View Full Version : Self Creation Cosmology
After an abortive start in the new IR Forum I am beginning a new thread on the published theory of Self Creation Cosmology.
There has already been many posts on the subject in PF and I apologise for any repetition, but having been asked to post it here in A&C I here make a clean start!
The published papers are:-
On Two Self Creation Cosmologies (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1982GReGr..14..117B&db_key=AST&data_type=HTML&format=&high=3effdfa94828758)
A New Self Creation Cosmology (http://www.kluweronline.com/oasis.htm/5092775)
and here:
Self Creation Cosmology - An Alternative Gravitational Theory (http://novapublishers.com/catalog/product_info.php?products_id=1869)
Abstract from that most recent paper:
Self Creation Cosmology An Alternative
Gravitational Theory
Garth A Barber
June 10, 2004
Abstract
A question is raised about the premature acceptance of the standard cosmological model, the LambdaCDM’ paradigm; the non-metric, or semi-metric, theory of Self Creation Cosmology is offered as an alternative and shown to be as equally concordant as the standard model with observed cosmological constraints and local observations. In self-creation the Brans Dicke theory is modified to enable the creation of matter and energy out of the self contained gravitational and scalar fields; such creation is constrained by the local conservation of energy so that rest masses vary whereas the observed Newtonian Gravitation ’constant’ does not. As a consequence there is a conformal equivalence between self-creation and General Relativity in vacuo, which results in the predictions of the two theories being equal in the standard tests. In self-creation test particles in vacuo follow the geodesics of General Relativity. Nevertheless there are three types of experiment that are able to distinguish between the two theories. There are also other local and cosmological observations that are readily explained by self-creation, such as the anomalous sunwards acceleration of the Pioneer spacecraft and a secular spinning up of the Earth’s rotation that both ’coincidentally’ echo Hubble’s constant. Moreover, the most significant feature of self-creation is that it is as consistent with cosmological constraints in the distant supernovae data, the Cosmic Microwave Background anisotropies and primordial nucleo-synthesis, as the standard paradigm. Unlike that model, however, it does not require the addition of the undiscovered physics of Inflation, dark non-baryonic matter, or dark energy. Nevertheless it does demand an exotic equation of state, which requires the presence of false vacuum energy at a moderate density determined by the field equations. Consequently it is able to interface gravitation and quantum theories without creating a ’Lambda’ problem. In self-creation there are two frames of interpretation of observational data, which depend on whether energy or energy-momentum is to be conserved and whether photons or atoms respectively are chosen as the invariant standards of measurement. In the former frame the universe is stationary and eternal with exponentially shrinking rulers and accelerating atomic clocks, and in the latter frame the universe is freely coasting, expanding linearly from a Big Bang with rigid rulers and regular atomic clocks. A novel representation of space-time geometry is suggested. As the theory is readily falsifiable it is recommended that all three of the definitive experiments be performed at the earliest opportunity.
You may not be able to access these, however there is free access of the last two of these papers on the physics ArXiv and the published work can be recovered from there as follows:
1. The Principles of Self Creation Cosmology and its Comparison with General Relativity (http://arxiv.org/pdf/gr-qc/0212111 )
2. Experimental tests of the New Self Creation Cosmology and a heterodox prediction for Gravity Probe B (http://arxiv.org/pdf/gr-qc/0302026 )
3. The derivation of the coupling constant in the new Self Creation Cosmology (http://arxiv.org/pdf/ gr-qc/0302088 )
4. The Self Creation challenge to the cosmological concordance model (http://arxiv.org/pdf/astro-ph/0401136)
5. Self Creation Cosmology - An Alternative Gravitational Theory (http://arxiv.org/pdf/gr-qc/0405094)
The reason why I am posting on PF at all is because I value your informed and constructive criticism. From my Profile you will read: "I am a published independent researcher in cosmology". The key word here is independent it is very difficult to obtain valued and informed criticism if you are no longer in a university department. PF is for me a "physics department coffee lounge" where ideas can be suggested and knocked down or otherwise. I value that.
Predictions of the Theory
The theory is completely equivalent to GR in vacuo, therefore all tests to date which compare the geodesics of test particles and photons with observation are concordant with both GR and SCC.
The cosmological solution requires a homogeneous density; therefore the result differs from GR.
R(t) ~ t
k =+1
A finite but conformally flat model concordant with WMAP CMB anisotropies spectrum. (Not only first peak but also lack of large angle anisotropies)
\Omega_m = 2/9 (0.22)
\Omega_ L = 1/9 (0.11) (false vacuum)
\Omega_{total} = 1/3 (0.33)
1. GPB Geodetic precession
SCC: 5.5120 arcsec/yr
GR: 6.6144 arcsec/yr
GPB gravitomagnetic frame dragging precession
SCC = GR = 0.0409 arcsec/yr
2. LIGO interferometer 8km light path deflected towards the Sun by
2 x 10-12 metres vertically.
Also a 'Space Interferometer Experiment' is suggested in my papers that will test the same effect.
Deviation from the EEP by solid objects; 10cm Aluminium block in vacuo violation of EEP at one part in 10-17, three orders of magnitude smaller than present experimental sensitivity.
3. Casimir force 'bottoming out' detectable somewhere in the Solar field between the orbits of Jupiter and Saturn.(depending on instrument sensitivity)
SCC predicts the maximum Casimir force to be a function of space-time curvature.
4. Pioneer Spacecraft anomalous Sunwards acceleration of
cH = 6.6 x 10-8 cm/sec2
5. Earth decrease in day relative ancient solar eclipses (lunar orbit) at rate
H = 6 x 10-4 secs/day/century.
NB. Last two may have been already observed.
The following is an extract from my introduction to the “Comparison of the Mainstream and the Self Creation Freely Coasting models” thread and matches my work with a largely Indian team who have worked on what they call the "Freely Coasting Model (FCM)".
Introduction to FCM
The FCM is an empirical model, proposed by a team at the University of Delhi, in which the universe expands strictly linearly with time R[t] ~ t. Its motivation was the realisation that such a model would not require inflation to explain the horizon, flatness or smoothness problems of GR as they would not exist in the first place. It was then realised that the model was surprisingly concordant with cosmological constraints without the further addition of concepts such as DM or DE that remain undiscovered in laboratory physics. There have been several papers published and PhD’s gained exploring this alternative cosmological paradigm, viz:
1. A coasting cosmology (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1989ApJ...344..543K&db_key=AST)
2. Freely Coasting Cosmology (http://arxiv.org/abs/astro-ph/0209209)
3. A Concordant “Freely Coasting” Cosmology (http://arxiv.org/abs/astro-ph/0306448)
4. A case for nucleosynthesis in slowly evolving models (http://arxiv.org/abs/astro-ph/0502370)
5. Nucleosynthesis in a Simmering Universe (http://arxiv.org/abs/nucl-th/9902022)
and a PhD thesis available on the physics ArXiv:
6. GRAVITATIONAL LENSING IN STANDARD AND ALTERNATIVE COSMOLOGIES (http://arxiv.org/abs/astro-ph/0401542)
However the shortfall of this concordant empirical theory is that
it requires a mechanism to deliver the strict linear expansion.
Independently from the Indian team’s work I have developed SCC as an alternative gravitational theory that modifies GR to include a ‘non-minimally connected scalar field’.There are seven papers and eprints that are referred to above.(There have also been 47 other author citations in peer-reviewed journals.)
Self Creation Cosmology
The SCC scalar field follows that in the theory of Brans Dicke (BD) and is coupled to the distribution of matter in motion in the universe in order to fully incorporate Mach’s Principle. SCC modifies BD in that it allows the scalar field to act on particles and thus violates the equivalence principle. The presence of the scalar field in BD and SCC perturbs space-time. This is the reason BD is not concordant with solar system experiments. However in SCC the scalar field force operates on particles, but not photons, and corrects this perturbation. The geodesics of test particles and photons are the same in SCC as GR. SCC is concordant with all experiments to date, however there are several tests that easily falsify the theory, which do not test whether trajectories follow GR geodesics . One of these tests is being carried out at present, the Gravity Probe B satellite experiment, and the results will be known next year.
SCC has two conformal frames of measurement, the Jordan frame in which particle masses increase with gravitational potential energy and in which gravitational trajectories and cosmological evolution are calculated, and the Einstein frame in which particle masses are constant and in which other physics is most easily described.
The cosmological solution is not in general a vacuum solution, therefore SCC cosmology differs from that of GR. The empty universe solution reduces to the GR Milne model. When the Jordan conformal frame cosmological solution, (which turns out to be the same as Einstein's original cylindrical static model) is transformed into the SCC Einstein conformal frame it turns out to be a strictly linearly expanding solution - that is
it provides the linear expansion mechanism for the FCM.
Two differences with the LCDM standard model of GR is that the FCM predicts a baryon density of around 0.2 closure density, in other words there is no need for exotic Dark Matter, and the primordial output of the BB had high metallicity compared to the standard GR BBN. In other words DM does actually exist but originally it was baryonic and only now resides in some dark form. The question for the FCM and the SCC theory is: "In what form is this matter today?"
One clue is the ubiquitous presence of
1. re-ionisation in the IGM and
2. metallicity in early Lyman alpha forests.
These may be evidence of a fairly isotropic background of PopIII stars that formed at around z = 20. From the paper A very extended re-ionisation epoch? (http://arxiv.org/abs/astro-ph/0506486) there is also a suggestion that there was a late period of Pop III star re-ionisation that finished at z>=10.5. This would then date the end of such stars, the ‘transition red shift’.
As a comparison therefore, the active lifetime of Pop III stars in the two models is calculated to be: (Using LCDM values for the GR model)
For the onset of metallicity, i.e. 'ignition' of Pop III stars, z = 20
tz=20 = 182 Myrs. in GR
tz=20 = 657 Myrs. in SCC
for the transition period, i.e. the end of Pop III stars, z = 10.5
tz=10.5 = 450 Myrs. in GR
tz=10.5 = 1.31 Gyrs. in SCC
Thus the active lifetime of Pop III stars is
~270 Myrs in GR and ~650 Myrs in SCC, i.e. over twice as long. Note that if this late re-ionisation period does not in fact exist then the transition period is much earlier and the Pop III lifetimes drastically reduced.
However how massive are PopIII and how many of them were there? The SCC speculation is that given the primordial gas (PG) had some metallicity
[Fe/H] = log10(NFe/NH)PG - log10(NFe/NH)Solar = -5
that the first PopIII stars could be smaller than the standard model allows. Metallicity is important in radiating away heat to allow the proto-stars to collapse. The range ([102 - 104]Msolar) is suggested as they would leave behind IMBHs or the same mass range and this range seems to be concordant with observation. So DM consists of a background of IMBHs in the range [102 - 104]Msolar.
Will this idea work, that is does the hypothesis that DM consists largely of IMBHs fit observation?
Garth
Chronos
Jul21-05, 03:19 AM
... So DM consists of a background of IMBHs in the range [10^2 - 10^4]Msolar.
Will this idea work, that is does the hypothesis that DM consists largely of IMBHs fit observation?IMBH abundance is not ruled out, but is controversial. A sampler:
http://arxiv.org/abs/astro-ph/0405355
Cosmic Star Formation, Reionization, and Constraints on Global Chemical Evolution
http://arxiv.org/abs/astro-ph/0302101
Intermediate-Mass Black Holes in the Universe: A Review of Formation Theories and Observational Constraints
http://arxiv.org/abs/astro-ph/0202218
Constraints on primordial black holes and primeval density perturbations from the epoch of reionization
http://arxiv.org/abs/astro-ph/9902028
Constraints on the mass and abundance of black holes in the Galactic halo: the high mass limit
http://arxiv.org/abs/astro-ph/9511032
Constraints on massive black holes as dark matter candidates using Galactic globular clusters
Thank you Chronos for those interesting links, I wonder whether IMBHs have not already been detected and mis-identified as MACHO's POINT-AGAPE Pixel Lensing Survey of M31 : Evidence for a MACHO contribution to Galactic Halos (http://arxiv.org/abs/astro-ph/0504188).
The main controversy in accepting IMBHs as the major component of DM is mainstream BBN constrains \Omega_{baryon} = 0.04. My question is: if this limitation is lifted (by the FCM BBN) could the DM identification problem be solved?
Note: in my thread "Submitted Research: Self Creation Cosmology, by Garth" in the IR Forum ZapperZ rather cynically asked:I don't know if this is the appropriate place to ask this, but you have been here long enough to be able to answer this. In all the interactions you have had on here, who do you think has the expertise to be able to either comment, criticize, or judge the validity of your work?
My answer, which I never posted in that thread, was that yes there are some such as yourself Chronos, and others such as the 'Mentors', who have made constructive comments and criticisms of my work. One of the greatest contributions has been in providing such relevant links to physics ArXiv papers, and other academic web pages, as yours above, which enable me to keep up to date with a multitude of developments that otherwise I might well have missed. Thank you.
Garth
Chronos
Jul22-05, 12:33 AM
I think Zz has a point [albeit a little pessimistic], but any kind of reasonably informed feedback would seem better than nothing [not to mention we work pretty cheap]. Anyways, I have another recent selection that might be of interest:
http://arxiv.org/abs/astro-ph/0507439:
Title: Heavy Element Production in Inhomogeneous Big Bang Nucleosynthesis
Retraction
Since publishing my 2002 paper I have been pleased to discover that the Gravity Probe B satellite appeared to provide a test that could falsify SCC. Earlier I repeated the prediction in this thread.
1. GPB Geodetic precession
SCC: 5.5120 arcsec/yr
GR: 6.6144 arcsec/yr
GPB gravitomagnetic frame dragging precession
SCC = GR = 0.0409 arcsec/yr
The SCC prediction is more complicated than the GR calculation as freely orbiting bodies have an extra, Newtonian-like, scalar field force acting on them (but not on photons). Over the years I have worried that I may not have included all the extra factors complicating the calculation.
In all other solar system experiments the scalar field force exactly compensated for the perturbation of space-time curvature from the GR value. I worried that this did not appear to happen in the case of geodetic precession.
Today, to my dismay, I have realised that my geodetic calculation does not include the Thomas precession on the GP-B gyroscopes properly.
When the effect of the Thomas precession, due to the scalar field force accelerating the gyroscopes, is taken into account the SCC geodetic precession is equal to that of GR
So the above prediction should read:
1. GPB Geodetic precession
SCC = GR = 6.6144 arcsec/yr
GPB gravitomagnetic frame dragging precession
SCC = GR = 0.0409 arcsec/yr
Falsification of SCC will now depend on somebody performing the definitive test, which is photons are predicted to 'fall' at a rate 3/2 that of particles.
A horizontal laser such as the LIGO interferometers, compared to the Earth, should be perturbed towards the Sun. With a 8 km light path the perturbation is predicted to be 2 x 10-12 metres.
I will be publishing this correction shortly.
Garth
Falsification of SCC will now depend on somebody performing the definitive test, which is photons are predicted to 'fall' at a rate 3/2 that of particles.Does SCC envision any refractive effect to produce this discrepant infall rate? If not, how do you model a gravitational force that manages to affect massless photons 50% more efficiently than massive particles?
Does SCC envision any refractive effect to produce this discrepant infall rate? If not, how do you model a gravitational force that manages to affect massless photons 50% more efficiently than massive particles?
This is at the heart of SCC and why the split laser beam interferometer would be a definitive test; if photons do fall at the same rate as particles then SCC is dead in the water, there would be no resurrection, SCC would then simply be another of the invariant conformal gravity theories that have only re-writen GR in some inconvenient coordinate system.
In Brans Dicke an extra scalar field is introduced that is coupled to the trace of the stress-energy-momentum tensor (matter) by a coupling constant \lambda. Its presence perturbs the curvature of space-time and consequently BD is only concordant with solar system experiements if \lambda is vanishingly small. This has led to its demise.
SCC introduces a principle of mutual interaction (PMI), which states that the scalar field is a source for the matter-energy field if and only if the matter-energy field is a source for the scalar field, by coupling
\nabla _\mu T_{M\quad \nu }^{\quad\mu } to T_M, thus:
\begin{equation}
\nabla _\mu T_{M\;\nu }^{.\;\mu }=f_\nu \left( \phi \right) \Box \phi =4\pi
f_\nu \left( \phi \right) T_{M\;}^{\;}\text{ ,} \notag \end{equation}
so that for an electro-magnetic field, which is trace-free,
T_{em} =0,
\begin{equation}
\nabla _\mu T_{em\quad \nu }^{\quad \mu }=4\pi f_\nu \left( \phi \right)
T_{em}^{\;}=4\pi f_\nu \left( \phi \right) \left( 3p_{em}-\rho _{em}\right)=0 \notag
\end{equation}.
Photons thus travel on null-geodesics, whereas particles do not.
A remarkable feature of the PMI violation of the equivalence principle is that this ’scalar field force’ acts in a similar fashion to the gravitational force. It is proportional to the product of the masses of two freely falling bodies and inversely proportional to the square of their separation. Thus, if this force exists, it would be convoluted with the Newtonian gravitational force and affect the value of the Newtonian gravitational constant in all Cavendish type experiments.
Eotvos-type experiments, asking whether, "atoms all fall at the same rate", which tests the equivalence principle for different types of matter, would only find a violation at the 10-17 level, three orders of magnitude smaller than present experimental sensitivity. (Such violation depending on
\frac{p}{\rho c^2} for the materials being studied.)
The scalar field thus exerts an extra force, which acts on freely-falling ,particles but not photons, that perturbs them from their geodesic trajectories. It works out that this scalar-field force exactly compensates for the perturbation of space-time by the BD scalar field. Particles and photons both travel along the geodesics and null-geodesics of GR, the theory is conformally equivalent to canonical GR in vacuo, and thus all experiments (including now the GP-B geodetic measurement) that verify GR also verify SCC.
The crucial difference is the direct measurement of the rate of acceleration of photons and particles in a gravitational field; an extension of the Eotvos experiments: "Do particles and photons 'fall at the same rate'?
Garth
Retraction of the Retraction!!
GP-B is back as a resolution of the degeneracy between SCC and GR!!
As I said above the geodetic precession (SCC precession = 5/6 GR precession) has to be corrected in SCC by a Thomas precession. (that caused by the acceleration of a spin-axis in 4-space)
The Thomas precession for SCC is 1/6 the GR geodetic precession, so above I worried that the total N-S GP-B precession rate was going to be (5/6 + 1/6) GR geodetic precession = GR = 6.6"/yr. and if GP-B returned that value, as everybody expects, then SCC would be lost in the dust!
However after a careful analysis I have realised that the Thomas precession has to be subtracted from the geodetic and so the SCC prediction is:
(5/6 - 1/6)GR geodetic precession = 2/3 = 4.4096"/yr and we are back in business as soon as I have time to publish the correction.
So the above prediction should now read:
1. GPB Geodetic precession
SCC = 4.4096 arcsec/yr
GR = 6.6144 arcsec/yr
GPB gravitomagnetic frame dragging precession
SCC = GR = 0.0409 arcsec/yr
We wait and see! :smile:
Garth
Chronos
Dec15-05, 03:14 AM
Your model will fail for devious reasons, Garth. Look at the way they will apply corrections to GPB results. They will cancel out the very effects you are looking for. What I'm saying is you need the raw data to apply your model. Does that make any sense? You have a lot of work to do!
Your model will fail for devious reasons, Garth. Look at the way they will apply corrections to GPB results. They will cancel out the very effects you are looking for. What I'm saying is you need the raw data to apply your model. Does that make any sense? You have a lot of work to do!
Thank you Chronos for your comment.
The GP-B team are being very careful not to prejudge the issue, that is why the experiment's two sets of data are being kept separate.
The angular displacements of the gyros have to be related to the satellite telescope’s initial position, rather than its final position directed towards IM Pegasi.
The motion of IM Pegasi with respect to a distant quasar has been measured with extreme precision over a number of years using Very Long Baseline Interferometry (VLBI) by a team at the Harvard-Smithsonian Center for Astrophysics (CfA).
However, to ensure the integrity of the GP-B experiment, a ”blind” component was added to the data analysis by insisting that the CfA withhold the proper motion data until the rest of the data analysis is complete.
I trust the team to be objective in their analysis, whatever their result may be. If my model fails because it really has been falsified by experimental observation, then so be it, at least it has had the strength to be falsifiable!
Garth
Chronos
Dec16-05, 03:35 AM
May I toss you another bone, Garth? I like the way you think, so I'm always on the lookout things like this:
You Can't Get There From Here: Hubble Relaxation in the Local Volume
http://www.arxiv.org/abs/astro-ph/0512323
May I toss you another bone, Garth? I like the way you think, so I'm always on the lookout things like this:
You Can't Get There From Here: Hubble Relaxation in the Local Volume
http://www.arxiv.org/abs/astro-ph/0512323
Yes I had seen it, the bone for me to chew on is the statement: The most straightforward explanation (though not the only possible) is that there exists a large quantity of baryonic matter in this region so far undetected, and unassociated with galaxies or groups.
SCC predicts far more baryonic matter (all DM) than the standard model, perhaps this observation is picking it up?
Garth
Chronos
Dec17-05, 02:59 AM
That's pretty much why I culled that one out for your viewing pleasure, Garth! SCC has some interesting implications. I would like to think I'm not oblivious to them. Besides, I'd like to be remembered as the guy who stood up for you before you became famous! And if not, at least we drank wine together while proseletizing.
And if not, at least we drank wine together while proseletizing. :approve:
I'll drink to that!
Garth
Looking further into DM in the SCC scenario I wish to draw across a link from the Addressing Impossibilities in the Standard Cosmological Model (http://physicsforums.com/showthread.php?t=105441&page=3) thread.
The question in hand is that in SCC the overall desnity parameter
\Omega_{Total} = 0.33
of which one third is false vacuum energy
\Omega_{False Vacuum} = 0.11
(This false vacuum energy is detected by the Casimir force. The theory predicts that the Casimir force is limited with a maximum determined by the gravitational potential \frac{GM}{rc^2}. The limit being detectable somewhere between the orbits of Jupiter and Saturn with present sensitivities.)
This leaves a residue of \Omega_{residue} = 0.22
Nucleosynthesis in SCC is to be calculated in the Einstein conformal frame in which atomic masses are constant. In this frame the universe expands strictly linearly, it is a Freely Coasting Model (FCM).
Now, the FCM model (http://arxiv.org/abs/astro-ph/0306448) predicts a BBN baryonic density of about
\Omega_{baryon} = 0.2
which ties in nicely with the SCC prediction, as there is the odd 1% or so of neutrino density to include, together with other possible as yet undiscovered particle species.
The question is in what form is this baryonic material now to be found?
One possibility is that it resides in a population of IMBHs of around (102 - 104)MSolar.
A scenario thus presents itself: Out of the BB and close on the epoch of combination at the CMB Surface of Last Scattering many large PopIII stars form in the mass range ~ (102 - 104)MSolar. (SCC primordial metallicity is not zero as in the standard model but about [-5] (i.e. ~ 10-5 Solar) so these PopIII stars can form with smaller masses and more numerously than in the standard scenario.) After a short time < 106 years, these stars go hyper-nova (thus producing long-GRBs) and leave behind IMBHs of about half the progenitor's mass.
One question with this scenario was what about the ejected material that was not drawn into the IMBH?
Although PopIII stellar evolution is very hazy, virial arguments might suggest that half the mass is drawn into the IMBH and about half ejected. So, unless this ejected material went on to form further giant stars and further BHs there should be a lot of it left behind.
SpaceTiger's link in the other thread to Measured Cosmological Mass Density in the WHIM: the Solution to the 'Missing Baryons' Problem (http://lanl.arxiv.org/abs/astro-ph/0501126) provides an answer: it is WHIM!
\Omega_bWHIM (≥ 7 × 1014) = (2.4+1.9−1.1) × 10−[O/H]−1 %, consistent with both model predictions and the actual number of missing baryons.
[O/H] is needed; now in Table 1 they state at:
z = 0.011 [O/H] > -1.47 and at
z = 0.027 [O/H] > -1.32,
so the upper limit is:
\Omega_bWHIM > 4.3 × 100.47 % = 12.6%
and the lower limit:
\Omega_bWHIM > 1.3 × 100.32 % = 2.7%?
Which is indeed consistent with the standard model of about \Omega_b = 0.04, but also with a much higher \Omega_{WHIM} allowed by the FCM BBN.
The residue density in SCC now appears to be made up of:
\OmegaObserved galactic matter = 0.003
\OmegaWHIM ~ 0.1
\OmegaIMBH ~ 0.1
\OmegaNeutrinos, other matter, etc. = 0.017
Total: \Omega_{residue} = 0.22
Of course the numbers can be played about with a bit, the ratio of WHIM/IMBH being most plastic!
Garth
SpaceTiger
Jan2-06, 02:56 PM
\OmegaObserved galactic matter = 0.003
\OmegaWHIM ~ 0.1
\OmegaIMBH ~ 0.1
\OmegaNeutrinos, other matter, etc. = 0.017
Total: \Omega_{residue} = 0.22
So your model does require a sort of dark matter, does it not? You were forced to include an ad hoc term of \OmegaIMBH ~ 0.1 in order to put your number into concordance with your model's prediction. Such a population of black holes, although possible, is certainly not expected in a naive cosmological model. Why is this less ad hoc than weakly-interacting particles?
In addition, what you call the "false vacuum energy":
\OmegaFalse Vacuum ~ 0.11
is really a form of dark energy, is it not? And does it not fall victim to the same fine-tuning problem as the cosmological constant of the standard cosmological model?
ST Thank you for your important questions, let me take them one by one.So your model does require a sort of dark matter, does it not? You were forced to include an ad hoc term of \OmegaIMBH ~ 0.1 in order to put your number into concordance with your model's prediction. Such a population of black holes, although possible, is certainly not expected in a naive cosmological model. Why is this less ad hoc than weakly-interacting particles?
Yes, I have always said the model requires dark matter, the difference though between SCC and GR is that this is baryonic dark matter.
All the gravitational theory actually predicts is that
\OmegaMatter = 0.22, as the observed matter is much smaller than this the question SCC leaves unanswered is in what form this dark matter might be. The answer to this secondary question comes in several parts.
First is the Indian team's work on the FCM model, which quite independently found \Omegabaryon ~ 0.2, thus the DM is baryonic in this model, and also allows a little leeway for the neutrino density to be squeezed in.
The second part was your acknowledgement that IMBH's would fit the bill, except that in the mainstream model it is constrained by BBN
\Omegabaryon = 0.04. However in SCC without this constraint I was at a loss to explain why the IMBH formation efficiency was almost 100%.
The third part, your last link for me, answered that latter question; the IMBH formation rate need not be 100%; 50% IMBH and the remainder as WHIM was consistent with observation. Also a 50/50 IMBH/ejected-gas model makes good sense in a 'hand waving' sort of way. (My arms are going like windmills at the present!)
Thank you!
In addition, what you call the "false vacuum energy":
\OmegaFalse Vacuum ~ 0.11
is really a form of dark energy, is it not? And does it not fall victim to the same fine-tuning problem as the cosmological constant of the standard cosmological model?
Astrophysics is the science of understanding what goes on
'up there' (astro-) by understanding what goes on 'down here', in the lab, (-physics). Cosmology applies this understanding to the largest possible observable scales. Up to the 1970's it did a good job, the cosmological theory, GR, having been well established in laboratory and solar system experiments. However that relationship between cosmological theory and laboratory science began to change with the intoduction of Inflation, then DM then DE, which were introduced a posteriori to make the model fit without laboratory confirmation (yet?).
The false vacuum energy density is predicted by SCC in the local vicinity and is discovered in the laboratory as the Casimir force. The spherically symmetric solution is over determined in the theory yielding two separate solutions, but in flat space both solutions converge. However, they slightly diverge in the presence of space-time curvature and require a precise small false vacuum energy for consistency. This prediction may be tested if an experiment measuring the Casimir force is launched into the trans-Saturian solar gravitational field. This false vacuum energy requirement in the cosmological solution yields the \Omegafalse vacuum = 0.11. This is a predicted value by the cosmological equations (see A New Self Creation Cosmology (http://www.kluweronline.com/oasis.htm/5092775)) and is not fine tuned to fit.
Please continue to provide constructive criticism, I value your comments a lot.
Garth
SpaceTiger
Jan3-06, 03:09 AM
Yes, I have always said the model requires dark matter, the difference though between SCC and GR is that this is baryonic dark matter.
...
The third part, your last link for me, answered that latter question; the IMBH formation rate need not be 100%; 50% IMBH and the remainder as WHIM was consistent with observation. Also a 50/50 IMBH/ejected-gas model makes good sense in a 'hand waving' sort of way. (My arms are going like windmills at the present!)
Fair enough, but I'm not sure you've answered my question. Why is this less ad hoc than non-baryonic dark matter? It's much easier for mainstream physics to explain a weakly interacting and abundant particle species than a population of intermediate mass black holes that makes up 10% of the closure density. How do you envision them being formed?
The false vacuum energy density is predicted by SCC in the local vicinity and is discovered in the laboratory as the Casimir force.
Two things. First, I don't understand how you're distinguishing this from the traditional quantum explanation for the cosmological constant. In fact, as far as I can tell, your \Omega_{False Vacuum} is equivalent to \Omega_{\Lambda} from the quantum point of view. I understand that your theory of gravity is different, but you seem to be invoking the same source for the "dark energy" as in the most popular mainstream models.
Second, measurements of the Casimir Force tell us about the existence of the vacuum energy, but they tell us nothing of its magnitude. A measurement of a "force" is basically a measurement of dE/dx, not of E0. It's the latter that you need to constrain \Omega_{False Vacuum}.
This false vacuum energy requirement in the cosmological solution yields the \Omegafalse vacuum = 0.11. This is a predicted value by the cosmological equations (see A New Self Creation Cosmology (http://www.kluweronline.com/oasis.htm/5092775)) and is not fine tuned to fit.
The fine-tuning problem comes from the quantum end of things, not the cosmological end. You may be thinking of the less severe "cosmic coincidence problem", which asks why the cosmological constant would suddenly be turning on at this moment in cosmic history. For more information on the fine-tuning and cosmic coincidence problem, check out this paper:
The Cosmological Constant Problem and Quintessence (http://lanl.arxiv.org/abs/astro-ph/0202076)
Fair enough, but I'm not sure you've answered my question. Why is this less ad hoc than non-baryonic dark matter? Only in that it does not require the invocation of an unknown/undetected species of fundamental particle. It's much easier for mainstream physics to explain a weakly interacting and abundant particle species than a population of intermediate mass black holes that makes up 10% of the closure density. How do you envision them being formed?
From a dense ensemble of moderate mass (102 - 103 MSolar)PopIII stars, which also give rise to ionisation and (enhanced) metallicity in the early universe.The false vacuum energy density is predicted by SCC in the local vicinity and is discovered in the laboratory as the Casimir force.Two things. First, I don't understand how you're distinguishing this from the traditional quantum explanation for the cosmological constant. In fact, as far as I can tell, your \Omega_{False Vacuum} is equivalent to \Omega_{\Lambda} from the quantum point of view. I understand that your theory of gravity is different, but you seem to be invoking the same source for the "dark energy" as in the most popular mainstream models.
There is a subtle distinction between the cosmological constant on the left hand side of the GR field equation, which describes space-time curvature, and the false vacuum on the right hand side of the FE, which is entered as its density and pressure is a source of gravitation. One is the source (RHS) the other is the effect (LHS). This distinction is often blurred and confused because the 'equation of states' of the cosmological constant and false vacuum energy are almost identical, differing by the amount g_{\mu \nu} differs from \eta_{\mu \nu}, (although the equations of state are exactly identical in one quantum loop vacuum fluctuation.)
The local and tested Schwarzschild solution of GR has nothing to say of vacuum energy, in GR vacuum is simply that, empty vacuum of zero density and pressure. However the modern cosmological solution has to include a 'false vacuum' energy of some sort to 'balance the books', and of course it is also has the advantage of including quantum effects.
In SCC the local spherically symmetric solution requires the existence of a moderate false vacuum energy density for consistency. This is detectable, as the Casimir force, and makes a falsifiable prediction in the far solar system Casimir experiment proposed. It was not therefore a surprise when it then also cropped up in the cosmological solution. See my definition of astrophysical cosmology in my earlier post above.
Second, measurements of the Casimir Force tell us about the existence of the vacuum energy, but they tell us nothing of its magnitude. A measurement of a "force" is basically a measurement of dE/dx, not of E0. It's the latter that you need to constrain \Omega_{False Vacuum}. Agreed, but SCC suggests that there is a natural renormalised 'cut-off' Emax determined, and therefore limited by, the field equations of the gravitational theory. In the cosmological solution this resolves the 'Lambda problem'.
It is the cut-off, detected as a rounding off at the maximum Casimir force as two plates are brought arbitrarily close together, which measures the vacuum energy density.
The false vacuum density \rho = -p_{max} .
The pressure, Casimir force/plate area, is given by
p_{max} = \frac{F}{A} = -(\frac{\pi hc}{480})z^{-4}
where z is the plate separation at maximum Casimir force.
SCC suggests this density and hence maximum Casimir pressure is limited, the standard theory says it is (almost) infinite, a difference that can be resolved experimentally. (As I have said, with present experimental sensitivity the round off should be detected in the Solar field between the orbits of Jupiter and Saturn.)
The fine-tuning problem comes from the quantum end of things, not the cosmological end. You may be thinking of the less severe "cosmic coincidence problem", which asks why the cosmological constant would suddenly be turning on at this moment in cosmic history. For more information on the fine-tuning and cosmic coincidence problem, check out this paper:
The Cosmological Constant Problem and Quintessence (http://lanl.arxiv.org/abs/astro-ph/0202076)
Yes that is a fine paper, thank you. However my comment on 'fine tuning' was simply responding to your question:"does it (SCC) not fall victim to the same fine-tuning problem as the cosmological constant of the standard cosmological model?" As I said \Omega_{False Vacuum} = 0.11 is determined by the field equation and not a free parameter that is adjusted to fit observations.
Garth
SpaceTiger
Jan3-06, 03:54 PM
Only in that it does not require the invocation of an unknown/undetected species of fundamental particle.
It appears to require the existence of a much less plausible population of objects!
From a dense ensemble of moderate mass (102 - 103 MSolar)PopIII stars, which also give rise to ionisation and (enhanced) metallicity in the early universe.
So your model requires that for every solar mass of material that went into low-mass stars (<~ 1 solar mass) in the early universe, roughly one hundred solar masses went into IMBHs? This requires both an extremely top-heavy mass function and an extremely large star formation efficiency. Do you have any references that even suggest that such a thing might be possible? To my knowledge, it's difficult to even form structure in a purely baryonic universe. Dark matter halos act as seeds for the formation of galaxies and clusters.
In SCC the local spherically symmetric solution requires the existence of a moderate false vacuum energy density for consistency.
So, if I'm understanding you correctly, the difference is not that your model doesn't include dark energy, it's that your model requires it to survive. I suppose this can be viewed as a benefit, but it's a bit deceptive to say that you don't need dark energy.
Agreed, but SCC suggests that there is a natural renormalised 'cut-off' Emax determined, and therefore limited by, the field equations of the gravitational theory. In the cosmological solution this resolves the 'Lambda problem'.
So, to be clear, you're not just modifying gravity, but predicting a low high-energy cutoff for QED (and other QFTs) as well? And the value of this cutoff depends upon the local gravitational potential? The paper I linked addresses the issue of introducing a UV cutoff (Emax) to existing theory:
One way to avoid this is to assume that the Planck scale provides a natural ultraviolet cutoff to all field theoretic processes, this results in <T00>vac ≃ c[sup]5[/sup/G2hbar ∼∼ 1076 GeV4 which is 123 orders of magnitude larger than the currently observed value ρ ≃ 10−47 GeV4. A cutoff at the much lower QCD scale doesn’t fare much better since
it generates a cosmological constant E4QCD 10−3GeV4 – forty orders of magnitude larger than observed. Clearly the answer to the cosmological constant issue must lie elsewhere.
In other words, the simple cutoff you propose appears to be unphysical from the particle physics point of view. Could you elaborate on how SCC changes this fact? Is it more than a theory of gravity?
Thank you for your comments. It is important to distinguish between what the theory predicts and the astrophysics consequences of that prediction. The main problem as I described above is explaining why the baryonic DM is 'dark' today.It appears to require the existence of a much less plausible population of objects!
So your model requires that for every solar mass of material that went into low-mass stars (<~ 1 solar mass) in the early universe, roughly one hundred solar masses went into IMBHs? This requires both an extremely top-heavy mass function and an extremely large star formation efficiency. Do you have any references that even suggest that such a thing might be possible? To my knowledge, it's difficult to even form structure in a purely baryonic universe. Dark matter halos act as seeds for the formation of galaxies and clusters.Yes, in the early low metallicity universe the IMF is expected to be top heavy as metallicity is important in radiating away energy from the collapsing star. The paper Constraints on the IMF of the first stars (http://arxiv.org/abs/astro-ph/0510685) in the standard LCDM model suggests that Indeed, the physical conditions in primordial starforming regions appear to systematically favor the formation of very massive stars. In particular, (i) the fragmentation scale of metal-free clouds is typically 103 M⊙ (Abel,Bryan & Norman 2002; Bromm, Coppi & Larson 2002) (ii) because of the absence of dust grains the radiative feedback from the forming star is not strong enough to halt further gas accretion (Omukai & Palla 2003). (iii) since the accretion rate is as large as 10−3-10−2 M⊙yr−1, the star grows up to >~ 100M⊙ within its lifetime (Stahler, Palla & Salpeter 1986; Omukai & Nishi 1998; Ripamonti et al. 2002)...............
