Redshift z

[quantumtopology]

Hi, everybody

Coldcreation, we have a lot of in common regarding cosmological views, so I'm glad to find at last someone I can empathize with in this issues. I also feel that where I have intuitions and glimpses you have developed a complete discourse backed with refererences, you really seem well informed, just curious do you have a physics degree? are you a profesional astronomer/cosmologist?

Now to the point, one of the things I found weird is that you also knew the reference from von Brzeski, I thought I was the only one:D, noone that I know of seems to have heard of it. And the ones that I showed it to told me it was crap. But I from my poor knowledge of math and physics can't find what specifically is wrong with it. Gladly you consider it sound science too.

I completely agree with your take on supernovae Ia observations.

Honestly I think anybody that tackles this without prejudices should have serious doubts about L-CDM model or any expansionist model.

Have you check the gurzadyan reference?

Regards

[coldcreation]

Coldcreation, we have a lot of in common regarding cosmological views, so I'm glad to find at last someone I can empathize with in this issues.

 

Glad to hear that. And a belated welcome to Hypography. :)

 

 

Have you check the gurzadyan reference?

Regards

 

I'm not sure which reference you are referring to. I did a quick search and found this one:

 

The Complexity of our Curved Universe

 

But not sure if this is the one you mean. This ePrint seems to be fairly standard in its methodology, as well as in the conclusions drawn, though the open (or hyperbolic) topology may not be as favored as the flat model, for several good reasons. His discussion of flat, positively and negatively curved universes are all expanding models based on mainstream cosmology.

 

Anyway, pressed for time now, but please link-me-up when you get a chance, if there is another Gurzadyan paper you would like me to look at, or any other work by someone else on the topic at hand.

 

 

PS. As far as the von Brzeski work is concerned, I have not looked into it as deeply as I probably should. There may be something, or there may be nothing to it. That's pretty much where modest and I left the discussion to rest. Hopefully we can pick up from where we left off.

 

 

CC

[quantumtopology]

Hi, thanks for the welcome.

Here you have a couple of links, but I hve only focused on the implications with respect to space, I know this is mainstream cosmology but at least he comes up with a novel way of looking at the COBE, WMAP data wich all the rest of cosmologists analyze in a narrow form as leading inexorably to a flat space.

http://www.icra.it/People/Vahe_articles/New_Scientist/The_origin_of_time.pdf

[astro-ph/0503103] Elliptic CMB Sky

Actually I found the references in the Penrose Road to reality book, where he advocates for a hyperbolic universe for his own reasons.

I feel that if the redshift idea is to go somewhere first we must gather all the possible clues leading to a hyperbolic space independently of the redshift itself just not to fall in circular reasoning, the nonlinear accelaration of distant objects is another clue, I would like to have more data about the angular size-redshift relation with z>1.6, the last I read is from Gurvits 1998 and was pretty inconclusive, do you happen to know any more recent observational paper on that matter?

Definitily I also should reread the brzeski paper, maybe then we might discuss it.

[quantumtopology]

One question,Coldcreation, your proposal is a 4-manifold hyperbolic spacetime and von Brzeski I think only refers to visible 3D space with hyperbolic geometry. Could you explain to a layman how the two relate?

I mean the space component of the hyperbolic 4-manifold is also hyperbolic and t?hus von brzeski space could belong to a hyperbolic 4-manifold? This may be very basic questions but I lack knowledge in differential geometry.

For instance de Sitter space is considered the lorentzian analog of positive curvature elliptic space, so when we say is hyperbolic we must be refering to some component of the manifold right?

Please can someone get me out of this confusion?

thanks in advance

[coldcreation]

One question, Coldcreation, your proposal is a 4-manifold hyperbolic spacetime and von Brzeski I think only refers to visible 3D space with hyperbolic geometry. Could you explain to a layman how the two relate?

 

I mean the space component of the hyperbolic 4-manifold is also hyperbolic and thus von brzeski space could belong to a hyperbolic 4-manifold?

 

For instance de Sitter space is considered the lorentzian analog of positive curvature elliptic space, so when we say is hyperbolic we must be refering to some component of the manifold right?

 

Hopefully von Brzeski incorporates the time dimension into his equations with the three spatial dimensions. I don't see how t could be avoided. Again, I haven't read his work recently. I should, now that you mention it.

