"de sitter effect" and cosmology history

[modest]

A good study on the different methods would be the Carroll 1992 paper I've been quoting: http://preposterousuniverse.com/writings/cpt92.pdf

 

It gets into the problems and advantages of different methods of distinguishing cosmological models, and was written before the 1998 SN1a observations.

 

~modest

[quantumtopology]

I found this paper on the "Einstein Studies" series http://books.google.es/books?id=5mGZno8CvnQC&printsec=frontcover&dq=the+expanding+worlds+of+general+relativity&source=bl&ots=FbaHK42Hxu&sig=91Z4qSh-r804ID5jrDwgApNWVBY&hl=es&ei=jsnzS6r7FI7Hsgbo1fX8Cw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CB0Q6AEwAA#v=onepage&q&f=false

that I think my clarify previous misunderstandings about de Sitter's "model" or perhaps it'd be better to call it "spacetime geometry". After reading it (specially pge 329) I see that discussions about whether de sitter universe is expanding or not are meaningless if one doesn't specify the model and the preferred metric and coordenates this is also clear from the controversy Einstein and deSitter had in 1916-1918 , see this http://www.tc.umn.edu/~janss011/pdf%20files/Einstein-De%20Sitter.pdf

 

Regards

[modest]

I apologize for the delay in responding. I've been very occupied.

 

I found this paper on the "Einstein Studies" series The expanding worlds of general ... - Google Libros

that I think my clarify previous misunderstandings about de Sitter's "model" or perhaps it'd be better to call it "spacetime geometry". After reading it (specially pge 329) I see that discussions about whether de sitter universe is expanding or not are meaningless if one doesn't specify the model and the preferred metric and coordenates

 

Yes, I agree. Eddington alluded to this in the previous quote in the thread about artificially detaching the kinematic motion of a de Sitter universe from the de Sitter effect.

 

As odd as it might seem, it is today most common to *not* use de Sitter's metric in describing a de Sitter universe, but rather to use the FLRW metric. Both metrics work (they both describe the same physical model) and both are an exact solution of GR, but the latter is more intuitive and simple. It's easier to analyze and compare to other models, I guess you might say.

 

this is also clear from the controversy Einstein and deSitter had in 1916-1918 , see this http://www.tc.umn.edu/~janss011/pdf%20files/Einstein-De%20Sitter.pdf

 

Yeah, I've read that. It mostly deals with the mistaken impressions that Einstein originally had with de Sitter's model, but it is indeed a very good paper and puts things into the proper historical perspective. I'm sure I've quoted it on Hypography before. Good find

 

~modest

[quantumtopology]

One thing that bugs me about this thogh is the following:

General relativity is supposed to be a coordinate invariant theory, so that in principle you can choose them arbitrarily and have the same physical outcome after applying the theory to some problem. But in the de Sitter's particular application of hte general relativity theory a change in coordinates completely alters the physical outcome, giving a static solution with certain coordenates and non-static solutions with others, which we'll agree are different physical outcomes, otherwise nobody would differentiate both alternatives and we'd save lots of arguments.

Any thoughts?

[modest]

One thing that bugs me about this thogh is the following:

General relativity is supposed to be a coordinate invariant theory, so that in principle you can choose them arbitrarily and have the same physical outcome after applying the theory to some problem. But in the de Sitter's particular application of hte general relativity theory a change in coordinates completely alters the physical outcome, giving a static solution with certain coordenates and non-static solutions with others, which we'll agree are different physical outcomes, otherwise nobody would differentiate both alternatives and we'd save lots of arguments.

Any thoughts?

 

Look at Eddington's quote again:

 

Allusion has been made to the fact that the recession of the galaxies in the present theory of the expanding universe is not precisely the effect forseen by de Sitter. It may be well to explain the manner of the transition. The phenomenon that is generally called the “de Sitter effect” was a rather mysterious slowing down of time at great distances from the observer; atomic vibrations would be executed more slowly, so that their light would be shifted to the red and imitate the effect of a receding velocity. But besides discovering this, de Sitter examined the equations of motion and noticed that the real velocities of distant objects would probably be large; he did not, however, expect these real velocities to favour recession rather than approach. I am not sure when it was first recognized that the complication in the equations of motion was neither more nor less than a repulsive force proportional to the distance; but it must have been before 1922. Summarizing the theory at that date, I wrote—“De Sitter’s theory gives a double explanation of this motion of recession: first, there is the general tendency to scatter according to the equation [math]d^2r/ds^2 = 1/2 \lambda r[/math]; second, there is the general displacement of spectral lines to the red in distant objects due to the slowing down of atomic vibrations which would be erroneously interpreted as motion of recession.” I also pointed out that it was a question of definition whether the later effect should be regarded as a spurious or a genuine velocity. During the time that its light is traveling to us, the nebula is being accelerated by the cosmcal repulsion and acquires an additional outward velocity exceeding the amount in dispute; so that the velocity, which was spurious at the time of emission of the light, has become genuine by the time of its arrival. Inferentially this meant that slowing down of time had become a very subsidiary effect compared with cosmical repulsion; but this was not so clearly realized as it might have been. The subsequent developments of Freedmann and Lemaitre were geometrical and did not allude to anything so crude as “force”; but, examining them to see what has happened, we find that slowing down of time has been swallowed up in the cosmical repulsion; it was a small portion of the whole effect (a second order term) which had been artificially detached by the earlier methods of analysis.

 

Theories of the Universe: From ... - Google Book Search

 

When the equations of motion in de Sitter's metric are not ignored both FLRW and de Sitter's metric give equivalent physical predictions.

 

In both cases two masses will recede from one another. In de Sitter's metric they will be forced apart in a static metric (essentially, they move through static space) and in FLRW they will follow the metric expansion of space away from one another (essentially, space expands and objects tend to follow along). Either moving through space or having space expand, the physical situation is the same: the two objects are moving apart.

 

Likewise, if you look further into the comparison, you will find that objects in de Sitter's universe are accelerated toward a cosmic horizon that is at a fixed position where they are time dilated more and more eventually becoming non-visible. In FLRW with de Sitter parameters the cosmic horizon shrinks toward the center observer overtaking objects and making them non-visible. It is two different descriptions of the same physical phenomenon.

 

~modest

[quantumtopology]

Hi, Modest

 

I would like to come back for a moment to the conversation about page 28 in http://www.spsnational.org/radiations/2008/ecp_bigbang2.pdf .

I wanna center in the solution

[math]A^{\prime} = 0[/math]

without lambda presented in this page of the paper (like you said the

[math]A^{\prime} = 0[/math]

with lambda is the well known Eintein Universe).

 

The problem with this solution (according to the author of the article) was that it rendered a hyperbolic infinite space that Einstein couldn't admit, my question is if this solution has been ever developed as a model, I see the solutions at infinity transforms the metric in minkowskian or model C(eq. 18), but the local solutions would be valid righ?, Ok, I'm noticing that if it's valid only locally then is not a cosmological model. Nevermind. Just thinking out loud.:eek_big: