Where did the energy in the CMB go to?

[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.