Redshift z

[Erasmus00]

The third is a de Sitter solution (1916, Mon. Not. RAS 76, 699), (1916, Mon. Not. RAS 77, 155) and (1917, Mon. Not. RAS 78, 3).

 

As far as I can tell, this metric is only a solution for empty space with a non-zero cosmological constant. This clearly isn't our universe (which isn't empty).

-Will

[coldcreation]

As far as I can tell, this metric is only a solution for empty space with a non-zero cosmological constant. This clearly isn't our universe (which isn't empty).

-Will

 

For an interesting read, on the Einstein-de Sitter exchanges (1916-1917) regarding the cosmological implications of GR and the controversy that ensued, viz the de Sitter empty world-view, look at pages 84 and 85 here: Conceptual Developments of 20th Century Field Theories,*By Tian Yu Cao

 

Obviously the universe is not empty...

 

 

 

CC

[modest]

As far as I can tell, this metric is only a solution for empty space with a non-zero cosmological constant. This clearly isn't our universe (which isn't empty).

For an interesting read, on the Einstein-de Sitter exchanges (1916-1917) regarding the cosmological implications of GR and the controversy that ensued, viz the de Sitter empty world-view, look at pages 84 and 85 here: Conceptual Developments of 20th Century Field Theories,*By Tian Yu Cao

 

Obviously the universe is not empty...

 

While I honestly hesitate to interject...

 

Your link would seem to support completely what Will is saying. Furthermore, the most interesting development discussed is on page 86:

 

Mathematically, it was a Russian meteorologist, Alexander Friedmann (1922, 1924), who showed that systems A and B were merely limiting cases of an infinite family of solutions of the field equations with a positive but varying matter density: some of them would be expanding, and others contracting, depending on the details of the counterbalancing.

 

(A) is Einstein’s cylindrical space-time and ( is De Sitter's hyperbolic space-time and they are both cases of varying matter density described by Friedmann.

 

Do you see how the world has quickly moved past this debate? Both cases are varying ends of a scale fully since described eloquently. In fact, Einstein and De Sitter both quickly found the logic in Friedmann's analysis and abandoned their debate and models A and B.

 

-modest

[PhysBang]

I also like the claim on page 86 that de Sitter wrote that "there cannot be the slightest doubt that Lemaitre's theory is essentially true," Lemaitre's theory, in this context, being the relativistic model (with the cosmological constant/dark energy) used in the standard cosmological model today.

[coldcreation]

While I honestly hesitate to interject...

Your link would seem to support completely what Will is saying. Furthermore, the most interesting development discussed is on page 86:

(A) is Einstein’s cylindrical space-time and (:naughty: is De Sitter's hyperbolic space-time and they are both cases of varying matter density described by Friedmann.

 

Do you see how the world has quickly moved past this debate? Both cases are varying ends of a scale fully since described eloquently. In fact, Einstein and De Sitter both quickly found the logic in Friedmann's analysis and abandoned their debate and models A and B.

 

 

Basically, what I attempt to suggest, without going into the tedious cosmological details (for now), is that there are two ways of looking at redshift z from the point of view (the rest frame) of any observer. Namely, the universe is either expanding and (nearly) flat, or it is hyperbolic and static. From an observational perspective, the two are (or were, rather, see below) indistinguishable.

 

Said differently, I argue on observational grounds that the general relativistic quasi-stationary (non-expanding yet dynamic and evolving) universe with global spacetime curvature simulates the same cosmological redshift that is today interpreted as an effect due to receding galaxies in an expanding universe (a change in the scale factor due to expanding space). And, the geometry that best describes the former is that of de Sitter (as predicted originally by Lobachevski): hyperbolic. Certainly, the exact metric for this model (most likely of the de Sitter form, with variations of the parameters, particularly of the mass-energy density, not dark matter) would still need to be ascertained in light of recent astronomic data (based on SNe Ia).

 

Before the 1998 SN survey it would have been impossible to distinguish between the two models (not between model A, B or FLRW): we must distinguish between lambda-CDM and the de Sitter static metric (with the required modifications).

