Comparison of the Mainstream and the Self Creation Freely Coasting models

[Garth]

SpaceTiger has created a very valuable thread on Mainstream Cosmology. For good scientific practice it is important to compare standard theories with testable alternatives, however ST's thread is not the place to do it. The theory of Self Creation Cosmology (SCC) presents itself as such a testable alternative theory and there are several posts about it on these forums. However, sometimes my posts have been taken as an intrusion, therefore I have started this new thread for a specific discussion on both the SCC and the Freely Coasting models. In so doing, I am looking for critical analysis as well as general comments about that comparison and I have been grateful for all the reasoned criticism posted so far.

Introduction

The Freely Coasting model 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 realized 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: A coasting cosmology
astro-ph/0209209]Freely Coasting Cosmology[/URL]
astro-ph/0306448] A Concordant “Freely Coasting” Cosmology[/URL]
astro-ph/0502370] A case for nucleosynthesis in slowly evolving models [/URL]
nucl-th/9902022] Nucleosynthesis in a Simmering Universe [/URL] and a PhD thesis available on the physics ArXiv:
astro-ph/0401542] GRAVITATIONAL LENSING IN STANDARD AND ALTERNATIVE COSMOLOGIES [/URL]
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 been developing an alternative gravitational theory, SCC, that modifies GR to include a ‘non-minimally connected scalar field’. I have published seven papers and eprints, viz:
The original paper, Barber, G.A. : 1982, Gen Relativ Gravit. 14, 117. 'On Two Self Creation Cosmologies'.
http://www.kluweronline.com/oasis.htm/5092775, Astrophysics and Space Science 282: 683–730, (2002)
but the new theory can be recovered in five electronic pr/eprints that followed;
gr-qc/0405094] Self Creation Cosmology - An Alternative Gravitational Theory [/URL] to be published in "Progress in General Relativity and Quantum Cosmology. " Nova Science Publishers, Inc. New York.
astro-ph/0401136] The Self Creation challenge to the cosmological concordance model[/URL]
gr-qc/0302088 ]The derivation of the coupling constant in the new Self Creation Cosmology[/URL]
gr-qc/0302026 ]Experimental tests of the New Self Creation Cosmology and a heterodox prediction for Gravity Probe B[/URL]
and
gr-qc/0212111 ] The Principles of Self Creation Cosmology and its Comparison with General Relativity[/URL]
There have also been 47 other author citations in peer-reviewed journals.

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. One of these is being carried out at present, the Gravity Probe B satellite experiment, and the results will be known next year.

It 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 masss are constant and in which other physics is most easily described.

When the Jordan frame cosmological solution, (which turns out to be the same as Einstein's original cylindrical static model) is transformed into the SCC Einstein frame it turns out to be a strictly linearly expanding solution - that is it provides the linear expansion mechanism for the "Freely Coasting" model.

More to come...

Garth

 

[Garth]

Taking up the lead from my post #66 on ST's “Review of Mainstream Cosmology” thread I here compare time-lines between the standard model, R(t) ~ t^2/3, and the SCC model R(t) ~ t.

The look back time t_l as a function of red shift z is given by:
In GR
t_l/t_H = (2/3)(1 - 1/(1 + z)^3/2)
In SCC
t_l/t_H = (1 - 1/(1 + z))



With t_H = 10.2/h Gyrs.
WMAP determines h = 0.72 so t_H = 14.2 Gys.
and the age of the universe = 2/3t_H = 9.44 Gyrs. in GR
and the age of the universe = 14.2 Gyrs. in SCC.

Using t_z=x to be the age of an object now observed at a red shift x we have:

For "re-combination" - the surface of last scattering of the CMB, z = 1000,
t_z=1000 = 300,000 yrs. in GR
t_z=1000 = 14.2 Myrs. in SCC

for the onset of metallicity, i.e. Pop III stars, z = 20
t_z=20 = 100 Myrs. in GR
t_z=20 = 676 Myrs. in SCC

for quasar 'ignition' z = 8
t_z=8 = 350 Myrs. in GR
t_z=8 = 1.58 Gyrs. in SCC

for 'modern' metallicity in Quasar SDSS J1030+0524 z = 6.28
t_z=6.28 = 480 Myrs. in GR
t_z=6.28 = 1.95 Gyrs. in SCC.

The comparison shows that there is considerably more time for the development of Pop III stars, Quasars and early metallicity than in the mainstream model.

The longer nucleosynthesis period results in a baryonic density of over 20% closure density and a primordial metallicity 10⁸ times that of GR primordial metallicity.

The problem with the SCC model is there would be no primordial deuterium and the observed D has to be produced by another process such as spallation. (See Deuterium production by high-energy particles )

Garth

 

[pervect]

I think there may be some problems with using the "matter dominated" formula for lookback times for standard cosmology.

A quick web search turned up

http://home.att.net/~numericana/answer/cosmos.htm#lookback

which has the cautionary note

"If the Universe was indeed dominated by ordinary matter, it would be younger than the oldest stars in it !"

However, while this web page quotes two different simple lookback formulas, I didn't find anything like as a "standard" lookback formula. I think Ned Wright's javascript calculator could be useful here

http://www.astro.ucla.edu/~wright/CosmoCalc.html

However, I couldn't quite follow his posted derivation of the formulas

 

[Garth]

I think there may be some problems with using the "matter dominated" formula for lookback times for standard cosmology.

A quick web search turned up

http://home.att.net/~numericana/answer/cosmos.htm#lookback

which has the cautionary note

"If the Universe was indeed dominated by ordinary matter, it would be younger than the oldest stars in it !"

[As I said] [Edit: This addition was lost in transmission!] The lookback time can be extended into the past by cosmological acceleration.

However I was using the formula primarily to derive a time-line from the beginning t = 0. Here the problem is whether there was enough time in the standard model for evolved objects to form and produce metallicity.

The point being, of course, is to compare that with the greater times available in SCC.

Note as well, that while the SCC/freely coasting model does not have acceleration, it has an age for the universe that is comfortable with the ages of the oldest stars and globular clusters.

In this respect this model is more concordant with observation than the standard model.

