Redshift z

[coldcreation]

'Tolman proved Einstein wrong', that's funny! Einstein said that ALL static solutions are WRONG - including Tolman's list of 3. If Tolman is right and there are only 3 static solutions then they are ALL wrong according to Einstein.

 

-modest

 

You miss the point: The SNe Ia data.

 

In other words, the equations themselves do not allow us to determine which model best represents the real world: Only empirical observations can do that.

 

Tolman only proved that, in effect, three static solution were possible (in addition to the non-static solutions: the three Friedmann models, or FLRW).

 

So no one, not even Einstein, could have known which metric would eventually emerge victor. And again, we still may not know now, though the SNe Ia data is compelling, for a variety of possibilities (yes, even acceleration, lambda-CDM).

 

 

Do you wish to retract your geometrically flat, linear expansion regime claim in light of the SNe Ia data?

 

 

 

 

 

CC

[coldcreation]

.

 

 

So we have two views of nature, exemplified by either static solutions or non-static solutions to the Einstein field equations. In both species, there are (thought to be) three possible geometries: spherical, Euclidean, hyperbolic. And, in both cases, the geometry must be determined empirically.

 

In the case of the static metric, the geometry of the universe is directly determined by the mass-energy density of the universe which induces a nonzero curvature on the global spacetime manifold.

 

In the case of the non-static metric the recession velocity determines the geometric structure of the universe, resulting in a closed, flat, or open universe. The long-distance relationship to general relativity is that gravity determines the velocity, or rate of expansion. If there is enough force of attraction the velocity slows, causing a deceleration, and so on. Redshift, then, has virtually nothing to do with the general postulate of relativity or non-Euclidean spacetime.

 

 

An essential theme of general relativity is that the matter density of the manifold determines the space curvature. But to determine a fully viable notion of global curvature (and its raison d’être: the mass-energy density) that leads to the observed redshift, or “temporal displacements” requires some extrapolation from relativity, or at least an interpretation.

 

Einstein’s law of gravitation applicable to interstellar and extragalactic space must be supplemented with a hitherto poorly defined coefficient: the cosmological constant, lambda. Any definitive conclusions about the average mass-density of the universe or its geometric topology will undoubtedly have to include lambda, as the term represents an indispensable characteristic or property of spacetime.

 

Keep in mind, this is not obligatorily ‘new physics’ that introduces ad hoc concepts (dark energy) into a theory. This type of extrapolation is far less chimerical than the extrapolations based on Newtonian gravity or ‘relativistic’ instabilities leading conventional cosmologists to believe that space and time along with all the mass-energy in the entire cosmos were once upon a time wrapped up into one point of infinite density and curvature.

 

 

Light curves and redshift z of distant supernovae (SNe Ia) were raising the peculiar specter that Einstein’s constant was real. Remember that lambda (Einstein's so-called greatest blunder) was originally introduced to mediate equilibrium, staticity, in a gravitationally attractive, unstable universe. Yet, the observations had then to be interpreted in such a way that they would not viscerally oppose the finely tuned expansion of inflation, or Hubble's law, or even the favored critical Friedmann model.

 

The possibility that the new dark energy-like "greatest blunder" might revive some of the anti-big-bang rhetoric of the early 50s loomed. That is to say, confronted with choice of reintroducing the fudge factor or sacking eight decades of theoretical cosmology, physicists had to scramble fast, and scramble fast they did. It seemed the only way out was to change the constant.

 

If everyone is avoiding disagreement in order to save current theory, neither physicists from Cambridge England nor Cambridge Massachusetts are joining forces out of some resurrection of the old equilibrated romance between gravity and lambda. The mood at least in the United States is a quintessentially pragmatic one, emerging more out of a sense of self-preservation than a sentimental attachment to the cosmological constant as a kind of first principle.

 

 

 

CC

[modest]

So we have two views of nature, exemplified by either static solutions or non-static solutions to the Einstein field equations. In both species, there are (thought to be) three possible geometries: spherical, Euclidean, hyperbolic. And, in both cases, the geometry must be determined empirically.

