[coldcreation]

Originally Posted by Overdog

Is he saying that the universe really is curved, always has been, and that we're just looking at it the wrong way?

The idea is similar to what Lobachevsky had envisaged (1823 - 1826): that the universe is hyperbolically curved, as opposed to Euclidean. This prospect had been considered to some extent, too, by W. de Sitter (1917), H. Weyl (1921), I.E. Segal (c.1976), G.F.R. Ellis (1977), A.M. Coldcreation (1997).

In other words, rather than redshift being an effect on radiation as it propagates through an expanding manifol (where the scale factor, or size, of the universe is dynamically changing, getting larger with time), this interpretation of redshift z is based on the geometry of spacetime, i.e., z is attributed to an effect due to a relative curvature of the manifold.

So, as the opening post states, there are to possible interpretations for cosmological redshit z that are virtually indistinguishable from one another observationally:

(1) A change in the scale factor to the metric (often called Doppler effect, (implying the expansion of space and the recession of objects in it, i.e., the radius of the universe changes with time t).

(2) The general relativistic curved spacetime interpretation (implying a stationary yet dynamic and evolving universe.

Originally Posted by Overdog

Is it possible that as we look out into space that we are looking back to a time when the universe was more curved than we see it today, and this might explain the red shift?

That depends on what you mean by "more curved." Certainly the departure from linearity increases with distance from an observers frame of reference. Curvature on the surface of the Earth manifests itself with increasing distance as well. Locally it appears flat, even though globally curvature is more or less homogeneous (it is not more curved in the land of Ozzz than it is in the land of Bull).

The idea that redshift z is due to the propagation of light (radiation across the entire spectrum) though a global pseudo-Lobachevskian four-dimensional hyperbolically curved manifold should not be discounted until it is shown empirically the untenability of the theory. There are ways to potentially test the idea against observations. The classical test is the Tolman surface brightness test, for example.

A Tolman surface brightness test is a comparison of the surface brightness of galaxies as a function of their redshift (measured as z). Such a comparison was first proposed in 1930 by Richard C. Tolman as a test of whether the universe is expanding or static. Different physicists have claimed that the results support different models.

In a simple (static and flat) universe, the light received from an object drops inversely with the square of its distance, but the apparent area of the object also drops inversely with the square of the distance, so the surface brightness would be independent of the distance. In an expanding universe, however, there are two effects that reduce the power detected coming from distant objects. First, the rate at which photons are received is reduced because each photon has to travel a little farther than the one before. Second, the energy of each photon observed is reduced by the redshift. At the same time, distant objects appear larger than they really are because the photons observed were emitted at a time when the object was closer. Adding these effects together, the surface brightness in a simple expanding universe (flat geometry and uniform expansion over the range of redshifts observed) should decrease with the fourth power of (1+z).

This test, designed to determine whether the universe is static or expanding, assumes that a static universe is flat (something which would not be the case). So it seems the test would have to be modified somehow, since light propagating through a curved spacetime would likely reproduce the same observations as an expanding universe, i.e., surface brightness in a stationary universe (with a hyperbolic geometry) should decrease with the fourth power of (1+z). The rate at which photons arrives is reduced because each photon has to travel through a curved spatiotemporal continuum. And, the energy of each photon observed is reduced by the redshift z.

Originally Posted by Overdog

Or is this idea just crazy?

“Dreams are often most profound when they seem the most crazy.” (Sigmund Freud)

“The world's crazy when it comes to beauty.” (Richard Bach)

“Every really new idea looks crazy at first.” (Alfred North Whitehead)

Originally Posted by Overdog

EDIT:
I'm picturing his idea as saying the curvature undulates like a sine wave?

Like a Pringles potato chip.



CC

[Overdog]

Originally Posted by coldcreation

...Like a Pringles potato chip.

Ok, I think I understand it now, thanks for the explanation.

So, if curved like the Pringles potato chip...does that mean the universe would be closed? Could it be curved like that and still be open, and even expanding too?