 

Also, I'm not really making a proposal. I simply point out that light traveling through a universe where there is a change in the scale factor to the metric (due to expansion), or traveling through a curved spacetime continuum (one that is static and hyperbolic) will be very difficult to differentiate one from the other: both could be consistent with the observed redshit z.

 

Both too, interestingly enough, both interpretations correspond to the spacetime description brought about by Einstein's general relativity—according to which the geometrical relationships of the non-Euclidean continua are treated with respect to standard measuring techniques of both distance and time relative to the constancy of the velocity of light, and with respect to our relative rest-frame.

 

So the simpler point is that there are two possible interpretations for cosmological redshift z that show wavelength independence over 19 octaves of the spectrum. Both interpretations are consistent with observations.

 

 

Redshift increases with distance and time in the four-dimensional manifold. The Gaussian curvature of the geometrical spacetime continuum can be established by measurements at the telescope, obtained from data of both the metric properties and the time intervals.

 

The redshift can, on empirical grounds, be interpreted as a departure from linearity (from flatness)—a lengthening of the wave between two epochs that increase with distance in a four-dimensional curved manifold. Any observer will find she is located at the center (but of course there is no center): and this is so for both interpretations of z.

 

In this sense, redshift z constitutes actual physical evidence of a curved spacetime nature, just as it does for expansion hypothesis.

 

 

From the local viewpoint, the global curvature interpretation of redshift is less intuitive since we live in a field that varies inversely proportional to distance. In reading the literature, it is evident that the differing aspects between local and homogenous fields are misunderstood. For example Sandage (1993) writes of the prime question set in the 1930s to find the form of the redshift-distance relation: “It is either linear if the expansion is real or parabolic in the static (but highly unphysical) metric of de Sitter.” He also remarks, “However, the stumbling block was always then, and is yet today, the necessity to find a suitable standard measuring rod whose properties (static and/or evolutionary over time) are known. This assurance must be had before any putative “standard rod” can be used to mark, and thereby to measure, the geometry.”

 

See Sandage, A.R. 1993, The Deep Universe, Saas-Fee Advanced Course 23, Lecture Notes 1993, Swiss Society for Astrophysics and Astronomy.

 

 

Consider, now, the simplest example of an isotropic two-dimensional curved space, namely the surface of a hyperbolic manifold. This two-space is isotropic because the degree of curvature is the same at all points in the two-space (shaped like the surface of a saddle, or a Pringles potato-chip). If we extend our model to three spatial dimensions we are no longer looking at a saddle shape; we have the curved volume of a hypersphere.

 

The fourth associated dimension, the temporal coordinate, varies proportionally with the curvature of the three-dimensional volume. We are in possession of a four-dimensional singularity-free non-expanding, non-contracting continuum, the physical attributes of which are described by general relativity and consistent with that which is observed in nature.

 

 

 

Interestingly enough, the deviation from linearity observed in spectra of distant supernovae Ia (1998) does not contradict the curved spacetime model; quite the contrary. See this discussion for example SNe Ia, Implications, Interpretations, Lambda-CDM...

 

Note: Just as there are problems with the expansion scenario, there are problems with the curved spacetime scenario (e.g., there doesn't appear to be enough mass to cause such a curvature).

 

 

Let me know if that answers your question satisfactorily.

 

 

CC

[quantumtopology]

Thanks I think I undertand it better, but in the von Brzeski paper they talk about L3 space or Lobachevskian(hyperbolic) 3D-space, I guess it also means 4-spacetime hyperbolic space.

 

Another question, could a negative curvature imply a graviy of different sign that the one produced by positive curvature geometry? I guess if positive curvature is produce by normal mass-energy , a negative curvature should be produced by negative mass-energy like the one some particle physicists talk about in "vacuum negative energy" , to explain "casimir effect" ,"exotic matter" etc, does this make any sense?:D

[coldcreation]

Thanks I think I undertand it better, but in the von Brzeski paper they talk about L3 space or Lobachevskian (hyperbolic) 3D-space, I guess it also means 4-spacetime hyperbolic space.

 

I assume the same (though again I need to look at the paper(s) in question) since it follows that a photons traversing 3-D space would conform to the geodesic of that given space, i.e., to whatever geometry is operational. And thus the interpretation of redshift as due to a curved spacetime phenomenon is not violated.

 

Recall that the most compelling way to test the Lobachevsky hypothesis—regarding the fundamental geometry of the universe and the concept of hyperbolic space —is through the study of how the spectrum of light emanating from distant objects is altered as it propagates through the manifold.

