Redshift z

[quantumtopology]

I found this ingenious explanation to redshift z that I believe to be equivalent to the explanation of redshift in hyperbolic 3D space given by von Brzesky in von Brzeski, G. (2006). Big Bang as a Fatal Mistake of Edwin Hubble. Cosmological Red-shift and Related Electromagnetic Phenomena in Static Lobachevskian (Hyperbolic) Universe.. PHILICA.COM Article number 63. but sort of explained backwards, in the following quote mathis is saying that light is less curved wrt us because we are in a motion that describes a much tighter curve (elliptical) than light straighter path while Brzeski assumes the observer or origin to be in Euclidean(flat) space and light reaching us from distant objects following a geodesic in negatively curved space, but the outcome is the same, we register light redshifted because it comes from a space where light is less curved (more straight) to an obeserver(the earth) in a more curved space(due to gravitational field of sun an center of the galaxy) in mathis quote or if we set our point of view in flat space, light reach us from a negatively curved space (hyperbolic) in Brzeski view.

 

 

On Hubble and the CBR by Miles Mathis

"I have shown that curvature can cause a redshift by creating sideways motion relative to light. But can I show that light from more distant sources would be shifted more? Yes. Since we are comparing curvatures, all I have to do is show that more distant light is curved less. This is easy to do, since, in general, the universe is curved more at smaller scales than at larger scales. General Relativity shows us that the universe as a whole is curved, but the universe is not as curved as a galaxy, and a galaxy is not as curved as a star. The curvature decreases at larger scales, by definition. If the curvature increased for larger scales, the larger scales could not be larger, could they? They would be pulled back on themselves, and would be smaller. Therefore, light traveling longer distances can be considered to be “larger-scale” light. Its total bend may be quite large, but its bend per unit length is less than nearer light, simply because it got here from so far away. If it had the same bend per distance traveled as nearer light, it could not have gotten here from there. More distant light is bent less by a tautology, since to get here from there, it had to travel a straighter path. The universe is curved less at larger scales, and it is the universe that determines the path of the light. Light diverted by smaller scale curvatures could not have gotten here from so far away.

 

Since more distant light is curved less, the difference between its own curvature and our curvature will be greater. Therefore our sideways motion relative to it will be greater, and the redshift will be greater. "

[modest]

Furthermore, just to let both you know (QT and modest) that Explanation 2 is almost complete.

 

We'll call the previous post "prelude to Lobachevskian curvature #1" :)

 

Comes from post 514 in the context of local versus global physics, it seems tha from Einstein and Friedmann equations a universe filled with radiation (no matter) would have R=0 or no curvature but intuitevely one would think that since radiation has energy density the Ricci scalar shouldn't be zero but I am not sure about this, if the Ricci scalar is zero then the Ricci tensor is also zero and therefore the stres energy tensor T should equal zero, is this compatible with a universe filled with radiation, with an energy density three times its pressure. Looks like something is wrong here but I don't know what.

 

A zero T is expected and implies conservation of energy-momentum. The link I gave in the other thread: Stress-energy tensor - Wikipedia, the free encyclopedia shows.

 

The Ricci tensor or scalar should probably not be so readily called "the curvature of spacetime". For example, the scalar is zero everywhere outside the horizon of a Schwarzschild solution while it is only asymptotically flat which is to say: not flat at all.

 

I don't feel qualified enough (and I doubt anyone participating in this thread is) in tensor calculus to analyze the particulars. I can, however, stand by my statement. As you say, from post 514,

 

Perhaps something for us to chew on: radiation pressure acts to stabilize a star against collapse, but globally with the universe as a whole, radiation pressure acts to add to the gravitational field, increasing the curvature, pushing the universe closer to wanting to collapse

 

Both density and pressure push the universe to collapse. If you want to see it derived from Einstein's tensor equation, the often quoted source would be: Dynamics of Homogeneous and Isotropic cosmologies

 

I'll quote from directly under eq. 11.18:

The effective gravitational energy is given by [math]\rho[/math] + 3P; the pressure also contributed to gravitation. Note that p < - [math]\rho[/math]/3 implies repulsive gravitation.

 

This is nothing more or less than I was saying and the consequences are as follows: any homogeneous and isotropic universe that is static today and has some matter/energy content will collapse in the future according to GR—it will begin collapsing immediately. To reject such a conclusion is either to reject GR or homogeneity and isotropy as good approximations.

 

That would explain the much talked about problems GR has with energy conservation globally.

 

Conserving energy/momentum is not a problem of energy conservation.

 

If the universe is infinite, certainly gravitation would be a local phenomenon and GR would describe a local deviation of spacetime but couldn't be applied to the universe as a whole where R would tend to zero as distance from the local perturbation tends to infinite.

