Where did the energy in the CMB go to?

[turbo]

Pardon me for being impolite. Chronon is espousing a bunch of crap.

I am a late-comer to the cosmology table (middle-aged amateur astronomer). The best way for me to learn is to compare models (new and old) and see where they differ in assumptions, methodology, etc. You can learn as much or more from a failed experiment as you can from a successful one, if you are willing to take the time to study the process and the observations and determine where the model's predictive power failed. It is very easy to adopt "status quo" thinking and avoid considering non-mainstream ideas, but that habit leads to stagnation and the perpetuation of error.

...Another of the qualities of science is that it teaches the value of rational thought as well as the importance of freedom of thought; the positive results that come from doubting that the lessons are all true. You must here distinguish--especially in teaching--the science from the forms or procedures that are sometimes used in developing science. It is easy to say, "We write, experiment, and observe, and do this or that." You can copy that form exactly. But great religions are dissipated by following form without remembering the direct content of the teaching of the great leaders. In the same way, it is possible to follow form and call it science, but that is pseudo-science. In this way, we all suffer from the kind of tyranny we have today in the many institutions that have come under the influence of pseudoscientific advisers.

We have many studies in teaching, for example, in which people make observations, make lists, do statistics, and so on, but these do not thereby become established science, established knowledge. They are merely an imitative form of science analogous to the South Sea Islanders' airfields--radio towers, etc., made out of wood. The islanders expect a great airplane to arrive. They even build wooden airplanes of the same shape as they see in the foreigners' airfields around them, but strangely enough, their wood planes do not fly. The result of this pseudoscientific imitation is to produce experts, which many of you are. [But] you teachers, who are really teaching children at the bottom of the heap, can maybe doubt the experts. As a matter of fact, I can also define science another way: Science is the belief in the ignorance of experts.

When someone says, "Science teaches such and such," he is using the word incorrectly. Science doesn't teach anything; experience teaches it. If they say to you, "Science has shown such and such," you might ask, "How does science show it? How did the scientists find out? How? What? Where?"

It should not be "science has shown" but "this experiment, this effect, has shown." And you have as much right as anyone else, upon hearing about the experiments--but be patient and listen to all the evidence--to judge whether a sensible conclusion has been arrived at.

In a field which is so complicated [as education] that true science is not yet able to get anywhere, we have to rely on a kind of old-fashioned wisdom, a kind of definite straightforwardness. I am trying to inspire the teacher at the bottom to have some hope and some self-confidence in common sense and natural intelligence. The experts who are leading you may be wrong.

I have probably ruined the system, and the students that are coming into Caltech no longer will be any good. I think we live in an unscientific age in which almost all the buffeting of communications and television--words, books, and so on--are unscientific. As a result, there is a considerable amount of intellectual tyranny in the name of science.

Finally, with regard to this time-binding, a man cannot live beyond the grave. Each generation that discovers something from its experience must pass that on, but it must pass that on with a delicate balance of respect and disrespect, so that the [human] race--now that it is aware of the disease to which it is liable--does not inflict its errors too rigidly on its youth, but it does pass on the accumulated wisdom, plus the wisdom that it may not be wisdom.

It is necessary to teach both to accept and to reject the past with a kind of balance that takes considerable skill. Science alone of all the subjects contains within itself the lesson of the danger of belief in the infallibility of the greatest teachers of the preceding generation.

So carry on. Thank you.

I'm pretty keen on epistemology, so it's enlightening to find out whether a cosmologist has tried to make a "clean-slate" start, and if not, what prior assumptions he has embraced. Milne apparently started with Special Relativity and the things then-known by observational astronomers, and constructed a cosmological model from those priors that did not require curved space-time. His model may not have been entirely correct, but it appears to have been quite valuable to the progression of cosmology, including his "cosmological principal", which is a crucial feature of the standard model. Again, Chronon, thanks for the link.

 

[chronon]

Thank you for the link to your page. I've got to spend some time tracking down Milne.

