Redshift z

[quantumtopology]

Here is the paper. pages 1 to 6

friedmann 1924.pdf

[modest]

Here is the paper. pages 1 to 6

 

Yeah, it is like I was thinking. Quoting p.2006:

 

Summarizing, we can say that the stationary world with constant negative curvature of space is only possible for vanishing or negative density of matter; the interval corresponding to this world is expressed through the formulae (D91 ), (D92 ) and (D9 9 3 ) given above.

 

You should see this is consistent with my statement:

There are many methods to distinguish between models. To rule out a static, isotropic, homogeneous, general relativistic model one simply needs to note 1) the universe has at least some energy density and 2) the Hubble constant is non-zero.

#1 rules out all but Einstein's model. His is the only static solution of the three with mass (i.e. energy density which would include mass or radiation). His is also the only one that is not spatially open.

 

~modest

[quantumtopology]

No, the equations follow from GR assuming isotropy and homogeneity. Redshift and scale factor are not assumptions but conclusions. They follow from 1) GR 2) isotropy 3) homogeneity. If those three things are true then you get redshift and a scale factor (i.e. the two Friedmann equations I gave).

 

I know this. When I talk about assumptions I mean the fact that you are already assuming H not zero in the first place. And attributing it to Friedmann and his equations, and clearly he gave solutions for H=0 and H different from zero, without favouring any of them.

 

If you take a look at the paper I attached you'll find new static solutions that you seemed to ignore. And I'm glad you said in the previous post that the energy density may or may not be zero, because that means you can't inmediately discard the solutions with negative curvature and vanishing density.

[quantumtopology]

Once again rule number two is equivalent to say : a rule to discard a static model is : that it's not static.

 

Ad rule number one I agreed to being a requisite to standard formulations of GR but you surprised me saying it might not be strictly necesary in GR, and in that case, as the solutions by Friedmann I just sent you show, is not a valid rule either, as these are exact formally perfectly valid solutions of the GR equations and don't have positive energy density.

[modest]

I think I just figured out what is confusing you. I'm not ruling out static models as not static, or ruling out static models as not consistent with GR. I'm ruling out static models as not being consistent with out universe (not consistent with observation). When I said:

1) the universe has at least some energy density and 2) the Hubble constant is non-zero.

I mean that observing mass in our universe rules out the possibility that our universe is de Sitter's static model. Observing H₀ rules out the possibility that our universe is Einstein's static model.

 

I'm saying that if you observe #1 and #2 then you can rule out the three static GR solutions (rule out our universe as being one of them).

 

If you re-read the last few posts in that context I believe things will make sense to you.

 

~modest

[quantumtopology]

Ok, so we are back to our fundamental disagreement about observations , motive of this thread, but I think we can share some basic premises:

 

there exist solutions to GR equations for isotropic, homogenous, static universes with negative curvature (hyperbolic) wich basic problem ( a big one, it seem since this observation looks evident at first sight) seems to be that they give energy densities not positive , besides the crux of this discussion ,wich is is they have H=0 whis is the same as saying they are static so it's kind of redundant to repeat it since its stated inthe first phrase of this paragraph.

 

Would you concede this basic agreement?

[modest]

Ok, so we are back to our fundamental disagreement about observations

 

I guess so.

 

I think we can share some basic premises:

 

there exist solutions to GR equations for isotropic, homogenous, static universes with negative curvature (hyperbolic)

 

Yup Like they say here:

 

[math]v’ = 0[/math]

or [math]\rho_{00} + p_0 = 0[/math]

or both [math]v’ = 0[/math] and [math]\rho_{00} + p_0 = 0[/math]

lead respectively to the Einstein, to the de Sitter, and to the special relativity line elements for the universe as we may now show in detail...

Relativity, thermodynamics, and ... - Google Books

 

The [math]\rho_{00} + p_0 = 0[/math] model (universes where density plus pressure equals zero). Such is called a de Sitter universe.