 

"couldn't be applied"? I do hope you have a source proving that the entire foundation of modern cosmology and astrophysics is impossible.

 

Einstein perceived this problem in his 1917 cosmology paper and thus sought to solve it with the cosmolgical constant, that he never liked anyway, when appearance of expansion was found and after the initial resistance, he finally saw expansion as a way to solve his probem with infinty and to get rid of his loathed lambda.

 

The value of lambda (either negative, positive, or zero) can only be known by making measurements and observations. It is not something to be a priori rejected and Einstein believed the same:

 

“The postulate of general relativity requires the introduction of the [cosmological constant] into the field equations. It will be our factual knowledge of the composition of the starry heavens, of the apparent motions of the stars, and of the state of spectral lines as a function of conditions far from us that will allow us empirically to answer the question whether the [cosmological constant] equals zero or not. Conviction is a good mainspring, but a bad judge!"

-

source

 

I found this ingenious explanation to redshift z that I believe to be equivalent to the explanation of redshift in hyperbolic 3D space given by von Brzesky in von Brzeski, G. (2006). Big Bang as a Fatal Mistake of Edwin Hubble. Cosmological Red-shift and Related Electromagnetic Phenomena in Static Lobachevskian (Hyperbolic) Universe.. PHILICA.COM Article number 63. but sort of explained backwards, in the following quote mathis is saying that light is less curved wrt us because we are in a motion that describes a much tighter curve (elliptical) than light straighter path while Brzeski assumes the observer or origin to be in Euclidean(flat) space and light reaching us from distant objects following a geodesic in negatively curved space, but the outcome is the same, we register light redshifted because it comes from a space where light is less curved (more straight) to an obeserver(the earth) in a more curved space(due to gravitational field of sun an center of the galaxy) in mathis quote or if we set our point of view in flat space, light reach us from a negatively curved space (hyperbolic) in Brzeski view.

 

 

On Hubble and the CBR by Miles Mathis

 

I've read it. CC brought it up in post #330.

 

~modest

[quantumtopology]

A zero T is expected and implies conservation of energy-momentum.

The Ricci tensor or scalar should probably not be so readily called "the curvature of spacetime". For example, the scalar is zero everywhere outside the horizon of a Schwarzschild solution while it is only asymptotically flat which is to say: not flat at all.

I don't feel qualified enough (and I doubt anyone participating in this thread is) in tensor calculus to analyze the particulars. I can, however, stand by my statement.

 

Yes, there were some misundertandings due to lack of familiarity with tensor calculus.

First of all R=0 does not imply a flat manifold, in order to get a flat manifold the Riemannian tensor should be zero, and also when we see T=0 doen't mean the stress-energy tensor is zero but its trace, In conclusion in a universe filled with radiation you have R=0 and T=0 but the curvature is not zero and the energy tensor is not zero either (only its trace is), so that should solve my paradox wich was only derived from my poor knowledge of tensor calculus.

 

 

Both density and pressure push the universe to collapse.

Yes, but please apply it to stars for now, I say it only for the sake of the discussion, in order not to close doors beforehand, after all that is one of the final conclusions we are triyng to refute (certainly CC is), among other things that wouldn't apply in an infinite universe.Even in the case of expansion model for k=0 and k=-1

 

 

This is nothing more or less than I was saying and the consequences are as follows: any homogeneous and isotropic universe that is static today and has some matter/energy content will collapse in the future according to GR—it will begin collapsing immediately. To reject such a conclusion is either to reject GR or homogeneity and isotropy as good approximations.

Again you are referring to Einstein universe which is finite(though unbounded).

 

 

Conserving energy/momentum is not a problem of energy conservation.

I am talking about a problem realized and acknowled by every mainstream relativist. There is even a math tool developed to try to cope with it , the landau-lifshitz pseudotensor. I honestly think that conservation of energy/momentum is related to energy conservation, if it's not please explain.

 

 

"couldn't be applied"? I do hope you have a source proving that the entire foundation of modern cosmology and astrophysics is impossible.

Ok, you have a point there, but have you noticed that this 4 year old thread postulates that redshift is not due to expansion and if so the entire foundaton of modern cosmology is indeed impossible? :)

 

The value of lambda (either negative, positive, or zero) can only be known by making measurements and observations. It is not something to be a priori rejected and Einstein believed the same:

 

You must know the cite about the "biggest blunder" and you have to be aware (if you have read some biography of Einstein) of his feelings about this constant, that is all I have talked about, not about the value of lambda.

 

I've read it. CC brought it up in post #330.

 

Sorry, I missed that post, I'll take a look at it.

 

 

Regards

[quantumtopology]

I checked post 330, I was aware of that link : the Brzeski one, CC and I had talked about it in this thread, I thought you were referring to the Maltis link, but i think i'm the fisrt to post it here, anyway if you read them maybe you could give us your thoughts on the comparison I stablished between those two approaches to redshift.

