Comparison of the Mainstream and the Self Creation Freely Coasting models

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Garth

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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 realised that the model was surprisingly concordant with cosmological constraints without the further addition of concepts such as DM or DE that remain undiscovered in laboratory physics. There have been several papers published and PhD’s gained exploring this alternative cosmological paradigm, viz: A coasting cosmology
[URL [Broken]astro-ph/0209209]Freely Coasting Cosmology[/URL]
[URL [Broken]astro-ph/0306448] A Concordant “Freely Coasting” Cosmology[/URL]
[URL [Broken]astro-ph/0502370] A case for nucleosynthesis in slowly evolving models [/URL]
[URL [Broken]nucl-th/9902022] Nucleosynthesis in a Simmering Universe [/URL] and a PhD thesis available on the physics ArXiv:
[URL [Broken]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'.
'A New Self Creation Cosmology, a 'semi-metric' theory of gravitation' , Astrophysics and Space Science 282: 683–730, (2002)
but the new theory can be recovered in five electronic pr/eprints that followed;
[URL [Broken]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.
[URL [Broken]astro-ph/0401136] The Self Creation challenge to the cosmological concordance model[/URL]
[URL [Broken] gr-qc/0302088 ]The derivation of the coupling constant in the new Self Creation Cosmology[/URL]
[URL [Broken]gr-qc/0302026 ]Experimental tests of the New Self Creation Cosmology and a heterodox prediction for Gravity Probe B[/URL]
and
[URL [Broken]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
 
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Garth

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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) ~ t2/3, and the SCC model R(t) ~ t.

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



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

Using tz=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,
tz=1000 = 300,000 yrs. in GR
tz=1000 = 14.2 Myrs. in SCC

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

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

for 'modern' metallicity in Quasar SDSS J1030+0524 z = 6.28
tz=6.28 = 480 Myrs. in GR
tz=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
 
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pervect

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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 [Broken]

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
 
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Garth

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pervect said:
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 [Broken]

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
 
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Chronos

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

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Expansion

i) Expansion

Chronos said:
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:
SpaceTiger said:
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
 
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Garth

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2. The Big Bang Theory

From 'Review of Mainstream Cosmology".
SpaceTiger said:
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 travelled 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
 
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pervect

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Garth said:
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
 

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Thank you perfect.
perfect said:
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
 
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pervect

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Garth said:
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.
 

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pervect said:
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
 
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pervect

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Garth said:
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 travelled 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 travelling 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).
 

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pervect said:
the current defintion of the SI meter is
The meter is the length of the path travelled 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.
pervect said:
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.
pervect said:
The GR approach would be to say that the photon travelling 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 :blushing:.

Garth
 
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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

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Garth said:
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.
 

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pervect said:
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

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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

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Chronos said:
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
 
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Garth

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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), here.
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 [Broken].
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 25o, 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
 
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Garth

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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

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Chronos said:
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 [Broken]
 
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Garth

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pervect said:
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 [Broken]
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
 
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Chronos

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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

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Chronos said:
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
Tuv;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
 
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