 

And if redshift is taken as evidence of hyperbolicity (as opposed to a change in the scale factor to the metric), then observations are clearly consistent with the description of a non-Euclidean continuum, i.e., the the concept of hyperbolic space developed by Lobachevsky between 1823 and 1826 (a concept that would find itself embedded in the Riemann space, 1854, of constant ‘negative’ curvature) is not contradicted by observations.

 

 

• When redshift z is interpreted as such, the 1998 supernovae results clearly demonstrate that parallel lines diverge with distance, that the sum of angles of a cosmic triangle measures less than 180 degrees.
   
   
  
• Had the large shells of radiation and material emitted by distant supernovae Type Ia appeared to have a smaller area than they would in a topologically flat space, making the source look very bright, then that would have ruled out Lobachevsky's hypothesis.
   
   
  
• Had the visible universe appeared smaller, older, and with a greater mass-energy density than previously suspected, then that would have ruled out Lobachevsky's hypothesis.
   
   
  
• The fact that observations show an unexpected dimness of early SNe Ia, giving the impression that they are further away than their redshifts indicate, altering the predicted structure of the cosmos according to the pre-1998 standard model, corroborates with Lobachevsky's hypothesis.
   
   
  
• The SNe Ia data indicates that light from very remote objects takes longer to reach Earth—as if time and space (and the light propagating through it) were continually and increasingly ‘stretched’ with larger distances: exactly what would be expected in a hyperbolic spacetime continuum (and exactly what would be expected if the universe was accelerating).

 

 

Of course, if the hyperbolic spacetime interpretation of redshift z to be considered a realistic alternative—to the current interpretation of z according to the LCDM model—a model is required that includes a viable alternative for the observed CMB blackbody radiation as well as the formation and observed abundance of the light elements. Not only that, a viable qualitative and quantitative analysis must be made that explains how the universe and its constituents do not collapse gravitationally or disperse (in addition to other things like galaxy formation, age of stars and so on).

 

Much of this work has already been completed by the likes of Fred Hoyle, Geoffrey Burbidge, and Jayant Narlikar, especially with regards to the CMB and light element formation. See this seminal work by Hoyle and Burbidge for example: The Origin of Helium and the Other Light Elements where the topic of CMB is also discussed in detail. But much work still remains.

 

 

 

Another question, could a negative curvature imply a graviy of different sign that the one produced by positive curvature geometry? I guess if positive curvature is produce by normal mass-energy , a negative curvature should be produced by negative mass-energy like the one some particle physicists talk about in "vacuum negative energy" , to explain "casimir effect" ,"exotic matter" etc, does this make any sense?:)

 

This is an excellent question. Let me post the above first, and come back to this question in a little while. The answer is not at all evident from an intuitive point of view, nor from an interpretational viewpoint. The short answer is that locally gravity represents one type of curvature, not two, and it's usually considered negative. That concept is slightly different than the geometrical notion of closed, open of flat (spherical, hyperbolic and Euclidean) spacetime when considering the shape or fate of the universe.

 

 

CC

[quantumtopology]

Ok coldcreation

I found this interesting page related to spacetime curvature that also helped me clear up things the curvature: from geometry to cosmology specially the part entitled "the geometry of the universe" that connects it with the SNIa observations

Now, with respect to CMB, as you know and I think you've talked about it in this thread, there are many problems with the interpratation of CMB as " the remains of the Big Bang", I have always considered that CMB tell us nothing about billion years ago, and a lot about current time and local place.In the von Brzeski paper they make their own interpretation of the CMB as the wavefront of the horosphere that I have yet to understand completely.

For one the 2.7º K temperature was admittedly never quite predicted by the BBT, so their supporters centre in the blackbody quality of the radiation. Well there are other ways to get that kind of spectrum i.e. :the unruh radiation, from the unruh effect defined as: "the prediction that an accelerating observer will observe black-body radiation where an inertial observer would observe none. In other words, the background appears to be warm from an accelerating reference frame" (taken from wikipedia). Of course the temperature that would yield this using g as accelaration is many orders inferior to the one registered with the antennas but perhaps the temperature we detect is that of the space that surrounds us with peaks from the stars giving a mean of 2.7º K. I'm just speculating here , needless to say, I am not proposing anything , just letting ideas flow :)

Regards

[quantumtopology]

This is a rather solitary place lately, where is the action?;)

[coldcreation]

Yes, the key in that link regarding the time component in relation to curvature is the effect has been experimentally demonstrated by Pound and Rebka in 1959. Yes, the key in that link regarding local curvature and the relation to the time component is the Pound and Rebka experiment (1959) which showed that clocks run at different rates at different places in a gravitational field.