When I was writing the web page I read the book:
Relativity, gravitation and world-structure by Edward Arthur Milne

You might be interested in the notes I made about this book. (My intention is eventually to add 'further reading' notes for each page to my website, but I haven't got round to it yet)

Interesting how he derives results from 1st principles. Doesn't like curved space. Rejects finite, unbounded universe - real/image distinction - somewhat muddled. (Obviously never played Asteroids.)
Particle horizons= continuous creation (sees Particle horizons as now) .
At one stage seems to adopt the 'cancelling forces' view of gravity, as Newton did. However, later he seems to criticize Newton's adoption of this point of view.
A random spread of velocities means that some particles will gravitate towards their place of rest. He sees this as a possible explanation of Dust clouds, and of cosmic rays. However, he does have particles reaching the velocity of light, so something is surely wrong.

So Milne was trying to find an alternative to General relativity, whereas today the 'Milne Universe' is thought of as a particular model within the framework of general relativity.

 

[Garth]

Again I'll try to emphasise the difference between space and spacetime. General relativity tells us about the intrinsic curvature of spacetime. It allows considerable freedom of how we coordinatise spacetime. What we think of as space depends upon our choice of coordinate system.The space in the Milne universe is hyperbolic in the usual coordinate system. The spacetime is flat. The case which is usually referred to as 'flat', k=0, has curved spacetime, flat space (in the usual coordinate system)When I talk about movement or stretching, this is with respect to space, not spacetime

I have taken some time to answer this post as I have been very busy and I needed time to do a little calculation and look up your links.

First thank you for correcting my slack choice of words, space stretches in the expanding universe, I am well aware of the difference between the curvature and evolution of space and the curvature of space-time. It was late and I was hasty in my post. However, what space-time is doing in the standard modes of the R-W metric Friedmann models is a more complicated question.

You have to distinguish between the Milne model, the empty limit of the Friedmann models of homogeneous and isotropic GR, and Milne Cosmology or 'Kinematic Relativity' which is a non-GR alternative cosmology and of which I have been aware for some time and to which I referred in my paper.

It is in Kinematic Relativity that space-time is flat. In the empty Friedmann model k = -1 and R = t, the 'Milne model', the universe spatially expands linearly and 3D space is hyperbolic embedded in a 4D manifold. The space-time of this model can be said to be not 'flat', in the sense that not all the components of its Riemann tensor R^a_bcd are zero, even though it can be embedded into flat Minkowski space-time by a transformation of coordinates.

The point I was making was that in the standard GR cosmological solution 'empty space' had a non-trivial structure.

 

[chronon]

It is in Kinematic Relativity that space-time is flat. In the empty Friedmann model k = -1 and R = t, the 'Milne model', the universe spatially expands linearly and 3D space is hyperbolic embedded in a 4D manifold. The space-time of this model can be said to be not 'flat', in the sense that not all the components of its Riemann tensor R^a_bcd are zero, even though it can be embedded into flat Minkowski space-time by a transformation of coordinates.

I'm not convinced about that - I think the Riemann tensor is zero. However, I'm rather out of practice in doing GR calculations, so I may have to think about it for a while. (I tried Googling: Milne "Riemann Tensor" , but all the hopeful looking quotes were to subscription only websites of journals)

 

[hellfire]

I'm not convinced about that - I think the Riemann tensor is zero. However, I'm rather out of practice in doing GR calculations, so I may have to think about it for a while. (I tried Googling: Milne "Riemann Tensor" , but all the hopeful looking quotes were to subscription only websites of journals)

I believe all components of the Riemann tensor are zero in the Milne universe. The Weyl tensor is zero, as it is zero in any Robertson-Walker model, and the components of the Ricci tensor are also zero, since $\ddot a = 0$ and $\dot a = \sqrt{-k}$. This makes sense, since all components of T_uv are zero and space is homogeneous and isotropic. Thus space-time is flat (although it expands) and space is curved k = -1.

 

[turbo]

I'm not convinced about that - I think the Riemann tensor is zero. However, I'm rather out of practice in doing GR calculations, so I may have to think about it for a while. (I tried Googling: Milne "Riemann Tensor" , but all the hopeful looking quotes were to subscription only websites of journals)

Here's a way to find (at least sometimes!) copies of these papers without paying $20-30 per article. At the journal page, highlight the title of the article and Google search on that title. This process is GREATLY simplified if you use Firefox as your browser - just highlight the title, right-click on it, and in the pop-up menu choose "Search Web for..." Firefox will open your default search engine in a new tab (preserving the page you are on currently in another tab).

