Testing cosmology, without assuming GR?

[Nereid]

Regular readers to GA&C here in PF will know only too well that some of our prolific posters feel the mainstream work is rather too heavily model-laden for their taste ... and others that this characterisation quite unfair.

Wrt those who are comfortable with the redshifts of galaxies (and SN) being mostly cosmological, and who would like some reassurance that the leading researchers aren't ignoring alternatives (esp to GR), I recently came across this paper, by Tegmark: "Measuring the metric: a parametrized post-Friedmanian approach to the cosmic dark energy problem" (astro-ph/0101354). The abstract says, in part "We argue for a “parametrized post-Friedmanian” approach to linear cosmology, where the history of expansion and perturbation growth is measured without assuming that the Einstein Field Equations hold"

 

[Chronos]

Good link, Nereid. I am familiar with, and probably too comfortable with Tegmark's works. I am a sucker for conclusions that soundly agree with observational evidence.

 

[turbo]

Tegmark is engaging in a bit of epistemology (we need a lot more of this!) when he observes that (as pointed out by Eddington) it is possible to define matter in such a way that Einstein's field equations are satisfied by default. As Garth has pointed out many times, the degree to which observation agrees with theoretical prediction is highly dependent not only on the model, but on the definitions and assumptions by which the model is used to interpret observation.

I will not presume to speak for his model - I do not understand much of it and so would likely miss some important underlying assumptions if I did so, but here is a case in point from a ZPE standpoint:

Let us assume:
1) mass polarizes and densifies the EM fields of the quantum vacuum and creates gradients in the ZPE fields in "empty" space.
2) EM waves propagate through these fields.

I model "gravitational" lensing as a purely optical effect - EM waves entering a denser propogating medium slow down and are bent (or not) in accordance with classical optics. The important refractive contibutions are made by 1) density gradients in that medium and 2) the orientation of those gradients with the wavefront of the impinging EM wave. (Classically, the refractive index of the lens and shape and orientation of the lens.) So far, so good. Now here's where the definitions come in:

If we need to keep the GR rule that the speed of light in a vacuum MUST be constant (regardlesss of the density of the propagating EM fields), we can slap on any number of epicycles to make this work.

1) We can define space in accordance with ZPE field density (denser field=smaller fine structure) and say that light invariably crosses s units of space in t units of time. This definition allows a unit of space to be any size dictated by local conditions (gravitational field in GR) and allows the speed of light to remain invariant (light crosses one unit of space s in time t) as long as our clocks slow down in the vicinity of space with smaller fine structure. This is in accordance with GR's clock slowing in the presence of a gravitational field.

2) We can keep clock time invariant, and keep the speed of light invariant. In this scenario, the only way to balance the books (with the classical optical model) is to assume that in the presence of mass, space is stretched out, so it takes longer for light to cross these units of space (from the viewpoint of an outside observer). You may recall seeing similar representations in descriptions of black holes, where the fabric of the universe is drawn into a very skinny elongated horn and outside observers see an infalling object taking longer and longer to traverse each bit of space as the object falls into the black hole.

3) We can make clocks and rulers vary inversely, keeping neither as a strict constant.

You can see where this is going, I'm sure...

My point is that when confronted by an observation that does not fit the prediction of a theory, there are plenty of ways to use assumptions and definitions to make theory fit observation. This is not a bad way to check for faults in the model, but when incongruities arise later, it is best to go back to the basics and see if the assumptions and definitions that were so self-consistent and useful years ago might be at fault (epistemology!). Curved space-time in the presence of mass is a useful model, for instance - at least on the scales of planets and moons, etc, but it has some shortcomings at galactic and larger scales and it poses severe problems for QFT, making unification a formidible, if not impossible task. Maybe the curved space-time model needs to be re-examined - maybe we need a mechanism by which gravitation can be expressed in a flat reference frame, instead of a mathematical model that predicts the results of gravitation as curvature with no mechanism by which the curvature arises.