 

The attempt has been made before, albeit without success: In 1977, George F. R. Ellis (Department of Applied Mathematics, University of Cape Town, South Africa) published a virtually unknown paper, entitled Is the Universe Expanding? Ellis shows that “spherically symmetric static general relativistic cosmological space-times can reproduce the same cosmological observations as the currently favored Friedmann-Robertson-Walker universes.” (Ellis, G.F.R. 1977, Is the Universe Expanding?, General Relativity and Gravitation, Vol. 9, No. 2 (1978), pp. 87-94).

 

There is a close analogy between the Friedmann models and the model proposed by Ellis, but the differences are astounding. What was previously ascribed to a time variation in an expanding frame is now ascribed to a spatial variation in properties of a static universe, as we observe the past light cone (in the look-back time). Weyl had considered this possibility in 1921, when he still sought a middle ground between the Einstein and de Sitter models (Kerszberg 1989 p.392). Ellis urges "a closer investigation of the field equations and astrophysical aspects of these models" and considers that the interpretation of an expanding universe (an idea that was first put forth by de Sitter) "is based on the assumption of spatial homogeneity, which is made on philosophical rather than observational grounds."

 

 

!977 was the year of the Sacco and Vanzetti condemnation.

 

 

CC

[PhysBang]

Before the 1998 SN survey it would have been impossible to distinguish between the two models (not between model A, B or FLRW): we must distinguish between lambda-CDM and the de Sitter static metric (with the required modifications).

 

The attempt has been made before, albeit without success: In 1977, George F. R. Ellis (Department of Applied Mathematics, University of Cape Town, South Africa) published a virtually unknown paper, entitled Is the Universe Expanding? Ellis shows that “spherically symmetric static general relativistic cosmological space-times can reproduce the same cosmological observations as the currently favored Friedmann-Robertson-Walker universes.” (Ellis, G.F.R. 1977, Is the Universe Expanding?, General Relativity and Gravitation, Vol. 9, No. 2 (1978), pp. 87-94).

It is not unknown to me; indeed, I have it right here. Ellis soon abandoned the paper because there were observable features of the universe that he was not able to reproduce. Take a look at his later work around the same time. Additionally, if you take the time to read Ellis' work, you will find that his model is radically different from your own model. In his model, the cosmological redshift is caused by the gravitational potential between one centre of the universe and the other centre of the universe that our galaxy is located near.

There is a close analogy between the Friedmann models and the model proposed by Ellis, but the differences are astounding.

I have no idea what analogy you could be drawing.

What was previously ascribed to a time variation in an expanding frame is now ascribed to a spatial variation in properties of a static universe, as we observe the past light cone (in the look-back time).

If you are talking about the redshift, the redshift is entirely gravitational.

Weyl had considered this possibility in 1921, when he still sought a middle ground between the Einstein and de Sitter models (Kerszberg 1989 p.392). Ellis urges "a closer investigation of the field equations and astrophysical aspects of these models" and considers that the interpretation of an expanding universe (an idea that was first put forth by de Sitter) "is based on the assumption of spatial homogeneity, which is made on philosophical rather than observational grounds."

I don't really want to address whether or not Ellis was right on this point (I'm going to be writing on that in a month or two, if I'm lucky), but he isn't right on this point today. There are numerous sky surveys out there to build actual evidence for general, first-approximation, homogeneity of the kind required for the standard cosmological models.

[modest]

Basically, what I attempt to suggest, without going into the tedious cosmological details (for now), is that there are two ways of looking at redshift z from the point of view (the rest frame) of any observer. Namely, the universe is either expanding and (nearly) flat, or it is hyperbolic and static. From an observational perspective, the two are (or were, rather, see below) indistinguishable.

 

Your statement here would seem to suggest a hyperbolic space-time produces one kind of redshift while a flat space-time produces another. This isn't the case as you and I both know; so, I think we have to get into those tedious cosmological details.

 

For one: can a matter-filled hyperbolic universe with De Sitter like time be described? Has it ever? I'd really like to honestly see that model.

