Concordance model, ΛCDM or Lambda-CDM, extending from the big bang-inflation epoch 13.7 Gyr ago to the present cosmological time. This schematic diagram attempts to illustrate the accelerated expansion in two-dimensional spherically symmetric form.



Though the surface background appears to be related to the CMB radiation thermal fluctuations, it was actually realized from the HUDF image using specific effects.




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