Even better, you can go to the Mozilla site and add Google Scholar to your tool bar and even make it your default search engine. Google Scholar will pull up the pay-as-you-go journals, but it will usually also pull up free archives, and it will identify citations and do other nice things.

 

[pervect]

For the metric
$$a(t)^2 (d \chi^2 + sinh(\chi)^2(d\theta^2 + sin(\theta)^2 d\phi^2)$$

which should be the FRW metric of interest (with k=-1, i.e. negatively curved spacelike hypersurfaces)

with a(t) = t

I get all components of R = 0, which implies that the Ricci and the Einstein are also zero (which means it's the zero density soulution as desired). Which also means that while the space-like hypersurfaces which perserve isotropy aren't flat, the space-time as a whole is flat, as other posters have remarked (and Google turns up a number of web pages which say the same thing).

However, while this is a flat spacetime, I don't think it satisfies the necessary conditions for conserving energy ("asymptotic flatness"). In spite of the similarity in names, flat does not necessarily imply asymptotically flat.

 

[Garth]

I believe all components of the Riemann tensor are zero in the Milne universe. The Weyl tensor is zero, as it is zero in any Robertson-Walker model, and the components of the Ricci tensor are also zero, since $\ddot a = 0$ and $\dot a = \sqrt{-k}$. This makes sense, since all components of T_uv are zero and space is homogeneous and isotropic. Thus space-time is flat (although it expands) and space is curved k = -1.

and chronon and pervect

The Ricci tensor is the trace or contracted form of the Riemann and that is zero throughout
R^a_bad = R_bd = 0,
its components can cancel each other out
R⁰_b0d + R¹_b1d + R²_b2d + R³_b3d = 0, so one can have
R_bd = 0 even if an individual
R^a_bad is not zero. Of course the trace can vanish even with an individual non zero R^a_bcd if it is 'off-diagonal'.

As I said above, the solution to the empty GR cosmological case is not the same as SR flat Minkowski space-time, it has a structure imposed by the cosmological boundary conditions imposed on the Einstein field equation.

And hellfire as we have recently established it is 3D space that expands not 4D space- time!


Garth

 

[hellfire]

Thank you for your clarification Garth. You may be right. I did not perform the calculations and I was relying only on my (probably bad) intuition. To calculate all components of the Riemann tensor is actually a lot of work; may be you could tell me which one(s) you expect to be non-zero, that I can convince myself...

 

[Garth]

In order to be sure I have just calculated all 256 components of the Riemann tensor for the Milne universe metric! (Allowing for asymmetries of course). Whereas what I have said about all the components of the Riemnann tensor not neccessarily being zero for the all the components of the Ricci tensor to be zero is in general correct, in the particular case of the Milne metric the components of the Riemann tensor are zero. The Milne space-time is flat and I apologise for misleading anyone.
Garth

 

[Garth]

So to recap, the solution to the empty GR cosmological case is not the same as SR, its space hypersurface has a structure imposed by the cosmological boundary conditions imposed on the Einstein field equation. Although it is rather academic to talk about such a non-Euclidean 3D geometry in an empty universe as there would be nobody around to measure it.

The reason I thought some of the components of the Riemann had to be non-zero was the (incorrect) intuition that that had to be so in order for its space-time to impose the hyperbolic geometry on its space foliations.

Garth

 

[hellfire]

Whereas what I have said about all the components of the Riemnann tensor not neccessarily being zero for the all the components of the Ricci tensor to be zero is in general correct, in the particular case of the Milne metric the components of the Riemann tensor are zero.

Anf if I was correct in my reasoning, this is due to the fact that space is homogeneous and isotropic. Since we know that the Ricci tensor is zero, then we have e.g. R₀₀ = R⁰₀₀₀ + R¹₀₁₀ + R²₀₂₀ + R³₀₃₀, the first being zero due to the antisymmetry of the Riemann tensor and the others are zero because they must be equal. Correct?

 

[pervect]

In order to be sure I have just calculated all 256 components of the Riemann tensor for the Milne universe metric!