 

If we accept your interpretation of redshift we must ignore good observations of the CMB and light element abundance. That's a tall order to fix a problem that isn't broke. We also must explain why stars seem not to be infinitely aged - or at least aged in the order of hundreds of billions of years. It seems like none of the evidence we've found since 1917 has supported a pencil-on-its-tip universe model. The best astronomy is based in or at leaset supported by observation - which all seems to point to the primordial atom.

 

1977 was the year of the Sacco and Vanzetti condemnation.

 

I hope you're referring to his model here and not De Sitter himself - who was well regarded and recognized at a genius in his time.

 

-modest

[coldcreation]

Your statement here would seem to suggest a hyperbolic space-time produces one kind of redshift while a flat space-time produces another. This isn't the case as you and I both know; so, I think we have to get into those tedious cosmological details.

 

Redshift is redshift. The difference between the two is the cause of redshift (which until definitive evidence on observational fronts sways the balance in favor of one model or the other, is based on interpretation).

 

Although de Sitter ended up adhering to non-static cosmological solutions with the reserve that “this hypothesis may at some future stage of the development of science have to be given up,” his work assumes the responsibility as a forerunner to the stationary evolving universe where the redshift is closely related to the relativistic effect that caries his name (the de Sitter effect). From the point of view of any observer, a distant object appears as though it is embedded in a hyperbolic universe where the redshift increases with distance, and is in fact nearly proportional to the distance. However, the greater the distance, the greater the deviation from linearity.

 

De Sitter used GR with the cosmological constant to construct a model of the universe where the gravitational force of attraction was everywhere in equilibrium with the force of 'repulsion' (lambda). He then removes all the force of attraction (by eliminating matter) and is left with the cosmic substratum that nevertheless retained curvature of both space and time. A free particle introduced in the manifold would either appear accelerated, or embedded in a curved spacetime manifold, as seen from the spectral shifts.

 

It should not occasion unwarranted amazement that from a stationary frame of reference in a non-expanding empty universe, the de Sitter effect should resemble an expanding model. The spectrum of any light source introduced into the manifold would appear redshifted (provided it was far enough away for the effect to become apparent). The only thing left to do would be to determine whether this effect was due to the receding motion of the light source, inducing a Doppler-like effect, or whether the redshift was due to temporal displacements proportional to distance in a curved spacetime continuum.

 

 

For one: can a matter-filled hyperbolic universe with De Sitter like time be described? Has it ever? I'd really like to honestly see that model.

 

Yes, a matter-filled hyperbolic universe with De Sitter like time was described by de Sitter himself. Recall, one of the two 1917 de Sitter models had matter (the model B discussed above did not).

 

 

If we accept your interpretation of redshift we must ignore good observations of the CMB and light element abundance. That's a tall order to fix a problem that isn't broke.

 

But this is not my interpretation of z. It was predicted by the general postulate of relativity, articulated by de Sitter, and arguably observed in nature.

 

The CMB and light element abundance, at least according to Hoyle and Burbidge in this work that I've linked previouslydoesn't seem to pose much of a problem.

 

 

We also must explain why stars seem not to be infinitely aged - or at least aged in the order of hundreds of billions of years. It seems like none of the evidence we've found since 1917 has supported a pencil-on-its-tip universe model. The best astronomy is based in or at leaset supported by observation - which all seems to point to the primordial atom.

 

Au contraire. The pencil problem is not exclusive to one model or the other. Fred Hoyle pointed out the problem with great lucidity:

 

“This picture…generalizes…the big-bang view of the Universe' date=' in which the entire Universe originates like the pencil balanced on its point. The balancing must be ultrafine. The density range in the cloud from the first moment contemplated in the theory…until the present is so vast that the pencil has to be balanced to an accuracy of about I part in 10 (60th). Written out in full, 1 part in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. How is this incredible balance achieved? There is no answer from the big-bang supporters, except with the implication of divine adjustment.” (Fred Hoyle 1994, 1997, p. 402) [/quote']

 

 

The ‘flat’ Euclidean one–to–one relation between the energy density to the critical density (omega), and the spatial curvature of the universe, predicted by the preferred Friedmann model (omega = 1), suffers from the same problem that Newton was forced to attribute to supernatural force: Like balancing a pencil on its point, flat today. It is impossible to explain why there is a perfect (or very nearly perfect) equilibrium or fine-tuning between the apparent velocities of receding galaxies, against the ‘attractive’ force of gravity.