By modeling the structure of the accretion flow and the evolution of the protostar, Tan & McKee (2004) have recently shown that radiative feedback becomes dynamically significant at protostellar masses ≈ 30M⊙, and are likely to constrain the mass of first stars in the range 100 − 300M⊙. Although star formation would take longer (the standard Jean's time scale) than in the standard model there is more time available in the SCC early universe because of the strictly linear expansion.
So, if I'm understanding you correctly, the difference is not that your model doesn't include dark energy, it's that your model requires it to survive. I suppose this can be viewed as a benefit, but it's a bit deceptive to say that you don't need dark energy. I actually say it does not require 'unknown' DE, but I take your point since I often leave off the 'unknown' as it takes too long to describe the vacuum energy's derivation.So, to be clear, you're not just modifying gravity, but predicting a low high-energy cutoff for QED (and other QFTs) as well? And the value of this cutoff depends upon the local gravitational potential? Yes The paper I linked addresses the issue of introducing a UV cutoff (Emax) to existing theory:
In other words, the simple cutoff you propose appears to be unphysical from the particle physics point of view. Could you elaborate on how SCC changes this fact? Is it more than a theory of gravity?It is just a theory of gravity but one in which the principle of the local conservation of energy in the Jordan conformal frame requires the vacuum in a gravitational field to have a small negative density. There are two points to make: the nature of this vacuum density is concordant with observations of the Casimir force and this is testable in the experiment proposed above. I agree that the simple cut-off "appears to be unphysical from the particle physics point of view", but then would not the same criticism equally apply to vacuum in GR?
Garth
SpaceTiger
Jan3-06, 07:43 PM
Thank you for your comments. It is important to distinguish between what the theory predicts and the astrophysics consequences of that prediction. The main problem as I described above is explaining why the baryonic DM is 'dark' today.
Yes, I think we're on the same page here. I wouldn't expect the theory of structure formation in your hypothetical universe to have been worked out in detail, but the problem is that my intuition tells me it's not even close to being possible. Perhaps we can explore this further...
Yes, in the early low metallicity universe the IMF is expected to be top heavy as metallicity is important in radiating away energy from the collapsing star. The paper Constraints on the IMF of the first stars (http://arxiv.org/abs/astro-ph/0510685) in the standard LCDM model suggests that Although star formation would take longer (the standard Jean's time scale) than in the standard model there is more time available in the SCC early universe because of the strictly linear expansion.
I agree and understand that Pop III stellar populations would be expected to have a top-heavy IMF, but I'm asking for quantitative support for the extreme requirements of your model. Not only do you have to put an utterly negligible amount of the mass into low-mass stars, but you need to put about half of your entire baryon budget into stars at a very early period in the evolution of the universe.
For the former requirement, you would need to find a calculation of a theoretical IMF in which the integrated total mass of these heavy stars exceeded the integrated total mass of stars that we can observe today (i.e. that are long-lived) by a factor of at least 100. Really, the majority of the stars we see in the observable universe are not from such an ancient population, so you probably need more like a factor of ~1000. It might be worth computing this more precisely.
For the latter requirement, you need to show that a reasonable spectrum of density perturbations will naturally evolve such that half of your baryon budget is collapsed into these heavy stars at high-redshift. For this, you will presumably need to do a calculation similar to that of Press & Schechter (see the "Classic Papers" thread for the link), taking into account this extra time that is provided by your linear expansion.
I object because it doesn't sound to me like it would work. I'll gladly concede the point if you can give me quantitative support.
There are two points to make: the nature of this vacuum density is concordant with observations of the Casimir force and this is testable in the experiment proposed above.
One could also then say that some forms of dark energy in the standard model are also concordant with these observations. This would not apply to the more exotic types of dark energy (like quintessence), but those are not the only ones considered in the mainstream model. The zero-point energy has not been ruled out as a source for the apparently accelerating expansion.
I agree that the simple cut-off "appears to be unphysical from the particle physics point of view", but then would not the same criticism equally apply to vacuum in GR?
Absolutely, that's why there's a fine-tuning problem!
The headache I have with SCC is that primordial baryogenesis had to persist much longer than predicted by most other models. That does not seem to fit observational evidence. Specifically, it does not explain how the universe cooled so quickly.
I agree and understand that Pop III stellar populations would be expected to have a top-heavy IMF, but I'm asking for quantitative support for the extreme requirements of your model. Not only do you have to put an utterly negligible amount of the mass into low-mass stars, but you need to put about half of your entire baryon budget into stars at a very early period in the evolution of the universe.
For the former requirement, you would need to find a calculation of a theoretical IMF in which the integrated total mass of these heavy stars exceeded the integrated total mass of stars that we can observe today (i.e. that are long-lived) by a factor of at least 100. Really, the majority of the stars we see in the observable universe are not from such an ancient population, so you probably need more like a factor of ~1000. It might be worth computing this more precisely.
For the latter requirement, you need to show that a reasonable spectrum of density perturbations will naturally evolve such that half of your baryon budget is collapsed into these heavy stars at high-redshift. For this, you will presumably need to do a calculation similar to that of Press & Schechter (see the "Classic Papers" thread for the link), taking into account this extra time that is provided by your linear expansion.
I object because it doesn't sound to me like it would work. I'll gladly concede the point if you can give me quantitative support.Thank you it is good to see more precisely where the problems lie - the calculations that are needed may take a little time, Rome, and the standard model, wasn't built in a day!One could also then say that some forms of dark energy in the standard model are also concordant with these observations. This would not apply to the more exotic types of dark energy (like quintessence), but those are not the only ones considered in the mainstream model. The zero-point energy has not been ruled out as a source for the apparently accelerating expansion.Except the slight matter of a factor of 10140 or so Lambda problem? As you say Absolutely, that's why there's a fine-tuning problem!
Thank you for your comments.
Garth
SpaceTiger
Jan4-06, 02:53 AM
Thank you it is good to see more precisely where the problems lie - the calculations that are needed may take a little time, Rome, and the standard model, wasn't built in a day!
Quite alright, take your time!
Except the slight matter of a factor of 10140 or so Lambda problem?
Yes, the hope remains that a field theory (not just of gravity) will come along in which this balance is quite natural. Meanwhile, others are suggesting that perhaps it's simply a matter of the anthropic principle -- a universe that was lamda-dominated at an earlier time would not have been habitable to life. I'm not the person to ask about particle physics, however, I work mainly on the cosmological side. :smile:
The headache I have with SCC is that primordial baryogenesis had to persist much longer than predicted by most other models. That does not seem to fit observational evidence. Specifically, it does not explain how the universe cooled so quickly.
BBN continued far longer in the FCM, the universe did not cool as quickly, that is the point. But how do you measure the rate at which the universe cooled except from the BBN relative abundances?
The problem the FCM/SCC model does have is with deuterium, which instead has to be made by a spallation process, perhaps in shocks associated with the formation and demise of PopIII stars.
From Concordant "Freely Coasting Cosmology" (http://arxiv.org/abs/astro-ph/0306448)Energy conservation, in a period where the baryon entropy ratio does not change, enables the distribution of photons to be described by an effective temperature T that scales as a(t)T = constant. With the age of the universe estimated from the Hubble parameter being ~ 1.5 × 1010 years, and T0 ~ 2.7K, one concludes that the age of the universe at T ~ 1010K would be some four years [rather than a few seconds as in standard cosmology]. The universe would take some 103 years to cool to 107K. With such time periods being large in comparison to the free neutron life time, one would hardly expect any neutrons to survive at temperatures relevant for nucleosynthesis.
However, with such a low rate of expansion, weak interactions remain in equilibrium for temperatures as low as ~ 108K. The neutron - proton ratio keeps falling as n/p ~ exp[−15/T9]. Here T9 is the temperature in units of 109K and the factor of 15 comes from the n-p mass difference in these units. There would again hardly be any neutrons left if nucleosynthesis were to commence at (say) T9 ~ 1. However, as weak interactions are still in equilibrium, once nucleosynthesis commences, inverse beta decay would replenish neutrons by converting protons into neutrons and pumping them into the nucleosynthesis channel. With beta decay in equilibrium, the baryon entropy ratio determines a low enough nucleosynthesis rate that can remove neutrons out of the equilibrium buffer at a rate smaller than the relaxation time of the buffer. This ensures that neutron value remains unchanged as heavier nuclei build up. It turns out that for baryon entropy ratio \eta ~ 5×10−9, there would just be enough neutrons produced, after nucleosynthesis commences, to give ~ 23.9% Helium and metallicity some 108 times the metallicity produced in the early universe in the standard scenario. This metallicity is of the same order of magnitude as seen in lowest metallicity objects.
The only problem that one has to contend with is the significantly low yields of deuterium in such a cosmology. Though deuterium can be produced by spallation processes later in the history of the universe, it is difficult to produce the right amount without a simultaneous over production of Lithium [19]. However, as pointed out in [1], the amount of Helium produced is quite sensitive to \eta in such models. In an inhomogeneous universe, therefore, one can have the helium to hydrogen ratio to have a large primordial variation. Deuterium can be produced by a spallation process much later in the history of the universe. If one considers spallation of a helium deficient cloud onto a helium rich cloud, it is easy to produce deuterium as demonstrated by Epstein [19] - without overproduction of Lithium.
Interestingly, the baryon entropy ratio required for the right amount of helium corresponds to \Omegab ~ 0.2.
Garth
Why n0bdy uses information quants?;
Why n0bdy uses information quants?;:confused:
And welcome to these Forums murdoc!
Would you like to restate your question, or was it just an observation?
Garth
There is a further reported conundrum with the Mainstream theory that may be resolved in SCC (http://en.wikipedia.org/wiki/Self_creation_cosmology).
As recently posted by Chronos in the thread quasar anomalies (http://physicsforums.com/showthread.php?t=113862) M.R.S. Hawkins of the Royal Observatory Edinburgh, published a paper Time Dilation and Quasar Variability (http://www.arxiv.org/abs/astro-ph/0105073) that reported a problem with the concept of cosmological expansion. It appears that the variablitiy of distant quasars does not appear to show cosmological time dilation as the standard model requires.
The mystery deepens because cosmological time dilation is observed in distant Supernova and slow Gamma Ray Burster light curves.
There may be other explanations for this anomaly, however, SCC provides a ready solution to this problem.
In the SCC Jordan frame the universe is static and red shift is due to a variable mass effect.
In SCC this mass varies with the scalar field (and inversely with G so GM = const.), but only if it is non-degenerate mass.
Fully relativistic energy and degenerate mass, p = +\frac13 \rho, is decoupled from the scalar field and would not vary. Hence although, on the one hand, matter accreting onto objects constructed of such matter, for example neutron stars and black holes, would show cosmological red shift, on the other hand, as the central engine is degenerate, there would be no cosmological red-shift effect in the variability of that radiation.
Therefore supernovae and GRBs, which have exploding ordinary stars as their central enegine, would be expected, by SCC, to be affected by the variation in mass and exhibit cosmological time dilation, whereas quasars, which are assumed to have massive black holes as their central engine, would not be expected by the theory to exhibit a dilation in their variation.
This is what seems to be observed.
Garth
SpaceTiger
Mar13-06, 12:59 PM
Fully relativistic energy and degenerate mass, p = +\frac13 \rho, is decoupled from the scalar field and would not vary. Hence although, on the one hand, matter accreting onto objects constructed of such matter, for example neutron stars and black holes, would show cosmological red shift, on the other hand, as the central engine is degenerate, there would be no cosmological red-shift effect in the variability of that radiation.
I'm a bit confused by this argument, Garth. You admit that there should be cosmological redshift (and, presumably, time dilation) in the radiation emitted from the accretion disk, but then claim that the radiation's variability wouldn't show this effect. Since the variable radiation arises from the accreting matter, shouldn't it be dilated?
I'm a bit confused by this argument, Garth. You admit that there should be cosmological redshift (and, presumably, time dilation) in the radiation emitted from the accretion disk, but then claim that the radiation's variability wouldn't show this effect. Since the variable radiation arises from the accreting matter, shouldn't it be dilated?
First, this is very new to me and I am only beginning to work out the implications of 'quasar variablity non-time dilation' in the SCC scenario. I may not have it right yet!
The basic premise is that it appears that observations confirm time dilation in the light profiles of distant supernovae, and, less certainly, of long GRBs, yet it is not observed in quasar variability.
One difference between these two classes is that the engines of supernovae and GRBs(?) are exploding non-degenerate (but massive) stars and the engine of a quasars is degenerate matter that has collapsed into a black hole.
Therefore there may be an explanation for this observation in SCC because in that theory the scalar field is coupled to non-degenerate matter and decoupled from degenerate matter.
How would this work?
In SCC there are two conformal frames, in the Einstein frame the cosmos evolves very much as in the mainstream model except the expansion is strictly linear with time, the universe is conformally flat the DM is all baryonic and the DE is a predetermined and measureable amount of false vacuum energy.
In the Jordan frame the universe is static and cylindrical (closed), particle masses increase exponentially with time because of the interaction of the scalar field and rulers 'shrink', cosmological red shift is a variable mass effect.
There are two processes involved in observing quasar variability, which may be understood in the Jordan frame.
The first is the red shift observed in emission lines from the accretion disk. The atoms in the past were less massive and therefore emitted at a lower frequency than at present, which is observed as a cosmological red shift.
Secondly the time scale of the variability is dependent on the size of the accretion disk itself. This diameter is determined by the gravitational field which itself is dependent on the mass of the central black hole.
Whereas the masses of individual atoms increase over cosmological time the mass of the black hole does not, because it does not interact with the scalar field. Its mass increases only through accretion, it does not increase cosmologically.
Therefore the time scale of the variability of the quasars emission should not be red-shift dependent.
The question of whether the light curve of a super nova should show time dilation in a variable mass cosmology was discussed by Narlikar & Arp in the paper: TIME DILATION IN THE SUPERNOVA LIGHT CURVE AND THE VARIABLE MASS HYPOTHESIS (http://www.journals.uchicago.edu/ApJ/journal/issues/ApJL/v482n2/5714/5714.pdf)
I would appreciate comment and constructive criticism!
Garth
SpaceTiger
Mar13-06, 08:28 PM
TIME DILATION IN THE SUPERNOVA LIGHT CURVE AND THE VARIABLE MASS HYPOTHESIS (http://www.journals.uchicago.edu/ApJ/journal/issues/ApJL/v482n2/5714/5714.pdf)
Well, I'm far from an expert on variable mass cosmologies, but it appears that their arguments are dependent on the variable mass of the emitting particles, not of the source of gravity. That is, they say that the timescales of atomic emission would be scaled up by their lower masses. In your model, I would think the same argument should apply to the matter accreting onto the black hole, despite the constancy of the mass of the black hole itself.
EDIT: No, I take it back. The emission should be affected by redshift, but the variability is from purely geometric arguments. If the mass of the black hole is the same, then the geometric size should be the same. You're instead stuck with the problem of how the black hole manages to accrete so much with such a strongly diminished Eddington luminosity (goes as the particle masses^3).
EDIT: No, I take it back. The emission should be affected by redshift, but the variability is from purely geometric arguments. If the mass of the black hole is the same, then the geometric size should be the same. You're instead stuck with the problem of how the black hole manages to accrete so much with such a strongly diminished Eddington luminosity (goes as the particle masses^3).
Then we agree, although I am not so sure I understand how a BH behaves in the Jordan frame of my theory! One key factor is G also varies cosmologically,
m = m0exp(Ht) for normal matter and
G = G0exp(-Ht).
The question is whether the cosmological decrease in G (increase in \phi) applies to the mass, and hence affects the gravitational field, inside the BH event horizon, and as that field smoothly matches the metric outside the event horizon, affects the orbital dynamics of the accretion disk.
Although in the past this enhanced value of G will alleviate the deficient Eddington luminosity somewhat. However, I don't quite understand how a diminished Eddington luminosity is a problem with matter accretion. Surely with less stuff being ejected, it will be easier to accrete mass? Or are you thinking about the last stages of a massive star evolving into a BH?
Garth
SpaceTiger
Mar14-06, 12:28 PM
Although in the past this enhanced value of G will alleviate the deficient Eddington luminosity somewhat. However, I don't quite understand how a diminished Eddington luminosity is a problem with matter accretion. Surely with less stuff being ejected, it will be easier to accrete mass? Or are you thinking about the last stages of a massive star evolving into a BH?
A diminished Eddington Luminosity causes two problems. First, it will make it hard to explain the brightest quasars. If the Eddington Luminosity were that much smaller at high redshift, we should see strong luminosity evolution in the quasars. To my knowledge, there are no strong trends in this direction until very high redshift (where the black holes are presumably much smaller on average). The other thing is that it exacerbates the pre-existing problem of explaining how SMBHs reached such large masses by the present epoch and how we see such massive and bright quasars at high redshift. The Eddington Limit, though not strict, certainly is valid to within a factor of order unity. It might be worth pumping some numbers to figure out the limiting luminosities in your model at various redshifts and, along with that, the inferred minimum masses of the black holes hosting high-z quasars. The evolving G does help your case a bit (it cancels out one factor of exp(Ht)), but your Eddington luminosity still diminishes steeply with redshift.
Thank you SpaceTiger, I was being a bit thick when you first mentioned the Eddington luminosity!
I will obviously have to start thinking about a theory of Super-Eddington accretion...
Garth
SpaceTiger
Mar14-06, 02:04 PM
I will obviously have to start thinking about a theory of Super-Eddington accretion...
Even in the mainstream model, there have been observations that suggest a possible need for this and, I'll tell you now, it's not easy to get more than a factor of order unity above Eddington. The standard derivation of the Eddington luminosity assumes spherical symmetry, so it's not exactly applicable to accretion from a disk, but the geometrical correction factors are not large (and I'm not immediately sure which direction they go). There's a great deal of literature on this, so you might try a search.
The problem is a bit more complicated in the Jordan frame.
The calculation of the Eddington mass limit from the Eddington luminosity uses the observational relationship
\frac{L}{L_\odot} \sim (\frac{M}{M_\odot})^3
which cannot be depended upon when masses and G are varying cosmologically. Basically the luminosity created by the same stellar core will be less at earlier times because of the lesser atomic masses relative to the present day.
It is easier to calculate physical processes, such as nuclear luminosity, in the Einstein frame of the theory in which particle masses and G are constant. In which case the Eddington luminosity and mass limit are the same as in the mainstream theory. It is the way that gravitational orbits varies over cosmological time that is better described in the Jordan frame
Garth.
SpaceTiger
Mar15-06, 01:42 AM
The calculation of the Eddington mass limit from the Eddington luminosity uses the observational relationship
\frac{L}{L_\odot} \sim (\frac{M}{M_\odot})^3
We're talking about quasars (i.e. black holes). The relationship you're quoting is for main sequence stars. I meant that a quasar observed to have a particular luminosity must at least be massive enough that it doesn't blow itself apart with its own radiation. This fact doesn't rely on the observed mass-luminosity relation of anything. The Eddington luminosity doesn't come from any fancy physics, just radiation pressure, Thomson scattering, and gravity.