 

 

However, and off-topic as it might be, they discuss the bending of light due to a very intense gravitational field mentioning The Einstein Cross as a "magnificent demonstration." This is the worst example they could have used. It his highly contested that this is a gravitationally lensed object. One simply needs to look at the illustration (or simulation) above the photo in that link to see that the predicted distortion for such an occurrence resembles not in the least what would be expected.

 

Clearly, a lensed images should be oval-shaped (or cressent-shaped), very elongated circularly, typical of a lensed object. Objects in The Einstein Cross, on the other hand are not oval along the circular path. Three of the objects are visibly pointing in the direction of the central object, the fourth is nearly spherical. The way it works is straight forward. The further the background object (say to the right) the less elongated (or distorted) its image. The closer it moves toward the center of the foreground object, the greater the distortion, until, in this case, the quasar is directly behind the foreground body: at which point distortion (flattening to cressent, ring or semi-ring shape) should be at its maximum.

 

Theoretical calculations of gravitationally lensed objects, when resolved in luminous isophotes, should be be elongated (extended in cressent-shape) by a factor of 4 or 5 to one along the circumference (Peter Schneider et al). Furthermore, the probability of such a lensing event, where the four quasars are within four arc sec of a galaxy nucleus, was calculated by Fred Hoyle to be less than two chances in a million.

 

Too, there is a gaseous connection between at least one of the quasars (east) in the ultraviolet exposures, which includes the Lyman alpha line (the strongest emission line of the most abundant material of the quasars) that extends directly into the central galactic nucleus, passes through it, and connects to the adjacent quasar, i.e. the east and west quasars have a luminous bridge (an Alpha lyman filament of low density gas) between them.

 

Finally, the small dwarf galaxy, judging from its morphological appearance (Arp 1998), located in the center of the system does not possess the mass necessary to produce a lensing of this magnitude. (Arp, Seeing Red, 1998, p. 173-176)

 

Conclusion: clearly, gravitational lensing is not operational in the Einstein Cross. It is impossible to see how the observations can be accounted for in the lensing scenario.

 

 

____________________

 

 

An important note on the geometry of the universe:

 

In the two scenarios discussed in this thread, there are two interpretations of what is meant by the geometry of the universe.

 

In the standard model, the universe is hyperbolic, spherical of flat (Euclidean) depending on the rate of expansion in relation to the mass-energy density (simply put). In the case where the universe has a negative curvature (a saddle-shaped surface in reduced dimension) the circumference is larger that 2pR. Yet, despite SNe Ia data it is thought that the geometry of the Universe is flat. This means that a mysterious repulsive force that physics cannot explain yet is required, along with a large cold dark matter component.

 

If the universe were static, yet hyperbolic, as viewed from the rest frame of an observer, the geometry would have nothing to do with expansion, or the rate of expansion (obviously). It has to do with the mass-energy content in relation to the curvature of the manifold. In this case where the universe has a negative curvature (a saddle-shaped surface in reduced dimension) the circumference of the visible universe is also larger that 2pR. This infers that a

large mass-energy density is required (unless something else is responsible) that physics cannot explain yet. Note that a mysterious repulsive force is not required.

 

Note too that in both interpretations there is a difference between the local curvature and the global curvature.

 

I'll see if I can elaborate on that in my next post.

 

 

____________________

 

 

Now, with respect to CMB: The two interpretations above require two different interpretations for the observed CMB.

 

Current assumption has it that the universe has never been colder than the 2.726 ± 0.01 K (almost three degrees above absolute zero, or 0 K), the temperature of the omnipresent cosmic microwave background (CMB) radiation that bathes the universe. The temperature of the cosmos is thought to have been extraordinarily high in the past and cooled to the ultra-low temperature now observed.