 

One mistake that upon reading the older posts I find is that CC spoke about the Brzeski paper in terms of "spacetime curvature", when it is clear( and judging by his responses,also Modest saw this clearly) that the paper only talks about "space curvature".

 

In my opinion the Brzeski paper doesn't directly address GR or FRW metrics since it only treats space, and gives a redshift explanation in terms of space only as a conformal stretching of wavelenghts, in that sense has nothing to do with the desitter effect that deals with time, it is a purely geometrical explanation, based in hyperbolic geometry and the conformal deformation of the perceived wavelength (stretching) that therefore has nothing to do with the light itself nor the photons(no change in energy, no tired light etc)

 

http://www.philica.com/uploads/images/124/Image/deformation_fig4.jpg

 

 

So far noone has been able to refute the geometrical part, which seems to be sound mahematically.

So as long as nobody refutes (either mathematically or physically) that in a hyperbolic space , regardless of the cosmological model at this moment, E-M wavelenghts are seen as stretched proportional to distance-and this has nothing to do with GR, we are not talking about spacetime nor gravitation here-, I am entitled to believe that Doppler-cosmological and gravitational ways are not the only ways to get a redshift. (BTW, there is at least another way, called the Wolff effect).

 

Regards

[coldcreation]

I am curious about how you will do that if you keep your idea of an apparent global positive curvature that clearly ignores the principle of equivalence and arbitrarily affects light but not matter, since you said those problems would be solved in Explanation 2.

 

The notion I'm getting lately is that maybe GR is not suited for a cosmological solution,

it could be that GR only works locally, that is, wherever there is mass there is a local distorsion of spacetime. That would explain the much talked about problems GR has with energy conservation globally. If the universe is infinite, certainly gravitation would be a local phenomenon and GR would describe a local deviation of spacetime but couldn't be applied to the universe as a whole where R would tend to zero as distance from the local perturbation tends to infinite.

Einstein perceived this problem in his 1917 cosmology paper and thus sought to solve it with the cosmolgical constant, that he never liked anyway, when appearance of expansion was found and after the initial resistance, he finally saw expansion as a way to solve his probem with infinty and to get rid of his loathed lambda.

 

I see it is like this: Local physics is global physics. Strange it would seem indeed if the physical laws governing the universe locally (everywhere) were different than the laws governing the universe globally (everywhere).

 

That leaves only three possibilities: (1) GR is a global theory, (2) GR is a global theory, or (3) GR is a global theory.

 

The only problem, so it seems, would be to interpreted general relativity in such a way as to maintain consistency both locally and globally.

 

Obviously right now that is lacking (quantum mechanics aside).

 

 

CC

[quantumtopology]

I see it is like this: Local physics is global physics. Strange it would seem indeed if the physical laws governing the universe locally (everywhere) were different than the laws governing the universe globally (everywhere).

 

That leaves only three possibilities: (1) GR is a global theory, (2) GR is a global theory, or (3) GR is a global theory.

 

You are missing my point,(or I'm missing yours) you are taking local versus global in the trivial sense that any physical law must be valid in any point of the universe following the relativity principle that requires that any law of nature should be the same at all times and regardless of location. But that is not what we are discussing here. You can't possibly mean that any theory that describes some particular local physics can be considered a model of the universe because " Local physics is global physics". I could give you examples of local laws but I in no way want to appear as sarcastic , I think you get my point by now.

If that was the case cosmology would be unnecesary :) as every local theory would be a global theory of the universe.

 

 

 

The only problem, so it seems, would be to interpreted general relativity in such a way as to maintain consistency both locally and globally.

 

According to the first quote there shouldn't be any inconsistency: if you really see it like Local Physics is Global Physics.

 

You could consider instead GR to be an incomplete theory, wich every theory is anyway:

Remember that the map is not the territory.

 

Regards

[coldcreation]

You are missing my point,(or I'm missing yours) you are taking local versus global in the trivial sense that any physical law must be valid in any point of the universe following the relativity principle that requires that any law of nature should be the same at all times and regardless of location.

 

True, that's more or less what the discussion was about. Recall the idea that stars remain stable with pressure (that acts against gravity), but on the large scale pressure gravitates and so contributes to the global topology. That's what the discussion was about. My claim was that GR can be interpreted many ways. And that the discrepancy with observations locally is large when compared to observations globally (on the large scale); where lambda means nothing locally (it's contribution is virtually zero), gravity rules: yet on large-scales it dominated the universe.

 

I might be wrong, but if the same physical laws govern the universe at scales compatible with the solar system also govern the expansion, then someone has misinterpreted GR. That is my point.

 

 

According to the first quote there shouldn't be any inconsistency: if you really see it like Local Physics is Global Physics.