 

Indeed, the favored Friedmann model with a critical density expands outwards at a rate that precisely balances the inward force of gravity. That is like a pencil balancing on it head forever. That was the origin of the so-called fine-tuning problem. Fortunately the supernovae Type Ia observations (interpreted as acceleration) show non-linearity, ruling out The critical Friedmann model, and so too the fine-tuning problem. Great, one less thing to worry about. Well, almost. Inflation predicted a one to one expansion ratio, a flat universe with fine-tuning.

 

There is no fine tuning problem in a non-expanding universe. That's an old myth propagated by disgruntled nouveaux relativists and the likes. That problem arose 300 years ago with Newtonian mechanics. There is one thing though missing from contemporary physics that should be recognized before the fine-tuning problem disappears for good, regardless of whether the model is based on a stable or unstable background.

 

 

I hope you're referring to his model here and not De Sitter himself - who was well regarded and recognized at a genius in his time.

 

Yes, I was referring to his model. And, yes, I agree with you that de Sitter was highly regarded: he was a true relativist; the best, after Herr Einstein of course.

 

 

Regards,

 

CC

[modest]

Redshift is redshift. The difference between the two is the cause of redshift (which until definitive evidence on observational fronts sways the balance in favor of one model or the other, is based on interpretation).

 

It is the evidence of the primordial atom that rules out any interpretation of redshift that does not describe real expansion - the balance is long past swayed.

 

Yes, a matter-filled hyperbolic universe with De Sitter like time was described by de Sitter himself. Recall, one of the two 1917 de Sitter models had matter (the model B discussed above did not).

 

Models A B and C where not the different models De Sitter had in mind, but were comparisons between the models of different people. C was Mankowski's. Indeed there were not 2 De Sitter models. It was one solution to the field equations described 2 different ways or with 2 different metrics. The solution was that of a positive cosmological constant and devoid of matter resulting in a maximally symmetric hyperbolic space time. As Freidmann later found, this solution as well as Einstein's are simply the different geometries that result from different (matter density / cosmological constant) parameters.

 

De Sitter himself came to the conclusion that his model did not resemble our universe. It does not have appropriate matter content. It is and always was a mathematical construct apart from reality. A quote by De Sitter referencing models A and B:

 

Both the solutions must be rejected, and as these are the only statical solutions of the equations. The true solution represented in nature must be a dynamical solution.

 

-Willem de Sitter, 1931

 

Listen to the man he was a smart fella. What is the dynamical solution we should look to?

 

I have found the true solution, or at least a possible solution, which must be somewhere near the truth, in a paper by Lemaître... which had escaped my notice at the time.

 

-de Sitter to Shapley, 1930

 

This was in the early 30's before all the supporting evidence of expansion. We have since found corroborating evidence - indeed we have found no evidence against expansion to go along with all our corroborating evidence.

 

So, this debate was closed over 70 years ago. All these scientists who assumed any solution would have to be static got past their preconceptions and listened to the math and nature. The evidence since has been enormous.

 

- modest

[Little Bang]

Temporal displacement, is there any observational evidence that supports the idea?

[modest]

Temporal displacement, is there any observational evidence that supports the idea?

 

Temporal displacement?

 

is there another kind?

 

-modest

[coldcreation]

It is the evidence of the primordial atom that rules out any interpretation of redshift that does not describe real expansion - the balance is long past swayed.

 

There is no evidence of a primordial atom!

 

Now very far from dwelling on Friedmann’s anecdotal trivialities, Lemaître saw the primordial atom and the humble expansion of scenery as a living metaphor of parables from the Gospel. Indeed, the primordial atom echoed the full pictorial inventiveness of the Bible itself, albeit with the unforgiving apocalyptic splendor missing from the original version.