Well there's your problem, you think Euclidean is a shape.

I think we should back up a bit.

"three possible geometries: spherical, Euclidean, hyperbolic"

No, let's back up further...

A sphere is a shape. It does not have to be 3 dimensions - let's say it's 4 to keep with de Sitter's model. It is called a hypersphere. But, the hypersphere must be inside a space to describe its shape. Remember - a sphere is a shape.

In Euclidean space de Sitter's model is in the shape of a hypersphere.

In Minkowski space de Sitter's model is a hyper-hyperbola.

So, shapes can be described inside different geometries. There are non-Euclidean geometries.

So, let's get back to that thing you said...

"three possible geometries: spherical, Euclidean, hyperbolic"

Now you see - this makes no sense at all. You've got 2 shapes and one geometry here. Are you trying to say that Euclidean geometry is spherical and Minkowski geometry is hyperbolic? I just don't see any understanding of the basics behind this statement.

In the case of the static metric, the geometry of the universe is directly determined by the mass-energy density of the universe which induces a nonzero curvature on the global spacetime manifold.

On a positive note you are no longer confusing a static metric with a globally static model. Very nice.

 

As far as what Einstein was saying - he was not saying that a non-expanding solution to the field equations is impossible. To say this would be rather calling himself an idiot for proposing one.

 

He was saying that the nature of redshift being isotropically red and increasing with distance is a dead giveaway. We live in a dynamic universe. It is NOT static. Einstein was notorious for holding on to his beliefs - and he came to this conclusion. Not because all the evidence wasn't yet in as you would have us believe. Because the nature of even the most preliminary evidence is incontrovertible.

 

Now, let me ask you a question as I see you have studied de Sitter's model in more depth:

Why do you believe his model is any more infinite in size than any other?

When you answer, keep this in mind:

In Einstein's solution you can travel in one direction for an eternity and cover an infinite distance.

In de Sitter's model as you approach the equator of the hypersphere you slow to a stop.

 

So, we get back to my very first statement on this issue. I see nothing that your model and de Sitter's have in common.

[coldcreation]

Before I respond to your last post let me say this:

 

 

Recall that the beauty of the critical Friedmann model resides in its symmetry, in its one-to-one relation between the density of the universe and its spatial curvature, in its simplicity, in its finely-tunned linear relation between redshift and distance, between the rate of expansion and the attractive force of gravity (lambda aside), leading to an flat, isotropic, homogeneous, Euclidean geometry.

 

Whereas, the beauty of the de Sitter model is that the universe itself remains stable, static, stationary, in equilibrium finely poised between catastrophic centripetal gravitational collapse and centrifugal outward expansion (and does so without the fine-tuning of ad hoc parameters). It allows us to determine the spatiotemporal curvature based on the non-linear redshift-distance relation, meaning the redshift-distance relation does not have be a one-to-one relation. Too, it is Lorenz invariant, all observers (at time t) live in an isotropic, homogeneous universe where redshift z increases with distance and remains wavelength independent over the entire 19 octave spectral range, in accord with observation.

 

Of course then, the questions beg: How does the de Sitter universe remain stable? How is the apparent fine-tuning justified? What prevents galaxy clusters from gravitationally merging into one great massive fireball?

 

 

CC

[modest]

 

In the case of the static metric, the geometry of the universe is directly determined by the mass-energy density of the universe which induces a nonzero curvature on the global spacetime manifold.

 

CC

 

Well, I debated if I should mention this or not- but here it is. In essence what de Sitter did was prove that a metric field without matter could be described in a GR model. Einstein believed that the g-mu-nu field should be completely determined by matter - which is (I guess) what you are saying here. Einstein coined the term Mach's Principle as a postulate against the de Sitter solution for this reason. Einstein eventually accepted that the de Sitter model was a counterexample to Mach’s Principle and was fully matter free and consistent with GR.