Agreed, but I understood you to be saying that one problem was how such SMBHs formed in the first place, (i.e. via massive PopIII stars) once formed the Eddington limit would not apply to a black hole, would it?
As I said in my post #37, the problem with doing such calculations in the Jordan frame is the whole of nuclear and astro physics has to be reworked with the variable particle mass scenario. It is much easier to work it in the Einstein frame, with standard physics and a modified GR gravitational field. As, for example, in BBN where the cosmology and BBN becomes that of the Freely Coasting Model.
Garth
SpaceTiger
Mar15-06, 11:28 AM
Agreed, but I understood you to be saying that one problem was how such SMBHs formed in the first place, (i.e. via massive PopIII stars) once formed the Eddington limit would not apply to a black hole, would it?
No, the problem is both how the SMBHs grew and how quasars can be so bright at high redshift. Yes, the Eddington limit does apply to a black hole, just as it does to any gravitating radiator. I suggest reviewing the derivation of the Eddington limit (if you can't find it, I'll be happy to reproduce it).
No, the problem is both how the SMBHs grew and how quasars can be so bright at high redshift. Yes, the Eddington limit does apply to a black hole, just as it does to any gravitating radiator. I suggest reviewing the derivation of the Eddington limit (if you can't find it, I'll be happy to reproduce it).
Yes, thank you. I am interested in how the Eddington limit applies to a BH accretion disk and jet, the quasar 'engine'.
Garth
SpaceTiger
Mar15-06, 12:22 PM
Yes, thank you. I am interested in how the Eddington limit applies to a BH accretion disk and jet, the quasar 'engine'.
The easiest way to derive it is to just consider the force of radiation pressure versus the gravitational force. Assume a gas made of purely ionized hydrogen in the Newtonian approximation, the gravitational force on a hydrogen atom is given by:
F_g=\frac{GM_{BH}m_H}{r^2}
If the hydrogen atom is to remain in orbit around the black hole (in the disk), this force must be greater than that provided by radiation pressure. The free electrons present a greater cross section to the radiation than the hydrogen ions, but electromagnetic forces will couple the ions and electrons, so a force on the electron is effectively a force on the protons as well. The radiation force on an electron is:
F_r=Flux \times \sigma_T / c = \frac{L\sigma_T}{4\pi r^2c}
where c is the speed of light and \sigma_T is the Thomson cross section. The point at which the radiation force overwhelms gravity is found by equating these two forces:
\frac{L\sigma_T}{4\pi r^2c}=\frac{GM_{BH}m_H}{r^2}
leading to...
L_{Edd}=\frac{4\pi GM_{BH}m_Hc}{\sigma_T}
There are several complications that arise in real accretion disks. First of all, the chemical composition is not entirely hydrogen. It is mostly hydrogen, though, so this won't be a big correction. Second of all, gravity isn't exactly Newtonian in the inner accretion disk. Again, an order unity correction. Finally, it assumes isotropic emission from the accretion, which is just a geometrical correction factor. None of these things, it turns out, make a big difference. The Eddington luminosity is still a good approximation to the maximum luminosity of an accreting black hole. If it radiates more strongly than this, then the surrounding matter is expelled and cannot accrete any further.
Thank you ST, very clear and the same as the Eddington luminosity of the envelope of a large star. Of course - we are talking about a 'thick disk', I keep thinking of an accretion disk as a thin affair!
The Thomson cross section is given by:
\sigma_T = \frac{8\pi}{3}\frac{e^4}{c^4m_e^2}
so the luminosity is proportional to particle masses cubed, thank you.
As I said in SCC it is easier to do the gravitational physics in the Jordan frame and leave everything else to the Einstein frame and be careful how you integrate the two. I make no claim that i understand this problem fully in the SCC scenario but you have given me some good pointers. Thank you again.
Garth
Putting some numbers in
\sigma_T = \frac{8\pi}{3}\frac{e^4}{c^4m_e^2} = 6.7 \times 10^{-29} m^2
L_{Edd}=\frac{4\pi GM_{BH}m_Hc}{\sigma_T}
c = 3 \times 10^8 km/sec
G = 6.7 \times 10^{11} MKS
m_H = 1.7 \times 10^{-27} Kg
so
L_E = \frac{4 \pi \times 3 \times 10^8 \times 6.7 \times 10^{-11} \times 1.7 \times 10^{-27} M}{6.7 \times 10^{-29}} MKS
L_E \sim 17 M MKS
now M_\odot = 2 \times 10^{30} kg.
and L_\odot = 3.8 \times 10^{26} MKS.
so
\frac{L_E}{L_\odot} = \frac{17 \times 2 \times 10^{30}}{3.8 \times 10^{26}} \frac{M}{M_\odot}
i.e. \frac{L_E}{L_\odot} \sim 10^5 \frac{M}{M_\odot},
which if the variable mass ~ 1/(1 + z) effect is taken into account, becomes:
\frac{L_E}{L_\odot} \sim 10^5 \frac{M}{M_\odot}\frac{1}{(1 + z)^2},
Now for the most luminous quasars L \sim 10^{12} L_\odot out at z = 6, we have for the standard theory:
M = 10^7 M_\odot
and for SCC
M = 5 \times 10^8 M_\odot
not too outrageous?
I hope I have counted all the OOMs correctly!
Garth
SpaceTiger
Mar15-06, 08:53 PM
Now for the most luminous quasars L \sim 10^{12} L_\odot out at z = 6, we have for the standard theory:
M = 10^7 M_\odot
and for SCC
M = 5 \times 10^8 M_\odot
not too outrageous?
Actually, the most massive quasar that has been reported at high-z (by SDSS) has ~3 x 109 Msun in standard theory. With the same correction factor, that brings your most massive SMBH to ~1.5 x 1011 Msun. That's pretty tough to reconcile with local observations of central black holes.
Actually, the most massive quasar that has been reported at high-z (by SDSS) has ~3 x 109 Msun in standard theory. With the same correction factor, that brings your most massive SMBH to ~1.5 x 1011 Msun. That's pretty tough to reconcile with local observations of central black holes.
Thank you ST, as a point of information, that most massive quasar has a mass 300 x my estimate, does it therefore have a luminosity of 3 \times 10^{14}M_\odot or are my numbers out? (i.e. \frac{L_E}{L_\odot} \sim 10^5 \frac{M}{M_\odot}).
Your final point is interesting to study in the SCC Jordan frame. If the mass of the SMBH is decoupled from the scalar field then it should not grow cosmologically whereas ordinary matter will. (Ordinary matter: m = m_0 exp(Ht)).
However, our measurements define particle masses to be constant, in which case we are working in the Einstein conformal frame of SCC. In this case degenerate matter will appear to decrease in mass as time progresses as measured against a standard non-degenerate mass, such as that of the Sun.
This means that a SMBH that had a mass of M \sim 1.5 \times 10^{11} at ~ z = 6 will today appear to have a mass of
M \sim \frac{1.5 \times 10^{11}}{1 + z}M_\odot = \sim 2 \times 10^{10}M_\odot
Is the core of M87 at 3 \times 10^{9}M_\odot the present observed SMBH? In which case I am about one OOM out, however, that object is still 'local' cosmologically speaking and more massive BHs could be lurking further away.
On the other hand, in my 'hand waving' mode: might this just give another explanation for the end of the 'quasar epoch', apart from them simply running out of accreted 'fuel', i.e. that epoch lies that between the earliest time such a large object could form and the time before their mass 'decreased' below some critical lower limit?
Garth
SpaceTiger
Mar16-06, 03:08 PM
Thank you ST, as a point of information, that most massive quasar has a mass 300 x my estimate, does it therefore have a luminosity of 3 \times 10^{14}M_\odot or are my numbers out? (i.e. \frac{L_E}{L_\odot} \sim 10^5 \frac{M}{M_\odot}).
I get \frac{L_E}{L_\odot} = 38,000 \frac{M}{M_\odot}, leading to ~10^{14} L_\odot.
So which is the "real" mass in your model? In other words, how much mass has been accreted from ordinary matter?
Yes I must have pushed a key on my calculator twice or something -I have the same problem with mobile phones, my fingers are too big - I was brought up on the slide rule, this calculation would have been a doddle!
I have reworked it making no approximations until the last and get the figure
\frac{L_E}{L_\odot} = 3.28 \times 10^4 \frac{M}{M_\odot}
So which is the "real" mass in your model? In other words, how much mass has been accreted from ordinary matter?
Mass is measured by comparing it to a standard, e.g. the Sun, at the epoch of the measurement.
So actually 1.5 \times 10^{11} M_\odot real mass was accreted at z ~ 6, which in the FCM occurs at t = 2Gyr. The Sun continues to grow in mass (and G diminish) by a factor (1 + z) from the time @ z until the present day. Comparing the old quasar with the modern Sun the quasar (with no further accretion) will appear to have a mass today of M \sim 2 \times 10^{10} M_\odot as I said above.
Garth
SpaceTiger
Mar17-06, 04:06 AM
So actually 1.5 \times 10^{11} M_\odot real mass was accreted at z ~ 6, which in the FCM occurs at t = 2Gyr. The Sun continues to grow in mass (and G diminish) by a factor (1 + z) from the time @ z until the present day. Comparing the old quasar with the modern Sun the quasar (with no further accretion) will appear to have a mass today of M \sim 2 \times 10^{10} M_\odot as I said above.
I don't really buy this argument. If the black hole's actual mass is remaining constant, then we should measure the same mass at two epochs when comparing to the same standard (e.g. the present-day sun). The fact that the sun's mass is changing is irrelevant, since we're only using it as a standard at one epoch.
Either way, though, you still have to explain how you built up over 100 billion solar masses in under two billion years with a strongly diminished Eddington limit.
I don't really buy this argument. If the black hole's actual mass is remaining constant, then we should measure the same mass at two epochs when comparing to the same standard (e.g. the present-day sun). The fact that the sun's mass is changing is irrelevant, since we're only using it as a standard at one epoch.What actually changes in the Jordan frame is the rest mass of non-degenerate atomic particles from which the standard mass (http://pda.physorg.com/lofi-news-standard-silicon-mass_3244.html) is made, the Sun's mass, as a collection of such particles, is a convenient unit in which to express stellar, galactic & BH masses.
Remember in this conformal frame the rate of atomic clocks is also changing relative both to the (inverse) frequency of a photon sampled from the peak emission of the CMB, and also to ephemeris time.
Atomic clocks depend on the conservation of energy-momentum, i.e. rest mass (SCC Einstein frame), standard photon clocks (carefully defined), and ephemeris clocks (in SCC but not GR), depend on energy being locally conserved (SCC Jordan frame).
Such a clock drift between atomic and ephemeris time would reveal itself as an apparent sunwards acceleration of cH of the Pioneer spacecraft.
Either way, though, you still have to explain how you built up over 100 billion solar masses in under two billion years with a strongly diminished Eddington limit. Agreed.
Working in the Einstein frame of constant atomic masses.
The process is by Jean's mass gravitational homogolous collapse of a baryonic density of ~20% closure, without the benefit of DM, in a linearly expanding universe.
As I have posted elsewhere:
In a Jean's collapse it is an overdensity that is important to get a nebula to collapse out of a homogeneous cosmological background.
In the FCM at the Surface of Last Scattering (SLS) at z ~ 1000, with
h = 0.71 and T = 30000K, the density is \rho = 3 \times 10^{-21} gms/cc.
With anisotropy fluctuations at the 10-5 level the overdensity at the SLS is
\rho = 3 \times 10^{-26} gms/cc.
The Jeans' Mass
M_J = 10^{-10}\sqrt{\frac{T^3}{\rho}}M_\odot
so the raw Jean's mass is 3 \times 10^5 M_\odot[/tex] and the intial collapsing halos from the overdensity will be masses of [itex]10^8 M_\odot forming and fragmenting 106 yrs after Last Scattering at t = 13 Myrs i.e. forming at t = 14 Myrs, the process finishing t ~ 108yrs. at ~ z = 100.
The Jeans Length works out as 12000 lgt.yrs, i.e roughly one halo per ~ 104 lgt.yrs, or an average of one every 107 lgt.yrs. today.
If the density anisotropies are at the ~ 10-5 level and kinetic energies of forming halos follows the potential energy of these wells, their relative velocities would be expected to be of the order 10-2.5c, which is the OOM of our own galaxy's motion relative to the CMB.
To an OOM I take a lower limit typical velocity for these halos to be ~ 10-3c, (300 km/sec), collisions between them would be expected every ~ 107 yrs.
About 104 mergers would be required to make up a typical spiral halo, or elliptical galactic, mass of 1012 MSolar.
Thus such halo masses might form after, a very hand waving estimate, ~ \sqrt N of 107 x 102 = 109 yrs, which would be seen today in the FCM model at z = 13, and onwards at lower z towards the present. This is where the earliest galaxies appear to have formed Detecting Reionization in the Star Formation Histories of High-Redshift Galaxies (http://arxiv.org/abs/astro-ph/0510421)
To form the object discussed above about 10% of such a galactic halo mass of 10^{12} M_\odot would then be required to collapse right down to a black hole and quasar; there is about another 10^{9} years for this to happen.
The fine details I will have to leave to you!
Thank you for your continued constructive criticisms they are much appreciated.
Garth
SpaceTiger
Mar17-06, 12:44 PM
What actually changes in the Jordan frame is the rest mass of non-degenerate atomic particles from which the standard mass (http://pda.physorg.com/lofi-news-standard-silicon-mass_3244.html) is made
I understand that, but it doesn't address the point. Our standard is at z=0, not z=6. The fact that its mass changes with time seems to be irrelevant. Our standards will not change significantly during the course of our observations and we can safely use it to interpret our observations at z=6, z=3, or z=2, as long as we account for the other changes in physical system (that is, G, the particle masses at z=6, the clocks, etc.).
To form the object discussed above about 10% of such a galactic halo mass of 10^{12} M_\odot would then be required to collapse right down to a black hole and quasar; there is about another 10^{9} years for this to happen.
The fine details I will have to leave to you!
That would be quite a task, considering that Pop III stars are thought to be limited to about 1000 M_\odot.
You also might want to look into trying to fit the WMAP data. Models without non-baryonic matter have been shown to be a very bad fit, particularly at the third peak.
I understand that, but it doesn't address the point. Our standard is at z=0, not z=6. The fact that its mass changes with time seems to be irrelevant. Our standards will not change significantly during the course of our observations and we can safely use it to interpret our observations at z=6, z=3, or z=2, as long as we account for the other changes in physical system (that is, G, the particle masses at z=6, the clocks, etc.). The standard is at z = 0 in the laboratory 'here and now' on Earth. We out from our laboratory back in time to the limits of the universe and interpret what we see there by what we know here. The mass of that object was estimated from its luminosity:
\frac{L_E}{L_\odot} = 3.28 \times 10^4 \frac{M}{M_\odot}
so
M_E \geq 3 \times 10^{-5} \frac{L_q}{L_\odot}M_\odot
this is the standard theory mass, in the SCC Jordan frame we have to allow for a diminished mH and an increased G, so the mass necessary to 'contain' the quasar's luminosity Lq is:
M_E \geq 3 \times 10^{-5} (1 + z)^2 \frac{L_q}{L_\odot}M_\odot
This is the mass of a distant supermassive quasar seen as it crossed our light cone in the distant past. We ask what about a similar but much nearer quasar of equal amount of accreted matter, which we might observe as it crossed out light cone at a much later time and therefore much closer to us?
In the SCC Jordan frame, during the time between the events of these two quasars crossing our light cone, atomic masses increased, rulers shrank and clocks 'speeded up' all relative to the energy, wavelength and inverse frequency of a photon sampled from the CMB. The effect of that would be that the second quasar would appear to be reduced in mass by the \frac{1}{1+z} factor.
The difference between the SCC Jordan frame and GR is that masses genuinely do increase with gravitational potential energy, it is not simply an effect of measurement in an inconvenient coordinate system.
That would be quite a task, considering that Pop III stars are thought to be limited to about 1000 M_\odot. In which case we need a merger of 108 of them, or 103 proto-halos of 108MSolar;with distances and velocities mentioned above this might take less than 109 years, but my hands are going like windmills at this point!
You also might want to look into trying to fit the WMAP data. Models without non-baryonic matter have been shown to be a very bad fit, particularly at the third peak.Yes I have no expertise here except to point out that that intepretation is model dependent, I wonder what the third and other peaks look like in the conformally flat, 'cylindrical 'universe of the SCC Jordan frame?
Garth
SpaceTiger
Mar17-06, 03:28 PM
T In the SCC Jordan frame, during the time between the events of these two quasars crossing our light cone, atomic masses increased, rulers shrank and clocks 'speeded up' all relative to the energy, wavelength and inverse frequency of a photon sampled from the CMB. The effect of that would be that the second quasar would appear to be reduced in mass by the \frac{1}{1+z} factor. Again, I already know that your theory makes the first statement, but I don't see how it leads to the second. We've accounted for the increase in atomic masses. Are you perhaps referring to the effective time dilation that goes into measuring a "luminosity"? Remember that, in the standard model, luminosities are inferred with a time correction and redshift correction built in, so you should make sure that this is consistent with the corrections you expect in your model. I have no expertise except to point out that the interpretation is model-dependent. Yes, but the point is obvious, and most of the models that are significantly different from \Lambda CDM (e.g. relativistic MOND) have been ruled out at large confidence levels. Considering that the CMB is the strongest single test of standard cosmology, I'd say this is pretty important. Even without a detailed fit, you'll need to figure out how you could produce a large third peak in the power spectrum without non-baryonic dark matter.
Again, I already know that your theory makes the first statement, but I don't see how it leads to the second. We've accounted for the increase in atomic masses. Are you perhaps referring to the effective time dilation that goes into measuring a "luminosity"? Remember that, in the standard model, luminosities are inferred with a time correction and redshift correction built in, so you should make sure that this is consistent with the corrections you expect in your model. Of course! Lq in my post above is the luminosity uncorrected for red shift. If the mass has been derived from the corrected cosmological luminosity then that effect has already been accounted for.
The (1 + z)^2 factor, which is a time dilation effect in GR and the SCC Einstein frame, is the variable mass and G effect in the SCC Jordan frame.
In the SCC Jordan frame there is no detectable time dilation caused by the curvature/expansion of space, hence no 'quasar variablity time dilation', red shift is a varying mass effect. The universe is static.
Consequently the most massive SDSS quasar has a mass of just 3 \times 10^9M_\odot as in GR, so we just require 0.3% of a galactic halo to collapse down into a black hole. [Note 0.3% is \sim \sqrt{10^{-5}}, equal to the 'overdensity' Jeans' mass factor]
I believe you may well be correct about the mass reduction effect. Comparing the BH with a solar mass both at z = 6 and then both at
z = 0 will produce such an effect, but as you rightly point out we are not doing that. :blushing:
Even without a detailed fit, you'll need to figure out how you could produce a large third peak in the power spectrum without non-baryonic dark matter.