 

Lemaître was no ordinary esprit, not a genius either. He used a descriptive, relatively banal language that he complemented in terms of his reinvention. But let’s recognize, honestly, there is no terminology or mathematics to articulate what happens at the moment of creation: a brutal rupture of symmetry, a primeval atom, infinite temperature, matter-antimatter asymmetry, super-radioactive processes, a simple quantum, highly unstable atom, everything (including space) sprouts from a point. Nothing seems to work. Everything has a terribly artificial linguistic physiognomy -- and that despite of the bastardization of simple everyday words.

 

By 1932, in such studies as the “primeval atom” hypothesis (later known as the big bang), it is apparent that Lemaître was no longer following the lead of Einstein or de Sitter in their hermetic approach to cosmology -- they had little interest in such a conflagration -- Lemaître was on a path leading to abstraction and to the almost total disintegration of recognizable form.

 

He was intelligent , yes, but at the same time not entirely comfortable with deliberately great ideas, the kind of generalizations about space, time, and evolution that governed the high ambitions among his brethren. In his work he wrote, “in atomic processes, the notions of space and time are no more than statistical notions.” It was supposed that during the act of cosmologizing, Lemaître’s social and mystical views did not persist, that he was saved by his quasi-obsession with scientific problems. However, on this score history is mistaken. It was the social and mystical in combination with the purely mathematically pictorial that led Lemaître away from nature, into an abstraction based on vast or epic synthetic ideas.

 

 

 

De Sitter himself came to the conclusion that his model did not resemble our universe. It does not have appropriate matter content. It is and always was a mathematical construct apart from reality. A quote by De Sitter referencing models A and B:

 

Indeed, what ultimately counts is how the model(s) fair against observation (s).

 

In 1929, Hubble published a famous paper entitled A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebula. In this work he writes: “The outstanding feature, however, is the possibility that the velocity-distance relation may represent the de Sitter effect, and hence that numerical data may be introduced into discussions of the general curvature of space.” (1929 was also the year of black Thursday at the New York Stock Exchange, the beginning of a long recession).

 

Hubble continues: “In the de Sitter cosmology, displacements of the spectra arise from two sources, an apparent slowing down of atomic vibrations and a general tendency of material particles to scatter. The latter involves an acceleration and hence introduces the element of time.” (Hubble 1929). Hubble should have written that the de Sitter effect is the slowing down of clocks with distance (that is the element of time).

 

The fact is that Hubble tended to attribute the redshift to a “de Sitter effect” meaning that that the redshift is not essentially caused by the recession or radial velocities of galaxies but by variations in time-like intervals; clocks would appear to slow down with increasing distance.

 

His use of the Doppler formula for calculating “apparent velocities” was strictly for “convenience” and simplicity. He very shrewdly left open the possibility that at some time in the future, when observational data would yield less “dubious” results, that an “ultimate interpretation” (as yet “unknown”) might be equally compelling, if not more so.

 

In a 1931 letter (addressed to the Dutchman de Sitter) Hubble wrote; “The interpretation, we feel [Hubble and Humason], should be left to you and the very few others who are competent to discuss the matter with authority” (from Kragh 1996).

 

Now, with the SNe Ia data on our hands, history is repeating itself.

 

 

Listen to the man he was a smart fella. What is the dynamical solution we should look to?

 

The word dynamic here refers not to a changing scale factor, but the dynamics involved in evolutionary processes. A model can be dynamic yet non-expanding.

 

The questions remain, nonetheless, how far is the physical shift of status away from the Einstein-de Sitter or Eddington interpretation; does the legitimization of lambda (not its new its new aka, dark energy) affect the reopening of a wide range of world-views embraced under the heading non-expanding or stationary? And how will it affect contemporary cosmology, physics of the twenty-first century? How, since the cosmological constant relates to gravity as a counter-force, or opposing stress tendency inherent in space, are the notions of symmetry and equilibrium reshaped by this exchange?