What I was asking about the undulation idea...what if 15 billion years ago the universe was curved like the potato chip, but then over the 15 billion years it has now flattened out, and in another 15 billion years it would be curved the other way and the the light would then start to be blue shifted? Would there be any way we would be able to tell if the universe were undulating like this? Or would this be something we would have easily spotted if it were happening?

EDIT:
Or is the idea just rediculous...because maybe it can't curve the other way...?

[Southtown]

Excuse me for answering cc, but the answer to Overdog's question, from what I know of cc's posts, is no. The curvature of a potato chip only serves to describe the distortion of space by gravity to a magnitude defined by distance. Project it into four dimensions. There is no "negative" of distortion.

Peace out.

[Overdog]

Originally Posted by Southtown

Excuse me for answering cc, but the answer to Overdog's question, from what I know of cc's posts, is no. The curvature of a potato chip only serves to describe the distortion of space by gravity to a magnitude defined by distance. Project it into four dimensions. There is no "negative" of distortion.

Peace out.

Ok, thanks...that makes sense.

[coldcreation]

The following illustration is a hyperbolic general relativistic spacetime manifold in reduced dimension. The observer (in accord with his or her rest frame) is located at the origin (in the center of the manifold).

Fig. 1. Hyperbolic Spacetime Manifold

Several points:

• Locally, the universe appears Euclidean, flat (the red central area corresponding to the Local Supercluster).
  
• The further out one looks, the greater the deviation from linearity.
  
• The spherical shells appear to be dilated with distance.
  
• The deviation from linearity is largest at the horizon.
  
• Events appear to take longer in the look-back time, than they would locally where the universe appears flat.
  
• The visible horizon is at the outer edge of the illustration, from where the degradation of the photon energy along the line-of-sight is such that it is no longer detectable at the telescope.

The following diagram shows a cross-space (in reduced dimension), a symmetric ground-state hyperbolic spacetime: the grid pattern of Fig. 1 viewed from above. Again note, the observer is centered at the origin.

Fig. 2. Symmetric groundstate hyperbolic cross-space manifold.

Spatiotemporal increments increase with distance. The result is both time dilation and the redshifting of light emitted by the source. Objects appear larger at greater distances. Note that the grid pattern lines (which represent spherical shells centered on the observer and line of site) appear (again from the origin) to become further way than expected in a flat spacetime regime, i.e., the spatial increments and the photon travel time become larger with distance. Events appear to take longer in the look-back time, than they would locally. The outer blue circle looks as if its half the distance to the horizon, but it is actually much further when judged from the spatiotemporal increments (grid-circles, or spherical shells).

The energy of each photon wave packet is degraded or diluted in energy (not due to the stretching of the wavelength in the travel time as a result of the expansion of space) due to the propagation through curved spacetime continuum. One factor comes as every photon packet is degraded in energy by (1 + z) due to the redshift (regardless of its cause). The second factor of (1 + z) is due to the dilution in the rate of photon arrival resulting from the distortion of the path length in the travel time relative to the observer (this effect is known as time dilation). Neither factor would be present if the universe was static and flat.

• Spacetime dilation with increasing distance in a static, stationary general relativistic non-Euclidean, geometrically hyperbolic four-dimensional continuum manifests itself as redshift z that increases with distance.
  
• This is a relative effect since hyperbolicity is observed from any and all reference frames (always located at the origin).
  
• Curvature is homogeneous and isotropic (with, of course, local deviations in linearity due to the uneven distribution of massive bodies which are associated with local humps or bumps in the spacetime geometry).

Redshift z, then, can be interpreted as an effect caused by the global curvature of spacetime, i.e., as opposed to a Euclidean manifold where cosmological redshift z is not present (unless the universe expands).

The interpretation of cosmological redshift z due to the expansion of space remains a viable interpretation of the empirical data. Further empirical tests need to be devised and carried out to differentiate between the two models.