Is that the same third peak around which the power spectrum (http://map.gsfc.nasa.gov/m_ig/060911/PowerSpectrum75.png) data goes "a bit 'wobbly'"? :wink:
Garth
SpaceTiger
Mar17-06, 06:14 PM
Is that the same third peak around which the power spectrum (http://map.gsfc.nasa.gov/m_ig/060911/PowerSpectrum75.png) data goes "a bit 'wobbly'"? :wink:
From WMAP data alone, yes, but actually there have been several other experiments that did a better job of measuring the high-l multipoles and found a very clear peak (which is, by the way, consistent with WMAP). See the WMAP paper for the overlay with power spectra from other experiments. The third peak is detected at very high significance by several experiments.
I'll comment on the rest when I get back later. I could only think of one factor of (1+z) difference in the luminosity inference from the models. Note also that this doesn't solve the growth problem that arises from the low Eddington luminosity.
I'll comment on the rest when I get back later. I could only think of one factor of (1+z) difference in the luminosity inference from the models. Note also that this doesn't solve the growth problem that arises from the low Eddington luminosity.
The standard cosmological luminosity takes two factors of (1 + z) into account, one for the fact that from an object at red shift z the photons are arriving less frequently by a factor of (1 + z), and the second because each photon carries less energy by a factor of (1 + z).
Your reference to "low Eddington luminosity" is where I became confused and assumed that you had not taken the (1 + z)2 factor into account in the luminosity. There is no further "low Eddington luminosity" effect in the SCC Jordan frame, it is the (1 + z)2 luminosity correction in GR.
Garth
SpaceTiger
Mar17-06, 09:58 PM
Your reference to "low Eddington luminosity" is where I became confused and assumed that you had not taken the (1 + z)2 factor into account in the luminosity. There is no further "low Eddington luminosity" effect in the SCC Jordan frame, it is the (1 + z)2 luminosity correction in GR.
Well, I should say "low" in the sense that your theory decreases the amount of matter the black hole can accrete, even if it doesn't increase the inferred mass of the black hole. I'm not 100% confident we've accounted for all of the quirks of your cosmology, but it's clear that this asymmetry between the masses of relativistic degenerate matter and non-relativistic matter still exists.
Well, I should say "low" in the sense that your theory decreases the amount of matter the black hole can accrete, even if it doesn't increase the inferred mass of the black hole. I'm not 100% confident we've accounted for all of the quirks of your cosmology, but it's clear that this asymmetry between the masses of relativistic degenerate matter and non-relativistic matter still exists.
Well, I said I'm not sure I fully understand the behaviour of BHs in my theory!
It is necessary to solve the Schwarzschild solution with a SCC/BD scalar field in the strong gravity case and let the central mass collapse. I have not yet had the time to do that, and I'm not sure I would get it right even if I did without outside help.
However I do understand that in the case of high z BH accretion the amount of matter, i.e. number of atoms, a BH can accrete is the same as in GR, however the amount of mass is reduced because of the variable mass effect. There is no other red shift to worry about, so the effect of this reduced mass, and increased G, in the SCC Jordan frame is the same as the (1 + z)^2 red shift effect on the luminosity in GR . The two SCC/GR scenarios are conformally equivalent.
Thank you for the discussion it has been illuminating. :smile:
Garth.
Not to take this interesting exchange off track, but, as Garth mentioned earlier, in SCC it rests on the assumption that the variability observed/observable in the optical part of the EM spectrum of QSOs arises essentially from just one component - the accretion disk.
Don't you, Garth, also need to establish that the jet, broad line region, etc are negligible contributors to the observed variability, in all stages of the quasars' evolution? Also, whatever the SMBH is, in SCC, don't you also need to establish - in some detail - the behaviour of the accretion disk? For example, no matter which theory (or combo of theories) is used to model such disks, the integrated emission includes significant contributions from very different (physical) regimes, doesn't it?
Hi Nereid, yes a good point. It is instructive to note that of all the energy produced by matter falling into the BH of a quasar that roughly half goes into the jet and half 'falls down the plughole' into the event horizon and only a small proportion is emitted as radiation. The jet and consequent radio lobes are powerful emitters, however the time scale of variability, and the Hawkins paper was looking at between 1 week to 1 year, depends on the size of the emitter. My understanding is the jet is much larger than the disc, extending many 1000's of light years and the structure within it ~ light years across, so would not the jet vary on a longer time scale?
Of course it is claimed by Baganoff & Malkan, ApJ. 444 1995, Gravitational microlensing is not required to explain quasar variability that because wavelength is inversely proportional to temperature, which depends inversely with the radius from the BH, that the variability is not expected to show dilation. However Hawkins refutes this.
To make it clear, I do agree that you need to not only to understand the behaviour of the accretion disk, but also you first need to fully understand the black hole in the SCC theory. All I have been engaged in is some 'back of the envelope' calculations to see how the land lies.
My basic point is simply that if it can be established that distant S/N and GRB light curves show time dilation and the variability of quasars do not, then my suggestion is the significant difference between them is that the 'engines' of former class consist of non-degenerate matter and the 'engine' of the BH is degenerate. SCC offers a ready distinction in the predicted behaviour between the two classes.
Garth
Is that the same third peak around which the power spectrum data goes "a bit 'wobbly'"? From WMAP data alone, yes, but actually there have been several other experiments that did a better job of measuring the high-l multipoles and found a very clear peak (which is, by the way, consistent with WMAP). See the WMAP paper for the overlay with power spectra from other experiments. The third peak is detected at very high significance by several experiments.
Such as here (http://cosmologist.info/notes/Moriond2006.ppt)? (You have to press <Page Down> once.)
Garth
SpaceTiger
Mar21-06, 03:37 PM
Such as here (http://cosmologist.info/notes/Moriond2006.ppt)? (You have to press <Page Down> once.)
Sorry Garth, I can't load it on this computer. Could you just summarize it briefly or give me a paper reference?
Sorry Garth, I can't load it on this computer. Could you just summarize it briefly or give me a paper reference?
http://cosmologist.info/notes/Moriond2006.ppt
is a series of lecture slides by Antony Lewis of the IoA, Cambridge, England. The second slide shows the power spectrum and the WMAP3 data with Acbor, Boomerang, CBI & VSA readings superimposed.
Whereas the other experiments do trace the predicted \Lambda CDM third and even fourth peaks and beyond fairly well, the WMAP3 data goes, as I said "a bit wobbly". In particular the errors bars at l= ~870 and beyond do not even reach the predicted curve. I know that in this region the WMAP3 data has a problem with noise, but I wondered how those error bars were determined? Either the power spectrum here is less well determined than declared or there seems to be an inconsistency between WMAP3 and the different experiments and the predicted model.
Garth
SpaceTiger
Mar21-06, 07:03 PM
http://cosmologist.info/notes/Moriond2006.ppt
is a series of lecture slides by Antony Lewis of the IoA, Cambridge, England. The second slide shows the power spectrum and the WMAP3 data with Acbor, Boomerang, CBI & VSA readings superimposed.
Whereas the other experiments do trace the predicted \Lambda CDM third and even fourth peaks and beyond fairly well, the WMAP3 data goes, as I said "a bit wobbly".
That's right, WMAP isn't the primary constraint on the third peak. They use ACBAR, CBI, etc. to fit to the high multipoles, though none of the experiments (including WMAP) are inconsistent with one another. See the WMAP parameters paper for more detail.
In their paper Cosmic Conspiracies (http://arxiv.org/abs/astro-ph/0604011) Scott & Frolop point out:The now standard vanilla-flavoured LambdaCDM model has gained further confirmation with the release of the 3-year WMAP data combined with several other cosmological data-sets. As the parameters of this standard model become known with increasing precision, more of its bizarre features become apparent. Here we describe some of the strangest of these ostensible coincidences. In particular we appear to live (within 1sigma) at the precise epoch when the age of the Universe multiplied by the Hubble parameter H0 t0 = 1.
Note that in the SCC (http://en.wikipedia.org/wiki/Self_creation_cosmology) linearly expanding model
R(t) ~ t, H0 x t0 = 1 at all epochs.
Garth
SpaceTiger
Apr4-06, 05:55 AM
In their paper Cosmic Conspiracies (http://arxiv.org/abs/astro-ph/0604011) Scott & Frolop point out:
:rofl:
That paper is hilarious. Check out some of the references.
(and in case you haven't already, check the date of submission)
:rofl:
Cosmic coincidences
That paper is hilarious. Check out some of the references.
(and in case you haven't already, check the date of submission)
Well of course: (Dated: 1st April 2006)
Douglas Scott = website (http://www.astro.ubc.ca/people/scott/)
Ali Frolop = April Fool ,
They were obviously sponsored by the Church of Scientology :biggrin:
H0t0 = 1.03 ± 0.04 needs no further explanation, but nevertheless is consistent with a linearly expanding model.
Garth
hellfire
Apr5-06, 09:09 AM
A question for my understanding. The fact that the theory contains a frame in which mass evolves and the universe is static, is this a direct consequence of conformal invariance, or is it also related to that principle of energy conservation in the preferred frame? What if you do not impose that second principle?
A question for my understanding. The fact that the theory contains a frame in which mass evolves and the universe is static, is this a direct consequence of conformal invariance, or is it also related to that principle of energy conservation in the preferred frame? Yes, both, the conformal transformation is chosen so that energy is locally conserved. However, it is not an invariant conformal transformation, which is where SCC differs from other conformal gravity and scalar field theories. What if you do not impose that second principle?Then you are in another theory, if you now impose conformal invariance then you end up with either the standard Brans Dicke or one of the other conformal gravity theories.
Garth
hellfire
Apr7-06, 03:03 AM
I was under the impression that in oder to claim that there exists an equivalent description of expansion, with static space and evolving masses, one has to rely on conformal invariance. It seams I am wrong. May be you could elaborate a bit.
I was under the impression that in oder to claim that there exists an equivalent description of expansion, with static space and evolving masses, one has to rely on conformal invariance. It seams I am wrong. May be you could elaborate a bit.
A good point.
The real question is how do you measure anything - especially at astronomical/cosmological distances? How do define a standard unit and then 'transport' that unit across space and time to make the comparison?
In order not to be in an "Alice in Wonderland" croquet situation trying to hit a hedgehog as a ball with the head of a flamingo as a croquet stick, where the bat stick and ball keep moving, you need something that does not move, that is invariant across space-time. The foundation of GR is the Einstein Equivalence Principle (EPP) with the consequent conservation of energy-momentum and invariance of particle rest masses under translations across space and time. 'Atomic' rulers (made of 'steel') are 'rigid' and 'atomic' clocks are 'regular'. Any conformal gravity theories maintaining this principle must be conformally invariant transformations. Some have argued that such transformations result in just GR dressed up in some inconvenient coordinate system.
In SCC the EEP is replaced with the Principle of Mutual Interaction, here the two conformal frames represent two different invariances of measurement.
In the Einstein frame particle masses are constant and energy-momentum is conserved, however energy is not locally conserved. Atoms remain the standard unit against which mass, length (their size) and time (their atomic frequencies) can be compared.
However in the Jordan conformal frame it is energy that is locally conserved, the energy of a 'standard' photon (carefully defined) is constant and its energy, wavelength and frequency are the measures of mass (E/c2), length and time (\nu^{-1}).
In order for this to be possible the BD coupling constant \omega = -3/2 in which case the normal theory becomes degenerate and ill defined and the SCC conformal transformation of its Jordan frame results in canonical GR in vacuo.
Garth
hellfire
Apr7-06, 04:05 AM
Thank you for your answers, Garth. I am making an effort to understand this, but I still have no success.
here the two conformal frames represent two different invariances of measurement.
But how does this claim follow? To my understanding this implies a kind of unphysical degree of freedom (a gauge) that leaves physics invariant. However, you wrote that it is not an invariant conformal transformation.
My thanks to Garth, SpaceTiger, et al for all the good links. Although this is more philosophy than science you might want to check out: www.self-creation.net and for a non-professional's 2003 prediction concerning WMAP3 data you might want to check out: http://physics.about.com/b/a/2003_10_15.htm?terms=bb+electronics
aguy2
Thank you for your answers, Garth. I am making an effort to understand this, but I still have no success.
But how does this claim follow? To my understanding this implies a kind of unphysical degree of freedom (a gauge) that leaves physics invariant. However, you wrote that it is not an invariant conformal transformation.
Thank you for that observation and question, sorry about the delay I have not had the time to answer properly until now.
First consider the Brans Dicke theory (BD):
The BD Lagrangian density, in which energy-momentum is conserved, is given by
L^{BD}[g,\phi ]=\frac{\sqrt{-g}}{16\pi }\left( \phi R-\frac{\omega }{\phi }g^{\mu \nu }\nabla _{\mu }\phi \nabla _{\nu }\phi \right) +L_{matter}[g]
where R is the curvature scalar, \omega a coupling constant and L_{matter}[g] is the Lagrangian density for ordinary matter minimally coupled to the scalar field, i.e.
\nabla _{\mu }T_{M\;\nu }^{\;\mu }=0 .
This ensures the rest mass of a particle m(x^{\mu }) , at x^{\mu } , is constant for all x^{\mu },
m(x^{\mu })=m_{0}
BD is a specific case of Jordan's general theory [Jordan, (1959)] and so this representation is known as the Jordan conformal frame (JF). However Dicke in 1962 showed that this Lagrangian can be conformally transformed into a form in which G is a constant and m(x^{\mu}) varies, which is termed the Einstein conformal frame (EF) in the
literature. The conformal dual is given by
L^{BD}[\tilde{g},\widetilde{\phi }]=\frac{\sqrt{-\tilde{g}}}{16\pi G_{N}}\left[ \tilde{R}-\left( \omega +\frac{3}{2}\right) \tilde{g}
^{\mu \nu }\tilde{\nabla }_{\mu }\tilde{\phi }\tilde{\nabla }
_{\nu }\tilde{\phi }\right] +\tilde{L}_{matter}[\tilde{g},\tilde{\phi }]
where \tilde{R} is the curvature scalar in the EF metric \tilde{g}^{\mu \nu }, conformally dual to g^{\mu \nu } according to
g_{\mu \nu }\rightarrow \tilde{g}_{\mu \nu }=\Omega ^{2}g_{\mu \nu } in which \Omega ^{2}=\phi G_{N}
The scalar function \tilde{\phi }=\ln \phi is the BD field in the EF and \tilde{L}_{matter}[\tilde{g},\tilde{\phi }] is the EF Lagrangian density for the ordinary matter, which is now non-minimally coupled to the scalar field, i.e. in the EF \nabla _{\mu }T_{M\;\nu}^{\;\mu } \neq 0.
The principle of Least Action can now be applied to this JF action to obtain the gravitational and scalar field equations and the equivalence principle is guaranteed in this frame.
Conformal duality has also been applied to GR in order to include a scalar field as an additional source of gravity. (See, for example, Quiros' paper Dual geometries and spacetime singularities (http://arxiv.org/abs/gr-qc/9905071)) In this case, in contrast to BD, ordinary matter is non-minimally coupled to the scalar field in the JF and it is minimally coupled in the EF. In this case the Lagrangian density in the JF is given by
L^{GR}[g,\phi ]=\frac{\sqrt{-g}}{16\pi }\left( \phi R-\frac \omega \phi
g^{\mu \nu }\nabla _\mu \phi \nabla _\nu \phi \right) +L_{matter}[g,\phi ]
and in the EF
L^{GR}[\tilde{g},\tilde{\phi }]=\frac{\sqrt{-\tilde{g}}}{16\pi G_N}\left[ \tilde{R}-\left( \omega +\frac 32\right) \tilde{g}^{\mu\nu }\tilde{\nabla }_\mu \tilde{\phi }\tilde{\nabla }_\nu \tilde{\phi }\right]+\tilde{L}_{matter}[\tilde{g}].
In this case applying the principle of least action produces the gravitational field equation and the scalar field wave equation in which:
\tilde{\Box }\tilde{\phi }=0
i.e. the scalar field is decoupled from matter and Mach’s principle as understood by BD has been lost.
SCC adapts this conformal gravity action to include the original BD field equation. This is possible if \omega = -\frac32 when the scalar field drops out of the EF action and \phi becomes indeterminate, the principle of the local conservation of matter is used instead to fix \Omega and determine \phi.
Its JF Lagrangian density is therefore, (with \omega general),
L^{SCC}[g,\phi ]=\frac{\sqrt{-g}}{16\pi }\left( \phi R-\frac{\omega }{\phi }
g^{\mu \nu }\nabla _{\mu }\phi \nabla _{\nu }\phi \right) + L_{matter}^{SCC}[g,\phi ]
the conformal dual, by a general transformation
\tilde{g}_{\mu \nu }=\Omega ^{2}g_{\mu \nu } , is
L^{SCC}[\tilde{g},\tilde{\phi }] =\frac{\sqrt{-\tilde{g}}}{16\pi }\left[ \tilde{\phi }\tilde{R}+6\tilde{\phi }\tilde{\Box }\ln \Omega \right] +\tilde{L}_{matter}^{SCC}[\tilde{g},
\tilde{\phi }] [/itex]
[tex] -\frac{\sqrt{-\tilde{g}}}{16\pi }\left[ 2\left( 2\omega +3\right)
\frac{\tilde{g}^{\mu \nu }\tilde{\nabla }_{\mu }\Omega \tilde{\nabla }_{\nu }\Omega }{\Omega ^{2}}+4\omega \frac{\tilde{g}^{\mu \nu }
\tilde{\nabla }_{\mu }\Omega \tilde{\nabla }_{\nu }\tilde{\phi }
}{\Omega }+\omega \frac{\tilde{g}^{\mu \nu }\tilde{\nabla }_{\mu }
\tilde{\phi }\tilde{\nabla }_{\nu }\tilde{\phi }}{\tilde{\phi }}\right] .
With m\left( x^{\mu }\right) =\Omega \tilde{m}_{0} where m\left( x^{\mu }\right) is the mass of a fundamental particle in the JF and \tilde{m}_{0} its invariant mass in the EF then SCC has \Omega =\exp \left[ \Phi {N}\left( x^{\mu }\right) \right] , and we select the SCC EF by requiring G = \phi^{-1} to be constant, then the Lagrangian density in the EF is given by
L^{SCC}[\tilde{g},\tilde{\phi }]=\frac{\sqrt{-\tilde{g}}}{16\pi G_{N}}\tilde{R}+\tilde{L}_{matter}^{SCC}[\tilde{g}]+\frac{3\sqrt{
-\tilde{g}}}{8\pi G_{N}}\tilde{\square }\tilde{\Phi }_{N}\left(\tilde{x}^{\mu }\right) ,
which becomes canonical GR when \tilde{\square }\tilde{\Phi}_{N}\left(\tilde{x}^{\mu }\right) = 0 in vacuo.