I view redshift and lensing as optical effects in a flat-frame universe with invariant rulers and invariant clocks, in accordance with Occam's Razor (nowadays often simplified to the KISS rule ). We're all pretty familiar with how redshift and lensing are explained in GR, so I won't get into that. Garth's model treats redshift in a VERY different manner. I believe that he would argue that there is no gravitational redshift, and that perceived redshift is a result of mass gained by the receiving instrument. That makes my head hurt. Nevertheless, it is interesting to me that he can keep SCC self-consistent (to the extent I can grasp it) and mostly consistent with GR, while making testable predictions.

 

[Garth]

Garth's model treats redshift in a VERY different manner. I believe that he would argue that there is no gravitational redshift, and that perceived redshift is a result of mass gained by the receiving instrument. That makes my head hurt. Nevertheless, it is interesting to me that he can keep SCC self-consistent (to the extent I can grasp it) and mostly consistent with GR, while making testable predictions.

To be precise; in the Jordan conformal frame of SCC there is time dilation equal, as normal, to [-g₀₀]^1/2, which in the Jordan frame metric of SCC is 3/2 the GR value. So it might be thought that there would be a gravitational red shift 3/2 the GR value. However in that frame energy is conserved with the effect that that time dilation applies to atoms as well as to photons. [Think of the de Broglie wavelength of the atom] As the observed red shift is actually a comparison of the energy of the photon with the total energy of the atom it interacts with, this effect is unobservable. What is observed is the increase of mass of the atom due to its subsumed gravitational potential energy.

SCC interprets gravitational red shift, between the bottom and the top of a gravitational potential well, as a gain of total energy, because of the gain in potential energy, of the atom rather than a loss of potential energy of the photon.

I hope this helps.

Garth

 

[turbo]

Thank you, Garth. That helps.

 

[Nereid]

So Garth, is the approach which Tegmark outlines one which you could use to analyse observational results, wrt SCC?

turbo-1: AFACS, only ideas which place high-redshift galaxies, quasars, and supernovae at distances much, much closer than ~> 1 billion Mpc would not be able to make use of Tegmark's approach. The best way to address these ideas, IMHO, is to ask for realistic physical models (within these ideas) of the objects otherwise known as high-redshift galaxies (etc). AFAIK, none of the three such alternative ideas have anything remotely close to such models (the Arp/Burbidge, plasma cosmology, and CREIL).

For example: there are lots of very good observations of high-z SN, and except for the redshift, they seem to behave just like 'local' SN a very long way away (with one important caveat, and a few small qualifications). So, if they're not distant SN, what are they? And if they are distant SN, why isn't their observed redshift cosmological?

 

[turbo]

turbo-1: AFACS, only ideas which place high-redshift galaxies, quasars, and supernovae at distances much, much closer than ~> 1 billion Mpc would not be able to make use of Tegmark's approach. The best way to address these ideas, IMHO, is to ask for realistic physical models (within these ideas) of the objects otherwise known as high-redshift galaxies (etc). AFAIK, none of the three such alternative ideas have anything remotely close to such models (the Arp/Burbidge, plasma cosmology, and CREIL).

My comments were not intended to comment on the applicability of Tegmark's paper to any alternate cosmologies, but to point out that questioning "givens" (epistemology) is a healthy thing. I have quoted Einstein's statement on epistemology a few times on this board, so I won't do it again, but it bears repeating that when a model begins to deviate from observation, one should go back and re-examine the foundations of that model (however sacred!) before tacking on epicycles. GR's curved space-time model is predictive on macro scales (smaller than galactic scales and larger than quantum scales), but divergences occur at the extremes, indicating that it is somehow either inaccurate or incomplete.