What program did you use to get your result? I used GRTensorII, and the metric I posted, to get the same result - that all the coefficients of the Riemann were zero. I'm assuming you did use a program, it would be very messy not to mention tedious to carry out that calculation by hand.

 

[Chronos]

I still naively assert the CMB energy was never lost, merely diluted by expansion.

 

[Garth]

What program did you use to get your result? I used GRTensorII, and the metric I posted, to get the same result - that all the coefficients of the Riemann were zero. I'm assuming you did use a program, it would be very messy not to mention tedious to carry out that calculation by hand.

The pencil and paper programme! Its not too messy if you do it methodically, I had a few exciting moments with non-zero results, which demanded double checking only to find that in fact they were zero, and that gave me a deep feeling and confidence in the Riemann tensor. Its like walking or cycling rather than riding in a car, even though its slower you get a feel for the countryside.
For my sins I am now working my way through the Riemann for a general Friedmann model to answer hellfire's question, I'll let you know how I get on!

Garth

 

[Garth]

I still naively assert the CMB energy was never lost, merely diluted by expansion.

Chronos in a GR dust universe matter is not lost but its density is diluted.
rho_matter ~ R^-3

however with radiation there is a red shift effect on top of the dilution effect so
rho_radiation ~ R^-4.

Radiation is more than diluted, so where does its energy go?

Garth

 

[Garth]

Anf if I was correct in my reasoning, this is due to the fact that space is homogeneous and isotropic. Since we know that the Ricci tensor is zero, then we have e.g. R₀₀ = R⁰₀₀₀ + R¹₀₁₀ + R²₀₂₀ + R³₀₃₀, the first being zero due to the antisymmetry of the Riemann tensor and the others are zero because they must be equal. Correct?

Well, empty, (and therefore?) homogeneous and isotropic.

In the other Friedmann models space is homogeneous and isotropic, that is the cosmological principle by which the Einstein field equation is solved, but they in contrast do contain matter and therefore they have non-zero Ricci and Riemann tensors.

The Milne model is devoid of a source of gravitation and therefore the components of its Riemann are everywhere zero.

I have now calculated (by hand!) several components of the Riemann tensor for the general R-W metric,
dtau² = dt² - R²(t){dr²/(1-kr²) + r²dtheta² + r²sin²theta.dphi²} (N.B. c = 1)
the result is:
R⁰₀₀₀ = 0 identically.
R¹₀₁₀ = -d²R/dt²/R
R²₀₂₀ = -d²R/dt²/R
R³₀₃₀ = -d²R/dt²/R

R₀₀ = R⁰₀₀₀ + R¹₀₁₀ + R²₀₂₀ + R³₀₃₀ = -3d²R/dt²/R

so these components are not all zero simply because space is homogeneous and isotropic. However if you substitute k = -1 and R = t, the Milne model, then they do reduce down to zero.

The other components of the Ricci tensor work out to be
R₁₁ = {Rd²R/dt² +2(dR/dt)² + 2k}/(1-kr²)
R₂₂ = r²{Rd²R/dt² +2(dR/dt)² + 2k}
R₃₃ = r²sin²theta{Rd²R/dt² +2(dR/dt)² + 2k}

so
R⁰₀ = +3d²R/dt²/R
R¹₁ = d²R/dt²/R +2(dR/dt/R)² + 2k/R²
R²₂ = d²R/dt²/R +2(dR/dt/R)² + 2k/R²
R³₃ = d²R/dt²/R +2(dR/dt/R)² + 2k/R²

so the Curvature scalar is
R = R⁰₀ + R¹₁ + R²₂ + R³₃ = 6d²R/dt²/R + 6(dR/dt/R)² + 6k/R²

and finally the Einstein tensor G_ab = R_ab – 1/2 .g_abR = 8piGT_ab

and the time-time component is
G₀₀ = R₀₀ – 1/2 .g₀₀R = -3d²R/dt²/R + 3d²R/dt²/R + 3(dR/dt/R)² + 3k/R² = 8piGrho

from which we get the GR cosmological density equation

(dR/dt/R)² + k/R² = 8piGrho/3 so my working checks out!

Garth

 

[Beyond-Numbers]

...space stretches in the expanding universe, I am well aware of the difference between the curvature and evolution of space and the curvature of space-time.