This argument can be found in the 2002 Astrophysics and Space Science paper A New Self Creation Cosmology (http://www.kluweronline.com/oasis.htm/5092775) and the eprint The Principles of Self Creation Cosmology and its Comparison with General Relativity (http://arxiv.org/pdf/gr-qc/0212111 ).
IMHO I think both BD and conformal gravity have not gone far enough in modifying GR; the SCC approach may be wrong, and if so then it is surprising that it produces such a concordant gravitational and cosmological model, but the next and real test will be GP-B!
Garth
I should have included, but I was trying not to make the post too long, that the key difference between SCC and BD/conformal gravity is the way \phi transforms.
A dimensionless quantity is needed that acts as the invariant of the transformation.
In BD/conformal gravity that dimensionless invariant is Gm2, conformal gravity theories then simply 'rewrite' GR in an inconvenient [and some would say unphysical (see On the Energy-Momentum tensor of the Scalar Field in Scalar-Tensor Theories of Gravity (http://arxiv.org/abs/gr-qc/9904003))] coordinate system and the change in m is only an artefact of this coordinate system.
In SCC the invariant of the transformation is the dimensionless Newtonian potential \Phi, which in the spherically symmetric case: \Phi = \frac {GM}{rc^2}. As a result Gm is an invariant, and masses 'really' increase with gravitational potential energy.
hellfire
Apr9-06, 01:07 PM
Thank you for the detailed answer and for the link to Quiros' paper. Conformal duality is a new concept to me.
In that paper it is written that "the choice G ~ 1/\phi, m = const., leads to the Jordan frame (JF) BD formalism". However, in your wikipedia article it is mentioned that the masses are constant in the Einstein frame. Could you please clarify the terminology?
The terminology is also unclear to me in this part of Quiros' paper:
In BD theory, for example, matter minimally couples in the JF so the test particles follow the geodesics of the Riemann geometry in this frame, i.e. JFBD theory is naturally linked with Riemann geometry. This means that EFBD theory (conformal to JF one) should be linked with the geometry that is conformal to the Riemann one (the Weyl-type geometry). For general relativity with an extra scalar field just the contrary is true. In this case matter minimally couples in the Einstein frame and then test particles follow the geodesics of the Riemann geometry precisely in this frame, i.e. EFGR is naturally linked with Riemann geometry and, consequently Jordan frame GR (conformal to EFGR) is linked with Weyl-type geometry
After reading this I got the impression that one may also define conformally dual solutions in general relativity. Could you help me to understand this paragraph?
Thank you for the detailed answer and for the link to Quiros' paper. Conformal duality is a new concept to me.
In that paper it is written that "the choice G ~ 1/\phi, m = const., leads to the Jordan frame (JF) BD formalism". However, in your wikipedia article it is mentioned that the masses are constant in the Einstein frame. Could you please clarify the terminology? Yes, certainly.
Quiros is claiming that conformal transformations result in two equivalent descriptions of the same physical situation. He then uses the conformal frame to eradicate singularities.
BD is formulated in the Jordan frame, where the JF here is defined as that frame in which energy momentum is covariantly conserved, G varies and (in BD) mass is constant. Its Einstein dual is that frame in which G is constant and m varies, but energy-momentum is no longer conserved.
Basically you have two conformally related frames, what you actually label them is up to you.
Quiros' reverses the BD convention and has a geometric dual set of conformal Lagrangians of GR plus a scalar field. It starts in the Einstein frame (EFGR) in which m is constant and energy-momentum covariantly conserved but plus an extra scalar field, and then conformally transforms into the Jordan frame (JFGR). Subsequently this Jordan frame is used to explore the behaviour of the scalar field particularly concerning singulariites, while noting that here energy-momentum is not covariantly conserved.
SCC follows this latter approach of having an EF in which masses are constant and e-m conserved. However, having set \omega = - \frac32, in which any conformal transformation goes onto canonical GR, SCC instead selects the particular transformation that locally conserves energy, but not energy-momentum, in the JF.
The terminology is also unclear to me in this part of Quiros' paper:
In BD theory, for example, matter minimally couples in the JF so the test particles follow the geodesics of the Riemann geometry in this frame, i.e. JFBD theory is naturally linked with Riemann geometry. This means that EFBD theory (conformal to JF one) should be linked with the geometry that is conformal to the Riemann one (the Weyl-type geometry). For general relativity with an extra scalar field just the contrary is true. In this case matter minimally couples in the Einstein frame and then test particles follow the geodesics of the Riemann geometry precisely in this frame, i.e. EFGR is naturally linked with Riemann geometry and, consequently Jordan frame GR (conformal to EFGR) is linked with Weyl-type geometry
After reading this I got the impression that one may also define conformally dual solutions in general relativity. Could you help me to understand this paragraph?As I said scalar tensor/JFGR theories do the reverse of BD; particles follow geodesics, (e-m conserved,) in the JF of BD but the EF of scalar tensor/EFGR theories. Photons follow geodesics in both frames.
Garth
Continued from the Gravity - Integrating General Relativity with "Gravitons" (http://physicsforums.com/showthread.php?t=122348) thread.Garth, can you include the logical sequence that led you to SCC ---a theory is never discovered in the way it is presented.
In 1964, at the age of 16, I was studying mathematics at an advanced high-school level ,and cosmology at an 'intelligent layman’s' level when I had what you might call a “vision”, or visual concept, of cosmological space and time that has never left me. Later, after gaining a mathematics degree, I had the tools to develop it.
This was a cosmological model I called “Radial Atomic Time cosmology” RAT for short! It required the universe to be spherical (positive curvature: k = +1) and expand strictly linearly with time (R(t) = t).
Through a friend at the Institute of Astronomy at Cambridge University it was shown to Martin Rees (who is now the Astronomer Royal). Martin Rees encouraged me to develop it and have it published but recommended that first I needed further study.
So I studied for a part-time MSc. in Astrophysics and Cosmology at Queen Mary College, London University, with the model as my project. I realised that earlier I had been naïve (obviously). Nevertheless the RAT put me on a trail to seek linear expanding models, which required modification of GR. I noticed the Large Numbers Hypothesis (LNH) could also lead to a linear expansion while the Brans Dicke theory (BD) modified GR.
My dissertation was called "On an integrated approach to cosmology" and sought to integrate GR, the LNH and BD. By now the linear expanding model had been put on one side. In this dissertation my modification of BD, itself a modification of GR, led to the first SCC paper in 1982. (The name SCC was only devised later)
Brans himself criticised that original theory in a paper published five years later. Consequently I put the theory to one side and continued in ministry at universities and colleges, meanwhile lecturing part-time in extra-mural and undergraduate courses in astronomy and cosmology. One evening whilst lecturing on Inflation theory and its resolution of the horizon/density/smoothness problems in GR cosmology it dawned on me that these problems would not exist in the first place in my original RAT model!
I was determined to rework my 1982 theory in order to overcome Brans' objection and a new theory emerged. That was in 1995. I took a further five years to work this theory into a coherent whole and another two years before it saw the light of day as ‘A New Self Creation Cosmology’ published in a peer-reviewed journal, ‘Astrophysics and Space Science’. (282 pg 683-730, 2002)
Starting with BD, which modifies GR to fully include Mach's Principle, I introduced mass creation by relaxing the conservation of energy-momentum as in all the SCC theories. In the new theory I included the local conservation of energy to constrain this mass creation by the Principle of mutual Interaction:"The scalar field is a source for the matter-energy field if and only if the matter-energy field is a source for the scalar field." Everything flowed from that.
After many years of working the final cosmological model turned out to be nothing else but my 'naïve' RAT model, everything had finally clicked into place!!
The theory is eminently testable and falsifiable, although I hardly expected anybody to take it seriously enough to spend serious money on an experiment. It was therefore a surprise and delight to realise that, over the same 40 years that my theory had been gestating, another team around the globe at Standford university had independently been slogging away at developing the Gravity Probe B experiment in order to test GR, an experiment that incidentally would also falsify SCC! (See Alternative theories being tested by Gravity probe B
I realise that the above story scores high on the John Baez crackpot index!:biggrin: But at least the theory is falsifiable.
It has been a long time and the result should finally be known next year (April 2007). :smile:
Garth
gptejms
May31-06, 01:22 PM
It's difficult to follow such a long thread,so I've just had a quick look at your wikipedia article.A few questions that come to mind(of course many of them would be at the level of a GR (informed) layman):-
1.In your equation d^2r/dt^2 = -del phi,you seem to be using 3-acceleration,not 4-acceleration--why?--because phi does not depend on t?--but phi can depend on t.
2.Isn't adding the scalar field term a little ad-hoc?Physically,why should such a term be there at all?What does it represent?
3.What's so sacrosanct about the linear expansion---why are you after it in the first place?
4.If there is a thing called gravitational potential energy in GR,does it not make it non 'self contained'--you are borrowing the gravitational potential from Newton's laws(even the equation d^2r/dt^2=- del phi is borrowed).
Also,since the only manifestation of gravity in GR is that of curvature of spacetime(and motion is along geodesics),doesen't gravitational potential energy look out of place?
More later.
It's difficult to follow such a long thread, I have moved this reply to the "Self Creation Cosmology thread.so I've just had a quick look at your wikipedia article.A few questions that come to mind(of course many of them would be at the level of a GR (informed) layman):-
1.In your equation d^2r/dt^2 = -del phi,you seem to be using 3-acceleration,not 4-acceleration--why?--because phi does not depend on t?--but phi can depend on t. That equation is the normal definition of the dimensionless Newtonian potential in units with c = 1. The gravitational force produces a 3-acceleration.
2.Isn't adding the scalar field term a little ad-hoc?Physically,why should such a term be there at all?What does it represent? Mach's Principle - here SCC is following the Brans Dicke theory. Even without Mach's principle many alternatives to GR include a scalar field.
3.What's so sacrosanct about the linear expansion---why are you after it in the first place?The linear expansion is not sacrosanct, it is a product of the SCC cosmological solution. However, it does then produce a very interesting cosmology see A Concordant “Freely Coasting” Cosmology (http://arxiv.org/abs/astro-ph/0306448).
4.If there is a thing called gravitational potential energy in GR,does it not make it non 'self contained'--you are borrowing the gravitational potential from Newton's laws(even the equation d^2r/dt^2=- del phi is borrowed).
I am 'borrowing' it from physical experiment actually, is there a problem with a concept consistent with observation?Also,since the only manifestation of gravity in GR is that of curvature of spacetime(and motion is along geodesics),doesen't gravitational potential energy look out of place?GR replaces a real Newtonian gravitational force with space-time curvature. This makes the concept of gravitational potential energy (i.e. the work done against the real gravitational force) in GR problematic.
The problem comes in GR when you try to locally conserve energy; where does the energy used in lifting a body from rest to a higher level at rest go to? Into the gravitational field? But in the momentarily stationary but freely falling frame that field is locally Minkowskian.
Einstein discussed the problems of fully including Mach's principle and the non-local conservaiton of energy in GR, Noether tackled the latter question early on and Brans & Dicke independently tackled the former one later, I have treated the two questions together.
Garth
That equation is the normal definition of the dimensionless Newtonian potential in units with c = 1. The gravitational force produces a 3-acceleration.
Ok,so that was a stupid question to ask.One is so used to seeing 4-vectors in relativity,that a 3-acceleration looks out of place.Anyway,the question remains--that you are borrowing the Newton's law directly rather than deriving it out of first principles of your theory.May be you can justify that by saying that you get the Newton's law in the flat spacetime approximation from your equations(as is done in GR too)--a'right,but that leaves something to be desired.
Mach's Principle - here SCC is following the Brans Dicke theory. Even without Mach's principle many alternatives to GR include a scalar field.
As I said you are talking to an informed layman as gar as GR is concerned--you need to explain to me how the scalar field helps take care of Mach's principle(provided you have the patience to do that!).
The linear expansion is not sacrosanct, it is a product of the SCC cosmological solution. However, it does then produce a very interesting cosmology see A Concordant “Freely Coasting” Cosmology (http://arxiv.org/abs/astro-ph/0306448).
Pl. list out the essential features of FCC.
borrow it from physical experiment actually, is there a problem with a concept consistent with observation?
No,there's no problem with that except that one would have preferred it coming out of first principles of your theory (or any other theory)--but you could call that a bias.
The problem comes in GR when you try to locally conserve energy; where does the energy used in lifting a body from rest to a higher level at rest go to? Into the gravitational field? But in the momentarily stationary but freely falling frame that field is locally Minkowskian.
If you do work on a body,the energy has to go into 'that body'---how can it go into the field(is that GR's position?)?Well,in Newtonian mechanics the energy goes into the gravit. potential energy of the body--either one has to introduce a similar concept in GR,or put it into the rest mass as you say.
I've a question here:-you hit a ball with a bat--it follows a parabolic motion(very easy to describe in Newtonian mechanics)--how do you derive the equation of motion in GR?Does the force applied get into the stress energy density tensor--how?
Pl. also give me a reference to the BD paper.
Ok,so that was a stupid question to ask.One is so used to seeing 4-vectors in relativity,that a 3-acceleration looks out of place.Anyway,the question remains--that you are borrowing the Newton's law directly rather than deriving it out of first principles of your theory.May be you can justify that by saying that you get the Newton's law in the flat spacetime approximation from your equations(as is done in GR too)--a'right,but that leaves something to be desired.
As with GR in SCC Newtonian gravity is used to set up the field equations in such a way that it is the first order approximation; in GR Newton is used to derive the factor 8\piG in front of the stress-energy-momentum tensor, in SCC it is used as well, with other requirements, to determine \omega & \lambda.
However once the field equations have been set up and actually the parameters are found to take on simple values, \omega = -3/2, \lambda = 1, then Newton does fall out from the first principles of the theory, which are: that GR be modified first to include Mach a la BD, and then BD modified to include the local conservation of energy.As I said you are talking to an informed layman as gar as GR is concerned--you need to explain to me how the scalar field helps take care of Mach's principle(provided you have the patience to do that!).I define Mach's Principle as: "The phenomenon of inertial ought to arise from accelerations with respect to the general distribution of mass in motion in the universe." Thus the inertial masses of elementary particles ought not to be fundamental constants but should be the result of the particles' interaction with some cosmic field. The simplest generally covariant field equation for such a scalar field is
\Box \phi =4\pi \lambda T_{M}
T_{M} is the trace, (T_{M\;\sigma }^{\;\;\sigma }), of the energy-momentum tensor describing all non-gravitational and non-scalar field energy and \lambda is some undetermined coupling constant of the order unity.
In BD, following GR, the equivalence principle holds and so the scalar field affects particles motion through changes in the curvature of space-time but not in any other way. Particle masses remain constant and the scalar field affects the measurement of G instead. \phi \sim 1/G and 1/ \phi replaces G in the field equation.
One consequence is Dicke's version of Mach's Principle (http://en.wikipedia.org/wiki/Mach%27s_principle), which states "The gravitational constant should be a function of the mass distribution in the universe"
In SCC it is particle masses that vary and G is measured to be constant. Requiring Newton as the first approximation determines \lambda = 1.
Pl. list out the essential features of FCC.
FCC = Freely Coasting Cosmology (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1989ApJ...344..543K&db_key=AST)
The universe behaves as if there is no cosmological gravitational deceleration or DE acceleration. It behaves as if it were empty, i.e. the Milne Friedmann model.
R(t) = t and k = -1 throughout cosmological history.
This simple model turns out to be surprisingly concordant without Inflation, and with no acceleration it does not require DE either. Furthermore the baryon density instead of being ~ 0.04, is ~ 0.2 and so it identifies DM as baryonic in nature.
The essential difference between the FCC and SCC is in SCC
R(t) = t and k = +1. The change of curvature does not affect the early universe where matter-energy density predominates.
Furthermore, the 'conical-model' universe is conformally flat, as is the real universe determined by the WMAP data.
I've a question here:-you hit a ball with a bat--it follows a parabolic motion(very easy to describe in Newtonian mechanics)--how do you derive the equation of motion in GR?Does the force applied get into the stress energy density tensor--how?
There are standard GR texts that deal with this question. The force imparts a velocity to the ball which then follows a geodesic through curved space-time. The trajectory is the same under Einstein as under Newton. In SCC the geodesic is different from that of GR but there is a further scalar-field force acting on the ball that corrects for this.Pl. also give me a reference to the BD paper.
Brans C. & Dicke R.H. Physical Review, vol. 124, Issue 3, pp. 925-935 11/1961
Mach's Principle and a Relativistic Theory of Gravitation (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1961PhRv..124..925B&db_key=PHY&d ata_type=HTML&format=&high=4332cfe20030582)
I hope this helps.
Garth
Thanks for patiently answering all my questions.
Is BD's paper(or the basic equations of the paper) available online somewhere?
EDIT:Though one question remained unanswered:-does the energy(of lifting) go into the gravit. field according to GR?If so,why?
AFAIK the BD paper itself is not available for free online, you can pay to download it from the link I gave above. However a brief introduction with equations can be found here (http://en.wikipedia.org/wiki/Brans-Dicke).
There is no answer to where the energy goes, except to say "Into the field".
Lift a brick and put it on a higher shelf, it has moved from one potential level to another, but where has the energy used lifting it gone to?
On the lower shelf the brick disturbed the otherwise symmetrical Schwarzschild space-time around a completely spherical (for the sake of argument) Earth. After being lifted up it now disturbs the space-time at a different level. This change of disturbance is where the energy has gone, according to some.
However as I said above if the observer is on the higher shelf and falls off, momentarily they would be stationary yet in free-fall.
By the equivalence principle the space-time around them will now seem in the observer's frame of reference to be Mikowskian in a small enough region around the observer, which now contains a stationary but upwards accelerating brick.
So where has the energy gone?
The real answer lies in the fact that in GR energy is not conserved in general!
In GR the world lines of the brick in its two locations are at an angle to each other, not because of any mutual velocity, but because of the change of gravitational field - the r in the factor 2GM/rc2 of the metric has increased - and there is a mutual time dilation that affects the measurement of energy, which is detected by gravitational red shift.
However, my point in SCC is that this time dilation should affect the masses of fundamental particles as well - the De Broglie hypothesis (http://en.wikipedia.org/wiki/De_Broglie_hypothesis) - especially if in String Theory the masses are represented by the frequency of vibrations of strings.
While 'time-dilation' red shift is therefore undetectable as it affects the photon and the apparatus measuring it, the cosmological and gravitational red shift that is detected is then caused by the increase of the apparatus' rest mass with gravitational potential energy.
SCC equates the increase in inertial mass by GPE with the increase of mass caused by the Machian scalar field. Everything follows from this.
Garth
On the lower shelf the brick disturbed the otherwise symmetrical Schwarzschild space-time around a completely spherical (for the sake of argument) Earth. After being lifted up it now disturbs the space-time at a different level. This change of disturbance is where the energy has gone, according to some.