 

I should note, however, that such a model is only trivially static. If you actually did put stuff in it then the stuff would scatter. That is why the wiki link for Einstein's static universe (which is not hyperbolic) says:

 

The Einstein universe is one of Friedmann's solutions to Einstein's field equation for dust with density [math]\rho[/math], cosmological constant [math]\Lambda_E[/math], and radius of curvature [math]R_E[/math]. It is the only non-trivial static solution to Friedmann's equations

Static universe - Wikipedia, the free encyclopedia

 

But, the [math]\rho_{00} + p_0 = 0[/math] universes do not have mass density, radiation density, or radiation pressure so they can be called static.

 

wich basic problem ( a big one, it seem since this observation looks evident at first sight) seems to be that they give energy densities not positive

 

 

besides the crux of this discussion ,wich is is they have H=0 whis is the same as saying they are static

 

I'm not sure if H has to equal zero in a de Sitter universe. In fact, I think it would not be zero. "static" in the technical sense means that the energy density of space does not change over time.

 

so it's kind of redundant to repeat it since its stated inthe first phrase of this paragraph.

 

Which paragraph?

 

~modest

[quantumtopology]

This paragraph!:

 

there exist solutions to GR equations for isotropic, homogenous, static universes with negative curvature (hyperbolic) wich basic problem ( a big one, it seem since this observation looks evident at first sight) seems to be that they give energy densities not positive , besides the crux of this discussion ,wich is is they have H=0 whis is the same as saying they are static so it's kind of redundant to repeat it since its stated inthe first phrase of this paragraph.

 

 

The model (universes where density plus pressure equals zero). Such is called a de Sitter universe.

 

You keep bringin up de Sitter universe, but remember I'm not referring to this but to the solutions with negative curvature, de sitter's universe is define as a positive curvature manifold. see de Sitter space - Wikipedia, the free encyclopedia.

[coldcreation]

...

 

 

 

Figure 7A, below, like Figure 6A, is a polar coordinate system representation in schematic diagram form. It is a cross section of the visible universe. In addition to being on an oblique angle I gave the manifold some perspective. It differs from Figure 6A in that the 'spherical' shells centered on the origin (the observer rest-frame) represent increments of 1.35 billion light-years (1.35 Gly) in the look-back time. There are ten shells, so the horizon is now at its proper distance of 13.5 Gly and redshift z is plotted accordingly. The concept is identical, it's just more accurately represented. Let's have a look:

 

 

 

 

Figure 7A

The cross-section of a homogenous and isotropic four-dimensional spherically symmetric globally curved geometrically hyperbolic pseudo-Lobachevskian spatiotemporal manifold (a cross section of the visible universe), that mimics observations currently understood as an accelerated expansion in a virtually flat (or quasi-Euclidean) space.

 

 

The striking feature observed here (as in all of the diagram A series) is that the incremental distances of 1.35 Gly 'spherical' shells centered on the observer (at O) appear to increase spatiotemporally in nonlinear fashion, the further one gazes into the look-back time, as if stretched, dilated, or both, relative to the observer's frame of reference.

 

Again, there are two ways to interpret Figure 7A. The most common way, or the generally accepted way is that the universe is expanding, and doing so at an accelerated rate.

 

Here below is an example of the redshift vs. look-back time on which Figure 7A is based. This is a table that converts some (cosmological) redshifts into "lookback" times.

 

 

 

 

 

Here is another plot from ESO, where the Gly plot is linearly expressed, contrary to the redshift plot: Redshift distribution of CDFS sources. (Click on the conic image to enlarge it)

 

 

The other way to interpret the data (along with other generally accepted means of determining distance mentioned above), is that the universe is hyperbolically curved, in accord with general relativity, and stationary (non-expanding).

 

But the argument has been raised that general relativity requires the universe to either expand or collapse (i.e., GR does not allow a stationary universe). I argue that this pseudo-Newtonian interpretation of GR is untenable, and that the concept is inconsistent with observations relating to self-gravitating bound systems (e,g,. the Local Group, or the solar system).