Differentiation between the two hypotheses (a linear expanding model and a non-linear static model) should manifest itself at the greatest scrutable distances. Again, objects and events should appear further away and to take longer (respectively) in a non-linear spacetime regime (static universe), than in a linearly or isotropically expanding spacetime.

Supernovae Type Ia data seems to support (or at least does not contradict) the spacetime dilation with distance redshift in a static, stationary general relativistic non-Euclidean, geometrically hyperbolic four-dimensional continuum model. Whereas in order to maintain linearity and isotropy in an expanding model parameters (e.g., DE and CDM) had to be reinvented and tweaked profusely (combined resulting in 96% of the suspected mass-energy density of the cosmos).

Falsification of the curved spacetime approach should be executable by showing that no mechanism could be possibly be responsible for curving spacetime to the degree observed throughout the universe. In another way, if global curvature of the manifold is due to the non-negative mass-energy density of all undifferentiated components (collectively), i.e., if it is an effect due to gravity, it must be shown that there is enough mass-energy available to cause such an effect (cosmological redshift z). So there would appear, if gravity is the cause, to be a missing-mass-energy density (a dark component or two) here as well.


If there is another cause to the non-Euclidean nature of global spacetime then it is not at all clear what that could be, unless the nature of the vacuum itself is non-Euclidean with or without matter. But I don't understand how that could be determined empirically.

I believe this problem can be reconciled, but it would require a level of sophisticated mathematical expertise beyond my current capabilities.


There are ways, however, quantitatively, qualitatively and conceptually (or based on educated guessing) of resolving certain aspects of this issue without the need of such expertise: and, without the introduction, ad hoc, potentially fictitious non-baryonic material or obscure form of vacuum energy. That will be the topic of the next few posts...




CC

[Pluto]

G'day from the land of ozzzzz

Coldcreation has the right information or should I say that I agree with what he says.

I thought this paper maybe of interest

[0804.4008] Revealing the High-Redshift Star Formation Rate with Gamma-Ray Bursts

Revealing the High-Redshift Star Formation Rate with Gamma-Ray Bursts

Authors: Hasan Yuksel, Matthew D. Kistler, John F. Beacom (Ohio State University), Andrew M. Hopkins (University of Sydney)
(Submitted on 25 Apr 2008 (v1), last revised 1 Jul 2008 (this version, v2))

Abstract: While the high-z frontier of star formation rate (SFR) studies has advanced rapidly, direct measurements beyond z ~ 4 remain difficult, as shown by significant disagreements among different results. Gamma-ray bursts, owing to their brightness and association with massive stars, offer hope of clarifying this situation, provided that the GRB rate can be properly related to the SFR. The Swift GRB data reveal an increasing evolution in the GRB rate relative to the SFR at intermediate z; taking this into account, we use the highest-z GRB data to make a new determination of the SFR at z = 4-7. Our results exceed the lowest direct SFR measurements, and imply that no steep drop exists in the SFR up to at least z ~ 6.5. We discuss the implications of our result for cosmic reionization, the efficiency of the universe in producing stellar-mass black holes, and ``GRB feedback'' in star-forming hosts.

[coldcreation]

Thanks for the link Pluto, I'll check it out.


...Continued from above.

It is interesting to compare two cosmologies, especially when one of them is the potential outcome of the standard model. Let's look at the geometry of spacetime in an open expanding universe and then compare it to a model with a similar (or identical) geometry.

Before the introduction of the concordance model, Lambda-CDM, which was the result of a modification of the Friedmann models based on the SNe Ia data (interpreted as an accelerated expansion), there were three possible large-scale geometries. They were called open, closed and flat.

Recall, the density of an expanding universe determines its geometry and there is a direct relation between the geometry of the universe and its fate (see the density parameter). If the mass-energy density exceeds the critical density, then the geometry of space is closed and positively curved like the surface of a sphere: parallel photon paths converge eventually. If the density of the universe is exactly equal to the critical density, then the geometry of the universe is flat, Euclidean. If the density of the universe is less than the critical density, the geometry of space is open, negatively curved like the surface of a saddle.