 

Perhaps all you are saying here is that matter helps determine the geometry of the universe - if that's the case, never mind my objection.

 

In the case of the static metric the recession velocity determines the geometric structure of the universe, resulting in a closed, flat, or open universe. The long-distance relationship to general relativity is that gravity determines the velocity, or rate of expansion. If there is enough force of attraction the velocity slows, causing a deceleration, and so on. Redshift, then, has virtually nothing to do with the general postulate of relativity or non-Euclidean spacetime.

Again I hesitate to respond because I'm a little confused by your point. Are you saying that we cannot understand the nature of redshift without knowing the curvature of space? You say that redshift has nothing to do with relativity. Do you mean expansion has nothing to do with relativity or that redshift has nothing to do with expansion. In any case, some GR solutions have redshift and some do not. Redshift is an observation of the universe. It should be used when comparing GR models to reality just like any other observation (CMBR for example)

 

I'm not even going to touch the redshift in non-Euclidean space comment

[coldcreation]

Well there's your problem, you think Euclidean is a shape.

 

Obviously, when I use the word Euclidean, it refers to Euclidean geometry., where a meter is always a meter, no matter what distance from the observer, and one second is always a second, when comparing identical clocks at, say, different altitudes in a gravitational field.

 

 

A sphere is a shape. It does not have to be 3 dimensions - let's say it's 4 to keep with de Sitter's model. It is called a hypersphere. But, the hypersphere must be inside a space to describe its shape.

 

Not true, A hypersphere does not have to be "inside a space" to describe the geometric structure of spacetime. The boundary can extent to infinity, either spatially, temporally, or preferably both, thereby, there is no "outside" space, or inversely the manifold is not contain inside of a space.

 

You would be correct if the horizon did not extend to infinity, but then you would be left with the daunting task of having to describe the boundary condition in physical or quantitative term (or easier, discarding its metaphysical nature from the theory itself).

 

 

 

...

So, let's get back to that thing you said..."three possible geometries: spherical, Euclidean, hyperbolic"

Now you see - this makes no sense at all. You've got 2 shapes and one geometry here. Are you trying to say that Euclidean geometry is spherical and Minkowski geometry is hyperbolic? ...

 

No, absolutely not.

 

We have two geometries (for the sake of this discussion): one Euclidean, the other two non-Euclidean. Of the latter, there are (again, for our purposes here) two: hyperbolic and spherical, one with 'negative' curvature, and the other with 'positive' curvature. That is a total of three possibilities (three geometries): One of which the structure is independent of gravity, two within which time is no longer independent of space but depends on distance, and only one of which is compatible with observations.

 

 

 

In the case of the static metric, the geometry of the universe is directly determined by the mass-energy density of the universe which induces a nonzero curvature on the global spacetime manifold.

 

 

 

On a positive note you are no longer confusing a static metric with a globally static model. Very nice.

 

I didn't think I was confusing them earlier either.

 

 

As far as what Einstein was saying - he was not saying that a non-expanding solution to the field equations is impossible. To say this would be rather calling himself an idiot for proposing one.

 

It would have been interesting to see what would have happened had Einstein not discarded the cosmological constant.

 

Anyway, as I mentioned above, Tolman (1929) showed that three static (non-expanding) solutions to the field equations were indeed possible.

 

 

 

He was saying that the nature of redshift being isotropically red and increasing with distance is a dead giveaway.

 

It is not though, since there are—even aside from the de Sitter effect redshift that increase non-linearly with distance in a stationary universe—other interpretations for redshift z. Albeit, the de Sitter redshift is the only one as far as I know that is wavelength independent (aside from the Doppler interpretation).

 

 

We live in a dynamic universe. It is NOT static. Einstein was notorious for holding on to his beliefs - and he came to this conclusion. Not because all the evidence wasn't yet in as you would have us believe. Because the nature of even the most preliminary evidence is incontrovertible.