 

The assumption in a static universe seems to be that the temperature of CMB it must have been extraordinarily low (exceedingly close to absolute zero) in the past and warmed to the temperature now observed. If so, then the formation of stars and galaxies present in the universe must have formed while the universe was cold. Thus my aka, Coldcreation. ;)

 

In that case it seems the explanation offered by Hoyle and Burbidge, that the energy density of the observed blackbody radiation being extremely close to the energy density expected from the production of helium from hydrogen burning (i.e., the CMB must be of stellar origin) seems inevitable (as opposed to a big bang origin). What remain to be shown, in my opinion, is an unambiguous mechanism for the thermalization that avoids the potentially ad hoc "iron wiskers" predicted and required by QSSC. Though, and in addition, Hoyle and Burbidge write:

 

This requires a time much greater than 10^10 yr, and there must be a physical mechanism operating that is able to thermalize the radiation that is initially released through hydrogen burning as ultraviolet photons from hot stars in starburst situations in galaxies. We have shown elsewhere that both of these conditions are fulfilled within the framework of the quasi–steady state cosmology (QSSC) (Hoyle, Burbidge, & Narlikar 1993, 1994a, 1994b, 1995).

 

 

 

CC

[quantumtopology]

 

In the standard model, the universe is hyperbolic, spherical of flat (Euclidean) depending on the rate of expansion in relation to the mass-energy density (simply put). In the case where the universe has a negative curvature (a saddle-shaped surface in reduced dimension) the circumference is larger that 2pR. Yet, despite SNe Ia data it is thought that the geometry of the Universe is flat. This means that a mysterious repulsive force that physics cannot explain yet is required, along with a large cold dark matter component.

 

If the universe were static, yet hyperbolic, as viewed from the rest frame of an observer, he geometry have nothing to do with expansion of the rate of expansion (obviously). It has to do with the mass-energy content in relation to the curvature of the manifold. In this case where the universe has a negative curvature (a saddle-shaped surface in reduced dimension) the circumference of the visible universe is also larger that 2pR. This infers that a large mass-energy density is required (unless something else is responsible) that physics cannot explain yet. Note that a mysterious repulsive force is not required.

 

I don't quite follow you here. Even in a universe like deSitter where there is density=0 there is a negative curvature,but it is attributed to lambda. I understand that matter curves the space positively ( or towards elliptic or circular curves if we do not wanna use the positive-negative terminology which could be confusing,so with this logic a hyperbolic universe would seem to require less matter than a spherical one . Maybe this is too naive , if there is misunderstanding from my part, please correct me.

 

 

 

Note too that in both interpretations there is a difference between the local curvature and the global curvature.

 

Any manifold is locally flat-euclidean (when its extension tend to zero) , I think. I don't know if this is what yo refer to.

 

The assumption in a static universe seems to be that the temperature of CMB it must have been extraordinarily low (exceedingly close to absolute zero) in the past and warmed to the temperature now observed. If so, then the formation of stars and galaxies present in the universe must have formed while the universe was cold. Thus my aka, Coldcreation. ;)

 

But then your static universe idea has a beginning of time , that is, it doesn't follow the cosmologic principle withj respect to time? Please explain

 

Finally you did not mention my comment about the Unruh effect, if you think it is nonsense you are free to express it, I'm just trying to learn :phones:

[coldcreation]

I don't quite follow you here. Even in a universe like deSitter where there is density=0 there is a negative curvature,but it is attributed to lambda. I understand that matter curves the space positively ( or towards elliptic or circular curves if we do not wanna use the positive-negative terminology which could be confusing,so with this logic a hyperbolic universe would seem to require less matter than a spherical one . Maybe this is too naive , if there is misunderstanding from my part, please correct me.

 

 

Let's just say that gravity is the curvature of spacetime, without for the moment saying whether it's positive or negative, spherical or hyperbolic. It is a departure from linearity, one way or another.

 

The idea that an empty universe has a curvature to it is intriguing. But lets place too the de Sitter model and lambda aside for a moment.

 

 

Lets imagine now a static universe that is completely empty, with no ground energy (an impossibility, but this is only a thought experiment). Let's assume the spacetime vacuum to be perfectly Euclidean, since there is nothing present that gravitates, thus no curvature (and again, no cosmological constant).

 

Now let's introduce the mass and energy of all the stars, all the galaxies and all the energy that comprises the universe we observe. Let's continue assuming, in our thought experiment, there is no expansion or contraction.

 

 

What would the universe look like? It certainly would no longer look Euclidean, with its galaxies creating local deviations in linearity (due to gravity). The distribution of matter would induce geometric variations, local humps, bumps and ripples in an otherwise smooth spacetime manifold. Though some would argue that all the humps and bumps in space due to objects such as stars and galaxies would all cancel out (photos gain energy as they 'fall' into a gravitational well, and they lose energy on the way out), leaving the overall impression of flatness. That view may not be justified (I'll come back to that).