My example about curved space-time and gravity was illustrative of that point. In my ZPE model, space-time is flat. The fine structure of space (as exemplified by the EM field of the quantum vacuum) is polarized and densified by the presence of matter. EM waves traveling through those fields slow when they encounter denser zones, just like EM waves slow when they encounter density gradients in any transmitting media, like air, water, and glass. In my model, the speed of light in a vacuum is not constant - the speed of light is dependent on the density of the media through which it propagates, just like everywhere else. This is basic optics.

Now, if this is the way the universe works, is it possible to make GR predictive and accurate, within reason? Here is where Tegmark's statement about definitions is important:

If (as in GR) we believe "empty" space is truly empty, or a close approximation thereof, and we believe that light traveling through "empty" space is not propagating through EM fields (and is therefore running at the absolute speed limit at all times), we are going to have to resort to space-time curvature to explain lensing. It would be pretty silly to discuss massless photons being bent by passing by a massive object simply due to gravitation. Then again, GR admits of no mechanism by which gravitation arises - it just explains the effects of gravitation in a way that can be explained as a curvature of the fabric of our universe. That's OK for a mathemetician perhaps, but less so for an engineer who need to know the "why" and "how" of things.

On the other hand, if we believe the quantum theorists, (and quantum theory is pretty predictive and accurate, so far!) we must see the quantum vacuum as a seething foam of particles, the EM field of zero point energy. We must logically be prepared to admit that EM waves in "empty" space propagate through this EM field. Like any other field, the ZPE EM field can be polarized and densified. Once we come to terms with this we have to be prepared to admit that these fields can affect the behavior of the waves that propagate through them, and we can model "gravitational" lensing in the language of optics. EM waves can be slowed and refracted by encountering density differentials in the media through which they propagate.

Tegmark says in the paper above that we can define mass in such a way as to make Einstein's field equations be satisfied by default. We need to realize that in GR, there are a lot of other "givens" that are similarly self-fulfilling. They make GR predictive across a range of scales, and because GR works so well across these scales, we have come to enshrine these "givens" as truths and never question their origins. One such "given" is the speed of light in a vacuum. No true vacuum can exist in our universe, according to Quantum Theory. The "speed of light in a vacuum" is an unacheivable ideal in the real world, and VSL is therefore not forbidden, but required.

 

[turbo]

For example: there are lots of very good observations of high-z SN, and except for the redshift, they seem to behave just like 'local' SN a very long way away (with one important caveat, and a few small qualifications). So, if they're not distant SN, what are they? And if they are distant SN, why isn't their observed redshift cosmological?

Nice red herring Nereid! Ok, I like some herring, but not the red ones... A redshifted supernova (pick the class) is a supernova at the distance implied by its redshift. People concerned about the nature of expansion (constant or inflating) look at the rise-times of these supernovae and try to figure out if time-dilation, reddening, misclassification of hypernovae as supernovae, etc, can nail down the nature of cosmological expansion. The basic concept that the redshifts of supernovae are indicative of their distances in accordance with the Hubble relationship is non-controversial to the quasar/intrinsic redshift bunch. One might quibble over the mechanism by which cosmological redshift arises (expansion, tired light, interaction of light with the media through which it propagates), but the basic Hubble relationship is non-controversial. What is controversial (and patently false) is the notion that all redshift not attributable to proper motion must be due to cosmological expansion. More on that just a bit later.

Arp and the Burbidges (and others) see quasars and AGNs and their intermediate evolutionary stages as a special class of objects with intrinsic redshifts. They posit that objects are created locally all over the universe, by ejection from galaxies, and that by some mechanism, these objects evolve from highly redshifted objects into more mature objects with more moderate redshifts. I have not read a single paper by any of them saying that distant objects do not have cosmological redshifts related to their distances. They DO say that some objects (typically young objects, like quasars) have excess redshifts in addition to the redshift arising from their proper motions and their cosmological distances, and that in some instances (quasars are the extreme examples), we improperly assign them great distances (and ages and luminosities) by misinterpreting the excess intrinsic redshifts as cosmological in origin.