 

No one is saying the universe is not dynamic. I simply state that the scale factor to the metric, the "radius of the universe," is not obligatorily changing (growing larger) as a function of time.

 

The only incontrovertible evidence to date (that can arguably determine which model is viable) appears to be the SNe Type Ia data, but the rest depends on the interpretation given to the deviations from linearity—in both redshift z and light curves—observed.

 

One of those interpretations requires profuse quantities of DE and DM, the other one not.

 

 

Now, let me ask you a question as I see you have studied de Sitter's model in more depth:

 

It's been a few years since I've studied the model(s), but go ahead...

 

 

Why do you believe his model is any more infinite in size than any other?

 

Your question make no sense. There is no such thing as "more infinite." So stating that (or asking if) a model is more infinite in size than any other means nothing.

 

As I mentioned above, all three models can be spatiotemporaly infinite (none more so than the another).

 

 

When you answer, keep this in mind:

In Einstein's solution you can travel in one direction for an eternity and cover an infinite distance.

In de Sitter's model as you approach the equator of the hypersphere you slow to a stop.

 

In a de Sitter spacetime, the observer is always located at the origin, at the 'center' of the hypersphere.

 

In accordance with observations, every observer is entitled (and in fact has no choice, due to the finite velocity of light) to consider herself in the center of the universe. Of course, the universe has no center, and so likewise, the center can be considered is everywhere.

 

So in the case of the FLRW metric and the de Sitter metric, the observer is situated at the origin.

 

 

So, we get back to my very first statement on this issue. I see nothing that your model and de Sitter's have in common.

 

What, then, in your opinion, are the differences?

 

 

 

CC

[coldcreation]

That was supposed to be, see bold type:

 

In the case of the non-static metric the recession velocity determines the geometric structure of the universe, resulting in an open, closed or flat universe. The long-distance relationship to general relativity is that gravity determines the velocity, or rate of expansion. If there is enough force of attraction the velocity slows, causing a deceleration, and so on. Redshift, then, has virtually nothing to do with the general postulate of relativity or non-Euclidean spacetime.

[modest]

What, then, in your opinion, are the differences?

Closed vs Open

Expanding vs globally static

 

I understand you want the redshift aspect of de Sitter space in your model. But, the principle is an aspect of the inertial effects in the de Sitter model. If you change the model you loose the aspect. It is not any solution that gives you the de Sitter effect. It is not your solution.

[coldcreation]

Closed vs Open. Expanding vs globally static

 

I understand you want the redshift aspect of de Sitter space in your model. But, the principle is an aspect of the inertial effects in the de Sitter model. If you change the model you loose the aspect. It is not any solution that gives you the de Sitter effect. It is not your solution.

 

 

You seem to have missed the point once again.

 

 

A hyperbolically symmetric general relativistic globally curved spacetime can reproduce the same cosmological observations as the currently favored Lambda-CDM model.

 

In this case the systematic cosmological redshifts—along with the large deviation from linearity exhibited in the redshift and light curves of distant Supernovae Type Ia—are interpreted as a de Sitter effect in a stationary, non-expanding universe, and the assumption that Euclidean space is expanding is replaced by the assumption that the spacetime is non-Euclidean from the point of view of any observer and the universe is stationary. That is, the special relativistic expanding inertial frame is replaced by a general relativistic curved spacetime stationary manifold. What was previously ascribed to a time variation in an expanding inertial frame—interpreted as resulting from an accelerated expansion in accord with the lambda-CDM model—is now ascribed to a spatiotemporal variations in properties of a static de Sitter universe.

 

Both interpretations are suggestive of an open, infinite universe in the direction of time, corresponding to non-Euclidean hyperbolic geometry.

 

 

So what I say is simple:

 

Recent observations permit two viable interpretations for the cause of cosmological redshift z.

 

One is that space is expanding (a relative Doppler-like effect), accelerating, the other involves a static metric solution to the Einstein field equations, the de Sitter effect.