 

 

 

Consider a photon propagating through space from a distant source (say near the visual horizon). First, there is an energy degradation as it leaves its source. This effect, though negligibly small for our purpose here, is called gravitational redshift. That energy loss will never be regained, no matter how many times it traverses humps or bumps as it propagates towards an observer from a great distance.

 

Consider too that gravity is everywhere present and thus so is the departure from linearity. So how would this non-linearity manifest itself (notice that I'm not saying the universe is hyperbolic or spherical, only that it is non-linear, i.e., there is a deviation from linearity)?

 

As this photon continues its voyage through space it is continually losing energy, since it is traveling through a non-linear regime (a kind of geodesic).

 

That continual loss of energy means that the photon will appear greatly redshifted by the time it reaches the observer. That factor comes because every redshifted photon is degraded in energy by (1 + z), no matter what its cause. But that's not all. There is another factor to consider, related to the dimension of time. Since space and time are inextricably linked, in accord with Einstein's general relativity, there is a second factor of (1 + z), due to the dilution in the rate of photon arrival. That dilution results precisely for the same reason there was an energy loss (to the first factor of (1 + z): only this time it corresponds to the dilation of the time-like interval between wave crests. The photon path is a geodesic (seen from the perspective of an observer it's really only a straight line to the source): it is distorted as it propagates.

 

Indeed this implies that the spatial metric increments, and temporal intervals, appear to be a greater with distance, there appears to be an increase in the path length in the travel time. This is the result of a global deviation in linearity due to gravity. We can say that observationally, that the metric property of space along with the time intervals appear to increase with distance from the observer.

 

Note: Both of these factors of redshift z are present in the standard model, where the first factor of (1 + z) is caused by a change in the scale factor to the metric (expansion). And the second factor is due to the 'stretching' of the path length in the travel time as the universe expands.

 

So one interpretation has both factors of (1 + z) caused by expansion, and the other interpretation has both factors of (1 + z) caused by curvature of the manifold.

 

In another way, according to our thought experiment, the dilution in the rate of photon arrival is not due to the stretching of the path length as a function of time. It is due to the cosmological non-linear geometric Gaussian curvature of the 3-space metric through which light must propagate. Redshift z, in this thought experiment, is a sign of the gravitational dilation of spacetime. The second factor that partakes in the redshift by the same ratio is due to time element that separates two epochs: The space-like and time-like interval becomes larger at greater distances, meaning that clocks appear to run slower the greater the distance. That is evidence of hyperbolicity; (the opposite would be true in a spherical manifold).

 

This is the relativistic phenomenon of time dilation and spatial dilation from the reference frame of an observer. Thus, redshift increases with distance and volume in a quasi-stationary universe.

 

 

Spacetime curvature (gravity) must be treated as a deviation or departure from linearity, i.e., the deviation occurs away from linearity, from a flat, Euclidean, Minkowski spacetime. We then let observations tell us the shape or degree of the curvature.

 

What type of curvature are we look at then? Hyperbolic.

 

Why would the universe appear hyperbolic, rather than spherical, again?

 

Observations show that he curvature of the universe is not spherical in the way described by Riemannian geometry or Einstein’s globally finite spherical space. This is where the framework of Lobachevsky’s non-Euclidean space, and to a certain extent de Sitters hypersphere, may be considered closely as viable representatives of the global properties of the universe. A metrically homogenous world is obtained by the equivalence of all points, in all directions—since the change is a continuous transformation—there is no reason why the hyperbolic curvature should not be everywhere continuous in a homogenous playing field.

 

 

 

Note this process is not a tired light hypothesis, since there would be no medium through which light would be traveling which would degrade the energy (other than the intergalactic medium, which is approximately equal to one hydrogen atom per cubic meter if I recall, practically negligible), and no scattering. This redshift would be wavelength independent, throughout the entire electromagnetic spectrum.

 

 

 

Any manifold is locally flat-euclidean (when its extension tend to zero) , I think. I don't know if this is what yo refer to.

 

I just assume that. Since I presume gravity to the curvature. Without mass-enegy, there is no gravity, no curvature. At least in the thought experiment above. Of course there is always ground state energy, zero point energy in the vacuum. So even if everything could be extracted from the universe, there would still be curvature, though it would be small.