 

The idea that the universe would expand or collapse gravitationally, rather than remain static (or stationary) can even be seen as nonsensical. Just as it would be nonsensical to say that the solar system must either disperse or collapse gravitationally. The motion of the objects in the solar system allows the maintenance of stability (for timescales exceeding 10 Gyr).

 

As long as objects in the universe (such as galaxies, or galaxy clusters and superclusters) remain in motion relative to one another, stability can be acquired and maintained, in accord with both classical Newtonian mechanics and Einstein's general theory of relativity. There is no need to extrapolate the problem of stability or instability to the entire universe. If the universe is infinite spatiotemporally it would make even less sense. An infinite universe would have no physical reason to expand or collapse. There is no center, or center of gravity towards which to collapse.

 

I used to think there might be some physical mechanism responsible for the maintenance of equilibrium between gravitating bodies, both locally and for the largest possible scales, somehow related to Einstein's cosmological constant. But it's a lot more simple than that.

 

 

I know what you're thinking; if it's that simple it can't be true.

 

I would argue that if it's that simple, it must be true.

 

 

The interesting twist here is that the cosmological constant is no longer required (gone, ...again), and could therefore be relegated back to being Einstein's greatest blunder (until it's next resurrection ). I never though a day would come where I would actually write that.

 

 

Indeed, local physics is global physics. The same physics described by celestial mechanics for local n-body gravitating systems is operational at all scales. It is thus possible for a universe (infinite spatiotemporally) along with the totality of mass-energy contained in it, to remain stable against gravitational collapse (or expansion). And the funny thing is that no modification of GR is required.

 

 

The detail of this idea will be the subject of the coming posts.

 

 

To be continued...

 

 

 

CC

[quantumtopology]

Indeed, local physics is global physics. The same physics described by celestial mechanics for local n-body gravitating systems is operational at all scales. It is thus possible for a universe (infinite spatiotemporally) along with the totality of mass-energy contained in it, to remain stable against gravitational collapse (or expansion). And the funny thing is that no modification of GR is required.

The detail of this idea will be the subject of the coming posts.

 

Can't wait to see how you pull out the trick.

[coldcreation]

Can't wait to see how you pull out the trick.

 

Oh, it's simple: in the same way you don't need static solutions to the Einstein field equations for local dynamics, you don't need static solution of the field equations for global dynamics.

 

 

CC

[quantumtopology]

Oh, it's simple: in the same way you don't need static solutions to the Einstein field equations for local dynamics, you don't need static solution of the field equations for global dynamics.

 

Well , I guess that might be a little too simple, expansion is a global solution and only works in global dynamics, space doesn't expand locally, so in the local dynamics it doesn't matter whether you choose a static or expanding model.

 

But I like the principle that if you don't need an expanding assumption to explain things locally ( and by locally I mean the Local Group of galaxies) and certainly expansion is not a minor assumption, it would seem totally unnecesary and against the Occam's razor, to postulate it for the global dynamics. Enter the redshift. And everybody knows the doppler effect produces redshift, but that doesn't mean all redshifts are due to the Doppler effect.

 

And in this thread it has been put forward the fact that in a hyperbolic geometry, in a universe with negative curvture, you also perceive a redshift related to distance that makes totally gratuitous the introduction of expansion. To me this is the key point to stablish if we want to make a believeable cosmological alternative

 

The possibility of a hyperbolical geometry of the univere is not some crazy idea that has just occurred to us, it's been proposed since the discovery of this geometry in the 19th century, and currently there are cosmologist and mathematicians like Roger Penrose that are championing this geometry for the universe.

 

Let's imagine that historically we had known before Hubble that one way to get a redshift related to distance is the hyperbolic spacetime curvature acting on light. Just like we learned by Einstein in the 1910's that another way to get spectral shifts is the gravitational field-another spacetime curvature or geometric action on light.