 

To understand this, it is essential to note that the "inertial effects" apparent in the de Sitter model are only "apparent" in nature, they are not Doppler-based, and so they are not a real inertial effect:

 

They are a relative effect in exactly the same way as gravitational redshifts and time dilation are not inertial in origin. This effect alters the spectral lines propagating from a distant light source, the redshift of which is determined by the geometrical structure of the spacetime manifold.

 

I am not presenting a new model here: that is general relativity, pure and simple.

 

 

 

CC

[modest]

You seem to have missed the point once again.

 

A hyperbolically symmetric general relativistic globally curved spacetime can reproduce the same cosmological observations as the currently favored Lambda-CDM model.

 

In 5 dimensions as far as redshift is concerned - yes.

But this is as dynamic a solution as any other - as de Sitter showed us.

[coldcreation]

In 5 dimensions as far as redshift is concerned - yes.

But this is as dynamic a solution as any other - as de Sitter showed us.

 

 

The "dynamics" apparent in the de Sitter model are only apparent in nature, they are not Doppler-based, and so not a real dynamical effect: There is no change in the scale factor. The radius of the universe remains infinite.

 

The apparent global dynamics of the de Sitter model is a general relativity based effect, similarly to local gravitational redshifts and time dilation. It is non-inertial in origin.

 

Again, this effect causes a redshift in the spectral lines of distant objects. Redshift in this case is determined by the geometrical structure of the spacetime manifold.

 

 

 

The cosmos explains general relativity more than GR explains the cosmos.

 

 

 

CC

[modest]

The "dynamics" apparent in the de Sitter model are only apparent in nature, they are not Doppler-based, and so not a real dynamical effect: There is no change in the scale factor. The radius of the universe remains infinite.

 

The apparent global dynamics of the de Sitter model is a general relativity based effect, similarly to local gravitational redshifts and time dilation. It is non-inertial in origin.

 

Again, this effect causes a redshift in the spectral lines of distant objects. Redshift in this case is determined by the geometrical structure of the spacetime manifold.

 

 

 

The cosmos explains general relativity more than GR explains the cosmos.

 

 

 

CC

 

Now you're back to thinking the de Sitter solution is globally static.

 

Perhaps in the time since de Sitter someone has worked out such a model with a fully coherent gravitational field, no density problems, no scale problems?

[coldcreation]

Now you're back to thinking the de Sitter solution is globally static.

 

Perhaps in the time since de Sitter someone has worked out such a model with a fully coherent gravitational field, no density problems, no scale problems?

 

The de Sitter solution exhibits a redhift. The interpretation or cause of that redshift will determine whether the universe is globally static or expanding. The de Siter effect is related to the observer-dependent time of identical clocks. The recession velocity interpretation (or expnading space) can apply as well, since both cause redshift. But by no means is that obligatorily or implicitly inherent within the de Sitter metric, on the contrary.

 

The Doppler interpretation was, too, at the time of Hubble, only seen as an "apparent recession." The expanding space concept came later.

 

 

In spite of the distinction between redshifts caused by the velocity of objects and the redshifts associated with the expanding universe' date=' astronomers sometimes refer to "recession velocity" in the context of the redshifting of distant galaxies from the expansion of the Universe, even though it is only an apparent recession.[26'] As a consequence, popular literature often uses the expression "Doppler redshift" instead of "cosmological redshift" to describe the motion of galaxies dominated by the expansion of spacetime, despite the fact that a "cosmological recessional speed" when calculated will not equal the velocity in the relativistic Doppler equation.[27] ... More mathematically, the viewpoint that "distant galaxies are receding" and the viewpoint that "the space between galaxies is expanding" are related by changing coordinate systems. Expressing this precisely requires working with the mathematics of the Friedmann-Robertson-Walker metric.

Source

 

So, again, to the best of my knowledge, there are two, and only two, interpretations for cosmological redshift z that are permitted by observations accross 19 octaves of the spectrum (i.e., that are wavelength independent and increase with distance).

