Conservation of energy is related to the time translation invariance. Unless one has a prior knowledge of the structure of space-time one is unsure of the validity of time translational invariance of the action. In general for a given arbitrary energy-momentum tensor, one has to solve for the unknown metric. For a special case of flat space-time, energy conservation will hold. Perhaps there are other special cases where time translation invariance is ensured, and consequesntly energy conservation.

Energy scale and length scale are related by the relation L=  ħ c / E; approximately one can write ħ c= 200 MeV fermi. In particle physics we use units ħ =c=1. Then one fermi is 200 MeV inverse. A decrease in energy scale is cooling, which is inversely related with length scale. That means in early universe larger wavelength of CMB radiation  is related with a fall in temperature.

Conservation of energy is related to the time translation invariance. Unless one has a prior knowledge of the structure of space-time one is unsure of the validity of time translational invariance of the action. In general for a given arbitrary energy-momentum tensor, one has to solve for the unknown metric. For a special case of flat space-time, energy conservation will hold. Perhaps there are other special cases where time translation invariance is ensured, and consequesntly energy conservation.

If we cannot talk about time translation invariance then we cannot talk about energy conservation.  Perhaps my cosmology professor was correct when he said, "On large length scales, energy is not a conserved quantity."  He was referring to dark energy but this could be another example. 

Dear Jeremy,

the energy of photons have an actual variation in the case of the doppler effect where there is an actual energy momentum variation of the photons.

In the case of the gravitational redshift there is not an actual variation of the energy of the photons if referred to the emitter.

SQ: In the case of the gravitational redshift there is not an actual variation of the energy of the photons if referred to the emitter.

That could work over short ranges, where the effect is similar to Doppler, but how do you apply that for photons that originated from beyond the Hubble Length, i.e. how do you calculate the energy when the rate of recession is greater than the speed of light?

George Dishman,

I don't work in cosmology, and I appologize if my question is naive: if the recession velocity of the source exceeds the speed of light, how do you at all see light coming from that source?

Please see, I heard of such ideas that extremely far cellestial objects may recede faster-than-light, but it seems to me that these are theoretical speculations close to the realm of science fiction. Of course, as I am no specialist in the domain, I may be wrong.

Some people here posed an interesting problem - so it seems to me: is the red displacement of Dopplerian nature? Can't it originate from the fact that the early Universe was different from the present one? A. Peres and D. Terno showed that in previous epoques of the Universe, the speed of light might have been different from today. Could this fact have something to do with the red displacement ? 

SDW: I don't work in cosmology

Neither do I Sofia, I'm just an interested amateur but I've done the cosmology course offered by Coursera (it's CalTech's first year course) so I have some background.

The speed of light is essentially a conversion factor for the units of distance and time so it's hard to see how it could change. Tests of the fine structure constant which is indirectly related show it hasn't changed by more than 7 parts per million in the last 10 billion years so I highly doubt that possibility. Until someone comes up with some serious evidence, I think that possibility will not be considered seriously.

The Hubble Length is defined as the distance where objects were receding at the speed of light and it corresponds to a redshift around 1.5. We can see galaxies out to a redshift of 11.09, galaxy GN-z11 which recently made the headlines. The space between us and it was expanding at 4.32 light years per year at the time the light we see was emitted, that has fallen to 'only' 2.24 light years per year now.

To understand how we can see that galaxy, you can search for "ant on a rubber rope" or look at the linked Wikipedia page.

https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope

https://www.spacetelescope.org/news/heic1604/

Dear George,

The story with the ant is an interesting mathematical exercise in itself. I looked in Wikipedia, but I have the impression that the calculus there is not entirely correct. I'll check it more deeply, and I'll return to you.

But, I didn't understand what you want to say with this example. Would you be so kind and tell me?

With thanks in advance,

Sofia

Hi Sofia,

There has been some confusion so let me backtrack a little.

Stefano said "In the case of the gravitational redshift there is not an actual variation of the energy of the photons if referred to the emitter."

I think his idea is to show that the energy remains the same in the frame of the source, it is only reduced when measured in the frame of the receiver. Something similar happens with Doppler shift and the aim would be to treat cosmological redshift in the same way. I've thought about that myself but hit the problem that speeds can be greater than the speed of light in cosmological expansion and the relativistic formula for kinetic energy is infinite at that speed. Hence my question to him, I wonder how he got round that limit.

You said "Some people here posed an interesting problem - so it seems to me: is the red displacement of Dopplerian nature? Can't it originate from the fact that the early Universe was different from the present one?"

The usual explanation is that the universe has expanded and the effect on the frequency of the photons is to reduce their energy and increase their wavelength by the same factor, i.e. they lose energy because the universe has expanded or as you say "the early Universe was different from the present one".

Modelling cosmological redshift using Doppler would be an interesting alternative but I'd like to know how they solve the problem of mapping the speed of expansion to something below that of light. The obvious way is to take the reduced energy and calculate the inferred speed but how does that relate to other distance measures?

George,

Stefano said "In the case of the gravitational redshift there is not an actual variation of the energy of the photons if referred to the emitter."

"Something similar happens with Doppler shift and the aim would be to treat cosmological redshift in the same way."

it is not similar at all. The Doppler shift is an actual variation of the electromagnetic energy of the photon in the RF of the source, it can be demonstrated as i did in this paper of mine.

Research On the Doppler effect of light, consequence of a quantum behaviour

SQ: In the case of the gravitational redshift there is not an actual variation of the energy of the photons if referred to the emitter."

How are you defining the frame of the emitter at the receiver location?

SQ: The Doppler shift is an actual variation of the electromagnetic energy of the photon in the RF of the source, it can be demonstrated as i did in this paper of mine.

I think you may have confused the issue by considering reflected light. If the light leaves the source at one frequency and is then measured some distance away but in the same reference frame, it should have the same frequency. Why would it change in flight?

Dear George and Stefano,

You are both very kind and competent. I am not at all competent in this domain, so, I am asking questions. Now, let me go slowly for being able to to understand what you say.

George, you say

"The usual explanation is that the universe has expanded and the effect on the frequency of the photons is to reduce their energy and increase their wavelength by the same factor, i.e. they lose energy because the universe has expanded . . ."

Oooo! That seems to me to have implications. On one hand Doplerian redshift, but on the other hand an opposite effect: in the early Universe (less expanded) the atom lines were displaced to the BLUE. So, the wavelength from the far galaxies should be determined by the competition between these two effects.

So, I understand, but probably I do some mistake. Would you correct me?

With many thanks,

Sofia 

SDW: in the early Universe (less expanded) the atom lines were displaced to the BLUE ... but probably I do some mistake.

Well that is a mistake. I don't know where you found that but it is wrong, you have been misled. The farther back in time we look, the greater the redshift.

SDW: On one hand Doplerian redshift, but on the other hand an opposite effect ..

There are two effects which have a lot in common, Doppler shift which can be red or blue and cosmological redshift which is always red. To an extent, this is an artificial split, the change of wavelength is due to the rate at which the distance between us and the source is varying and that rate can be thought of as having two components.

If you think of a group of galaxies in an old cluster, they are moving on a variety of orbits, mostly elliptical, but I find a good way to visualise it is like a swarm of bees flying round a nest in a tree. At any moment, some are moving towards you and some away and if you had good hearing, you could tell which direction each was moving because of the Doppler shift of the hum of their wings.

Now imagine you are walking away from the nest. The total Doppler for each bee depends both on your speed walking away and the direction of their flight.

Looking at distant galaxies works like that, we see the total shift due to both Hubble expansion and their speed within their host cluster. Of course there is no "nest" in that case, they just orbit around the centre of their combined mass.

The difference between the two components (as I said before) is that the rate of change of distance due to expansion can greatly exceed one light year per year, it isn't a motion through space which is limited by relativity but an expansion of gap between, while the motion of galaxies in a cluster is only around 1 per cent of the speed of light or less.

An easy figure to remember is that the Hubble expansion of distances is a rate of 1% in 140 million years, never think of it as a speed and you'll avoid a lot of confusion.

p.s. An example of blue shift is our nearest large neighbour, the Andromeda Galaxy which is moving towards us and will collide with the Milky Way in a few billion years.

George,

I am very impressed by what you said.

Among other things, I understand that if we don't succeed to beat the light velocity, more exactly to trick it, all the knowledge accumulated by the humankind is doomed to disappear in a few billions of years because of our neighbor, Andromeda. That's very, very sad.

Of course, before that, the humankind should be able to find another solar system, because our Sun is not a young star, and it gets older.

You also say that it's not that the far galaxies run away, but the space dilatates. The phenomenon seen by us is the same, isn't it? Then, how can one be sure which of the two interpretations of this phenomenon is correct? In my non-professional understanding, saying that the space dilatates means that you think that there where we see the most distant galaxies, the Universe ends, and there is nothing beyond. More exactly, a "beyond" does not exist. But, how can one check if there is a beyond or not?