The simplest version of inflationary theory (an extension of the big bang model) predicted that the density of the universe is very close to the critical density, that the geometry of the universe is flat, like a sheet of paper: a result confirmed by WMAP (with some serious tweaking of the parameters).

Consider the open universe and its geometry; where the expansion velocity is greater than mass density, space is negatively curved, like the surface of a saddle (in reduced dimension), the inner angles of a triangle sum to less than 180° and expansion continues forever. In another way, the density parameter is less than one, space has negative curvature and the universe will expand forever.

Fig. 3. Hyperbolic, expanding, open universe.

Now let's look at a static model that has a global spacetime manifold described by hyperbolic geometry. This model universe is non-expanding. Spacetime is curved like the surface of a saddle. Spacetime is said to be 'negatively' curved. The inner angles of a triangle sum to less than 180°. The universe has no edge. The universe is infinite spatiotemporally.

Fig. 4. Non-expanding universe with hyperbolic spacetime geometry.

Both illustration above are basically the same geometry (hyperbolic paraboloids) viewed from slightly different angles and with differing colors. Both models have redshift independent of wavelength throughout the entire spectrum. But there are fundamental differences between the two models:

• One is expanding and the other not.
  
  
• One has cosmological redshift z due to expanding space as it carries with it galaxy clusters. The same model has time dilation in the look-back time due to the stretching of space in the line-of-sight.
  
  
• One has redshift increasing with distance due to a relative motion. The other has redshift increasing with distance due to curvature.
  
  
• In other words, one has a hyperbolic geometry due to rate of expansion being greater than the critical mass-energy density, yet it virtually takes place in a geometrically Euclidean (or quasi-Euclidean) universe. This is a pseudo-Newtonian cosmology: the recession velocity determines the geometric structure of the universe. The long-distance relationship to GR 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.
  
  
• The other has a hyperbolic geometry due to the non-negative and nonzero mass-energy density of the universe (where all the mass and energy available in the manifold partake in the curvature); thus it is a gravitational effect (spacetime curvature) as described by Einstein's general principle of relativity.
  
  
• Said differently, one model describes a Newtonian world of events as a dynamic inertial picture changing in time and hurled onto the background of three-dimensional pseudo-Euclidean space, as opposed to a static picture on the background of a four-dimensional spacetime continuum, where Einstein’s gravitational spacetime curvature plays the key role.
  
  
• One has 96 percent of the mass-energy in the universe unaccounted for (made of something "dark"). The mass-density of the other still needs to be calculated.

The two models are very different, yet both have the same geometry. Observationally, both models are practically identical (putting aside the CMBR).

How, then, do we make the distinction, empirically, between an expanding pseudo-Newtonian inertial system and a static general relativistic universe when a beam of light is affected (curved) in a gravitational field exactly as if the source of a beam were traveling (away from us) at great velocity. Are we dealing with an inertial problem, or a gravitational problem? Clearly, the solution must come from general relativity and must differ drastically from the Newtonian solution when dealing with large distances.



CC

[Pluto]

G'day from the land of ozzzzzzzzz

Hello Coldcreation, I read your posts from many links. It seems to me that you know and understand what is happening.


These links may also be of interest
=================================================
[0802.1634] Bouncing Cosmologies
Bouncing Cosmologies

Authors: M. Novello, S.E.Perez Bergliaffa
(Submitted on 12 Feb 2008)

Abstract: We review the general features of nonsingular universes ({em i.e.} those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes. We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms. Observational consequences of such regular cosmologies are also considered, with emphasis in the behavior of the perturbations.