In other posts, I used the very simple model of a black hole that gradually accretes mass, to point out that conventional non-controversial physics can easily model an object that loses redshift as it matures and gathers matter. I did that (and continue to do so) in order to illustrate that an object CAN have a redshift that is not just due to its proper motion+cosmological distance, but also due to intrinsic properties, just like the steep gravitational field of a white dwarf adds to the redshift of that star. When we extrapolate from a white dwarf, to a neutron star, to a black hole (with an infinite redshift), you can see why I cringe when somebody tells me that bodies with intrinsic redshifts are "impossible", "chance projections", etc. Bodies with intrinsic redshifts exist, and we have routinely measured such redshifts, beginning many decades ago. Is it possible that bodies may exist with intrinsic redshifts many orders of magnitude greater than a white dwarf? Why not? I'd say it's a heck of a lot more likely than proving existence of a 200-400 billion solar mass quasar at a redshift equivalent to an age of 800 million years post-big-bang, with super-solar metallicity! Any one of those qualities (extreme mass, extreme youth, high metallicity so early in the BB universe) is a problem for the standard model, but all three of them together knock the heirarchical scheme and the 13.7Gy BB Universe on its ear. Clearly, the extreme redshifts (z~6) of such supermassive quasars are either in error, or we need a whole new cosmological model. Likely both.

The truth behind intrinsic redshifts of quasars will likely be more radical in effect and more basic in mechanism that we might expect. We already have evidence that GR gravity is not predictive on galactic scales, requiring the insertion of overwhelming masses of DM (and special distributions of such) to explain galactic rotation curves, galactic and cluster lensing and cluster binding. We might also find that GR gravity has problems modeling the behavior of light in very steep gravitational gradients and on very small scales (like in the neighborhoods of black holes). We know that GR breaks down near singularities - we should not be surprised to find divergences in GR gravity and gravitational redshift long before we get near a BH.

 

[Chronos]

...In other posts, I used the very simple model of a black hole that gradually accretes mass, to point out that conventional non-controversial physics can easily model an object that loses redshift as it matures and gathers matter. I did that (and continue to do so) in order to illustrate that an object CAN have a redshift that is not just due to its proper motion+cosmological distance, but also due to intrinsic properties...

. Refresh me. My memory is unreliable, but I'm sure we would have had memorable discussions on that topic.

 

[Garth]

Two questions Turbo-1.
1.

an object CAN have a redshift that is not just due to its proper motion+cosmological distance, but also due to intrinsic properties

In Arp's and the Burbiges' opinion are these intrinsic properties basically causing gravitational red shift? If so then you would need another mechanism for them in your theory would you not? If for high Z quasars the red shift is due to a local gravitational field then surely their spectra would be smeared out by the extent of their accretion discs, which would cover a vast range of gravitational potential, is this observed?

2. If the ZPE field does contribute significant density to vacuum, so that it could slow up light etc., would not its effects have been discovered at a local scale?

Nereid -

So Garth, is the approach which Tegmark outlines one which you could use to analyse observational results, wrt SCC?

Yes it can, but with the caveat that Turbo-1 expressed above, in that the analysis is theory dependent. In particular Tegmark says of his Fig.1 that the rho_eff has been determined by assuming the Friedmann equation is correct.
For scalar-tensor theories the Friedmann equation may be retained but the density has to be augmented by a 'dark energy' term, and care has to be exercised how this is done. SCC is not a straight forward scalar-tensor theory as it is not a strictly metric theory, it is 'semi-metric' - the energy-momentum tensor is not covariantly conserved. Also, as it is a static model in the Jordan frame, H takes on a different meaning so the standard analysis decomes degenerate, with the result:.
Omega_total = Omega_m + Omega_k + Omega_Lambda = 1 in metric theories
but
Omega_total = Omega_m + Omega_k + Omega_Lambda = 0 in SCC

Garth

 

[turbo]

Two questions Turbo-1.
1.
In Arp's and the Burbiges' opinion are these intrinsic properties basically causing gravitational red shift?