Garth

 

[Chronos]

Garth, does your model include a big bang, or is it a steady state thing? I forget [I'm old and should take notes].

 

[Garth]

Expansion

i) Expansion

Garth, does your model include a big bang, or is it a steady state thing? I forget [I'm old and should take notes].

Hi Chronos! Thank you for your question.
This question is answered by first asking: "How do we measure the universe 'out there' with standards of measurement defined in a laboratory 'down here'?" :-
a. What standard do you use?
b. How do you transport that standard measurement to the far ends of the universe in order to make the comparison, what conservation principle does it depend on?

In GR the principle of equivalence requires atomic masses to be constant, so by they are defined to be so when that principle is applied to our understanding of physical observations. Consequently, atoms are adopted as an appropriate basis of making measurements of mass, length and time. That is, the size of the atom determines the length of the ruler, and the frequency of atomic processes determines the 'rate' of the clock. [Here I am talking about the rate of an atomic process in a distant quasar/galaxy being compared with that of the same process here on Earth.]

The atom, in a gedanken experiment, is to be physically transported across the universe and assumed to retain its properties unchanged. However we may ask, what if the mass actually does increase, either with cosmological age, or say, with potential energy as it is raised in a gravitational field? Einstein pondered this and concluded that if the rest mass of an atom did increase with altitude (PE) then that would also apply to the standard kilogram as well. To make a comparison the two masses would have to be brought together and an increase would not be detected; therefore, he concluded, they can be safely thought of as constant.

Constant atomic mass also applies in the SCC Einstein conformal frame. In this frame the universe expands strictly linearly from a Big Bang, it is a Freely Coasting theory.

However we do not actually transport clocks and rulers across the universe, instead we have to rely on observation of photons that have come from those nether regions, and photons suffer cosmological red shift.

In the Jordan conformal frame of SCC atomic masses are defined to vary with gravitational potential energy: energy is locally conserved,
m = m₀exp[Phi]
where Phi is the dimensionless Newtonian gravitational potential.

In this frame of SCC the principle of the Local Conservation of Energy as measured in the preferred Machian frame of the Centre of Mass (Centroid) requires photons to be of constant energy, so by they are defined to be so when that principle is applied to interpret astronomical data here on Earth. In this frame photons become the standard measure of mass (their energy) length (their wavelength) and time (the inverse of their frequency).

In this frame, as energy is locally conserved, gravitational and cosmological red shifts are interpreted as a gain of energy (mass) by the apparatus rather than a loss of energy by the photon.

Gravitational orbits and cosmological evolution have to be calculated in this frame and it is found that:
a. trajectories of test particles are identical with the GR geodesics in vacuo. SCC is concordant with the GR experimental tests to date.
b. as (CMB) photons ‘expand with the universe’ (in GR as well as SCC) the universe, as measured by those photons, is static and eternal. (The ‘frequency’ of a CMB photon tends to infinity as t tends to zero)
c. it also works out that the universe is spatially spherical and therefore closed. The SCC Jordan frame universe is Einstein’s original static cylindrical model!

Therefore summing up, in answer to your question. Choose the appropriate conformal frame to analyse a situation.
1. The Einstein frame for nuclear processes, stellar formation and evolution etc. In this frame the universe is a linearly expanding big bang universe.
2. The Jordan frame for gravitational orbits and cosmological evolution. In this frame the universe is Einstein's static cylindrical universe.
It depends on how you look at it and how you measure it.

We can compare this with SpaceTiger's Review of Mainstream Cosmology thread:

1) Expansion
The universe is, without a doubt, expanding. The most striking evidence for this is the fact that nearly every object in the sky exhibits a redshift in the spectrum of light that is emitted from it. Furthermore, more distant objects are observed to have larger redshifts, exactly what you would expect for expansion. Alternative theories (such as Zwicky's "tired light hypothesis") were put forth and seriously considered in the first half of the 20th century, but have produced no correct predictions, nor are they consistent with any known physics. They have not been seriously considered by the mainstream for quite some time.

Note: The Jordan frame of SCC is the opposite of a 'Tired Light' theory, photons retain their energy, it is the apparatus that gains mass with cosmological time.

I hope this helps, do cross-examine me!

Garth

 

[Garth]

2. The Big Bang Theory

From 'Review of Mainstream Cosmology".

2) The Big Bang Theory There is a lot of confusion amongst the general public about what the Big Bang Theory is really saying and which aspects of it are taken as gospel truth by the scientific community. In its simplest form, you can think of the argument as follows:

"If space is expanding and the universe has a finite size, then it must have been much smaller in the past".

How much smaller? Well, the standard assumption is that the universe had a creation event and expanded from a singularity to its present size. Such a distant extrapolation can't possibly be verified by the current observations, but we can safely say that the universe expanded from a much smaller size than its current one. There is good observational evidence for an epoch of nucleosynthesis approximately one minute after the creation event (z ~ 10⁸). Physical models of the conditions in this early phase of the universe were able to predict the relative abundances of the light isotopes (including hydrogen, helium, and deuterium) to very high accuracy.

How does SCC compare with this excellent summary of the standard theory 'Big Bang'?

Again the question is: “If the universe is expanding how do you measure it? For example does the 'ruler' expand with the universe?"

In the SCC Einstein frame the atomic ruler has fixed length and the universe expands around it. Gravitational red shift is Doppler in nature and nucleosynthesis in SCC is similar to the standard theory albeit in a linear expansion with no inflation. Nucleosynthesis continues much longer than the GR ~3 minutes, for four years! To get the correct amount of helium the baryonic density has to be increased to over 20% closure, in others words equal to the Dark Matter component. So is DM baryonic after all? If so what form does it take today and why can't we see most of it? Also with that duration of nucleosynthesis all the Deuterium is destroyed. The D observed today has to be created in some other way - spallation for example?

In the Jordan frame the ruler (the wavelength of a CMB photon) does 'expand with the universe'; the universe is static and the BB has been projected back in time to the 'infinite' past. The universe is eternal. The mass of an atom increases exponentially with cosmological time:
m(t) = m₀exp(Ht)
where t is the time measured by the frequency of a CMB photon and
where t = 0 is the present epoch and m₀ its present mass.