 

Expansion would have never been seriously considered ,if only for reasons of economy of assumptions (using the least quantity of assumptions to explain something) to interpret Hubble's findings, it would have been attributed to the hyperbolic geometry of the universe.

[coldcreation]

Well , I guess that might be a little too simple, expansion is a global solution and only works in global dynamics, space doesn't expand locally, so in the local dynamics it doesn't matter whether you choose a static or expanding model.

 

The point is that even in the absence of static solutions for local dynamics (i.e., since static solution are not required to explain how objects manages to achieve orbital stability, however precarious) stability against gravitational collapse (or excessive velocity-induced dispersion) is achieved and maintained. If space is not expanding, then there is no reason to believe the same fundamental physical processes responsible for local stability are not operational globally. There is no static solution required by the Einstein field equations for a non-expanding universe (as was erroneously assumed by both Einstein and de Sitter in their 1916-1917 debates on the metric structure of the universe).

 

I will come back to this point.

 

 

But I like the principle that if you don't need an expanding assumption to explain things locally (and by locally I mean the Local Group of galaxies) and certainly expansion is not a minor assumption, it would seem totally unnecesary and against the Occam's razor, to postulate it for the global dynamics. Enter the redshift. And everybody knows the doppler effect produces redshift, but that doesn't mean all redshifts are due to the Doppler effect.

 

Precisely. In fact, the expansion redshift is not a true Doppler effect. And nor is redshift z in a stationary geometrically hyperbolic universe a true gravitational redshift effect. I will come back to this too.

 

 

And in this thread it has been put forward the fact that in a hyperbolic geometry, in a universe with negative curvture, you also perceive a redshift related to distance that makes totally gratuitous the introduction of expansion. To me this is the key point to stablish if we want to make a believeable cosmological alternative

 

Exactly.

 

 

The possibility of a hyperbolical geometry of the univere is not some crazy idea that has just occurred to us, it's been proposed since the discovery of this geometry in the 19th century, and currently there are cosmologist and mathematicians like Roger Penrose that are championing this geometry for the universe.

 

While this is true, I would assume that Penrose postulates hyperbolicity in an expanding universe. But that takes nothing away from the concept of geometry on global scales. Edit: I take that back. I'm looking at the Penrose diagram right now, and there may be an interpretation to be made related to a manifold that is stationary (independent of expansion). More on this soon. Thanks for that info. I was not yet aware of these diagrams. I do have to find a better source than Wiki for this. If you have one, please link-me. In the mean time I will see what I can muster-up online.

 

 

Let's imagine that historically we had known before Hubble that one way to get a redshift related to distance is the hyperbolic spacetime curvature acting on light. Just like we learned by Einstein in the 1910's that another way to get spectral shifts is the gravitational field-another spacetime curvature or geometric action on light.

 

There is a comparison that needs to be made with respect to both models (expanding and static). Recall that redshift z in an expanding universe is not a true Doppler effect. Redshift would be caused by the metric expansion of space itself: the averaged increase of metric (i.e. measured) distance between distant objects in the universe with time). That is, expansion is defined by the relative separation of parts of the universe, not by motion 'outward' into preexisting space. So redshift is not a true Doppler effect.

 

Similarly, in a static universe, redshift z is not a true gravitational redshift. It would be caused by the average curvature of spacetime which appears to increase hyperbolically with distance (i.e., measured) from the observer to distant objects in the universe with look-back time.

 

 

While special relativity constrains objects in the universe from moving faster than the speed of light with respect to each other, there is no such theoretical constraint when space itself is expanding. There is, however, the constraint of light speed when the universe is not expanding, since all observation are carried out from our (or any observer's) rest-frame. It is thus possible for two very distant objects to appear extremely redshifted and time dilated (as if spuriously "moving" away from each other at a speed greater than the speed of light) to such a point where the emitted light no longer reaches the observer (meaning that these objects cannot be observed from the local rest-frame). The size of the observable universe would thus appear to be just a small section of an infinite general relativistic hyperbolically curved spacetime continuum.