In that case,one has to quantify the energy change due to the change of disturbance and not just make a statement and shut up--hope they have done this.Anyway,the idea is interesting---so,do we conclude that the distortions of spacetime contain energy just as a field has energy?
However, my point in SCC is that this time dilation should affect the masses of fundamental particles as well - the De Broglie hypothesis (http://en.wikipedia.org/wiki/De_Broglie_hypothesis) - especially if in String Theory the masses are represented by the frequency of vibrations of strings.
Thanks for the news on de Broglie :smile:
While 'time-dilation' red shift is therefore undetectable as it affects the photon and the apparatus measuring it, the cosmological and gravitational red shift that is detected is then caused by the increase of the apparatus' rest mass with gravitational potential energy.
At the atomic level what happens to the energy levels(hence frequency of photons absorbed or emitted) when the rest mass changes---can check it up but leave it to you to answer.
In that case,one has to quantify the energy change due to the change of disturbance and not just make a statement and shut up--hope they have done this.Anyway,the idea is interesting---so,do we conclude that the distortions of spacetime contain energy just as a field has energy?I do not think anyone has calculated the energy change due to this disturbance. It is just a 'hand waving' explanation in GR to 'explain' where the energy goes to. As I said in GR energy is not conserved and the energy of a gravitating system is very difficult to define consistently in the first place. There has been much discussion on the subject in these forums.At the atomic level what happens to the energy levels(hence frequency of photons absorbed or emitted) when the rest mass changes---can check it up but leave it to you to answer.The rest mass increases with altitude, therefore the atoms at higher altitude emit radiation at higher frequency than those at lower altitudes.
The energy of the photon does not change, after all why should it? It has traversed curved space-time with no forces acting on it along a null-geodesic. No work has been done on, or by, the photon so why should its energy change?
When the photon emitted by an atom at lower altitude is compared with an exact equivalent emitted at a higher altitude gravitational red shift is observed. Of course the Pound and Snider experiment in 1965 absorbed, rather than emitted, the photon at the higher altitude.
Therefore in the SCC Jordan Frame, in which energy is locally conserved, gravitational red shift is interpreted not as a loss of potential energy by the photon but rather as a gain of potential energy by the apparatus measuring it. It is important to note that in this frame the frequency, and hence wavelength and energy, of a free photon is invariant, even when transversing space-time with curvature.
This argument only applies under the assumption of the Local Conservation of Energy, which holds in the Jordan Conformal fame of SCC. See The derivation of the coupling constant in the new Self Creation Cosmology (http://arxiv.org/pdf/ gr-qc/0302088) page 20 ff for details.
Garth
Drifted into other forums over the past few days.
However,to let not the inertia of discussion (and thereby some cosmic field!)break,let me ask you the following:-the cosmic field seems to obey an equation quite similar to the K.G. equation in the presence of matter(or other fields) and a wave equation in the absence of matter.Now is this a mere coincidence?Could the cosmic field be actually the K.G. field(or its sibling)associated with the distribution of mass?--in that case,it's quantum in origin!
Drifted into other forums over the past few days.
However,to let not the inertia of discussion (and thereby some cosmic field!)break,let me ask you the following:-the cosmic field seems to obey an equation quite similar to the K.G. equation in the presence of matter(or other fields) and a wave equation in the absence of matter.Now is this a mere coincidence?Could the cosmic field be actually the K.G. field(or its sibling)associated with the distribution of mass?--in that case,it's quantum in origin!
That is a very interesting observation....
One difference between SCC and GR is that in SCC a gravitational field, i.e. the presence of curvature, requires the vacuum to have a small and specific density (close to the Earth ~ 10-9 gm/cc) to make the solution of the scalar field equation consistent with that of the gravitational field equation. This limits the false vacuum density.
Cosmologically this becomes a moderate amount of DE (\Omega_{DE} = 0.11) and it therefore provides a natural explanation why DE is so small relative to the QM expectation and thus provides a solution to the "Lambda problem".
Exploring Klein-Gordon equations may therefore be the way forward to integrate SCC with QT.
Garth
An interesting discussion. I like the lifting brick example. I think the energy was always there. Lifting the brick simply loans the potential energy back to the universal gravitational field. The total energy of the universe, however, always remains exactly zero. Without gravity, a universe that contains matter behave very badly. Mach's principle does not globally conserve energy. . . which I believe is a local effect. GR, however, does globally conserve energy. This, again IMO, is where QT misses the mark. QT works well in the instantaneous subset, but fails miserably when pushed to the 4D model. Conclusion: QT is fundamentally unsound.
Hi Chronos, good to have your comments!An interesting discussion. I like the lifting brick example. I think the energy was always there. Lifting the brick simply loans the potential energy back to the universal gravitational field.
How? The total energy, rest mass and gravitational binding energy, of a Schwarzschild gravitational field measured at (null) inifinity is simply the Kepler mass M. It does not depend on the distribution of that mass within the spherically symmetric shell.The total energy of the universe, however, always remains exactly zero. Without gravity, a universe that contains matter behave very badly. Mach's principle does not globally conserve energy. . . which I believe is a local effect. GR, however, does globally conserve energy. In what frame is this 'global' energy to be measured?This, again IMO, is where QT misses the mark. QT works well in the instantaneous subset, but fails miserably when pushed to the 4D model. Conclusion: QT is fundamentally unsound.Or the other way round? It is GR that does not conserve energy (a frame dependent concept), rather it conserves energy-momentum (a frame independent concept) instead, which only translates into a conservation of energy under very special circumstances.
Garth
Hi Chronos, good to have your comments!
How? The total energy, rest mass and gravitational binding energy, of a Schwarzschild gravitational field measured at (null) inifinity is simply the Kepler mass M. It does not depend on the distribution of that mass within the spherically symmetric shell.In what frame is this 'global' energy to be measured?Or the other way round? It is GR that does not conserve energy (a frame dependent concept), rather it conserves energy-momentum (a frame independent concept) instead, which only translates into a conservation of energy under very special circumstances.
GarthAn interesting question Garth. But I do not understand your assertion that GR is frame dependent.
An interesting question Garth. But I do not understand your assertion that GR is frame dependent.
I didn't mean GR - it is energy in GR that is a frame dependent concept.
In SR two observers moving relative to each other would not agree on the total energy of a third body. Similarly in GR two inertial observers at different altitudes-potentials within a gravitational field would not agree on the total energy of a third body.
Let one inertial observer A be at the Centre of Mass of the Earth - freely falling yet stationary wrt the Earth. Now let a high up brick fall from rest, its rest energy/mass remains constant, yet it builds up speed and therefore its total energy increases as measured by A. Yet to another inertial observer B freely falling close alongside the brick its total energy remains the rest energy!
They would, however, agree on the rest mass, or rest energy, of the brick. This is the body's energy-momentum.
Garth
To introduce a Machian element, neither observer [earth or brick bound] would be able to 'prove' which body was moving in a two-body universe. Of course, introducing a third body changes everything.
Yes, motion is relative not absolute - even if there were three or more bodies present.
To make my example more precise, and to correct a false impression I may have created in post #92, if the brick was of negligible mass then its total energy as measured by observer A would be constant, taking A's assessment of the brick's varying time dilation factor into account. This is because there is a Killing Vector field for A's static Earth gravitational field. The two observers would make different assessments of the brick's total energy but both would be constant.
Where two measurements of total energy would differ between the two observers in the sense that one would remain constant and the other vary, is in their determination of the Earth's total energy.
To observer A at the centre of the Earth it would remain constant, however to observer B the Earth's total energy would increase as she accelerated towards the Earth. In B's frame of reference the Earth's field is not static and therefore there is no Killing vector to allow the conservation of energy.
My further point is to emphasise that the frame of reference in which the total energy of the brick is conserved is that frame 'selected by Mach's Principle' - that co-moving with the centre of mass of the system - i.e. A's.
Garth
Garth,
I have a question:-Suppose there are two identical atoms one above the other in a gravitational field(of the earth say).The atom at lower height(call it A) emits a photon.Say the atom B which is higher is prepared in its de-excited state i.e. it's ready to absorb a photon.The question is:-will it absorb the photon emitted by A?
According to GR the photon is red-shifted,so it does not have enough energy.According to SCC,the photon is not red-shifted but the rest mass of the atom has increased(thereby affecting its energy levels--energy levels obtained from a relativistic equation e.g. the K.G. equation contains the term mc^2,where m is the rest mass).The energy gap in fact widens due to increase in m,so the photon is again not absorbed.
So in both scenarios the photon is not absorbed(though due to different reasons).This may be the true situation but it leaves one a bit uncomfortable--one would expect the photon to be absorbed.What do you have to say?
Thank you gptejms for that interesting question.
Note: the expectations of this experiment is the same in GR and SCC.
In SCC there are two conformal frames of measurement, and the SCC Einstein frame in vacuo is canonical GR - so if the expectations were different in this case SCC would have a serious case of internal inconsistency!
The atoms of the absorbing medium would have thermal motion, so if the photons were only red shifted a little then some would still be absorbed.
If the red shift was cosmological then they would not be absorbed by the same transition, but of course they may be by another lesser energy transition. Why does this "leave you uncomfortable?"
Garth
No,there is no thermal motion here--also consider only two level atoms.Anyway,this is not the important point.
Regarding what leaves me uncomfortable:-what one is effectively saying here is that a laser won't operate if the pumping atoms(..don't remember the terminology) are separated from the atoms emitting the coherent light/laser beam in a gravitational field.Could be true---it's worth testing!
No,there is no thermal motion here--also consider only two level atoms.Anyway,this is not the important point.
Regarding what leaves me uncomfortable:-what one is effectively saying here is that a laser won't operate if the pumping atoms(..don't remember the terminology) are separated from the atoms emitting the coherent light/laser beam in a gravitational field.Could be true---it's worth testing!
Yes it might be worth testing, somebody with expertise in that field will have to give a more definitive answer.
But certainly unless the emitting and absorbing apparatus are at absolute zero there will be thermal motion of the atoms concerned.
Garth
But certainly unless the emitting and absorbing apparatus are at absolute zero there will be thermal motion of the atoms concerned.
Yes,of course.What I meant in my original question was that in the ideal case(where a delta function is emitted and absorbed by atoms)one would not see one atom absorbing what the other emitted if they were in a gravitational field.
Another question I wanted to ask you(something I didn't understand):-how does increase in rest mass of atoms translate to apparent red-shift of photons(which otherwise have the same energy in scc).You don't seem to be taking recourse to energy levels in your argument as I do.
Another question I wanted to ask you(something I didn't understand):-how does increase in rest mass of atoms translate to apparent red-shift of photons(which otherwise have the same energy in scc).You don't seem to be taking recourse to energy levels in your argument as I do.
There are two conformal frames of measurement in SCC.
In the Einstein conformal frame (GR with scalar field) the masses of fundamental particles remain constant and in vacuo the theory reduces to canonical GR. There is a conformal equivalence between SCC abd GR. The scalar field is decoupled from matter and space-time and exists as a 'ghost field'.
Energy-momentum is conserved wrt covariant differentiation, but not, in general, energy. Photons suffer gravitational and cosmological red shift, although as in GR there is no satisfactory explanation of where that energy goes to - it is simply not conserved.
In the Jordan conformal frame the scalar field is not decoupled and affects both space-time (as in BD) and the motion of particles through space-time. A scalar field force perturbs particles, but not photons, from their geodesic paths.
A consequence of the theory in vacuo is the scalar field force exactly compensates for the scalar field perturbation of space-time, so although particles do not follow geodesics of the SCC space-time they do follow geodesics of GR space-time.
It is this exact compensation in vacuo which results in the conformal equivalence between SCC and GR. Energy-momentum is not conserved but energy is locally conserved in general.
As a consequence in the Jordan frame photons do not suffer red shift. They do not lose or gain energy The energy of the photon does not change, after all why should it? It has traversed curved space-time with no forces acting on it along a null-geodesic. No work has been done on, or by, the photon so why should its energy change? (Remember gravitation in GR - and SCC - is explained as the effect of the curvature of space-time, not as a real Newtonian force.)
As I said in an earlier post above in the Jordan Frame, in which energy is locally conserved, gravitational red shift is interpreted not as a loss of potential energy by the photon but rather as a gain of potential energy, which increases atoms' rest mass in the apparatus measuring it.
Whereas no work has been done on or by the photon between the two levels, work has to be done on the apparatus to lift it from the lower to the higher level!
This increase in fundamental particles' rest mass changes the atoms' energy levels and it is this change that is measured as gravitational or cosmological red shift.
Garth
Whereas no work has been done on or by the photon between the two levels, work has to be done on the apparatus to lift it from the lower to the higher level!
This increase in fundamental particles' rest mass changes the atoms' energy levels and it is this change that is measured as gravitational or cosmological red shift.
You didn't mention the energy levels anywhere in your work.I think you took it in the sense of ratio of photon's energy to the rest mass(which goes down as the atomic clock goes up)--right?!--anyway,this way of looking at it is also fine,though the energy level approach is a better one.
There are two conformal frames of measurement in SCC.
In the Einstein conformal frame (GR with scalar field) the masses of fundamental particles remain constant and in vacuo the theory reduces to canonical GR. There is a conformal equivalence between SCC abd GR. The scalar field is decoupled from matter and space-time and exists as a 'ghost field'.
Energy-momentum is conserved wrt covariant differentiation, but not, in general, energy. Photons suffer gravitational and cosmological red shift, although as in GR there is no satisfactory explanation of where that energy goes to - it is simply not conserved.
In the Jordan conformal frame the scalar field is not decoupled and affects both space-time (as in BD) and the motion of particles through space-time. A scalar field force perturbs particles, but not photons, from their geodesic paths.
A consequence of the theory in vacuo is the scalar field force exactly compensates for the scalar field perturbation of space-time, so although particles do not follow geodesics of the SCC space-time they do follow geodesics of GR space-time.
It is this exact compensation in vacuo which results in the conformal equivalence between SCC and GR. Energy-momentum is not conserved but energy is locally conserved in general.
As a consequence in the Jordan frame photons do not suffer red shift. They do not lose or gain energy The energy of the photon does not change, after all why should it? It has traversed curved space-time with no forces acting on it along a null-geodesic. No work has been done on, or by, the photon so why should its energy change? (Remember gravitation in GR - and SCC - is explained as the effect of the curvature of space-time, not as a real Newtonian force.)
As I said in an earlier post above in the Jordan Frame, in which energy is locally conserved, gravitational red shift is interpreted not as a loss of potential energy by the photon but rather as a gain of potential energy, which increases atoms' rest mass in the apparatus measuring it.
Garth
I have questions on this part too.Are you saying that both in Einstein and Jordan frames,SCC in vacuo is equivalent to GR?In Einstein frame,the scalar field exists as a ghost field(in vacuo) whereas in JF,the scalar field affects both space-time and particles--the two effects cancel out in vacuo--is this what you are saying?
Now regarding vacuo--aren't you in vacuo all(or most of)the time?--you don't discuss what's happening in the earth's interior in GR.
You didn't mention the energy levels anywhere in your work.I think you took it in the sense of ratio of photon's energy to the rest mass(which goes down as the atomic clock goes up)--right?!--anyway,this way of looking at it is also fine,though the energy level approach is a better one.
Agreed.I have questions on this part too.Are you saying that both in Einstein and Jordan frames,SCC in vacuo is equivalent to GR?In Einstein frame,the scalar field exists as a ghost field(in vacuo) whereas in JF,the scalar field affects both space-time and particles--the two effects cancel out in vacuo--is this what you are saying?That is what I saidNow regarding vacuo--aren't you in vacuo all(or most of)the time?--you don't discuss what's happening in the earth's interior in GR.
Yes we are, which is why so far there has been a degeneracy in the tests, they have not differentiated between GR and SCC, so that tests that verify the one theory have verified the other also.
I have identified three tests that resolve this degeneracy:The GP-B geodetic precession, the locally measured bending of a light path towards a gravitating body such as the Sun or Earth (not the standard deflection test) and a bottoming out of the Casimir force in weak gravitational fields.
The first is being evaluated at present, the second produces a transverse bending of the LIGO 8 km laser light path of about 10-12m towards the Sun, which is too small to be detected as yet, and the third should be detectable away from the Sun's gravitational field somewhere between the orbits of Jupiter and Saturn with present experimental sensitivities.
The principle of equivalence is also broken and different matierials, e.g. gold and aluminium, should fall towards the Earth at different rates, but only at the one part in 1017 level three orders of magnitude smaller than present experimental sensitivity.
Garth
According to your theory,a particle moving at a constant velocity v has a rest mass different from the the one at rest.This is because in order to attain the constant velocity v, starting from rest, the particle has to accelerate and when the particle accelerates(it's as if it's in a gravit. field so) its rest mass changes.So do you mean SR needs to be modified(at least in the JF frame)?
J.Singh
According to your theory,a particle moving at a constant velocity v has a rest mass different from the the one at rest.This is because in order to attain the constant velocity v, starting from rest, the particle has to accelerate and when the particle accelerates(it's as if it's in a gravit. field so) its rest mass changes.So do you mean SR needs to be modified(at least in the JF frame)?
J.Singh
The fact that the mass of an object moving relative to an observer is observed to have a greater 'relativistic mass' or total energy because the object's kinetic energy is allowed for, as measured in the observer's frame.
SR does not need to be changed, in fact in its JF SCC is consistent with this SR 'energy principle' by also including gravitational potential energy in the rest mass.
Garth
Garth,
The increase in rest mass is not quite the same as a greater relativistic mass.In your case the rest mass may increase or decrease depending on whether the atom accelerates towards me(an observer at \infty )or away from me.This directional dependence,however,is a desirable feature!
This is because it explains the doppler effect in terms of energy levels of the source of light.If the source moves towards me,its rest mass increases thereby widening the gap between the energy levels--the reverse happens if the source moves away from me.So,it explains the relativistic doppler effect in terms of energy levels!You can't give such an explanation in SR,because relativistic mass does not depend on the direction of velocity.
I'll give you some background to my last post.A friend and class-fellow of mine came up with the following interesting problem(during the starting days of our M.Sc.):-There's a photocell and a (monochromatic)source of light at a certain distance from the photocell.The source of light emits light of frequency lower than what is required for the photoelectric effect.So there is no photoelectric effect.Now the source of light starts moving towards the photocell with some constant velocity--the resultant doppler effect is sufficient to take the frequency beyond the threshold(in photocell's frame).The question is would the photoelectric effect now be observed?If yes,where does the photon get the extra energy from?
I thought of discussing this in a separate thread,but since our discussion is heading towards similar issues,I've included it here.May be I should do both--discuss it here as well as start a separate thread.
J.Singh
The classic doppler effect is not the same as relativistic (total) energy change.
In classical doppler the red shift is proportional to velocity, whereas the total energy change - kinetic energy - is proportional to velocity2.