 

Exactly. But let's not confuse things like topology and the gravitational field of the moon. Certainly the same laws are operational, but things don't always happen the same at different scales. The key is that laws not be violated by a theory to explain things that don't jive here or there observationally. I think we're on the same page there.

 

You could consider instead GR to be an incomplete theory, wich every theory is anyway: Remember that the map is not the territory.

 

Sometimes it's not even that a theory is incomplete so much as it is a question of interpretation. What complicates matters further is that some physical laws are time reversible, while others (e.g., the second law of thermodynamics) are not.

 

But the issue that started this discussion, if I recall, was the idea (my claim) that matter is not affected by the global topology (spacetime curvature of the type de Sitter and Einstein hypothesized about as early as 1916) in a isotropic and homogeneous universe yet light is affected (as de Sitter suspected, known as the de Sitter effect which results in redshift z). To that, modest wrote:

 

Your idea breaks the fundamental postulate of GR—the equivalence principle. The nature of curved spacetime is the equivalence between accelerated inertial reference frames and gravity. To say that spacetime is globally curved yet there is no accelerated inertial reference frames just doesn't make sense. By the very definition, global curvature would have accelerated inertial reference frames, and again by definition matter would want to follow those inertial reference frames.

 

This is a classic case, where an interpretation of local phenomena is extrapolated to the large-scale, seemingly in accord with Einstein's equivalence principle, and somehow seemingly in accord with Newton's idea of gravity as an attractive force. The result is massive instability. Clearly someone (possibly myself) has misinterpreted GR.

 

I think this is one the most important problems of modern cosmology. The problems is not solved yet. But that does not mean there is no solution.

 

Stay tuned...:)

 

 

CC

[quantumtopology]

I might be wrong, but if the same physical laws govern the universe at scales compatible with the solar system also govern the expansion, then someone has misinterpreted GR. That is my point.

 

Agree

 

Clearly someone (possibly myself) has misinterpreted GR.

 

Probably :D

 

I think this is one the most important problems of modern cosmology. The problems is not solved yet. But that does not mean there is no solution.

Agree

 

Stay tuned...:hihi:

 

Sure, but a suggestion, after we discuss your explanation 2 , I think we should go back closer to the topic and discuss redshift mechanisms,

 

Regards

[coldcreation]

Sure, but a suggestion, after we discuss your explanation 2, I think we should go back closer to the topic and discuss redshift mechanisms.

 

Explanation 2 is not just an explanation of how stability is maintained globally. It actually gets right down to the core mechanism responsible for redshift z. As it turns out, both redshift and stability result from the same thing: Gaussian curvature within the framework of general relativity. :hihi:

 

 

CC

[modest]

Sorry guys, I've been extremely busy.

 

This is similar to your example above, modest, where all observers are entitled to consider themselves on the equator. Certainly other interpretations are permitted, but hers would 'appear' to be consistent with observations, even though we know the conclusion above (that we are deep in a well, or visa versa) is not the case in the real world, i.e., it is a false conclusion. The effect is a relative one.

 

Why would you say that it is *not* the case in the real world because it is relative? Global curvature means that geodesics converge with distance. From any point, geodesics will converge with distance away from that point. Its relative nature makes it no less real.

 

Likewise, our observer at the horizon is entitle to conclude, with her knowledge of special relativity (SR), that the entire Virgo Cluster is racing through space (or with space) close to, or precisely at the speed of light c. This is only an "apparent" affect based on her observations, and which is permitted by relativity, but it too is false, i.e., we are not really moving at the velocity c. That is, the conclusion is false. In order to bypass this problem it had to be invented the notion of expanding space. But general relativity says nothing of the kind. Just as GR says nothing about the existence of an infinite mass at the horizon.

 

Again, you claim that the relative nature of velocity makes it apparent rather than real. If Bob sees Alice moving away from him and Alice sees Bob moving away from her then the velocity is relative. This does not imply that the velocity is only apparent and somehow not real. It is, as it should be, both real and relative.

 

In an apparently expanding homogeneous and isotropic universe where redshift z is a classical Doppler effect, the conclusion that the physical spatial distance between observers cannot actually be increasing follows from the premise that the metric should treat every observer the same.

 

Your conclusion is non sequitur. It goes against Galilean relativity and makes no sense to me.

 

Quantumtopology had an interesting analogy above: A mirage. Mirages are a natural optical phenomenon that occur where light rays are bent, producing a displaced image of distant objects. They alter proper distances by a distortion process. The observer may incorrectly interpret the actual location of objects, or the shape of the horizon in the background. Light rays coming from a distant object travel through the air layers and all are bent. This is a real physical effect, and the curvature is naturally produced by temperature gradients, but the objects seen and perceived are not really where they appear to be (their position appears to be displaced). Viewed from a different location the mirage will either have a different shape, of will not be present at all.