 

Gravitational redshift, as opposed to a redshift z induced as photons propagates through a globally hyperbolic spacetime, is due to the effect caused on the wavelength of electromagnetic radiation originating from a source located in a region of stronger gravitational field, or at differing altitudes (and which could be said to have climbed 'uphill' out of a gravity well) are of longer wavelength when received by an observer in a region of weaker gravitational field (or at higher altitude). This would obviously not be the case when considering a globally isotropic hyperbolic field.

 

 

Expansion would have never been seriously considered, if only for reasons of economy of assumptions (using the least quantity of assumptions to explain something) to interpret Hubble's findings, it would have been attributed to the hyperbolic geometry of the universe.

 

Yes, and indeed it was for a while interpreted as a de Sitter effect in a stationary universe, as you know. But that idea quickly vanished in favor of a non-conventional pseudo-Newtonian precept of space and time; based in part on the solutions of Friedmann, but especially based on the mysticism Lemaître, with his radical speculation that the new hypothesis on the nature of space and time leads not just to an expanding universe, but to a chimerical primeval atom, a faint echo of Biblical creation.

 

 

 

Something has only just begun

 

 

CC

 

 

To be continued...

[modest]

de sitter's universe is define as a positive curvature manifold. see de Sitter space - Wikipedia, the free encyclopedia.

 

I'm sorry if I was confusing. De Sitter's metric can describe open, flat, or closed cosmologies. What I meant by "de Sitter universe" is a universe with no matter and a positive cosmological constant such that it is spatially open.

 

You'll see in the Friedmann paper you gave he compares static negative curvature to de Sitter's model at the top of the second page.

 

It could also be kept in mind, like CC said, the curvature of spacetime is not the same as the curvature of space. A positively curved Lorentzian manifold corresponds to a repulsive force of gravity (de Sitter space) and a negatively curved Lorentzian manifold corresponds to an attractive force of gravity (anti de Sitter space).

 

It has a separate meaning from the curvature of space which is best thought of as determining if the universe is open or closed (ie bound or unbound).

 

There are ten shells, so the horizon is now at its proper distance of 13.5 Gly and redshift z is plotted accordingly.

 

Glad I could help :)

 

The most obvious question is why D_{(look-back time)} = 13.5 is a horizon. Why can't you see things at D = 14? In an expanding model it makes sense that the universe is only so old. There would be a visible horizon at some point corresponding to the look-back time beyond which the universe was filled with matter too dense for light to get around.

 

But, if you're suggesting that things are static then I don't understand why D=13.5 would correspond to a horizon.

 

I would suggest that D=13.5 should correspond to z=∞. I think that would fix the problem, but the diagram has D(13.5)=z(10) which clearly seems problematic if you want D=13.5 to be a horizon (regardless if the horizon is an effect of redshift or time dilation).

 

The striking feature observed here (as in all of the diagram A series) is that the incremental distances of 1.35 Gly 'spherical' shells centered on the observer (at O) appear to increase spatiotemporally the further one gazes into the look-back time, as if stretched, dilated, or both.

 

I have a problem with that assertion. You drew the look-back time quadratically (as you say, "incremental distances of 1.35 Gly... appear to increase") but there is no reason that I can figure for you to have done that. You could just as easily had "incremental distances of 1.35 Gly... appear to decrease" and if you did that it would allow you to say "incremental distances of 1.35 Gly appear to decrease relative to redshift". In other words, between z=1 and z=2 there is quite a bit more look-back time than between z=3 and z=4.

 

In fact, let me plot what I mean to make clear. Plotting your redshift / look-back time data we get:

 

 

So the range 9 < z < 10 has a much smaller change in look-back time than 1 < z < 2. Hopefully you see what I mean. It is not the case that incremental distances of look-back time appear to increase relative to redshift. It is rather the opposite.