 

(1) The FLRW solution(s): where the metric describes the cosmological expansion (or stretching) of space (supplement that with lambda-CDM).

 

(2) The de Sitter solution(s): where the metric describes, globally, a hyperbolically curved spacetime manifold.

 

 

There are numerous reasons why the de Sitter solution is more desirable, elegant (a selection of which are mentioned here):

 

The regime can display both linear and nonlinear redshift-distance relations depending on distance, i.e., the closer the object the more linear will appear the relation. The divergence from linearity will manifest itself the further away the emitting object is from the observer. (Similarly, the surface of the earth appears flat locally).

 

The de Sitter metric does not require the ad hoc introduction of free-parameters (viz DE and DM). It is beautiful the way it is.

 

The de Sitter solution does not imply that all the energy and mass in the universe was wrapped up into a singular event of excruciatingly high-gigaton yeald (where the laws of physics are born, or die, depending on the direction of time).

 

The de Sitter solution describes how light 'travels' in a non-expanding, non-contracting, infinite spatiotemporal curved spacetime continuum.

 

The de Sitter metric is a compelling solution to the nonlinear SNe Ia data (one that does not require the accelerated-stretching-of-space concept) in that, by definition, nonlinearity is predicted.

 

 

 

CC

[Mike C]

If indeed the Doppler interpretation (1) is not correct, a wholesale revision of cosmology is required.

 

I have been doing this for years.

Doppler is easily refuted because of its implications that we are centrally located in the Universe.

The probability of this being true is infinately small since the universe is gigantic in size and the Geocentric theory has already been refuted.

 

That is why I had looked for another cause for this cosmological redshift.

So I posted another cause that is much more realistic and provided the evidence for it.

The title is 'The Expansion of the Light Waves' that I just now added on the Cosmology thread ..

 

Mike C

[Little Bang]

How does red shift imply that we are located at the center of the universe?

[Mike C]

How does red shift imply that we are located at the center of the universe?

 

The observed receding galaxies appear to be receding from our location equally all around us.

This inplies that we are in the center of the universe.

 

So with the 'expansion of space' idea that the BB'ers are promoting, they have eliminated the one central location with their 2 dimensional balloon analogy.

IMO, 2 dimensional space is not like 3 dimentional space.

3 dimensional space has a 'radial' expansion also and that does not seem to conform to the transverse expansion as the balloon analogy implies.

 

Mike C

[coldcreation]

How does red shift imply that we are located at the center of the universe?

 

The observed receding galaxies appear to be receding from our location equally all around us.

This inplies that we are in the center of the universe.

...

 

There is no center of the universe. Redshift z does not imply we are centrally located. There is nothing special about our observational location.

 

According to the standard model, a linear expansion regime is required. The redshift–distance relation had to be linear if the expansion scenario was to be considered real.

 

For expansion to be linear, i.e. when a light source was twice as far, it would travel twice as fast: four times as far, four times as fast, the distribution of matter had to be homogenous and isotropic. If this were not the case, the rate of expansion would vary from different locations at different times, because of the intervention of gravitational attraction. There cannot be a preferred position in the velocity field; otherwise it would violate the ‘cosmological principle.’

 

This basic assumption states that the Earth is not situated at any special location in the cosmos. It is assumed that any other observer would also observe the same large-scale features of the universe (at the present time). A variation of this principle purports that these same features would be observable at all times (called the ‘perfect cosmological principle’). Without a uniform expansion, our position would be considered unique, conceptually bringing us back to the time before Copernicus, when it was thought the Earth was in the center of the universe.

 

If one were to run the clocks backwards in this type of expanding manifold, all the galaxies would find themselves in a ‘free-fall’ towards any observer, and all the matter in the universe would reach the same point at the same time. This is the type of linear field that permits a singularity at the outset, as all objects would eventually collide at one point, regardless of where they were initially located.

 

 

 

CC