Cosmological red shift is caused by the atoms of the apparatus having gained mass since the epoch when the photon was emitted, the photon itself has not lost energy at all, indeed why should it, it has traveled across space-time 'instantaneously' along its light-like null-geodesic. No work has been done on or by the photon, so why should it loose energy? In this frame the standard model appears to be a 'tired light' model!

In the distant past atoms had hardly any mass and so were very large, the diameter of an atom is inversely proportional to its mass, other things being equal. The distant past in the Jordan frame was just as crowded as the Big Bang in the Einstein frame!

More to follow...

Garth

 

[pervect]

Therefore summing up, in answer to your question. Choose the appropriate conformal frame to analyse a situation.
1. The Einstein frame for nuclear processes, stellar formation and evolution etc. In this frame the universe is a linearly expanding big bang universe.
2. The Jordan frame for gravitational orbits and cosmological evolution. In this frame the universe is Einstein's static cylindrical universe.
It depends on how you look at it and how you measure it.

Garth

I'm not 100% sure if this is right, but my picture of your cosmology is this:

The Einstein frame in your model is the familiar and standard "big bang" model, in which the universe evolves with a(t). The difference is that the expansion is freely coasting.

Time measured in the Einstein frame is proper time, the time measured by clocks as we know them.

Your Jordan frame seems to be closely tied in with conformal time - which I would describe as an arbitrary rescaling of the time parameter used to make the geodesics of light 45 degree lines. (My view on this may be myopic).

Thus "time" in the Jordan frame is not the "physical time" measured by ticking clocks. Because the conformal time is the logarithm of the proper time, the time coordinate goes to minus infinity at the big bang.

What this means is that physically, as measured by a clock, the universe has a finite age. The causal structure of the universe is such, though, that any two points no matter how distant share a common history ( a consequence of the fact that conformal time extends back to infinity).

This is illustrated by the last diagram at the bottom of the following webpage:

http://www.astro.ucla.edu/~wright/cosmo_03.htm

 

[Garth]

Thank you perfect.

The Einstein frame in your model is the familiar and standard "big bang" model, in which the universe evolves with a(t). The difference is that the expansion is freely coasting.

Time measured in the Einstein frame is proper time, the time measured by clocks as we know them.

Correct

Your Jordan frame seems to be closely tied in with conformal time - which I would describe as an arbitrary rescaling of the time parameter used to make the geodesics of light 45 degree lines. (My view on this may be myopic).

Thus "time" in the Jordan frame is not the "physical time" measured by ticking clocks.

The Jordan SCC frame is a non-invariant conformal transformation of the Einstein frame and vice versa. However it depends on what clocks you deem to be physical as to whether this time is "physical time".

Photons are just as much part of the physical world as particles. Indeed in most of astronomy all we have of our objects of study are the photons received from them.

Whether you deem particles or photons as more physical depends on whether you want to conserve energy-momentum or energy respectively. Lift an apparatus, where does the energy used lifting it go? In GR it 'goes into the field' non-localised and the apparatus' rest mass remains constant. However a photon transmitted from one apparatus down below and received by an identical apparatus at the top of a 'cliff' is observed to suffer from gravitational red shift. Where did the photon's energy go to? No work has been done on or by that photon.

In GR the energy went 'into the field.' In the SCC Jordan frame the energy of lifting the apparatus goes into increasing its rest mass.

The measurement of frequency of the photon is a comparison of the energy of the photon relative to the mass of the apparatus, and red shift is the difference between such measurements at the bottom and top of the 'cliff'. SCC interprets such red shift as the apparatus really increasing in mass by the gain of potential energy and that increase is observed/measured by comparison with a photon.

Because the conformal time is the logarithm of the proper time, the time coordinate goes to minus infinity at the big bang.

What this means is that physically, as measured by a clock, the universe has a finite age. The causal structure of the universe is such, though, that any two points no matter how distant share a common history ( a consequence of the fact that conformal time extends back to infinity).

This is illustrated by the last diagram at the bottom of the following webpage:

http://www.astro.ucla.edu/~wright/cosmo_03.htm

That is a useful diagram that we have discussed in another Forum! If we deal with physical particles rather than mathematical points, in the SCC Jordan frame as t -> -∞ the particles increase in size d -> +∞ , so yes in the asymptotic limit as the universe is filled with infinite sized particles they all do overlap, yes they share a common history!

Garth

 

[pervect]

Whether you deem particles or photons as more physical depends on whether you want to conserve energy-momentum or energy respectively.

Alright, let's scratch "physical" clocks and replace it with "SI" clocks.

If we stick with SI units as closely as we can, would the age of the universe be finite in SI units?

There might be certain difficulties in maintaining a SI cesium clock all the way up to the big bang. The same issue arises with the SI meter (at some point a spacelike geodesic could not be a meter long.). Still, we can try and ask, if we had an SI meter, would a photon bounce across it a finite number of times since the big bang? (When the meter starts to become too long to fit in the universe without bending, we cut it in half, and require a photon to transverse the halved-meter twice to advance our time count once).

Lift an apparatus, where does the energy used lifting it go? In GR it 'goes into the field' non-localised and the apparatus' rest mass remains constant. However a photon transmitted from one apparatus down below and received by an identical apparatus at the top of a 'cliff' is observed to suffer from gravitational red shift. Where did the photon's energy go to? No work has been done on or by that photon.

At this point I'm mentally quite tied to the view that the gravitational field does do work on the photon, I'm afraid - which is the POV that the photon frequency does shift.

Since I suspect a lot of other people are mentally tied to this same POV, it might be worthwhile to give this POV a name. I think this POV is your "Einstein" frame.

 

[Garth]

All right, let's scratch "physical" clocks and replace it with "SI" clocks.

If we stick with SI units as closely as we can, would the age of the universe be finite in SI units?

There might be certain difficulties in maintaining a SI caesium clock all the way up to the big bang. The same issue arises with the SI meter (at some point a space-like geodesic could not be a meter long.). Still, we can try and ask, if we had an SI meter, would a photon bounce across it a finite number of times since the big bang? (When the meter starts to become too long to fit in the universe without bending, we cut it in half, and require a photon to transverse the halved-meter twice to advance our time count once).