[0801.2965] Cosmology and Cosmogony in a Cyclic Universe
Cosmology and Cosmogony in a Cyclic Universe

Authors: Jayant V. Narlikar, Geoffrey Burbidge, R.G. Vishwakarma
(Submitted on 18 Jan 2008)

Abstract: In this paper we discuss the properties of the quasi-steady state cosmological model (QSSC) developed in 1993 in its role as a cyclic model of the universe driven by a negative energy scalar field. We discuss the origin of such a scalar field in the primary creation process first described by F. Hoyle and J. V. Narlikar forty years ago. It is shown that the creation processes which takes place in the nuclei of galaxies are closely linked to the high energy and explosive phenomena, which are commonly observed in galaxies at all redshifts.
The cyclic nature of the universe provides a natural link between the places of origin of the microwave background radiation (arising in hydrogen burning in stars), and the origin of the lightest nuclei (H, D, He$^3$ and He$^4$). It also allows us to relate the large scale cyclic properties of the universe to events taking place in the nuclei of galaxies. Observational evidence shows that ejection of matter and energy from these centers in the form of compact objects, gas and relativistic particles is responsible for the population of quasi-stellar objects (QSOs) and gamma-ray burst sources in the universe.In the later parts of the paper we briefly discuss the major unsolved problems of this integrated cosmological and cosmogonical scheme. These are the understanding of the origin of the intrinsic redshifts, and the periodicities in the redshift distribution of the QSOs.

[modest]

Originally Posted by coldcreation

Further empirical tests need to be devised and carried out to differentiate between the two models.

Originally Posted by coldcreation

How, then, do we make the distinction, empirically, between an expanding pseudo-Newtonian inertial system and a static general relativistic universe when a beam of light is affected (curved) in a gravitational field exactly as if the source of a beam were traveling (away from us) at great velocity.

Here's what you do. First, identify some aspect of either model that is unique to that model. For example, the expanding model has some point in the past where all the matter and radiation we see would be bunched up really tightly together. As this is unique to expansion, any prediction based solely on this would be a very, very good indication of expansion.

Of course, you already see where I'm going, so I'll just get there: Cosmic microwave background radiation. It was predicted based on an expanding model and it screams real and actual expansion very loudly. It confirms the reality of the expansion that we see happening.

~modest

[coldcreation]

Originally Posted by Pluto

Hello Coldcreation, I read your posts from many links. It seems to me that you know and understand what is happening.

These links may also be of interest:
Bouncing Cosmologies
Authors: M. Novello, S.E.Perez Bergliaffa
(Submitted on 12 Feb 2008)
Cosmology and Cosmogony in a Cyclic Universe
Authors: Jayant V. Narlikar, Geoffrey Burbidge, R.G. Vishwakarma
(Submitted on 18 Jan 2008)

Thank you once again for the links Pluto. I will look at them and get back to you, if at all they deal with the same topic (Redshift z: expansion vs. curved spacetime).

Originally Posted by modest

Here's what you do. First, identify some aspect of either model that is unique to that model.

Yes, and the light elements, of course.

You bring up a good point, as long as the unique aspect of either model is related to z.

For now, I would like to stick with the subject here at hand: Redshift z and the possibility of distinguishing between two competing models; perhaps by means of observational data that shows linearity or nonlinearity of the redshift-distance regime (at moderate to great distances), or redshift against the count-magnitude relation, or redshift-angular diameter (angular size), Tolman surface brightness, the age of galaxies or globular clusters in relation to z, apparent size and surface brightness, or comparing Cepheid distances to local calibrators (the timing test related to the Hubble constant), observation selection bias in the Hubble diagrams, signal-to-noise ratio as a function of z, and last but not least an in-depth analysis of the SNe Ia data in relation to z and light curves.

The answer is to be found in there somewhere.

Originally Posted by modest

For example, the expanding model has some point in the past where all the matter and radiation we see would be bunched up really tightly together. As this is unique to expansion, any prediction based solely on this would be a very, very good indication of expansion.

There is a primary difference between the two competing models: the standard model needs a linear expansion regime. In that way all the matter observed in the universe would (if the clocks were turned back) reach t = 0 at the same time. Arguably, without this linear expansion there would be no big bang at the origin.