 

According to GR, the recession is real even if the velocity is apparent. I know that sounds absurd, so let me explain. Let me give an analogy first then a direct result of a de Sitter universe.

 

By analogy, consider someone on a L-Point exactly between two massive stars (in the center of a binary system we'll say). In a rotating frame all three objects are stationary. Our observer attaches two strings to two clocks and slowly lowers each clock toward each star.

 

Two things happen: as the clocks are lowered toward the stars they are time dilated (the center observer sees them redshifted) and imagining that the center observer stops the lowering motion of the clocks—the strings gain tension. In order to keep the clocks from falling into the stars a force must be applied.

 

So, in one sense the redshift that the center observer is seeing is only an apparent velocity, what you might call a mirage. As long as force is applied to the string, the clock is not receding from the center observer. But, if the string is cut then the clocks fall. The apparent velocity when the clocks are held in a fixed location is a real velocity when they are not fixed against their inertial path.

 

Two galaxies in our universe have no such string tying them together. They are really free-falling away from one another, and the apparent redshift (or de Sitter effect) is dwarfed by the actual velocity redshift. The former is a second order effect and the latter is a first order effect.

 

This can be shown deductively in a de Sitter universe and Eddington, as usual, does a very good job of explaining just this fact:

 

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

 

So that leaves me rather thinking the same as before and the same as QuantumT. If you want to divorce the apparent effect from the actual 'force' that comes along with it (or, equivalently, if you want to divorce the effect on light from the effect on mass) then you are divorcing your description from the theoretical backing of GR.

 

Gravity wants to affect light and mass. Both massless and massive particles want to follow their geodesic path. To say otherwise is to disagree with GR. I don't see anything in the rest of your post which curtails this objection. To make this idea work I think we would need to first recognize that we are disagreeing with GR, then build from the ground up a different theory of gravity which is consistent with both local and cosmic observations in the manner you outline. If we did that and the resulting theory gave predictions equivalent to standard cosmology then we could say that either interpretation of redshift is valid.

 

A couple minor points I guess:

 

All points on this manifold have the same value of gravitational potential, and it is nonzero.

 

There is no gravitational potential in the Einstein field equations. It is replaced by the metric tensor. Gravity is a geometric effect in GR

 

There is a difference between action and apparent action, just as there is a difference between force and pseudo force..

 

A pseudo force is a real force. A person in a centrifuge, for example, really is forced against the wall.

 

~modest

[modest]

First of all R=0 does not imply a flat manifold, in order to get a flat manifold the Riemannian tensor should be zero, and also when we see T=0 doen't mean the stress-energy tensor is zero but its trace, In conclusion in a universe filled with radiation you have R=0 and T=0 but the curvature is not zero and the energy tensor is not zero either

 

That makes better sense to me :hihi:

 

Both density and pressure push the universe to collapse.

Yes, but please apply it to stars for now

That can be done, but a star is not homogeneous unless it is infinite in size. This is a physical difference between our universe and a star.

 

If you imagine our visible universe is like a small sphere drawn somewhere inside a star situated anywhere in the star so long as the edge of the sphere does not intersect the star's boundary nor at the exact center as that would violate the anthropic principle—we could postulate that the star has uniform density and that the star's molecules represent galaxies.

 

The analogy is problematic in one sense—an observer in the center of the sphere in the star will not see radiation isotropically. Radiation in a star moves, by and large, from the center outward. This provides a pressure which keeps the star inflated against the collapse of gravity. Our universe is not like this. We see radiation isotropically.

 

If we neglect this physical difference between situations by postulating that the star has no radiation (it could equivalently be a nebula or any uniform distribution of mass) then the FLRW metric will exactly describe the evolution of this sphere. This is supported here:

In that case, we must ask if there is a white hole model for the universe that would be as consistent with observations as the FRW models. Some people initially think that the answer must be no, because white holes (like black holes) produce tidal forces that stretch and compress in different directions. Hence they are quite different from what we observe. This is not conclusive, because it applies only to the spacetime of a black hole in the absence of matter. Inside a star the tidal forces can be absent.

 

A white hole model that fits cosmological observations would have to be the time reverse of a star collapsing to form a black hole. To a good approximation, we could ignore pressure and treat it like a spherical cloud of dust with no internal forces other than gravity. Stellar collapse has been intensively studied since the seminal work of Snyder and Oppenheimer in 1939 and this simple case is well understood. It is possible to construct an exact model of stellar collapse in the absence of pressure by gluing together any FRW solution inside the spherical star and a Schwarzschild solution outside. Spacetime within the star remains homogeneous and isotropic during the collapse.

Is the Big Bang a black hole?