 

 

 

But then your static universe idea has a beginning of time , that is, it doesn't follow the cosmologic principle withj respect to time? Please explain

 

The cosmological principle is respected. Why wouldn't it be?

 

There is no beginning of time. Why would there be in an infinite, static, yet evolving universe?

 

Where did you deduce that from?

 

 

 

Finally you did not mention my comment about the Unruh effect, if you think it is nonsense you are free to express it, I'm just trying to learn ;)

 

I think the Unruh effect is interesting, but fail to see how (if it exists) is related to a static universe.

 

 

 

 

CC

[quantumtopology]

Thanks for your explanation, still I can't see why a hyperbolic static universe would require a higher mass-energy density than the original Einstein spherical universe for instance.

Regarding the CMB and the cosmological princple: in your phrase "The assumption in a static universe seems to be that the temperature of CMB it must have been extraordinarily low (exceedingly close to absolute zero) in the past and warmed to the temperature now observed. If so, then the formation of stars and galaxies present in the universe must have formed while the universe was cold." you seem to introduce an asymmetry, you imply a global way to differentiate the past from the present and future of the universe and the reference to a "creation" in your nick seems to confirm it. Surely I must bemissing something here ;)

When I bring up the Unruh effect is to stress that a blackbody quality of radiation doesn't have to mean it comes from the relic of a Big Bang in a expanding universe,like the supporters of BBTaffirm. But it's probably not a very fortunate example.

BTW have read my last post in the "de sitter cosmology history" thread. I think it helps clear up some of the debate you had in old posts with regards to whether de sitter universe was expanding or static. It turns out the geometry de sitter proposed admitted different coordenates and metrics, it could lead to static universe as was originally intended and also to FLWR universes(flat open and closed) depending on the metric and coordenates chosen. see this link pages 5 and 7 http://www.bourbaphy.fr/moschella.pdf

 

quantumtopology

[coldcreation]

Thanks for your explanation, still I can't see why a hyperbolic static universe would require a higher mass-energy density than the original Einstein spherical universe for instance.

 

You may have a point there. Could you explain that in further detail?

 

I'm assuming that to cause the type of deviation from linearity observed via redshift z, if indeed that interpretation is valid, that more mass-energy density would be required. How do you reconcile that dilemma?

 

 

 

Regarding the CMB and the cosmological princple: in your phrase "The assumption in a static universe seems to be that the temperature of CMB must have been extraordinarily low (exceedingly close to absolute zero) in the past and warmed to the temperature now observed. If so, then the formation of stars and galaxies present in the universe must have formed while the universe was cold." you seem to introduce an asymmetry, you imply a global way to differentiate the past from the present and future of the universe and the reference to a "creation" in your nick seems to confirm it. Surely I must bemissing something here ;)

 

I don't see what you mean. I hope you're not implying that a static universe does not evolve, or that there is a perfect balance between all that exists in the universe. Certainly there is an asymmetry between past and future. There is an 'arrow of time', consistent with the second law of thermodynamics and the non-decrease of entropy. That asymmetry is observed. But that's not the only asymmetry observed.

 

Obviously, if their existed a perfect balance between the tendency to coalesce and the opposite inclination to scatter (attraction and repulsion), no particles would ever convene to form atomic nuclei, hydrogen atoms, stars, galaxies, or anything else. There is also an asymmetry between matter and antimatter. See e.g., the baryonic asymmetry.

 

Manifestations occur at very low temperatures, for example, due to Poincaré resonances: dynamical processes lead to long-range correlations, despite the short-range character of forces between particles⎯an essential fact that leads to asymmetry and permits evolutionary patterns and emergent phenomena in agreement with the thermodynamic description of nature.

 

Bose-Einstein condensation, superconduction and superfluidity are remarkable examples of things that happen at ultra-low temperatures, not to mention dissipative processes, long-range correlations and new coherences related to dynamical non-equilibrium processes.

 

The name 'coldcreation' is derived from that type of 'creativity.'

 

If I don't understand you correctly regarding asymmetry let me know. Is that what you meant? Did I fill in what was missing?

 

 

When I bring up the Unruh effect is to stress that a blackbody quality of radiation doesn't have to mean it comes from the relic of a Big Bang in a expanding universe,like the supporters of BBTaffirm. But it's probably not a very fortunate example.