 

These are the most important questions of all, but to answer them it is essential to take account of another factor in the immensely increased strength of staticity, a factor so far hardly touched upon in this thread (since it is slightly off-topic): evolution and the formation of the large-scale structure of the universe.

 

 

This was in the early 30's before all the supporting evidence of expansion. We have since found corroborating evidence - indeed we have found no evidence against expansion to go along with all our corroborating evidence.

 

The only to corroborate the evidence (CMB anisotropies, large-scale structures, SNe Ia data) within the framework of the standard model is, as you know, is with an abundant supply of dark energy (not to mention CDM). So really, one could argue that there is no corroborating evidence once the metaphysical factor is removed. It is thus a question of belief, whether dark matter is real or not. My tendency is inclined toward the latter.

 

 

So, this debate was closed over 70 years ago.

 

I argue that the debate should be reopened in view of the recent extraordinary observations.

 

At the very least, a static hyperbolically curved general relativistic matter-filled de Sitter-like option should be explored and confronted head-on to the direct observational evidence. To the best of my knowledge, this has not been done since 1998.

 

 

All these scientists who assumed any solution would have to be static got past their preconceptions and listened to the math and nature. The evidence since has been enormous.

 

The starting-point in nature shows that nuclei, atoms, molecules, planetary orbits, galaxies, and clusters are observed to be very stable systems. And we have no reason to disbelieve the likelihood that the universe in its entirety is stable, and dependent on the same natural ubiquitous mechanism responsible for mediating stability on all scales: It has a name and is denoted by a Greek letter, lambda.

 

 

 

CC

[modest]

Both the solutions must be rejected, and as these are the only statical solutions of the equations. The true solution represented in nature must be a dynamical solution.

 

-Willem de Sitter, 1931

 

The word dynamic here refers not to a changing scale factor, but the dynamics involved in evolutionary processes. A model can be dynamic yet non-expanding.

 

You honestly looked at this quote, saw him say static versus dynamic, and though he didn't mean static and dynamic? Things are getting stretched a bit far.

 

-modest

[coldcreation]

Temporal displacement?

 

is there another kind?

 

-modest

 

This is not at all the type of temporal displacement inferred by the de Sitter effect.

 

The de Sitter effect is a genaral relativistic phenomenon called time dilation.

 

Time dilation is the phenomenon whereby an observer finds that another's clock which is physically identical to their own is ticking at a slower rate as measured by their own clock. This is often taken to mean that time has "slowed down" for the other clock' date=' but that is only true in the context of the observer's frame of reference. Locally (i.e., from the perspective of any observer within the same frame of reference, without reference to another frame of reference), time always passes at the same rate. The time dilation phenomenon applies to any process that manifests change over time.[/url']

 

A maximally symmetric non-Riemannian 4D de Sitter space has constant negative curvature. That is where the time dilation comes from (relative to the observers rest frame).

 

Here is an example of the de Sitter static metric that produces time dilation, i.e., temporal displacements, which manifests itself as cosmological redshift z, and that increases with distance (in a static universe).

 

Time dilation is observed, entre autre, in the spectra and light curves of SNe Ia.

 

 

 

CC

[modest]

This is not at all the type of temporal displacement inferred by the de Sitter effect.

 

The de Sitter effect is a genaral relativistic phenomenon called time dilation.

 

 

Yes, I know that. Little Bang was asking about "temporal displacement" which is some kind of time travel thing. If he meant gravitational time dilation or the de sitter effect - there is absolutely no way I could have known that. That's why I was asking him to clarify what he meant.

 

-modest

[PhysBang]

Here is an example of the de Sitter static metric that produces time dilation, i.e., temporal displacements, which manifests itself as cosmological redshift z, and that increases with distance (in a static universe).

Again, that metric is the one that is proved to not be static, as the static coordinates do not cover the entire space.

[Little Bang]

It appears that CC is saying that the red shift is due to temporal displacement, but the only temporal displacement that I am aware of is due to gravitational differences.