So, this distinction between local and cosmic solutions to general relativity is only a difference in the physical situation. Our universe is postulated to be homogeneous and isotropic. If a local nebula or star were homogeneous and isotropic then it would exactly follow the FLRW metric as it would be the appropriate solution to GR.

 

This is nothing more or less than I was saying and the consequences are as follows: any homogeneous and isotropic universe that is static today and has some matter/energy content will collapse in the future according to GR—it will begin collapsing immediately. To reject such a conclusion is either to reject GR or homogeneity and isotropy as good approximations.

Again you are referring to Einstein universe which is finite(though unbounded).

 

No. I'm explicitly referring to any homogeneous and isotropic universe which follows the physics of general relativity (ie any Friedmann universe).

 

Ok, you have a point there, but have you noticed that this 4 year old thread postulates that redshift is not due to expansion and if so the entire foundaton of modern cosmology is indeed impossible? :D

 

This thread is so far missing the predictions which would support or falsify the hypothesis. It is also missing a coherent theoretical foundation.

 

You must know the cite about the "biggest blunder" and you have to be aware (if you have read some biography of Einstein) of his feelings about this constant, that is all I have talked about, not about the value of lambda.

 

You should read the link I gave. Saying that the cosmological constant should not be part of the field equations is the same as saying that it has a value exactly equal to zero. In some derivations of GR, lambda arises quite naturally. With our current understanding of the vacuum expectation value in QFT it would be negligent to remove Lambda from the field equations because we know of at least one physical process which should give lambda a positive value.

 

Like Einstein said, it is by astronomical measurements that we empirically answer the question whether lambda equals zero or not. It is not something to be a priori declared. If you'd like to discuss it further then we should make a thread because we are increasingly getting off topic.

 

I checked post 330, I was aware of that link : the Brzeski one, CC and I had talked about it in this thread, I thought you were referring to the Maltis link, but i think i'm the fisrt to post it here, anyway if you read them maybe you could give us your thoughts on the comparison I stablished between those two approaches to redshift.

 

I see. Just skimming it over, it looks like pseudoscience.

 

So far noone has been able to refute the geometrical part... that in a hyperbolic space , regardless of the cosmological model at this moment, E-M wavelenghts are seen as stretched proportional to distance-and this has nothing to do with GR

 

If redshift is proportional to distance, things are static, and redshift is caused by hyperbolic space then angular diameter distance would be proportional to z^2. This is indeed falsified by observation. The Tolman surface brightness test would also falsify such an interpretation.

 

 

 

True, that's more or less what the discussion was about. Recall the idea that stars remain stable with pressure (that acts against gravity), but on the large scale pressure gravitates and so contributes to the global topology. That's what the discussion was about. My claim was that GR can be interpreted many ways. And that the discrepancy with observations locally is large when compared to observations globally (on the large scale); where lambda means nothing locally (it's contribution is virtually zero), gravity rules: yet on large-scales it dominated the universe.

 

I might be wrong, but if the same physical laws govern the universe at scales compatible with the solar system also govern the expansion, then someone has misinterpreted GR. That is my point.

 

Radiation pressure increases the strength of the gravitational field both locally and globally. In a star, for example, the radiation pressure increases the total energy of the star and it therefore curves spacetime more than it would without that pressure.

 

As I was saying to QT, the difference between the star (a Schwarzschild solution) and the universe (a FLRW solution) is in the situation. The latter is homogeneous and the former is not (a star has a boundary). The physics (general relativity) is exactly the same in both.

 

Sometimes it's not even that a theory is incomplete so much as it is a question of interpretation.

 

Believe me, CC. Saying that mass doesn't want to follow geodesics is very far removed from GR and nowhere near a correct interpretation. You are saying exactly the opposite of the main postulate of GR and claiming it is a correct interpretation.

 

It looks bad.

 

~modest

[coldcreation]

If Bob sees Alice moving away from him and Alice sees Bob moving away from her then the velocity is relative. This does not imply that the velocity is only apparent and somehow not real. It is, as it should be, both real and relative.

 

No one sees galaxies moving. All we see is redshift. The apparent velocity is either real, or it is spurious. In other words, the conclusion could be false and relative (meaning the velocity is only apparent).

 

Obviously if we could see galaxies move the problem would be solved.

 

 

According to GR, the recession is real even if the velocity is apparent. I know that sounds absurd...

 

According to GR the recession is either apparent and real, or apparent and spurious.

 

 

So, in one sense the redshift that the center observer is seeing is only an apparent velocity, what you might call a mirage. As long as force is applied to the string, the clock is not receding from the center observer. But, if the string is cut then the clocks fall. The apparent velocity when the clocks are held in a fixed location is a real velocity when they are not fixed against their inertial path.

 

Here we agree, finally, that the center observer is seeing only an apparent velocity. The rest of what you write works fine when the gravity field has a gradient: when the metric is not the same at all points.