 

To be consistent with your diagram we would need the curve to be a hyperbola. It is possible that you didn't mean that look-back time increases hyperbolically *with respect to redshift*, so the pertinent question would be: relative to what does the change in look-back time increase? To put it graphically:

 

 

The other observable clearly isn't redshift and you've previously indicated that it isn't galaxy count. It cannot be the case that "incremental distances of 1.35 Gly... appear to increase" relative to itself, so I think we need to put some consideration into this. As it stands, I see no reason to draw the diagram like diagram A rather than diagram B or C.

 

Again, there are two ways to interpret Figure 7A. The most common way, or the generally accepted way is that the universe is expanding, and doing so at an accelerated rate.

 

But, in standard cosmology the diagram would not look like you have drawn it. It would look like diagram C. The most natural thing in ΛCDM against which to compare look-back time is comoving distance. Just like the redshift / look-back time diagram above, a "comoving distance / look-back time diagram" would have positive rather than negative curvature in ΛCDM.

 

To demonstrate numerically (I'm too tired at the moment to plot another diagram), let D_C be comoving distance and D_L be the look-back time,

D

_L

= 1 Gyr, D

_C

= 1.038 Gly

D

_L

= 2 Gyr, D

_C

= 2.156 Gly

D

_L

= 3 Gyr, D

_C

= 3.365 Gly

D

_L

= 4 Gyr, D

_C

= 4.678 Gly

D

_L

= 5 Gyr, D

_C

= 6.109 Gly

D

_L

= 6 Gyr, D

_C

= 7.681 Gly

D

_L

= 7 Gyr, D

_C

= 9.420 Gly

D

_L

= 8 Gyr, D

_C

= 11.367 Gly

D

_L

= 9 Gyr, D

_C

= 13.582 Gly

D

_L

= 10 Gyr, D

_C

= 16.165 Gly

D

_L

= 11 Gyr, D

_C

= 19.293 Gly

D

_L

= 12 Gyr, D

_C

= 23.363 Gly

D

_L

= 13 Gyr, D

_C

= 29.698 Gly

You can see that the change in look-back time decreases at greater comoving distance. As D_L approaches the age of the universe D_C approaches 46 Gly (today's horizon in comoving distance).

 

So, you say that your diagram and the data that it represents can be interpreted two ways, but the diagram itself is not clear in what it represents. As far as I can tell, your choice to plot look-back time like diagram A ( where "incremental distances of 1.35 Gly... appear to increase") is arbitrary and doesn't seem to correspond to any data that I know or that you gave.

 

Here below is an example of the redshift vs. look-back time data upon which Figure 7A is based...

 

It seems to me that we cannot claim the data can be interpreted as static and hyperbolic unless the data is predicted with a static and hyperbolic model.

 

If we could get this same data (as well as other, and preferably directly observable data) by using a static model rather than using standard cosmology then I think saying "both interpretations are valid..." would be quite fine. That, I believe, should be the direction of investigation.

 

Otherwise, the idea that the data corresponds is an untested hypothesis and the assertion that it corresponds is an assumption.

 

The other way to interpret the data (along with other generally accepted means of determining distance mentioned above), is that the universe is hyperbolically curved, in accord with general relativity, and stationary (non-expanding).

 

So, my biggest objection is that we haven't done anything to determine if the above claim is valid or complete rubbish. As far as I can tell, it is right now a hollow claim. The focus of investigation should be on deriving a static model or method (or something) that predicts the observables that are right now being solved with standard cosmology and assumed compatible with some unknown static solution.

 

The idea that the universe would expand or collapse gravitationally, rather than remain static (or stationary) can even be seen as nonsensical. Just as it would be nonsensical to say that the solar system must either disperse or collapse gravitationally. The motion of the objects in the solar system allows the maintenance of stability (for timescales exceeding 10 Gyr).

 

As long as objects in the universe (such as galaxies, or galaxy clusters and superclusters) remain in motion relative to one another, stability can be acquired and maintained, in accord with both classical Newtonian mechanics and Einstein's general theory of relativity. There is no need to extrapolate the problem of stability or instability to the entire universe. If the universe is infinite spatiotemporally it would make even less sense. An infinite universe would have no physical reason to expand or collapse. There is no center, or center of gravity towards which to collapse.