With many thanks for your interesting explanations,

Sofia

 According to Noether's theorem, the homogeneity of space implies that  momentum is conserved.  For photons, this means that energy is also conserved.  The only way this can be squared with the observed cosmological red shift requires that the instruments used to measure  energy have evolved, gradually increased their own characteristic energy levels. Thus diffraction gratings, which are used to measure wavelength, have been continually shrinking.  These changes result from a systematic gradual increase in the rest mass of all objects.   I'm sure This will strike you as utterly insane, but it's the only way that Noether's theorem can be satisfied.  This problem and much more is presented in the attached paper presently being considered for publication in PhyRevD15. 

Please forgive me for stepping late into this discussion. There are two issues presented, I believe. One is that light passing through a gravitational field becomes slightly red shifted and the question is: what happens to the energy? The second is that as the universe cools, the cosmic temperature, which we now measure as the cosmic microwave background temperature, becomes less; therefore, what happened to the energy?

Regarding the first question: the path of light travelling through a gravitational field deviates from what it would be if the field did not exist. If you are able, and it is a rather extensive calculation, (although it can be done), the difference in momentum, before and after a photon has passed into and out of a gravitational well is incredibly slight, but it does exist. An example would be to consider that a photon passing through the gravitational field of the Sun before reaching us has travelled a slightly curved path (curvature is a complex term so bear with me here please) and is slightly red shifted. The energy goes into changing in the kinetic energy of the Sun. In other works, the photon moves the Sun very slightly. The gravitational field of the Sun has done work on altering the momentum of the photon in order to get it to change direction and as a result, the photon has shifted the Sun. This is a simplified view, but it works. NASA uses elastic collision calculations to slingshot probes into space by "bouncing" them off the gravitational field of Jupiter or other planet. Another way to "see" it is to consider that the photon has an extremely small momentum even though it has no "mass". You can do the calculation by solving the field equations, including the Faraday tensors along with the material stress-energy tensor, conserve overall momentum and energy; or you can do the calculation as a collision and get the same answer. By the way, as an added point, the light also becomes slightly polarized. I'll leave the proof of that as an exercise.

As to the second part of your question: the mathematics of a cooling and expanding universe uses the calculations of a free expansion of a gas into a vacuum. A hot gas, having a high blackbody temperature, expands and cools having a lower blackbody temperature. If you calculated all of the energy in the hot gas having a small volume and all the energy in the cooled gas having a large volume, they end up being the same. There is no loss of energy.

I hope that helps. 

Thanks Bruce. On the second point, what you say raises a question, perhaps you could clarify. The number density of the photons of the CMB falls as (1+z)3 as the volume increases obviously, so in any comoving volume the total number remains constant. However, the energy per photon falls due to the redshift by an additional factor of (1+z). That gives the fourth reduction in intensity necessary to match the Stefan-Boltzmann Law so that the spectrum remains a black body, but how can the total energy in the volume then remain constant?

JH: According to Noether's theorem, the homogeneity of space implies that momentum is conserved. For photons, this means that energy is also conserved.

Noether's Theorem relates a conservation to a symmetry, in the case of energy that is time translation symmetry. However, in an expanding universe, time translation does not leave it unchanged hence you can't apply Noether's Theorem directly.

JD: It is the spatial homogeneity that requires momentum be conserved.  

SDW: ... all the knowledge accumulated by the humankind is doomed to disappear in a few billions of years because of our neighbor, Andromeda. That's very, very sad.

As the HitchHiker's Guide to the Universe said, "Don't Panic" ;-)

Although the galaxies will collide and merge, stars are very small in comparison so it is unlikely that there will be many actual impacts, probably none. Some stars will be thrown out by "gravitational slingshot" effects but many new stars will also start forming due to the impact of the gas the galaxies hold.

SDW: Of course, before that, the humankind should be able to find another solar system, because our Sun is not a young star, and it gets older.

Yes, we'll need to leave around the same time, but Andromeda will give us twice as many to choose from ;-)

SDW: You also say that it's not that the far galaxies run away, but the space dilatates. The phenomenon seen by us is the same, isn't it?

Ye, we can measure redshift but it contains both effects.

SDW: Then, how can one be sure which of the two interpretations of this phenomenon is correct?