 

 

...the apparent redshift (or de Sitter effect) is dwarfed by the actual velocity redshift. The former is a second order effect and the latter is a first order effect.

 

This argument about the de Sitter effect, while likely true, does not rule out a first order redshift in a positively (spherically) curved spacetime, independent or radial velocity.

 

 

 

If you want to divorce the apparent effect from the actual 'force' that comes along with it (or, equivalently, if you want to divorce the effect on light from the effect on mass) then you are divorcing your description from the theoretical backing of GR.

 

Not at all. Geometric considerations bypass the 'force' problem.

 

 

Gravity wants to affect light and mass. Both massless and massive particles want to follow their geodesic path. To say otherwise is to disagree with GR. I don't see anything in the rest of your post which curtails this objection. To make this idea work I think we would need to first recognize that we are disagreeing with GR, then build from the ground up a different theory of gravity which is consistent with both local and cosmic observations in the manner you outline. If we did that and the resulting theory gave predictions equivalent to standard cosmology then we could say that either interpretation of redshift is valid.

 

Again, what you write is true of local fields. But irrelevant when it come to a global homogenous field. GR will do just fine. No need to invent something else.

 

What make you think that objects would be forced to move (geodesically) is a homogenous and isotropic gravitational field that permeates all of spacetime (if indeed such a field exists)?

 

 

 

There is no gravitational potential in the Einstein field equations. It is replaced by the metric tensor. Gravity is a geometric effect in GR

 

That is my point. :hihi:

 

CC

[modest]

No one sees galaxies moving. All we see is redshift. The apparent velocity is either real, or it is spurious. In other words, the conclusion could be false and relative (meaning the velocity is only apparent).

 

Obviously if we could see galaxies move the problem would be solved.

 

My point is that you err in thinking that if velocity is reciprocal the motion is apparent and not real. That is non sequitur. If Alice and Bob are moving away from one another in regular old special relativity then Alice expects Bob's clocks to run slow and Bob's light to be redshifted. Bob likewise expects Alice's clocks to slow and her light to be redshifted. The velocity is relative and in *no* way does that imply that the distance "cannot actually be increasing".

 

By no reasoning that I can fathom does the one thing imply the other.

 

Here we agree, finally, that the center observer is seeing only an apparent velocity. The rest of what you write works fine when the gravity field has a gradient: when the metric is not the same at all points.

 

With constant positive curvature geodesics converge with distance. Something with distance from me will fall with accelerated motion away from me and I will fall with accelerated motion from it. This is supported with the quote I gave from Eddington. If you cannot support an assertion otherwise then I don't think it would be productive to go back and forth on the issue.

 

This argument about the de Sitter effect, while likely true, does not rule out a first order redshift in a positively (spherically) curved spacetime, independent or radial velocity.

 

De Sitter space is exactly a positively curved spacetime. Two objects with constant distance between them, held in place against their inertial motion, will be redshifted relative to one another. This is the de Sitter effect. But, the amount of redshift is very small and dwarfed compared to the velocity redshift that you get when the two objects are not forced against their inertial motion to maintain constant distance.

 

When they are allowed to move as they wish they will accelerate away from one another in an amount proportional to the distance between them. The de Sitter effect is a second order effect and the velocity is a first order effect.

 

Not at all. Geometric considerations bypass the 'force' problem.

 

Force would be required in holding the objects together. Their tendency to scatter is geometric—they are following their inertial path.

 

Again, what you write is true of local fields. But irrelevant when it come to a global homogenous field. GR will do just fine. No need to invent something else.

 

You can't expect to invent an interpretation of GR which contradicts not only the exact solution of GR consistent with your description, but the main postulate of GR itself, and think it will pass as consistent with the theory.

 

It would be like saying that a football can be accelerated to the speed of light in special relativity relative to Tom with 5 Newtons of force because the speed is relative and not real. It is completely contrary to the theory.

 

General relativity is not whatever we imagine it to be. It has very specific answers.

Furthermore, the predictions of general relativity are fixed; the theory contains no adjustable constants so nothing can be changed. Thus every test of the theory is either a potentially deadly test or a possible probe for new physics. Although it is remarkable that this theory, born 90 years ago out of almost pure thought, has managed to survive every test, the possibility of finding a discrepancy will continue to drive experiments for years to come.

The Confrontation between General Relativity and Experiment

 

What make you think that objects would be forced to move (geodesically) is a homogenous and isotropic gravitational field that permeates all of spacetime (if indeed such a field exists)?

 

That is what positive spacetime curvature means! It means that two inertial frames with distance between them will accelerate away from one another. That is the very meaning of the thing. It's like asking why I think a blind person won't see the color red.

 

~modest

[coldcreation]

Believe me, CC. Saying that mass doesn't want to follow geodesics is very far removed from GR and nowhere near a correct interpretation. You are saying exactly the opposite of the main postulate of GR and claiming it is a correct interpretation. It looks bad.