The relativistic doppler effect can be obtained from the classical doppler by factoring in the relativistic energy change. It is the difference between the classical and relativistic doppler effects that can be explained "in terms of energy levels".
Garth
gptejms
Jun10-06, 04:02 AM
The classic doppler effect is not the same as relativistic (total) energy change.
In classical doppler the red shift is proportional to velocity, whereas the total energy change - kinetic energy - is proportional to velocity2.
Yeah,but I never had the classical doppler effect in mind while talking of this problem.For relativistic doppler effect(which's what I had in mind) k.e. is not proportional to v^2(nor is the red-shift proportional to v).
The relativistic doppler effect can be obtained from the classical doppler by factoring in the relativistic energy change. It is the difference between the classical and relativistic doppler effects that can be explained "in terms of energy levels".
Garth
I thought of this:-however,you have to bring in two different effects(to explain the relativistic doppler effect)namely the change in energy levels due to increase in relativistic mass m/(1-v^2/c^2)^0.5 (provided we assume relativistic mass affects energy levels) and classical doppler effect(in which case you appeal to the wave-picture,but we are seeking an explanation in terms of particle picture only).Due to obvious reasons,one can't take this line of reasoning forward.
gptejms
Jun29-06, 08:48 AM
Garth:
You didn't comment on the directional dependence of rest mass in SCC.Is there or is there not directional dependence of rest mass in SCC?
The increase in rest mass is not quite the same as a greater relativistic mass.In your case the rest mass may increase or decrease depending on whether the atom accelerates towards me(an observer at )or away from meI'm not sure I understand you. Why should acceleration affect rest mass?
In SCC (Jordan Frame) rest mass is a function of gravitational potential energy and so has a positional dependence, (but so has G in such a way that Gm is constant,) but not a directional one.
As I said above, if you are trying to explain classical doppler as a variable rest mass effect it will not work. Any such variations in rest mass would be \propto v^2 whereas classical doppler z is \propto v.
Garth
gptejms
Jun29-06, 12:25 PM
I'm not sure I understand you. Why should acceleration affect rest mass?
In SCC (Jordan Frame) rest mass is a function of gravitational potential energy and so has a positional dependence, (but so has G in such a way that Gm is constant,) but not a directional one.
'A particle undergoing acceleration' is the same as 'a particle moving in a gravit. field'--so according to your scc,every time a particle moves from rest to some constant velocity,its rest mass should change.
'A particle undergoing acceleration' is the same as 'a particle moving in a gravit. field'--so according to your scc,every time a particle moves from rest to some constant velocity,its rest mass should change.
First: the Equivalence Principle (EEP) does not hold for particles in SCC, the EEP only holds for photons or fully relativistic particles. It is a semi-metric theory.
Secondly even if the EEP did hold your statement would not be correct. 'A particle undergoing acceleration' would be equivalent to 'a particle in a gravitational field' not necessarily 'moving in a gravitational field'.
In GR a gravitational field and acceleration do not in themselves result in time dilation.
Time always passes at the tautological 'one-second-per-second'.
When the observation of one clock deep in the field is compared to the other clock in a laboratory well away from the field, it is the intervening space-time curvature between them that produces the time dilation effect. That is it is the change in g00 between the two locations.
In a similar way in SR it is the build up of relative velocity following a period of acceleration that produces time dilation between moving observers not the acceleration itself. If a clock falls off a laboratory bench it remains synchronized to its identical twin that remains on the bench while they are both momentarily stationary, even though one is accelerating and the other not.
Garth
gptejms
Jun30-06, 03:24 AM
Tell me what happens in the following situation according to scc:-an observer(photocell) accelerates towards a source of light.We know as a fact that it receives photons of higher and higher frequency as long as it accelerates(this could be quantified by the photo current).Now according to scc,since EEP does not hold for atoms,atoms of the source (or the photocell) do not undergo any change in rest mass.The photons do not undergo any change either.So,how do you explain the change in frequency of the received photons?
Tell me what happens in the following situation according to scc:-an observer(photocell) accelerates towards a source of light.We know as a fact that it receives photons of higher and higher frequency as long as it accelerates(this could be quantified by the photo current).Now according to scc,since EEP does not hold for atoms,atoms of the source (or the photocell) do not undergo any change in rest mass.The photons do not undergo any change either.So,how do you explain the change in frequency of the received photons?
If the experiment is carried out all at the same gravitational potential level then there is no difference between SCC and SR/GR.
As I posted above Classical Doppler is not a 'relativistic mass' effect, it is a geometric effect caused by the relative movement; literally the photons are being 'squashed up' if the source is moving towards and are therefore observed at higher frequencies.
This is indicative of the frame dependence of energy levels. What is the zero point when measuring energies? To first order the relative motion shifts the frequency by an amount that is proportional to velocity. On top of his classical shift we factor in a relativistic correction, which does take time dilation into account.
(Here my LaTex has become all screwed up again :frown:)
Garth
gptejms
Jun30-06, 02:13 PM
If the experiment is carried out all at the same gravitational potential level then there is no difference between SCC and SR/GR.
Of course,there is a difference--from GR perspective,the 'particle undergoing acceleration' is equivalent to a 'particle in a gravitational field'--so the change in photon's frequency can be explained.I don't see this happening in the case of scc--I don't see why the photon's frequency should change from the scc perspective.
As I posted above Classical Doppler is not a 'relativistic mass' effect, it is a geometric effect caused by the relative movement; literally the photons are being 'squashed up' if the source is moving towards and are therefore observed at higher frequencies.
This is indicative of the frame dependence of energy levels. What is the zero point when measuring energies? To first order the relative motion shifts the frequency by an amount that is proportional to velocity. On top of his classical shift we factor in a relativistic correction, which does take time dilation into account.
Yeah,this is one way of looking at it as I said in one of the posts above.There are two factors (1+v/c) (or (1-v/c)) coming from classical doppler and a factor of 1/(1-v^2/c^2)^1/2 coming from time dilation.
Of course,there is a difference--from GR perspective,the 'particle undergoing acceleration' is equivalent to a 'particle in a gravitational field'--so the change in photon's frequency can be explained. But as I have said repeatedly acceleration by itself does not produce time dilation, or red shift, only the relative velocity that subsequently builds up.I don't see this happening in the case of scc--I don't see why the photon's frequency should change from the scc perspective.
Are you talking about gravitational or relativistic doppler red shift?
If relativistic doppler red shift, with no gravitational potential difference between emitter and observer, then in SCC it is exactly as in SR/GR.
If you are talking about gravitational red shift, the predicted red shift in SCC is the same as in GR, however the explanation given is fundamentally different.
In the SCC (Jordan Frame) the local conservation of energy, and the consequential variation in rest mass, demand that gravitational mass is treated under the De Broglie hypothesis.
Mass is defined by the DeBroglie frequency of that particle.
The red shift caused by the curvature of space-time, a time dilation expressed by the metric component \sqrt{g_{00}} , is suffered not only by the photon but also by the atom with which it interacts and is thus undetectable.
The red shift that is detectable is caused by the increase in rest mass that fundamental particles undergo when raised to the higher level.
Gravitational red shift is interpreted not as a loss of gravitational potential energy by the photon, but as a gain of gravitational potential energy by the apparatus measuring it.
Thus the predicted red shift is equal to the difference in Newtonian potential and therefore identical with that of GR as confirmed in the Pound-Rebka experiment.
I hope this helps,
Garth
gptejms
Jun30-06, 03:50 PM
Are you talking about gravitational or relativistic doppler red shift?
Relativistic doppler is what I was talking about--what else could it be when I talked of an observer/photocell moving towards a source of light.
If relativistic doppler red shift, with no gravitational potential difference between emitter and observer, then in SCC it is exactly as in SR/GR.
See the whole point is this:-you can derive the rel. doppler effect formula from an SR perspective(the way it's done in textbooks) as well as from a GR perspective if you consider the period of acceleration required to attain a constant velocity v,starting from rest(one of the threads in sr/gr forum also discusses this).I don't see this happening in the case of scc--i.e. you can't derive rel. doppler effect from an scc perspective.
Relativistic doppler is what I was talking about--what else could it be when I talked of an observer/photocell moving towards a source of light.That's what I thought, but you kept referring to the 'particle undergoing acceleration' is equivalent to a 'particle in a gravitational field' But acceleration by itself does not produce time dilation/red shift.
See the whole point is this:-you can derive the rel. doppler effect formula from an SR perspective(the way it's done in textbooks) as well as from a GR perspective if you consider the period of acceleration required to attain a constant velocity v,starting from rest(one of the threads in sr/gr forum also discusses this).I don't see this happening in the case of scc--i.e. you can't derive rel. doppler effect from an scc perspective.If the significant thing is the relative velocity produced by the acceleration then the two theories are equivalent. However, I am not familiar with your derivation of rel. doppler from GR.
Garth
Type Ia Supernova are important as the whole of cosmological acceleration is based on the observation of distant SN Ia.
These supernovae are hydrogen deficient and show a strong Si II line.
The best agreement between the theoretical and observed spectra is obtained by modeling the explosion of an accreting carbon-oxygen white dwarf in a close binary system. The white dwarf accretes material from its companion until core carbon burning begins and it deflagrates, with the shock front moving slower than local sound speed.
The light curves of local Type Ia are sufficiently similar to each other that it is thought they can be used as standard candles.
This supernova model is by no means unquestioned.
At z ~ 1 these candles appear dimmer than was previously expected, an effect that is explained by their distance being greater than expected. This would have meant the universe had expanded faster than expected, hence the inference of cosmological acceleration caused by DE on which the present \LambdaCDM model is based.
At even higher red shift z > 1 their apparent magnitudes become brighter again, which would give a handle on how DE behaves, if that \LambdaCDM model is the correct interpretation of the data.
However. as I have previously posted, the linear expanding freely coasting model also fits the z ~ 1 SN Ia remarkably well.
In the Accelerating universe? (http://physicsforums.com/showthread.php?t=115260) thread I responded to Juan Casado in my post #5:
Another explanation for SNe Ia faintness
This explosions would seem farther away than they really are (were) because of a small negative curvature of space. In a slightly hyperbolic Universe, the wave front of light is spreading out faster than in a flat one (the light cone resembling a horn) so that luminosity distances would appear longer than they are.
In such scenario no dark energy would be needed.
You are correct, hyperbolic space will cause initially parallel light rays to diverge and objects will appear smaller, further away and fainter than in flat space, similar to a concave lens effect.
This effect is convoluted with the expansion rate of the universe, because an accelerating universe will also result in objects that will actually be further away than at the same red shift z in a non-accelerating or decelerating universe.
There is always a degeneracy in the interpretation of cosmological effects, however in this case both the curvature and expansion effects have already been taken into account in the models that then are compared to the observations of these distant Type Ia supernovae.
The standard model fits several parameters to the data, not only that of these standard candles but also the WMAP data, quasar lensing data and other cosmological constraints.
That mainstream fit does require DE.
However as an example of your suggestion see Figure 2 in the primary paper on the subject of high red-shift Type Ia supernovae: Perlmuter et al's paper:Measurements of Omega and Lambda from 42 High-Redshift Supernovae (http://arxiv.org/abs/astro-ph/9812133) (page 23)
The (\Omega_M,\Omega_{\Lambda}) = (0,0) plot being the empty, “Freely Coasting” ([URL=http://arxiv.org/abs/astro-ph/0306448) model universe which has hyperbolic space and no DE. (It also doesn't require undiscovered non-baryonic DM either, but that is another story!)
As a caveat I must also add that this (\Omega_M,\Omega_{\Lambda}) = (0,0) plot is not such a good fit at higher red-shifts where the supernovae begin to become brighter than expected.
Notice also that this cosmic acceleration interpretation depends on the assumption that Type Ia supernovae are standard candles. They are standard candles in our own galaxy, which is why this type of supernova is used as such, but that is no guarantee that they remain of the same intrinsic luminosity over cosmological time, especially if physical constants actually vary over such time scales.
There may be several alternative explanations for these observations.
Garth
Previously, as SCC mimics the Freely Coasting Model (FCM) I had assumed that SSC also fitted the SN Ia data.
However the above response to Juan Casado set me thinking.
The difference between SCC and FCM is the linear, freely coasting model has hyperbolic space, k = -1, whereas SCC is linearly expanding but with spherical space, with k = +1. This should make the SN Ia apparent magnitudes brighter in SCC than they appear in the k = -1 model, and hence to fit the data they must actually be less luminous than expected if they were standard candles.
But why should the SN Ia be less luminous in the past than the model suggests?
Here I am 'hand waving', but reasons could be - a selection effect as most distant SN are detected after peak luminosity, and the further away they are the more might be missed.
Or, at high z the progenitor stars might well be expected to have less metallicity than more recent ones.
Now these are speculations only, but perhaps no more so than the standard model's bland acceptance that their luminosities do not change over such cosmological time scales.
Garth
After an abortive start in the new IR Forum I am beginning a new thread on the published theory of Self Creation Cosmology................
I find it difficult to follow the details of this long thread, or to come to any conclusions about its central topic, namely SCC. I hasten to add that this is probably due to simple ignorance on my part. But I'm not quite sure of this.
A brief summary of the present standing of SCC in the cosmological cosmos (as it were), by someone other than its author Garth would be very helpful for one trying to assess the present situation in cosmology. If one takes Garth's comments in the links to his Arxiv papers at face value, this situation seems to me quite parlous.
Could some knowledgeable person (like Space Tiger?) perhaps lend a critical hand here?
Critical comments would be most welcome and also here (http://en.wikipedia.org/wiki/Self_creation_cosmology) as well. Please feel free to sensibly edit that Wikipedia article as its NPOV is in question because there has been only one main author.
Garth
Garth,
I find your work very interesting but unfortunately do not have the physics background to understand it. Are you suggesting that matter can be created?
Garth,
I find your work very interesting but unfortunately do not have the physics background to understand it. Are you suggesting that matter can be created?
Hi caston! And welcome to these Forums. :smile:
The theory actually suggests inertial mass is 'created', or rather grows exponentially with cosmological time.
The particle number is treated the same way as in the standard theory; the inertial mass of each particle, however, varies with gravitational potential energy.
To define potential energy you need a special frame of reference to measure it in, the theory also uses Mach's prinicple to define that frame as being that of the Centre of Mass/Momentum of the system.
Thus the theory modifies GR to include both the Local Conservation of Energy and Mach's Principle.
I hope this helps.
Garth
Thanks Garth,
Does energy travel through time at a different speed to us?
Thanks Garth,
Does energy travel through time at a different speed to us?
Try to rephrase the question; everything 'travels through time' at the tautological rate of one second per second.
The proper time elapsed between two events A & B depends on the worldline taken between them. If an observer Ann is travelling at speed relative to Bob and Ann accelerates out and then back so both of them start at A and end at B, then Ann experiences a lesser time elapse than Bob.
If the energy you are talking about is light energy, which travels at c relative to a massive object, then it will travel on a null geodesic, and if it is, say reflected off a mirror, to arrive back at B, it will experience no time elapse.
Garth
I was at the APS April meeting at which the first results of GP(B) were presented.
The plenary session was given in the grand ballroom with about 1000 people present and the acoustics were not too great, and I have only one good ear. Francis Everitt began by explaining the geodetic effect using the paper cone model, made from a circle of card with a thin pie slice cut out, which of course demonstrates only the space-curvature part of the effect (2/3 of the total). So I just heard him say "here we have 4.4 "/yr." and my heart gave a jump, "What did he say, what did he say?"!!
Even though the accuracy is not too great the data clearly shows 6.6"/yr, which is fatal to SCC. GP-B N-S gyro orientation (http://einstein.stanford.edu/cgi-bin/highlights/showpic.cgi?name=gyro_drift_plot.png)
I am left wondering about those effects that SCC did seem to promise to explain, for not only does it have the same predictions as GR in the other standard ((1 +\gamma)G/2) tests but also the Pioneer effect (cH), a spinning up of the Earth (H), no inflation, baryonic DM and an equality between Hubble Time and the age of the universe.
I can't help thinking even post GP-B that there must be something in it.
However, if the frame-dragging results come out also as GR then there will be no doubt.
Although there is a possibility of a modified version of SCC with an undetermined and small \lambda, like BD, which would keep many of the features of the present theory.
I have now generalised the theory and am writing it up for publication.
In the General Theory of Self Creation Cosmology (GSCC) the BD coupling parameter \lambda is left as an undetermined variable.
In both SCC and GSCC the conservation equation is replaced by a 'creation equation', which is determined by the 'Principle of Mutual Interaction' (PMI). The PMI states that: "The scalar field is a source for the matter-energy field if and only if the matter-energy field is a source for the scalar field.''
As the source for the scalar field is the trace of the stress-energy tensor, the PMI is delivered by coupling this trace to the divergence of the stress-energy tensor. A detailed calculation yields:
\nabla _\mu T_{M\;\nu }^{.\;\mu }=\frac {\kappa}{8\pi} \frac {\nabla _\nu \phi }{\phi }\Box \phi =\frac {\kappa}{2} \frac {\nabla _\nu \phi }{\phi } T_{M\;}^{\;}
Where \kappa is a 'creation' coupling constant.
Note: In the Brans Dicke theory
\omega_{BD} = \frac{1}{\lambda} - \frac{3}{2}
whereas in SCC and GSCC
\omega_{SCC} = \frac{1}{\lambda} - \frac{3}{2} - \kappa
so if \frac{1}{\lambda} = \kappa
then \omega_{SCC} = - \frac{3}{2} .
In GSCC the 'creation' parameter \kappa remains equal to 1/\lambda, so \omega = -3/2 as before, and the conformal equivalence between GSCC and GR in vacuo is retained.
The two conformal frames remain as before with energy being locally conserved in the Jordan conformal frame and energy-momentum conserved in the Einstein frame. In the Jordan frame the 'rest' masses of fundamental particles are variable, subsuming gravitational potential energy, and they are constant in the Einstein frame.
There is still the same clock drift between ephemeris and atomic clocks as in the original SCC and hence the Pioneer Anomaly is still predicted by GSCC.
The GP-B geodetic prediction becomes
\Omega = [(1 - \lambda/3)6.6 + 0.25] arcsec/yr.
(I have found an extra 0.25 arc/sec/yr precession due to cosmological time dilation (clock drift) that makes the original SCC prediction 4.65 arcsec/yr not 4.4 arcsec/yr.)
The frame dragging result is still the same as in GR.
Unfortunately GSCC predicts the total mass density parameter for the universe to be
\Omega_T = \frac{1}{3\lambda} = \frac{\kappa}{3},
so if \lambda is small, i.e. if the creation parameter \kappa is large, a lot of DM and DE is required and an attractive feature of the original theory is lost.
However, if \lambda about 1/3 can be accommodated by the final GP-B geodetic result, (which is about twice the value allowed by the present published value of the geodetic precession,) then the overall density parameter would about unity and concordance with the standard \lambdaCDM model total density would be obtained.
I will post more when I have published.
Garth
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