On the other hand, the non-expanding model (at least the one based on the curved spacetime redshift) has a nonlinear regime. It is the signature of nonlinearity that will make or break competing cosmologies. That signature has been observed repeatedly throughout the cosmos. It is there that more research and analysis of the data needs to be carried out.

Luckily, I must say, for the new post-1998 standard model (Lambda-CDM), there exists a set of parameters that can be used to flatten (or nearly flatten) the deviations from linearity observed. Luckily too, those same parameters (e.g., DE and CDM) can be used to tamper with (or make fit) other phenomena observed (e.g., the CMB), to a degree in which other observations too can be made to coincide.

Originally Posted by modest

Of course, you already see where I'm going, so I'll just get there: Cosmic microwave background radiation. It was predicted based on an expanding model and it screams real and actual expansion very loudly. It confirms the reality of the expansion that we see happening. ~modest

It is well known that all cosmologies predict a cosmic microwave background. It would be ludicrous to envisage a universe, within which trillion and trillion of stars emitting vast quantities of heat into the environment reside, where there no thermal background spectrum, and yes even in blackbody form.

So the CMB temperature (2.726 K) is by no means indicative solely of big bang cosmology. There is no empirical evidence that the CMB is a redshifted relic of a hot dense state thought to have existed some time in the past. The idea that the CMB is redshifted remnant is an extrapolation.

When taken at face value, the CMB blackbody radiation is simply a thermal spectrum, the source of which depends on the model in question.

Eddington had predicted a temperature. The constant temperature of intergalactic space, was also calculated by Nernst as just below 1° K—remarkably close to the value later observed in the CMB. The Nernst universe was devoid of expansion.

The CMB is off-topic in this thread (I will gladly begin a new thread on the subject if you wish to discuss it further), but I will interject (as I have done before) my favorite quote from a text written by Fred Hoyle on the subject:

“How, in the big-bang cosmology, is the microwave background explained? Despite what supporters of big-bang cosmology claim, it is not explained. The supposed explanation is nothing but an entry in the gardener’s catalogue of hypothesis that constitutes the theory. Had observation given 27 Kelvins instead of 2.7 Kelvins for the temperature, then 27 kelvins would have been entered in the catalogue. Or 0.27 Kelvins. Or anything at all.” (Hoyle 1994, 1997 p. 413)

See the Hoyle and Burbidge take on the CMB here THE ORIGIN OF HELIUM AND THE OTHER LIGHT ELEMENTS

In 1941, McKellar (1941) showed that there must be a radiation field present in the Galaxy with a temperature between 1.8 and 3.4 K. Penzias & Wilson’s (1965) measurements, followed by others and culminating in the COBE observations by J. Mather and his colleagues (cf. Fixsen et al. 1996), have shown that the cosmic microwave background (CMB) has a blackbody form at least out to radio wavelengths with T 2.728 K. The hot big bang cosmological model is not able to predict the temperature (cf. Turner 1993). But what is remarkable about the result that we have described here is that the energy density of the observed blackbody radiation is extremely close to the energy density expected from the production of helium from hydrogen burning.

If you wish to discuss further the relation redshift z - CMB, that is on-topic. For example, the standard model predicts that the CMB preserves its blackbody form during expansion, and that it is shifted to higher photon energies and radiation temperature by a factor of (1 + z), where T(z) = 2.726(1 + z) K, thus increasing the total energy-density by a factor of (1 + z)^4. If this were the case there should be observed certain epochs that were hotter than now.

The Lyman-alpha (Ly?) resonance line of hydrogen has been used (at a wavelength of 1216A) to trace hydrogen gas through its absorption of light emitted from quasars in the hopes of showing that the universe was hotter in the past. To the best of my knowledge (and I haven't read anything on the subject lately so my knowledge could be lacking) the results are inconclusive, for a variety of reasons.

Your move...



CC