Is Self Creation Cosmology a Viable Alternative to the Standard Model?

[Garth]

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

 

[gptejms]

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.

 

[Garth]

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 said

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.

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

 

[gptejms]

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

 

[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

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

 

[gptejms]

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.

 

[gptejms]

Photo-Doppler problem

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

 

[Garth]

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]

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]

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?

 

[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 )or away from me

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.

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]

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.

 

[Garth]

'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]

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?

 

[Garth]

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 )

Garth

 

[gptejms]

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.

 

[Garth]

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]

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.

 

[Garth]

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

 

[Garth]

A Problem fitting SN Ia in SCC?

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? 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 (page 23)

The (\Omega_M,\Omega_{\Lambda}) = (0,0) plot being the empty, [URL=[PLAIN]http://arxiv.org/abs/astro-ph/0306448[/URL] 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

 

[oldman]

What are the hassles with the self creation idea?

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?

 

[Garth]

Critical comments would be most welcome and also 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

 

[caston]

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]

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.

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

 

[caston]

Thanks Garth,

Does energy travel through time at a different speed to us?

 

[Garth]

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 traveling 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

 

[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. 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.

 

[Garth]

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