I do not presume to speak for them, especially in regard to the possible mechanism for intrinsic redshift. I was merely pointing out that we already know that some objects with extreme properties (for example, white dwarf stars) are known to have intrinsic redshifts, in this case due to gravitation. These intrinsic redshifts have been well-known for many, many years and are uncontroversial. It is therefore very puzzling to me (and somewhat infuriating) when otherwise smart people disparage the work of the Burbidges, Arp, et al and smugly proclaim that quasars DO NOT have intrinsic redshifts, when it has been proven that far less exotic, and far more common objects DO have intrinsic redshifts.

2. If the ZPE field does contribute significant density to vacuum, so that it could slow up light etc., would not its effects have been discovered at a local scale?

It is very difficult to separate the effects of a local ground state from observations, especially if it is a locally weak effect, and you are not looking for it (the Pioneer anomaly is just such an example).

I suggest that we may detect the slowing of light by the ZPE EM field by means of a very simple experiment. Using an interferometer, we can compare the speed of light through the gap in a Casimir device to the speed of light across an equivalent-length path in an equivalent vacuum. If the ZPE EM field mediates the propagation of light, we should see less interaction and faster light speeds across the "slightly" less dense ZPE fields in the Casimir device. This experiment might pose a problem in sensitivity, since most Casimir gaps are very tiny and the measured Casimir forces (proportional to the reduction in ZPE field density) are very weak. Regardless, with sufficient interferometer sensitivity and perhaps many, many transits of the gap by reflection (effectively extending the size of the gap), I believe the effect will be detected.

 

[turbo]

. Refresh me. My memory is unreliable, but I'm sure we would have had memorable discussions on that topic.

It wasn't that long ago, Chronos. Refer to the thread below, and scan the posts leading to post #13, posing a very simple thought-experiment. The discussion continued throughout much of the rest of the thread.

https://www.physicsforums.com/showthread.php?t=57373&page=1

 

[Garth]

I do not presume to speak for them, especially in regard to the possible mechanism for intrinsic redshift. I was merely pointing out that we already know that some objects with extreme properties (for example, white dwarf stars) are known to have intrinsic redshifts, in this case due to gravitation. These intrinsic redshifts have been well-known for many, many years and are uncontroversial. It is therefore very puzzling to me (and somewhat infuriating) when otherwise smart people disparage the work of the Burbidges, Arp, et al and smugly proclaim that quasars DO NOT have intrinsic redshifts, when it has been proven that far less exotic, and far more common objects DO have intrinsic redshifts.

Gravitational red shift of quasar spectra is of course accepted, the question is how much? As I asked above I am not aware of much smearing out of the quasars spectra as would be expected if a large proportion of a large quasar red shift was from this source.

I suggest that we may detect the slowing of light by the ZPE EM field by means of a very simple experiment. Using an interferometer, we can compare the speed of light through the gap in a Casimir device to the speed of light across an equivalent-length path in an equivalent vacuum. If the ZPE EM field mediates the propagation of light, we should see less interaction and faster light speeds across the "slightly" less dense ZPE fields in the Casimir device. This experiment might pose a problem in sensitivity, since most Casimir gaps are very tiny and the measured Casimir forces (proportional to the reduction in ZPE field density) are very weak. Regardless, with sufficient interferometer sensitivity and perhaps many, many transits of the gap by reflection (effectively extending the size of the gap), I believe the effect will be detected.

I think this is a good question for experiment to resolve, although the practicalities may be insurmountable.

Garth

 

[Nereid]

turbo-1: you have outlined your ideas at some considerable length here in PF, and also sketched those of Arp and Burbidge.

However, unless I've missed it, you have not provided:
a) a reference to work which shows how - quantitatively - the 'naked BH accreting matter from the IGM' accounts for even a significant subset of the range of good observations of quasars, in any detail (it's all been handwaving)
b) a reference to work which shows how - quantitatively - the ZPE effect on light (EM) accounts for even a significant subset of the range of good observations of galaxies, clusters, quasars, lensing (etc), in any detail (it's all been handwaving).