 

While I agree that there are other theories that explain the origin of the CMB, besides the big bang, I can't say whether the Unruh effect is an alternative for the CMB. I should read up on the effect. Something that bothers me about it is the need for an observer to be accelerating (the background appears to be warm from an accelerating reference frame).

 

What does an observer see from a non-accelerating frame? It is my understanding that an an inertial observer would observe no blackbody radiation. So I don't see how the Unruh can be reconciled with the CMB, which is observed from both accelerating and inertial reference frames.

 

In the hypothesis of a static, or stationary (non-expanding) universe, the observed CMB, (blackbody spectrum at a radiation temperature of 2.726 K) is not a remnant of a hot creation event that occurred 13.7 Gyr ago. There would have been no beginning. There was plenty of time for its production. The CMB could have been produced by stellar means (hydrogen burning stars, supernovae, etc.) over a time span exceeding 100 billion years (Burbidge, Hoyle, 1998), or even 600 Gyr, depending on the model. That's along time! Things happen. :phones:

 

 

CC

[quantumtopology]

"I'm assuming that to cause the type of deviation from linearity observed via redshift z, if indeed that interpretation is valid, that more mass-energy density would be required. How do you reconcile that dilemma?"end quote from cc

This indeed is an interesting dilemma, and I think it is at least vaguely related to the Einstein-de Sitter debate about the Machian principle, de Sitter insisted that in order to have curvature there was no need of matter or mass-energy density, you only needed with "the gravity of inertia" whilst Einstein disagreed and believed following Mach that the curvature, that is, gravity could only arise from matter. In de Sitter universe the cosmological term provided that curvature he attributed to "inertia". But at the same time like Einstein didn't like the term, he considered it inelegant. Now if we identify this "universe inertia" of de sitter with the deviation of linearity you talk about but that we don't believe to be the cosmological term we must find some alternative, and that is a tough one, I hope this clarifies my line of thought here.

On the asimmetries , of course I believe in an evolving universe on the local scale (local meaning galactic scale, but the universe as a whole in an isotropic and homogeneus with respect to time should look the same billions years ago and billions years from now, don't you think?

And I don't seriously mean currently the unruh effect as an alternative to CMB, it was just an example of how you would get a blackbody radiation if you were accelarating like we on earth are. In GR I take an inertial frame to be accelarting in its geodesic due to the gravity field as oposed to the inertial frame of SR or Newtonian systems which has uniform velocity.

 

quantumtopology

[modest]

I'm assuming that to cause the type of deviation from linearity observed via redshift z, if indeed that interpretation is valid, that more mass-energy density would be required. How do you reconcile that dilemma?

 

But GR is rather specific in that more energy density means more spherical. The most hyperbolic would be the models with zero mass.

 

~modest

[coldcreation]

[...]On the asymmetries , of course I believe in an evolving universe on the local scale (local meaning galactic scale, but the universe as a whole in an isotropic and homogeneus with respect to time should look the same billions years ago and billions years from now, don't you think?

 

Now I understand why you bring up the asymmetry problem.

 

An evolving isotropic and homogenous universe will, in principle, look the same from the viewpoint of any observer at a given time t.

 

That means that an observer situated anywhere in the universe, according some universal time (say, when the CMB spectrum is at a radiation temperature of 2.726 K) will see the universe just as we do.

 

Remember that as things evolve locally for us, they evolve 'locally' for any other observer. Here and now, it is 2010 and the CMB is 2.726 K. As we ponder the heavens though we are looking back in time t.

 

We see the universe evolving (assuming it's evolving). The time t, according to out telescopes is not 2010 anywhere else in the universe, nor would the CMB have the same temperature (if we could accurately measure it) at NGC 7319, since we see it as it was 390 million years ago. And if the temperature of the universe changes with time, the temperature of the CMB there will have changed by now. An observer located there, looking at the Milky Way, and measuring the CMB in our rest frame, will not find it to be 2.726 K.

 

So yes the universe might be homogenous and isotropic, but we cannot prove that since we see it different in the past. That is why the cosmological principle is based on philosophical grounds. It is just something we assume. And I assume it too.

 

That doesn't mean though that the universe should 'look' the same billions years ago (or billions years from now, if you could see the future), form any rest-frame.

 

The universe globally can evolve (and most believe that it does) without violating the cosmological principle.

 

 

I hope that common misconception has been cleared up.

 

 

 

But GR is rather specific in that more energy density means more spherical. The most hyperbolic would be the models with zero mass.

 

Good point. I'll come back to this.

 

 

CC