What is your SI metre rule constructed from, steel? In which case you are in the Einstein frame and the universe expands around it. However in fact we cannot transport a steel metre rule to the ends of space and back to the BB, all we can do is observe photons from those regions. (If you could transport it all the way back to the BB, a photon would bounce back and forth across it an infinite number of times!)
[Edit: Correction; the photon would bounce back and forth a finite number of times, but it would vibrate an infinite number of times. According to the steel rule the universe has a finite age, according to the photon its age is infinite. - Sorry about that!]
So keep the steel rule on Earth and define a metre with it, so many vibrations of a light wave emitted by a particular spectral line of Caesium for example, and use that photon to measure the universe. Now you are in the Jordan frame. The key point of SCC is the gravitational and cosmological field equation has to be solved in this frame.

At this point I'm mentally quite tied to the view that the gravitational field does do work on the photon, I'm afraid - which is the POV that the photon frequency does shift.

Since I suspect a lot of other people are mentally tied to this same POV, it might be worthwhile to give this POV a name. I think this POV is your "Einstein" frame.

But is the POV consistent with GR, or are you still partially stuck in a classical physics with its gravitational potential energy? Remember no forces are acting on the photon, the null-geodesic world-line of the photon simply passes through a space-time with curvature.

Many standard authors, MTW (pg 187), Weinberg (pg 85), use a kind of classical PE argument and energy-conservation to explain GR gravitational red shift so that POV is understandable; but are they being consistent within the GR paradigm?

However, do I expect GR to predict g. red shift? Yes!
Because energy is conserved? No! But because energy is not generally conserved in GR! (Remember we are deep in a gravitational field on Earth, there are no Killing vectors between the bottom and the top of the cliff. Energy is not conserved, rather energy-momentum is, but that is different.)

Garth

 

[pervect]

What is your SI metre rule constructed from, steel?
In which case you are in the Einstein frame and the universe expands around it.

That is what I more-or-less expected, however I have to point out that the current defintion of the SI meter is

http://physics.nist.gov/cuu/Units/current.html

The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

I presume that this doesn't change anything, and that the answer is still yes, we have a finite number of SI seconds since the Big Bang?

But is the POV consistent with GR, or are you still partially stuck in a classical physics with its gravitational potential energy? Remember no forces are acting on the photon, the null-geodesic world-line of the photon simply passes through a space-time with curvature.

The answer is a double yes - the POV is consistent with GR, and yes, I still am partialy stuck in classical physics with it's gravitatioanl potential energy.

The GR approach would be to say that the photon traveling from the bottom of the Earth to the top is following a geodesic as you say.

But since the space-time of the Earth is reasonably static, we DO have time-like Killing vectors at both the bottom and top of the cliff! If you don't like the actual example of the Earth, think of being in the exterior region of an idealized Schwarzschild metric where this is exactly true.

The product of any tangent vector of a geodesic and a Killing vector is a constant. Because k^a is a unit vector, the zeroeth component of the energy-momentum 4-vector of the photon, E_a is conserved. (This is also true for a free-falling particle). So the energy-momentum conservation law gives us gravitational redshift in the Schwarzschild metric without reference to any semi-classical concepts. If you have Wald, you can check out pg 137, or follow through with E = sqrt(-E_0 E^0) = sqrt(-E_0 g^00 E_0) = E_0 sqrt(-g^00), and remember that E_0 must be a constant for any given light ray. Since E=hv, this gives us the frequency.

In the expanding universe case of a flat FRW metric, we don't have any time-like Killing vectors, so we don't have a conserved energy. We do have some space-like Killing vectors, though, due to isotropy. These give us a conserved "momentum" in this case (very handy for actually solving for the geodesics).

 

[Garth]

the current defintion of the SI meter is

The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

I presume that this doesn't change anything, and that the answer is still yes, we have a finite number of SI seconds since the Big Bang?

Yes; the fundamental measurement question is: How do we measure time?" Using a caesium (cesium? American spelling?) atom in the definition places the time measurement firmly in the Einstein frame - it is equivalent to a steel rule but more accurate.

The answer is a double yes - the POV is consistent with GR, and yes, I still am partialy stuck in classical physics with it's gravitatioanl potential energy.

Although I find that POV (photons fighting a gravitational potential well) persuasive I don't find it consistent with the GR paradigm.

The GR approach would be to say that the photon traveling from the bottom of the Earth to the top is following a geodesic as you say.

But since the space-time of the Earth is reasonably static, we DO have time-like Killing vectors at both the bottom and top of the cliff! If you don't like the actual example of the Earth, think of being in the exterior region of an idealized Schwarzschild metric where this is exactly true.

The killing vector exists for the photon, which is why its energy is conserved, but not for the apparatus, that has to be carried up the cliff, against the field. Its geodesic would take it straight down again and its killing vector would not survive the crash at the bottom!

Note the correction in my last post above: "the photon would bounce back and forth a finite number of times, but it would vibrate an infinite number of times. According to the steel rule the universe has a finite age, according to the photon its age is infinite." You were correct about the photon and the ruler, sorry .

Garth

 

[Garth]

Further note: Wald (pg 137) has got it right, (i.e. gravitational red shift) he follows Synge (1955) in explaining grs as a time dilation effect, but then he 'spoils it' by saying

we would expect the energy of the photon to be degraded as it 'climbs out of the gravitational potential well'.

In GR? Exactly which force is it that is degrading the photon's energy?

Garth

 

[pervect]

Although I find that POV (photons fighting a gravitational potential well) persuasive I don't find it consistent with the GR paradigm.The killing vector exists for the photon, which is why its energy is conserved, but not for the apparatus, that has to be carried up the cliff, against the field. Its geodesic would take it straight down again and its killing vector would not survive the crash at the bottom!

LOL. Methinks the Killing vectors would survive the crash much better than the instrument package.