If and when you do have such references, please post them; in the meantime, what is to be gained by repeating the handwaving?

 

[Nereid]

Nereid -
Yes it can, but with the caveat that Turbo-1 expressed above, in that the analysis is theory dependent. In particular Tegmark says of his Fig.1 that the rho_eff has been determined by assuming the Friedmann equation is correct.
For scalar-tensor theories the Friedmann equation may be retained but the density has to be augmented by a 'dark energy' term, and care has to be exercised how this is done. SCC is not a straight forward scalar-tensor theory as it is not a strictly metric theory, it is 'semi-metric' - the energy-momentum tensor is not covariantly conserved. Also, as it is a static model in the Jordan frame, H takes on a different meaning so the standard analysis decomes degenerate, with the result:.
Omega_total = Omega_m + Omega_k + Omega_Lambda = 1 in metric theories
but
Omega_total = Omega_m + Omega_k + Omega_Lambda = 0 in SCC

Garth

Thanks Garth.

If I have understood your response correctly, the Tegmark approach is OK for testing SCC (and similar ideas), with

1) a possible tweak of equation 1,

2) confirmation that "the function H(z) is directly measurable in a variety of ways that make no assumptions about dark matter properties or gravitational field equations, but rely on spacetime geometry alone.", and

3) checking that 'gravity' in these alternatives "is well approximated by partial differential equations on large scales, these decouple into ordinary differential equations for each Fourier mode, since we are perturbing around a homogeneousmetric and derivatives become local in Fourier space"

 

[Garth]

Thanks Nereid those are good points, I will see whether I can answer them.

If I have understood your response correctly, the Tegmark approach is OK for testing SCC (and similar ideas), with

1) a possible tweak of equation 1,

Tegmark's equation 1 is fine, the FRW metric is derived for a maximally symmetric space relying only on the assumptions of homogeneity and isotropy. It is equation 2 that has to be interpreted carefully. As it stands it is incomplete; for, although the mean matter density also includes a curvature contribution, a contribution from any cosmological constant is also required as it is indeed added later by equation 4.

For our readers who do not know; the GR "a" evolution equation (Tegmark's equation 2) is
(a'/a)² = 8.pi.G.rho/3 - k/a² + Lambda/3
where a is the scale factor and a' its time derivative, so dividing through by
[H(t)]² = [a'(t)/a(t)]² we obtain
1 = 8.pi.G.rho/3H² - k/a²H² + Lambda/3H²
As we define
Omega_m = 8.pi.G.rho/3H²
Omega_k = - k/a²H²
and
Omega_Lambda = Lambda/3H²
we obtain the result I gave in my post above:
Omega_total = Omega_m + Omega_k + Omega_Lambda = 1 in metric theories.
In a static model such as the Jordan conformal frame of SCC a' = 0 and so we cannot divide through by it, the procedure becomes degenerate - however in SCC there is a well defined concept of Hubble's parameter H based on its measurement directly from red shift and not from a theory dependent recession.

2) confirmation that "the function H(z) is directly measurable in a variety of ways that make no assumptions about dark matter properties or gravitational field equations, but rely on spacetime geometry alone.", and

The main problem is the independent measurements of effective density are themselves theory dependent, as well as noisy as Tegmark remarks, standard candles, rulers and clocks are so hard to come by! Therefore the argument may be in danger of being circular.

3) checking that 'gravity' in these alternatives "is well approximated by partial differential equations on large scales, these decouple into ordinary differential equations for each Fourier mode, since we are perturbing around a homogeneousmetric and derivatives become local in Fourier space"

The 'freely coasting model', for which SCC gives a mechanism, is concordant with the WMAP data as has been published by the Indian team I have referred to elsewhere.

Garth