It's not a choice of one or the other, we measure the combination of both. For most purposes, that's all that's needed for any single galaxy. If we want to break it down, we can find the mean motion of a cluster just by taking the average (weighted by mass) and that relates to the Hubble expansion while the motion of the individual galaxies relative to the mean is their local speed within the cluster.

SDW: In my non-professional understanding, saying that the space dilatates means that you think that there where we see the most distant galaxies, the Universe ends, and there is nothing beyond.

No, that's not part of the model at all. We say space expands but that includes the region we can see but also whatever lies beyond, and that is assumed to be more of the same, more galaxies like those we can see. The basis of modern cosmology is called the Cosmological Principle and is always subject to ongoing testing. See the link below.

The limit of what we can see is only a tiny fraction of the whole, we are limited because light has only had 13.8 billion years to reach us.

https://en.wikipedia.org/wiki/Cosmological_principle

Dear George,

As an old-fashioned person, I believe that the most precious thing the humankind possesses, besides its very existence, is the knowledge. So, thanks for telling me that there is hope.

By the way, please be kind and tell me, what is the star closest to us, and likely to have developped around itself a solar system like ours? At which distance from us is there a chance to have appeared intelligent beings?

Now, I read, as you recommended (and thank you), the page in Wikipedia. It's very, very interesting.

But there is somethings which puzzles me: in our Universe do we see black hole exploding? And if "yes", does the space-time around them expand in addition to the general expansion of the space-time of the Universe? As to the opposite phenomenon, the formatio of a black hole contracts the space-time around itself?

With thanks and best regards,

Sofia (P.S. I ckecked the problem with the ant moving on an extending rubber rod. It is hard to say whether the ant would reach the end of the rod, because it takes an infinite time to reach that end.)

George: The energy density decreases, however, the total energy remains constant. I think we both agree on that. According to Wiki: "A very important difference between a gas of massive particles and a photon gas with a black body distribution is that the number of photons in the system is not conserved."

Perhaps that may provide a key to understanding it. Although Wiki is not any authority, it may lead to being able to work it out. The crux of that presentation is that photons interact with matter and the number of photons following the interaction is different than the initial number. 

Nevertheless, it is an interesting question if there is no matter available.

George,

"SQ: In the case of the gravitational redshift there is not an actual variation of the energy of the photons if referred to the emitter." How are you defining the frame of the emitter at the receiver location?"

It is undeniable  that same atoms cannot exchange their radiation across gravitational potentials (the emitted radiation is not absorbed by a twin atom), Pound and Rebka, Vessot and Levine.

In the case of the Gravitational redshift  there are two facts that show that the EM energy is preserved (and not exchanged during flight) across gravitational fields.

a) photon is massless, it cannot lose energy  across gravitational potentials, so the energy at the emitter has to be the same as the energy at the receiver. The redshift  is only how the receiver atom sees radiation differently from the same radiation received at the same gravitational potential.

b) the radiation power is preserved across gravitational potentials: watts emitted = watts received.

Same radiation is acquired redshifted at higher gravitational  potentials fabsorbed=femitted (1-gh/c2), but since clock rates have also a variation, the higher, the faster, Tabsorption=Temission (1-gh/c2)  the number of photons per unit time emitted by the same oscillator at different gravitational potentials will be different.

Hence Wemitted = h femitted/Temission = h fabsorbed/Tabsorption =Wabsorbed

since the energy per unit time is preserved there cannot be any energy stored in the gravitational field due to photons loosing their energy.

George,

"I think you may have confused the issue by considering reflected light. If the light leaves the source at one frequency and is then measured some distance away but in the same reference frame, it should have the same frequency. 

If you read well you see that I did not get confused.

Consider the DOPPLER RADAR:

 there is an "actual" energy difference between the photon which departs with a certain frequency and the same one which bounces back, returning with a different frequency (in a different instant obviously).

Since both the paths are identical in the hypothesys of inertiality, the variation of the energy of the photon  along one path has to be half of the one registered at the RF of the emitter (where the photon arrived going back and forth). In such case the variation of the energy of the photon at the absorber, in the RF of the emitter is that half.

the variation of the energy is given by the difference of speed between the moving objects, if they are departing the difference is negative, if they are approaching the difference is positive.

Why would it change in flight?"

Radiation does change at all during the flight, this is a must both in Doppler and gravitational redshift.