We seem to be getting into the issue that Pete always raises, about how the mass of a system is to be calculated if the system is not isolated. This is clearly the case here, the measuring system is not following a geodesic, though the photons are. So the time-like Killing vectors exist, but since the package isnt' following a geodesic, they don't help us find it's energy.

Currently I have no answer as to how to calculate the mass of a non-isolated system with full GR. It may even be a fundmanetally ambiguous notion, I'm not sure at this point.

I think that your scalar field starts to enter the picture somewhere around here, resolving the difficulties in SCC for the energy of an interacting system, but not saying anything about what the solution (if any) is for GR.

Note the correction in my last post above: "the photon would bounce back and forth a finite number of times, but it would vibrate an infinite number of times. According to the steel rule the universe has a finite age, according to the photon its age is infinite.

Ah - that helps a lot. Besides the warm fuzzy feeling of beign right :-), it gives me a clear mental picture of the situation.

 

[Garth]

We seem to be getting into the issue that Pete always raises, about how the mass of a system is to be calculated if the system is not isolated. This is clearly the case here, the measuring system is not following a geodesic, though the photons are. So the time-like Killing vectors exist, but since the package isnt' following a geodesic, they don't help us find it's energy.

Currently I have no answer as to how to calculate the mass of a non-isolated system with full GR. It may even be a fundmanetally ambiguous notion, I'm not sure at this point.

I think that your scalar field starts to enter the picture somewhere around here, resolving the difficulties in SCC for the energy of an interacting system, but not saying anything about what the solution (if any) is for GR.

I would be interested in your opinion on my calculation of red shift under the "local conservation of energy paradigm" in my eprint "The derivation of the coupling constant in the new Self Creation Cosmology" page 22-24.

Garth

 

[Chronos]

We still have issues in that model. SW and GZK effects are problematic in the Jordan reference frame, IMO. And so far as photons are concerned, time does not exist.

 

[Garth]

SW and GZK effects are problematic in the Jordan reference frame, IMO. And so far as photons are concerned, time does not exist.

Everything is measured with reference to a set of standards, mass, length, time here in a laboratory on Earth. The frequency of a 'standard photon' has to be ideally defined in a Machian centre of Mass freely falling frame of reference, however here on the Earth's surface will do for now. From our laboratory the rest of the universe may be 'mapped out', measured, using the photons received from that universe.

Time is defined by the number of vibrations of that photon as measured by an atomic process in the laboratory here on Earth, and from that number of vibrations, length and energy/mass too.

Remember that atomic masses are varying in the Jordan frame, therefore in order to examine a physical process such as the SW and GZK effects it is easier to transform into the Einstein frame in which masses are constant.

Now there is no intrinsic problem with the Sachs-Wolfe effect in the Einstein frame - it simply puts a constraint on cosmological parameters. Do you want to discuss numbers on this issue?

As far as the GZK effect is concerned I don't think anybody can explain the high energy cosmic rays or GRB's, do you? Can Gamma Ray Bursts Produce the Observed Cosmic Rays Above 10²⁰ eV?

7 Conclusion Given all of the above considerations, it would appear that there is no compelling reason to believe that GRBs can produce the observed flux of ultrahigh energy cosmic rays. Indeed, given the knowledge obtained from recent observations of GRBs, there appear to be many problems with this hypothesis, making it highly questionable.

Garth

 

[Garth]

But also note: Because of the significant energy loss by the GZK (Greisen-Zatsepin-Kuzmin 1966) mechanism, the present universe is not transparent to the highest energy cosmic rays (10²⁰ eV), http://prola.aps.org/abstract/PRL/v73/i26/p3491_1.

A very energetic cosmic ray of energy about (1.7-2.6) x 10²⁰ eV was observed by the Akeno Giant Air Shower Array on 3 December 1993 from the direction of galactic longitude l=131° and galactic latitude b=-41° within an error circle of 1.0° radius. If this cosmic ray were a proton; its origin could be extragalactic. However, the distance of the source cannot be much more than a few times 10 Mpc due to the energy loss during its travel from interactions with universal background radiation.

Therefore any sources contributing to the bulk of these cosmic rays should be within 500 Mpc of earth.

What could be their source? As such high energies are involved there might be a natural accelerator out there - but that would not result in an isotropic flux.

So, is the flux isotropic? http://www.journals.uchicago.edu/cgi-bin/resolve?id=doi:10.1086/307646 .

With the Akeno Giant Air Shower Array, 581 cosmic rays above 10¹⁹ eV, 47 above 4×10¹⁹ eV, and seven above 10²⁰ eV were observed until 1998 August. The arrival direction distribution of these extremely high energy cosmic rays has been studied. While no significant large-scale anisotropy is found on the celestial sphere, some interesting clusters of cosmic rays are observed. Above 4×10¹⁹ eV, there are one triplet and three doublets within a separation angle of 25^o, and the probability of observing these clusters by a chance coincidence under an isotropic distribution is smaller than 1%. The triplet is especially observed against expected 0.05 events. The cos(GC) distribution expected from the dark matter halo model fits the data as well as an isotropic distribution above 2×10¹⁹ and 4×10¹⁹ eV, but the fit with the dark matter halo model is poorer than the isotropic distribution above 10¹⁹ eV. The arrival direction distribution of seven 10²⁰ eV cosmic rays is consistent with that of lower energy cosmic rays and is uniform. Three of the seven are members of doublets above about 4×10¹⁹ eV.

Another possibility, which I would suggest as an educated guess, is that black holes must be involved - a lot of them roughly isotropically distributed across the sky. Is this evidence of a population of IMBH's making up the DM halo of our galaxy (10¹⁹ eV cosmic rays) and the IGM of our galactic cluster (10²⁰ eV cosmic rays)?

Garth

 

[wolram]

My favorite origin of cosmic rays is
http://www.universetoday.com/am/publish/new_explanation_cosmic_rays.html?352004
but these energetic rays are still an enigma.

 

[Garth]

Thank you wolram for that link - but would giant radio galaxies (GRG's) provide an isotropic flux if they were within a "few 10's of Mpc" of the Milky Way? (Note too at the heart of GRG is a BH)

Garth

 

[pervect]

And so far as photons are concerned, time does not exist.