 

It may look bad, but that is relative.:D

 

Believe me, modest, saying that mass doesn't want to follow geodesics in a homogenous and isotropic gravitational field is entirely in line with GR and possibly a correct interpretation. I am saying exactly the opposite as the mainstream interpretation of GR, and claiming it may be a correct interpretation. It doesn't look so bad after all.

 

I'm sorry to leave you hanging like this, with partial answers and bold assertions (pending Explanation 2). Another day or so should do. Today I finally got to the point where the main body of text is presentable. Just a couple sections need touching up. That will be done tomorrow, I hope (it's looking like it might be a good beach day).

 

Anyway, in the mean time, I'd like you to think about the question I posed above. Said differently:

 

Why would objects move along geodesics in a homogenous, isotropic gravitational field with no gradient, with a metric tensor that remains the same from point to point (i.e., everywhere)?

 

 

This is not a trick question.:D

 

Lets assume that curvature is either positive negative (or flat?). See if you can find the solution to the problem. And let's assume the validity of general relativity, which describes a homogenous globally curved background spacetime.

 

Hint: the answer has nothing to do with the classical Newtonian instability due to an attractive force. Nor does the answer have anything to do with the inherent instability associated with the FLRW models.

 

The answer has to do with pure geometry (i.e., GR).

 

Good luck.:hihi:

 

 

CC

[modest]

Why would objects move along geodesics in a homogenous, isotropic gravitational field with no gradient, with a metric tensor that remains the same from point to point (i.e., everywhere)?

 

The principle of extremal aging.

 

Geodesics as extremal curves

 

Hint: the answer has nothing to do with the classical Newtonian instability due to an attractive force. Nor does the answer have anything to do with the inherent instability associated with the FLRW models.

 

"Force" is required to deviate objects from their inertial path. They want geodesic motion, geometrically.

 

If you insist on disagreeing then please give a source.

 

~modest

[quantumtopology]

No. I'm explicitly referring to any homogeneous and isotropic universe which follows the physics of general relativity (ie any Friedmann universe).

 

And I disagree here, how can an isotropic homogenous infinite universe collapse? there is no center of gravity that it can collapse into, certainly it can colapse locally ( "black holes"), just think of our galaxy, or our local group, where expansion is not detected, are they collapsing? I believe they are stable over very long periods. Gravity vanishes with the square of distance and if there is infinite space, I am tempted to say that it won't collpse.

I'd be delighted if you could correct this maybe wrong reasoning but I ask you to do it with logical arguments rather than with authority based arguments.

 

I see. Just skimming it over, it looks like pseudoscience.

Well that is prejudiced, is everything out of mainstream pseudoscience? How could science advance then?

 

 

If redshift is proportional to distance, things are static, and redshift is caused by hyperbolic space then angular diameter distance would be proportional to z^2. This is indeed falsified by observation. The Tolman surface brightness test would also falsify such an interpretation.

 

I don't think angular distance would be proportional to z^2 in hyperbolic space, it wouldn't be a linear relation to begin with.I would have to learn more about hyperbolic geometry to predict how it would look in a redshift vs Angular distance chart. The Tolman surface test we've discussed enough about how it does not apply to hyperbolic universes. A question. You know k=-1 is also a solution of FRW metric in a expanding universe, do you absolutely rule it out?

 

 

Regards

 

QTop

[modest]

And I disagree here, how can an isotropic homogenous infinite universe collapse?

 

The distance between any and all sets of two points will decrease with time.

 

there is no center of gravity that it can collapse into

 

Neither is there a center of gravity for a closed, finite universe. This link might help:

 

It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space. (In other words, the universe is not expanding "into" anything outside of itself).

Metric expansion of space

 

Gravity vanishes with the square of distance and if there is infinite space, I am tempted to say that it won't collpse.

I'd be delighted if you could correct this maybe wrong reasoning but I ask you to do it with logical arguments rather than with authority based arguments.

 

I tend to give a lot of links supporting my assertions, not as an appeal to authority, but because doing so is a site rule.

 

Given a volume of space (a sphere) in a homogeneous universe the escape velocity of a particle at the sphere's edge is related to the density of the sphere by:

 

[math]\rho_c = \frac{3 V^2}{8 \pi G}[/math]

 

as shown here: Critical density for predicting a big crunch.

 

this relationship is true regardless of the size of the sphere (you can take the limit as volume approaches infinity and the relationship will be the same) because the density of any volume is the same.

 

If the universe is static then V=0 in which case any positive value [math]\rho[/math] causes collapse.

 

The Tolman surface test we've discussed enough about how it does not apply to hyperbolic universes.

 

I must have missed where you showed that. Can you point me to it.

 

~modest