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

[Garth]

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]

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.

 

[aguy2]

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[/url] and for a non-professional's 2003 prediction concerning WMAP3 data you might want to check out: [PLAIN]http://physics.about.com/b/a/2003_10_15.htm?terms=bb+electronics
aguy2

 

[Garth]

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) 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
[tex]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]
$$-\frac{\sqrt{-\tilde{g}}}{16\pi }\left[ 2\left( 2\omega +3\right) \frac{\tilde{g}^{\mu \nu }\tilde{\nabla }_{\mu }\Omega \tilde{\nabla }_{\nu }\Omega }{\Omega ^{2}}+4\omega \frac{\tilde{g}^{\mu \nu } \tilde{\nabla }_{\mu }\Omega \tilde{\nabla }_{\nu }\tilde{\phi } }{\Omega }+\omega \frac{\tilde{g}^{\mu \nu }\tilde{\nabla }_{\mu } \tilde{\phi }\tilde{\nabla }_{\nu }\tilde{\phi }}{\tilde{\phi }}\right]$$.

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 http://www.kluweronline.com/oasis.htm/5092775 and the eprint The Principles of Self Creation Cosmology and its Comparison with General Relativity.

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

 

[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)] 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]

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?

 

[Garth]

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

 

[Garth]

Continued from the Gravity - Integrating General Relativity with "Gravitons" 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 realized 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 realize 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 realize that the above story scores high on the John Baez crackpot index! But at least the theory is falsifiable.

It has been a long time and the result should finally be known next year (April 2007).

Garth

 

[gptejms]

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.

 

[Garth]

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.

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

 

[gptejms]

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.

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.

 

[Garth]

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$\pi$G 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, 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
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

I hope this helps.

Garth

 

[gptejms]

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?

 

[Garth]

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.

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 - 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

 

[gptejms]

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 - especially if in String Theory the masses are represented by the frequency of vibrations of strings.

Thanks for the news on de Broglie

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.

 

[Garth]

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 gr-qc/0302088]The derivation of the coupling constant in the new Self Creation Cosmology[/URL] page 20 ff for details.

Garth

 

[gptejms]

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!

 

[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!

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

 

[Chronos]

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.

 

[Garth]

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

 

[Chronos]

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.

Garth

An interesting question Garth. But I do not understand your assertion that GR is frame dependent.

 

[Garth]

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

 

[Chronos]

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.

 

[Garth]

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

 

[gptejms]

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?

 

[Garth]

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

 

[gptejms]

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!

 

[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!

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

 

[gptejms]

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.

 

[gptejms]

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.

 

[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