I'm not sure if this point has been addressed yet - the path a photon takes has an affine parameterization, which can be used to determine time and distance. It's usually used as a distance measure, see for example

http://relativity.livingreviews.org/open?pubNo=lrr-2004-9&page=articlesu4.html

 

[Garth]

I'm not sure if this point has been addressed yet - the path a photon takes has an affine parameterization, which can be used to determine time and distance. It's usually used as a distance measure, see for example

http://relativity.livingreviews.org/open?pubNo=lrr-2004-9&page=articlesu4.html

I did address the question of how 'light' can be used to measure time, thank you for clarifying it. My point is that you cannot just use a photon. In the SCC Jordan frame, with varying atomic masses, you have to have a physical, i.e. an atomic clock in a laboratory here on Earth, ideally in a freely floating laboratory at the Centre of Mass of the Earth, to define what a second is and what a 'standard' photon is and then use that photon to measure the universe, conceptually by 'radar'.

Garth

 

[Chronos]

A naive question again, Garth. How do we distinguish the Jordan frame from the Einstein frame? If all the measurement sticks change proportionately, how do we differentiate this from the GR point of view?

 

[Garth]

A naive question again, Garth. How do we distinguish the Jordan frame from the Einstein frame? If all the measurement sticks change proportionately, how do we differentiate this from the GR point of view?

You choose.

You have a kilogram standard mass, a steel metre rule and an atomic clock sitting in your laboratory here on Earth. How do you apply those standards to measure the universe at large, and back into the BB?

You have to adopt and choose a reasonable and consistent conservation principle that defines something that does not change when you mentally transport your standards to the ends of space and time. How do you know, for example, that atomic masses do not change over cosmological history?

So we apply the Conservation of Energy-Momentum enshrined in the field equation
T^u_v;_u = 0,
which enshrines the Einstein Equivalence Principle (EEP), and which determine particle masses to be constant. This is the basis, of course, of GR.

It is also the basis of the Einstein frame of SCC, which despite having an extra scalar field term in the gravitational field equation reduces to canonical GR in vacuo.

This conservation principle defines atomic masses to be constant, but thereby eliminates the possibility of a continuous creation out of gravitational and scalar field energies by the increase of atomic masses. [Note Hoyle's Continuous Creation postulated an extra Creation field to spontaneously create extra nucleons that then individually have constant masses. This approach (SSC) was been eliminated by detection of the CMB - I tried the alternative approach.]

This alternative approach violated the EEP by allowing the Brans Dicke Machian scalar field to interact with particles,(a "non-minimally connected" scalar field, in scalar-tensor theory parlance). This scalar field interaction (a force) now corrected the perturbation by the presence of that field on space-time. The theory is concordant with the GR tests to date - all in vacuo.

This Jordan frame is that frame in which gravitational, and therefore cosmological dynamical, equations have to be solved. To make a measurement in this frame you choose to adopt instead the Principle of the Local Conservation of Energy and thereby define the energy of a photon, as measured in the preferred frame co-moving with the Centre of Mass of the system, to be constant.

I hope this helps.

Garth

 

[Chronos]

I'm not trying to conserve energy locally, just globally. That is where the objection arises.

 

[Garth]

I'm not trying to conserve energy locally, just globally. That is where the objection arises.

Then you remain in the Einstein frame of SCC - that is GR.
However the theory also fully incorporates Mach's Principle, by including that scalar field, and the question is whether Mach's Principle & the Local Conservation of Energy are physically important or not.

The three distinguishing tests of SCC, the GPB geodetic measurement, the test of whether photons 'fall' at the same 'rate' as particles, and the test of whether the Casimir force is dependent on s-t curvature, are ways of empirically discovering the validity of this approach and falsifying it. Fortunately we won't have too long to wait...

Garth

 

[Garth]

3) Homogeneity and Isotropy

11. Where do we go from here?

If you wish to entirely change a paradigm, you must re-interpret all of the observational evidence in the context of the new paradigm before you can safely say that your theory is viable.

That is precisely my intention in this thread

3) Homogeneity and Isotropy
Most models of the universe assume that it is uniform to translations in space (homogeneous) and uniform in direction (isotropic). This does not mean that every point in space is the same on all scales (it obviously isn't), but rather that the universe is smooth on the largest scales. By analogy, the surface of a spherical balloon is homogeneous and isotropic, despite having small bumps and wiggles if you look at it closely enough. Although this point is not controversial (even believers in steady-state cosmology like homogeneity and isotropy), it is actually more difficult to prove than, for example, expansion. Difficult, but not impossible.

The first and most convincing line of evidence (if you believe the big bang) is the cosmic microwave background radiation. If it really is a fingerprint of the early universe, then its extreme uniformity implies homogeneity to one part in 104.

Smoothness was one of the set of three: the horizon, density and smoothness problems of the Friedmann model that Inflation provided an solution for. The reason these three parameters of the universe were problems, i.e. why was the sky isotropic if regions of it are not causally connected, why is its density close to unity, why was the universe so homogeneous, was caused by the deceleration of the universe. Deceleration over the entire age of the universe would have driven these parameters away from the Friedmann flat model solution. Inflation, on the other hand, a short violent exponential acceleration, had the ability of driving these parameters onto the flat model solution.

The strictly linearly expanding model, i.e. the freely coasting model, of which SCC is an example, does not have these problems in the first place, thus removing the need for inflation, the first of the mainstream model’s ‘epicycles’.

In SCC a scalar field is the source for the matter field and in the distant past it had the boundary condition of homogeneity. Matter in the earliest phases of the Jordan frame of SCC would have consisted of a homogeneous sea of virtual particles, which having very little mass would have a long life-time. Inertial mass was endowed onto these particles by the scalar field, a real input of energy that converted virtual into real particles.

The homogeneity of the earliest universe is not in doubt as the CMB is homogeneous to greater than one part on 10⁴, however how did the anisotropies of galactic clusters, galaxies, stars, planets and eventually people form from that smooth continuum? This will be the subject of a future post.

Garth

 

[pervect]

I'm not trying to conserve energy locally, just globally. That is where the objection arises.