Please forgive my intrusion. Like Turbo-1, I am new to this. I have read many books and parused the internet for years researching physics and QM. Garth: I am not singling you out, don't worry about that. I just have a problem with what you said; as it is widely accepted by everyone. Until recently I also thought this. I also thought time was the "4th dimension". I came to the conclusion that time as we know it MAY simply be a... peculiar bi-product of the first 3 dimentions. That is another topic, however, of a paper I wrote last night. The problem I have with what you said is: If space stretches and expands but at the same time is infinite, is contradictory and implies there is some sort of barrier/wall or edge to the KNOWN universe. If there were an edge it would have to be detectable as a heck of a lot more than CMB. No matter where the "edge" would be, it would have to be detectable in some manner from every point in the 3 dimensions as anything other than CMB. Therefore I put it to all of you to consider the Universe not infinite and expanding but rather infinite and NOT expanding. More logical than expanding would be to say it is more like an ocean. It seems to be expaning because that is how we are percieving the current "wave" in our position in the universe. At some point it will slow and change. This could also explain blue/red shifting. 'Course, I could be talking out my... whatever. This makes more sense to me than a contradictory statement. I must stress that I have never taken a single physics or QM course. If what I just said is BS, then I have some more reading to do.

 

[Garth]

Hi Beyond-Numbers welcome to these Forums!
The concepts of Special and General Relativity may seem counter-intuitive at times, because we do not in everyday life experience velocities near the speed of light or gravitation so strong that it would flatten every known physical structure. However elsewhere in the universe such extremes do exist and there our 'common-sense' breaks down. The description of the expanding universe that you find difficult to believe is absolutely standard GR cosmology. Elsewhere on these Forums, and indeed in this thread you will find that I question some of the assumptions, and interpretations of observations, which are made in that standard model, questions that either may expand the field of cosmology or, more probably, just my understanding of it.

That standard model determined by the questions I posted above, and others, describes a universe that is either expanding or contracting, it is either finite but unbounded, like the surface of a sphere, or infinite and unbounded, like an infinite plane or ‘saddle’, depending on the value of the average density of the universe. It is difficult to conceive of a space embedded in a 4-dimensional space-time but the mathematics can take us where our intuition fails. One consequence of the maths is that we may indeed be living in an infinite universe that is everywhere expanding. What into? You may well ask! Intuition may be failing here, or maybe, just maybe, the standard understanding of the mathematical model needs refining.
The particular question relevant to your idea is, “If the universe is expanding, how do we measure it?” What ruler do we use? . In GR the principle of the conservation of energy-momentum, and therefore the rest mass of individual atoms, defines the answer to be that the standard-ruler is made of atoms. So the size of an atom and the frequency of light emitted or absorbed by that atom are defined as the ‘standard ruler’ and ‘standard clock’. In such an interpretation photons mysteriously lose energy when they traverse gravitational fields, hence the subject of this thread, “Where did the energy in the CMB go to?”
However if we use a photon from the CMB as the standard ruler and clock, its wavelength being a measure of length and its frequency (inverted) a measure of time, then the CMB energy is conserved AND the universe is found to be static and eternal. Such a transformation is called a conformal transformation and was first explored by Fred Hoyle and Javant Narlikar in the late 1960’s. I have followed up this line of thinking in my work on ‘http://www.kluweronline.com/oasis.htm/5092775’.

I hope this helps.

Garth

 

[Chronos]

Chronos in a GR dust universe matter is not lost but its density is diluted.
rho_matter ~ R^-3

however with radiation there is a red shift effect on top of the dilution effect so
rho_radiation ~ R^-4.

Radiation is more than diluted, so where does its energy go?

Garth

Reverse engineering. Where does it go? I like to think it cannot simply twinkle out of existence. Because, in that case, the entire universe is eventually doomed to twinkle out of existence. And in that case we are left at the mercy of philosophers explaining how 'nothing' can arise from 'something' - a hideous concept. So permit me to offer an analogy:

I dissolve 1 gram of salt into 1 liter of distilled water. If I add more water to the solution the question becomes - "is salt lost or merely diluted"?