 

If the visible universe had a massive center with pockets of orbiting mass then I'd agree.

 

Someone might say that general relativity allows massive stars to collapse and form black holes and therefore it isn't surprising that the earth will one day collapse and become a black hole. But, that would be false because it ignores the fact that the earth is not a massive star. I don't think those kinds of analogies make good arguments.

 

~modest

[quantumtopology]

Precisely. In fact, the expansion redshift is not a true Doppler effect.

 

Recall that redshift z in an expanding universe is not a true Doppler effect. Redshift would be caused by the metric expansion of space itself: the averaged increase of metric (i.e. measured) distance between distant objects in the universe with time). That is, expansion is defined by the relative separation of parts of the universe, not by motion 'outward' into preexisting space. So redshift is not a true Doppler effect.

You stress this point with persistence. I am aware of this. But we can't deny that the cosmological redshift interpretation was triggered, historically and conceptually by interpreting redshifts as radial velocities in other words doppler effect. When telescopes got bigger and distances observed reached certain magnitudes, obviously not even with the relativistic doppler effect could the redshifts be managed correctly, so they had to be calculated in terms of the cosmological redshift that anyway is the logical choice with the Friedman equations and the FRW metric, but for many phisicists is still explained as a doppler shift in cosmological coordinates, or as an integration of infinitesimal doppler shifts ,(I've seen it explained this way by renowned physicists).

 

I would assume that Penrose postulates hyperbolicity in an expanding universe.

 

He does. My references of his preference for a hyperbolic universe come from his impressive book "The road to reality" and some interviews and popular articles.

He adheres to standard cosmology, but he is seen as a eccentric because he doesn't like inflationists hypothesis and has pointed out in many instances the thermodynamical improbability of the initial moments of the universe in the BBT. Sometimes I perceive in his writings that he has important doubts about the Standard model but he wouldn't admit it publicly, as he knows then he would be inmediately banned from "serious" science.(look what happened to good ol' Harp.) Again this is my perception and could be biased. :)

 

 

Similarly, in a static universe, redshift z is not a true gravitational redshift. It would be caused by the average curvature of spacetime which appears to increase hyperbolically with distance (i.e., measured) from the observer to distant objects in the universe with look-back time.

 

This is a very interesting theme, and I'll try to elaborate on it later

 

 

 

Something has only just begun

 

Actually continuing ;)

[quantumtopology]

Originally posted by Modest

The most obvious question is why D(look-back time) = 13.5 is a horizon.

 

In a hyperbolic non-expanding infinite universe you would still have a finite observational horizon based on the finite speed of light and the intrinsic geometry effect on light intensity (thus faintness of SNe Ia) and on light spectrum ,(this is actually a solution of Olber's paradox that relies on the geometric properties of hyperbolic geometry instead of on expansion) so the observable universe has a limit that is around those figures probably, and as it's been also said that this is another of the features that wouldn't allow us to distinguish the static from the expanding models

 

Originally posted by Modest

If the visible universe had a massive center with pockets of orbiting mass then I'd agree.

Someone might say that general relativity allows massive stars to collapse and form black holes and therefore it isn't surprising that the earth will one day collapse and become a black hole. But, that would be false because it ignores the fact that the earth is not a massive star. I don't think those kinds of analogies make good arguments.

 

Er.. I don't think this has anything to do with CC's analogies

 

What he implies is just the opposite, precisely in an infinite universe such thing as a massive center is unlikely,and the analogy of the earth collapsing I simply can't grasp.

[modest]

In a hyperbolic non-expanding infinite universe you would still have a finite observational horizon based on the finite speed of light and the intrinsic geometry effect on light intensity (thus faintness of SNe Ia) and on light spectrum

 

My point was that at such a horizon the redshift must be infinite.

 

Scientific Method

 

Confirmation bias

 

~modest