Garth's theory actually has a number that represents "the energy of the universe" that is a constant - you would probably call this a global quantity. Don't be confused by the name he has chosen to give his energy conservation principle. His energy conservation principle is different than that of GR's, because he includes the energy that is in his "scalar field" into the total energy.

GR does not have this notion - there is no notion of the "total energy of the universe", strictly speaking. Strictly speaking, one requires either a timelike Killing vector, or an asymptotically flat space-time to define energy. FRW spacetime in general doesn't have either notion, so it doesn't have a conserved energy.

GR's notion of energy has been called "improper" and "nonlocal". This was a matter of concern for a long time. Emily Noether explained why this had to be true - Hilbert noticed the problem after formulating the Hilbert action, and he asked Emily to work on the problem, which she did.

A quote from http://gsdl.enc.org/external/search/gsdl_view_catalog_record/0,4140,curl%253D%25252Fgsdl%25252Fexternal%25252Fresearchers%25252Fresearchers%25255Fscience%2526version%253Dgraphics%2526id%253D4290,00.shtm

Abstract: This paper presents a historical account of Emily Noether's proof of two thereoms which have had a great impact on modern physics. Emmy Noether proved two deep theorems, and their converses, on the connection between symmetries and conservation laws. Because these theorems are not in the mainstream of her scholarly work, which was the development of modern abstract algebra, it is of some historical interest to examine how she came to make these discoveries. The present paper is an historical account of the circumstances in which she discovered and proved these theorems which physicists refer to collectively as Noether's Theorem. The work was done soon after Hilbert's discovery of the variational principle which gives the field equations of general relativity. The failure of local energy conservation in the general theory was a problem that concerned people at that time, among them David Hilbert, Felix Klein, and Albert Einstein. Noether's theorems solved this problem. With her characteristically deep insight and thorough analysis, in solving that problem she discovered very general theorems that have profoundly influenced modern physics. This resource is appropriate for all users, particularly for girls and women, because it acknowledges women's contributions to STEM.

Garth's theory, because of the scalar field and the way it's constructed, DOES have a local (in the mathematical sense used in the paper above) defintion of energy. There is another confusing issue here - physicists and mathemeticians have totally different notions of what local energy conservation means.

Anyway, if you realize that Garth's theory has a different notion of energy, one that is always conserved in his theory (it's a true "proper" or local conservation, unlike GR's "improper" conservation) - a notion of energy that's different than the GR notion of energy because it includes the energy in a "scalar field" present in his theory, you'll be on the right track.

If you also go "hmmm, how does Garth's theory get around Noether's thoerem? Does it wind up not being diffeomorphism invariant, because the scalar field gives you in essence a preferred frame?", I *think* you'll be on the right track, though I'm not 100% sure of this point.

 

[Garth]

If you also go "hmmm, how does Garth's theory get around Noether's thoerem? Does it wind up not being diffeomorphism invariant, because the scalar field gives you in essence a preferred frame?", I *think* you'll be on the right track, though I'm not 100% sure of this point.

Thank you for that link, you may also be interested in Nina Byers Noether’s Discovery of the Deep Connection Between
Symmetries and Conservation Laws[/URL].

There were two questions left after the formulation of GR, treated separately: the local conservation of energy and the full inclusion of Mach's Principle. Emmy Noether dealt with energy-conservation early on and Brans and Dicke tried to deal with Mach's Principle in the 1960's.

SCC deals with both questions simultaneously.

The problem with the local conservation of energy is that the measurement of energy is frame dependent, in order to conserve energy you need to specify a frame of reference in which it is conserved, a preferred frame. I use Mach's Principle to select that frame.

The question of preferred frames in SCC is a deep one.
The field equations (Jordan frame) are manifested covariant, there are no preferred frames, although the matter field energy-momentum tensor is not conserved. (It is when conformally transformed into the Einstein frame). However if you select one particular fame, the 'Machian' Centre-of-Mass (Momentum) frame for the system in question then in that frame of reference energy is locally conserved.

I hope this helps.

Garth

 

[selfAdjoint]

Thank you for that link, you may also be interested in Nina Byers Noether’s Discovery of the Deep Connection Between
Symmetries and Conservation Laws[/URL].

There were two questions left after the formulation of GR, treated separately: the local conservation of energy and the full inclusion of Mach's Principle. Emmy Noether dealt with energy-conservation early on and Brans and Dicke tried to deal with Mach's Principle in the 1960's.

SCC deals with both questions simultaneously.

The problem with the local conservation of energy is that the measurement of energy is frame dependent, in order to conserve energy you need to specify a frame of reference in which it is conserved, a preferred frame. I use Mach's Principle to select that frame.

The question of preferred frames in SCC is a deep one.
The field equations (Jordan frame) are manifested covariant, there are no preferred frames, although the matter field energy-momentum tensor is not conserved. (It is when conformally transformed into the Einstein frame). However if you select one particular fame, the 'Machian' Centre-of-Mass (Momentum) frame for the system in question then in that frame of reference energy is locally conserved.

I hope this helps.

Garth

I would call the Machian principle not a question, as if physics demanded it, but a philosophical preference. Einstein was a Machian at first but found his theory did not support it and was able to abandon it. I am not criticising SCC, just pointing out that there does not appear to be a crying need to build Mach into one's theories.

 

[Garth]

I would call the Machian principle not a question, as if physics demanded it, but a philosophical preference. Einstein was a Machian at first but found his theory did not support it and was able to abandon it. I am not criticising SCC, just pointing out that there does not appear to be a crying need to build Mach into one's theories.

Yes, selfAdjoint, thank you for that observation. I was using the word 'question' to mean 'the question of whether it should be included or not', it may even be emphasised by calling it a 'problem' instead.
The 'question' about Mach's Principle is closely related to the 'question', or 'problem' of the local conservation of energy. Quoting from my link above to that paper of Byers:

The failure of local energy conservation in the general theory was a problem that concerned people at that time, among them David Hilbert, Felix Klein, and Albert Einstein.
Energy conservation in the general theory has been perplexing many people for decades. In the early days, Hilbert wrote about this problem as ‘the failure of the energy theorem ’. In a correspondence with Klein [3], he asserted that this ‘failure’ is a characteristic feature of the general theory, and that instead of ‘proper energy theorems’ one had ‘improper energy theorems’ in such a theory. This conjecture was clarified, quantified and proved correct by Emmy Noether.