 

[Garth]

I dissolve 1 gram of salt into 1 liter of distilled water. If I add more water to the solution the question becomes - "is salt lost or merely diluted"?

My point was that if rho_radiation ~ R^-3 then the energy of the CMB would be merely diluted, however in fact
rho_radiation ~ R^-4 so it is more than diluted. If you integrate the radiation density over the volume of the universe the total decreases with time. GR is quite happy with this as it doesn't set out to conserve energy in the first place, only energy-momentum, i.e. the 'rest' masses of individual atoms.

The measurement of gravitational/cosmological red shift is a measurement of the energy of the photon compared with the mass-energy of the atom it interacts with. A red shift is observed when the cosmological photon is compared with an equivalent laboratory photon. Each has been emitted/absorbed by the same, identified, atom, say sodium, and so either the energy of the photon has decreased or the mass-energy of the atom has increased.
GR understands the observation by the former interpretation, and so the photon has mysteriously lost energy, over and above the 'dilution' factor. GR is a type of 'tired light' theory! It interprets the red shift as a doppler effect, and that is self consistent, however it is not the only possible interpretation.

That then raises the question of "Where does the energy of a doppler shifted photon go?" The answer lies in the definition of energy levels by different observers in mutual motion.

Note that without relativistic effects being taken into account that in the classical doppler shift there is an interesting conundrum. If we treat light as a stream of particles, photons, energy seems to be lost in classical doppler shift as photon number is conserved while the energy of individual photons has decreased. Treat light as a stream of radiation, however, and the energy is not lost, the red shift being compensated by the extra time taken for the stream to be received!

Garth

 

[Chronos]

Note that without relativistic effects being taken into account that in the classical doppler shift there is an interesting conundrum. If we treat light as a stream of particles, photons, energy seems to be lost in classical doppler shift as photon number is conserved while the energy of individual photons has decreased. Treat light as a stream of radiation, however, and the energy is not lost, the red shift being compensated by the extra time taken for the stream to be received!

Garth

Interestingly enough, that is the same argument I had in mind for conservation of energy in the CMB photons. They were emitted at T ~ 3000k. Space has since stretched a 1000 fold and we now perceive them at an effective T~3k. I realize when you do all the math [gyod, you do tensors by hand?] it looks like energy is lost - but I can go the other way and claim the difference is recovered via gravity waves.

 

[Garth]

[gyod, you do tensors by hand?]

Only for fun!
In GR the density, either of matter or radiation is measured at a particular time-like slice across space-time. The measurement of energy is frame dependent, which is where this particular problem "Where did the CMB energy go?" comes from, and also its resolution. However the question is whether this is a satisfactory resolution. In SCC the Einstein conformal frame treats it as in GR, whereas the Jordan conformal frame finds this explanation unsatisfactory and treats photon energy as conserved. You have a choice.
Garth

 

[Chronos]

Only for fun!
In GR the density, either of matter or radiation is measured at a particular time-like slice across space-time. The measurement of energy is frame dependent, which is where this particular problem "Where did the CMB energy go?" comes from, and also its resolution. However the question is whether this is a satisfactory resolution. In SCC the Einstein conformal frame treats it as in GR, whereas the Jordan conformal frame finds this explanation unsatisfactory and treats photon energy as conserved. You have a choice.
Garth

Propose an experiment... I bet the house GPB will refute your theory. Permit me to add this... I think Garth is on the right track... but for the wrong reasons.

 

[Garth]

GPB is the experiment, and yes it could easily refute SCC, however it might also refute GR - are you not glad that you are living in interesting times!

(Also, of course, SCC has the space interferometer and the deep space Casimir force experiments to follow through should GPB come up trumps!)

BTW "I think Garth is on the right track... but for the wrong reasons."
What are the right reasons?

Garth

 

[hellfire]

Well, empty, (and therefore?) homogeneous and isotropic.

I think this does not follow. I can imagine a space which is empty and inhomogeneous (may be with some gravitational waves propagating through it).

R₀₀ = R⁰₀₀₀ + R¹₀₁₀ + R²₀₂₀ + R³₀₃₀ = -3d²R/dt²/R

so these components are not all zero simply because space is homogeneous and isotropic.