It is important to see the significance of this "failure of the energy theorem" in GR, for example:

In a laboratory on Earth (a 'supported frame of reference') you lift a stationary kilogram weight and put it on a shelf. Where has the energy used to lift it gone to? You have expended energy in lifting it and so your total energy, has gone down. Yet (in GR) the 'rest' mass of the weight has not altered, so where has the energy gone? The standard answer is "into the field".

In GR "there is transfer of energy to and from the gravitational field and it has no meaning to speak of a definite localization of the energy of the gravitational field in space...
At any given spacetime point one may choose a set of coordinates for which the gravitational fields vanish (g_uv reduces to the flat spacetime Minkowski metric and the Christoffel symbols vanish). This is guaranteed by the equivalence principle which states that one can always choose a coordinate system such that spacetime in the neighborhood of a given point is Minkowski (flat). Thus one may see why it is not meaningful to speak of a localized energy density for gravitational fields." " (Quoted from Byers' paper)

Thus, while it may seem that "there does not appear to be a crying need to build Mach into one's theories", is there a crying need to build in a local conservation of energy? That conservation requirement needs a frame of reference and that is why Mach is also required to select out such a 'preferred' frame.

The standard answer is to say there isn't a need for either, but the maverick in me has long suggested that in fact there is! As GPB is testing both theories at present we may not have to wait much longer to find out.

Garth

 

[Garth]

Age of the Universe

Next, from "Review of Mainstream Cosmology"

4) Age of the Universe
Firstly, there are globular clusters. From what we know about stellar evolution, we can model populations of stars and, under the assumption that they were all born at the same time, determine their age. When we do this with Milky Way globular clusters, we get an age of around 12 +- 3 billion years. Not technically a determination of the universe's age, but certainly a lower limit.

What about radioactive elements? Can we somehow use them to infer the age of the universe? It turns out that we can. Recent detections of Uranium-238 and Thorium-232 in stars have allowed us to use the traditional radioactive dating method to obtain an age of 12.5 +- 3 billion years. Again, a lower limit, but completely independent from and consistent with that from stars.

Finally, there are the measured cosmological parameters. When brought together and analyzed carefully, we can very tightly constrain the age of the universe to be 13.7 +- 0.2 billion years. It is very reassuring that this is consistent with both of the above ages. In fact, the standard model predicts that the Milky Way should have formed very early in the life of the universe, so the fact that the other two ages are of the same order (and not much less) is also consistent. One way to falsify the standard model would be to find something that is significantly older than 13.7 billion years. For a while, the globular cluster measurements were thought to represent such a falsification, but with the improvement of both our globular cluster measurements and our cosmological measurements, we are now finding nice agreement.

I thank ST for this clear exposition of the mainstream view.
It is important to note the age parameters, already posted, #2 on this thread, that have been determined by the standard interpretation of the WMAP data.
Hubble time, t_H is given by t_H = 10.2/h Gyrs.
where H = h.100 km/sec/Mpsc.
WMAP determines h = 0.72
so t_H = 14.2 Gys .

In a spatially flat, matter dominated dust Friedmann universe
R(t) = R₀(t/t₀)^2/3
and the present age of the universe = 2/3t_H = 9.44 Gyrs.

Thus the universe looks 'a bit young' for the components within it: i.e. the globular clusters and radioactive fossils. Furthermore, the universe would be even younger if the density or pressure were greater.

However all is not lost, acceleration in the past would have meant that the universe had been expanding more slowly in the ancient past and therefore is older than it at first seems today. This acceleration can be produced by inserting negative pressure into the Friedmann equations.

Therefore the observation that SN Ia in high red shift galaxies were fainter than expected was seized upon as a solution to two specific problems, as these observations provided evidence that the universe had accelerated in the past, if interpreted in the GR paradigm.
1. The universe 'is older than it looks' thereby resolving the age problem.
2. This negative pressure could be caused by Dark Energy that provided the extra cosmological density required for closure (Omega = 1).

But note that this DE has to be carefully modeled, in ST's words, "These things were invented to explain the data, not the other way around." (post #38 in "Mainstream" thread).

The mainstream model requires massive acceleration in the earliest universe - Inflation. However the expansion has to be that of a radiation dominated universe R(t) = R₀(t/t₀)^1/2 for BBN (primordial nucleosynthesis) to be correct. So DE is insignificant in this period, but then becomes significant in the 'dark ages' and early galactic age, but would appear to be insignificant again in the modern epoch otherwise we could detect it locally.

In comparison the Freely Coasting model, as produced by the SSC gravitational field equations, has a simple evolution R(t) = R₀(t/t₀) and the age of the universe is simply 14.2 Gys. The independently determined ages of its various components sits comfortably within this constraint, as do the formation of Pop III stars, quasars and the earliest galaxies.

There is no acceleration, no DE, and yet the model fits the distant SN Ia data, here, page 4 as recognised by Perlmutter here, page 24.

The middle solid curve is for (Omega M,Omega L) = (0,0). Note that this plot is practically identical to the magnitude residual plot for the best-fit unconstrained cosmology of Fit C, with(Omega M, Omega L) = (0.73,1.32).

Finally, as there is no requirement to make up the density closure because the total Omega = 0.33, why "multiply the entities" with the "invention" of DE?

Garth

 

[Kea]

In comparison the Freely Coasting model, as produced by the SSC gravitational field equations, has a simple evolution R(t) = R₀(t/t₀) and the age of the universe is simply 14.2 Gys.

Interestingly, this is similar to the age calculated by the recent Wiltshire Machian cosmology.

 

[Garth]

Interestingly, this is similar to the age calculated by the recent Wiltshire Machian cosmology.

That is interesting. Note that model also adds Mach to GR, and also finds it does not need DE to explain cosmological constraints. Does it have any specific falsifiable tests as SCC does?

Garth