You are right, but note that my claim was that if space is homogeneous and isotropic and the Ricci tensor vanishes, then all components of the Riemann tensor are zero.

 

[hellfire]

Such a transformation is called a conformal transformation and was first explored by Fred Hoyle and Javant Narlikar in the late 1960’s. I have followed up this line of thinking in my work on ‘http://www.kluweronline.com/oasis.htm/5092775’.

Could you please explain why and how a scalar field is needed in such theories? Is it needed in order to locally modify matter to explain redshift and have a physical equivalence with the expanding frame?

 

[Garth]

I think this does not follow. I can imagine a space which is empty and inhomogeneous (may be with some gravitational waves propagating through it).

And what would be the source of this inhomogeneous gravitational radiation?

You are right, but note that my claim was that if space is homogeneous and isotropic and the Ricci tensor vanishes, then all components of the Riemann tensor are zero.

Agreed.

Could you please explain why and how a scalar field is needed in such theories? Is it needed in order to locally modify matter to explain redshift and have a physical equivalence with the expanding frame?

The Brans Dicke scalar field was introduced to fully include Mach's Principle into GR. It does so, even though it keeps inertial masses constant by varying G. Self Creation Cosmology on the other hand varies particle masses (to include gravitational potential energy) and keeps the observed value of G constant. In fact it has two G's, on that is 'felt' by atomic matter and the other 'felt' by relativistic energy such as e-m radiation.
Experiment and observation have constrained the BD scalar field to be so weak most people ignore it, however interest in Dark Energy and the requirements of QG have kept interest in it alive. So far no experiment has yet been carried out that can distinguish between GR and SCC, until now - the GPB experiment, result due in a few months!

Garth

 

[Chronos]

Hi Garth! I think GPB will not support SCC. But you might still be right... will discuss that later. My reasons are very unorthodox... no ZPE involved...

 

[hellfire]

And what would be the source of this inhomogeneous gravitational radiation?

I think it does not need of any source to be part of a solution to the Einstein's equations. But you are right if you say that gravitational waves without any material source might not have any physical meaning.

The Brans Dicke scalar field was introduced to fully include Mach's Principle into GR. It does so, even though it keeps inertial masses constant by varying G. Self Creation Cosmology on the other hand varies particle masses (to include gravitational potential energy) and keeps the observed value of G constant. In fact it has two G's, on that is 'felt' by atomic matter and the other 'felt' by relativistic energy such as e-m radiation.
Experiment and observation have constrained the BD scalar field to be so weak most people ignore it, however interest in Dark Energy and the requirements of QG have kept interest in it alive. So far no experiment has yet been carried out that can distinguish between GR and SCC, until now - the GPB experiment, result due in a few months!

Thank you. One question more: how is the redshift explained in the frame where the universe is observed to be static? I assume the properties of matter must vary somehow. Is the scalar field needed for this?

 

[turbo]

Hi Garth! I think GPB will not support SCC. But you might still be right... will discuss that later. My reasons are very unorthodox... no ZPE involved...

If quantum theory is correct, the potential energy of the ZPE fields is tremendous, and there is no true "vacuum" in our universe, just the ZPE ground state plus or minus any fluctuations and polarization the field might be capable of. Any cosmology that does not include the mass/energy of the virtual particles of the ZPE will fail. I do not believe that we need to search for non-baryonic dark matter - the baryonic (though evanescent) virtual particles of the ZPE are already proven to exist by demonstrations of the Casimir force. If the EM field of the ZPE can be polarized by the presence of mass, we no longer need dark matter.

Andrei Sakharov and others hinted at the relationship between vacuum energy and gravity/inertia years ago. Others have studied the relation more recently, but a limitation of the papers that I have found is that the authors fail to treat the ZPE field as a real field, capable of polarization and density fluxes. This will have to be addressed before quantum theory and GR can be reconciled.

I have suggested before that we need to measure the speed of light between the plates of a Casimir device, to verify that the speed of light in that restricted ZPE field is higher than that in an unrestricted vacuum. Somebody currently involved in ZPE research has informed me that this expected result is called the Scharnhorst Effect, and that our instrumentation is not yet sensitive enough to detect that effect experimentally. It is nice to know that somebody else is on this track, though.