SQ: Consider the DOPPLER RADAR:

SQ: there is an "actual" energy difference between the photon which departs with a certain frequency and the same one which bounces back, returning with a different frequency (in a different instant obviously).

Yes, certainly.

SQ: Since both the paths are identical in the hypothesys of inertiality, the variation of the energy of the photon  along one path has to be half of the one registered at the RF of the emitter

The photon which reaches the target has the same frequency and energy as measured in the frame of the emitter as it had at the start. When it reflects off the target, its momentum is reversed hence the momentum of the target must increase (to conserve the total). That imparts a delta-v to the target which acquires extra kinetic energy. That's how a solar sail gets its thrust. That increased energy came from the photon so the reflected photon has a lower frequency than the incident photon. After reflection, the photon travels back to the receiver, again without loss on the journey.

That is quite different from the case of gravitational frequency shifts though there is an interesting link between them. I think Lev Okum wrote on that, but that's another story ;-)

The photon which reaches the target has the same frequency and energy as measured in the frame of the emitter as it had at the start.

Before reaching the target yes, then landing on the target it acquires the energy of the target. You can see it easily if you revisit the RDE with the energy and momentum conservation.

After reflection, the photon travels back to the receiver, again without loss on the journey.

During the journey yes. But it interacted with the reflector and back with original the emitter.

 If I measure the bounced photon from the same RF where it has been emitted and I find a frequency difference, that corresponds directly to an energy difference.

You are confusing the application of the Lorentz Transformations. it is not the inverse transformation which is applied in this case, the time is not reversed.

“…photon is massless, it cannot lose energy  across gravitational potentials…”

- photon has both – inertial and gravitational masses (though hasn’t so called “rest mass” because of moves in 3D space only) and  it loses energy [at moving] across gravitational potentials…

Cheers

SQ: If I measure the bounced photon from the same RF where it has been emitted and I find a frequency difference, that corresponds directly to an energy difference.

I think you misread my post, that's exactly what I said. The frequency change and energy loss occur on reflection, not while the photon is in transit. We seem to be fully in agreement on that.

If you consider the situation of the photon not being reflected but just measured by a receiver moving away from the source, the energy measured by the moving observer is reduced whereas if you measure it at the same location but at rest relative to the emitter, there is no change. Contrast that with what you said that started this discussion:

SQ: The Doppler shift is an actual variation of the electromagnetic energy of the photon in the RF of the source,

The energy is only different in the moving frame, not the source frame.

A photon moving upward in a gravitational field does not lose energy:  it will be received red shifted because it was red shifted on emission.  The red shift is caused by a phenomenon not yet recognized by the physics establishment: -  gravitational rest mass reduction. Here is a proof of the this important effect.

A direct examination of the gravitational red shift is sufficient to identify its cause.  The frequency spectrum emitted by every species of atom is determined by a formula involving species-specific quantum numbers, but in every case the leading factor in the formula is the  Rydberg frequency: e4i,me/h3 .  This formula holds for every location in the field, and the factor by which frequencies are reduced is the same for every species of atom. Thus the gravitational field somehow causes a decrease in the Rydberg frequency.  The imagined ‘time dilation effect’ cannot be held responsible, since none of the factors in PR is sensitive to the “flow of time.”  The obvious answer is a simple decrease in the electron rest mass, me , rather than some unimaginable change in the factor e4/h3.  The Bohr radius, a0=h2/e2me , increases with PR, implying the elongation of measuring rods, which in turn  insures the invariance of the measured speed of light. Happily, the idea that the flow of time itself is reduced by gravity may be dropped

SQ: a) photon is massless, it cannot lose energy across gravitational potentials, so the energy at the emitter has to be the same as the energy at the receiver. The redshift is only how the receiver atom sees radiation differently from the same radiation received at the same gravitational potential.

You are right that it is massless and that the frequency changes but since its energy is given by E=hν, the energy also changes.

SS: - photon has both – inertial and gravitational masses (though hasn’t so called “rest mass” because of moves in 3D space only) and it loses energy [at moving] across gravitational potentials…

The simplest way to understand mass in relativity is through the energy-momentum relation which is valid for any particle:

E2 = (pc)2 + (mc2)2

Turn that round to get

(mc2)2 = E2 - (pc)2

For a photon E=pc hence the (invariant) mass is zero. That is what scientists generally talk about, the concepts of "relativistic mass" and "rest mass" are best treated as archaic. As a result, as the frequency changes, both the energy and momentum reduce in proportion and since they are always equal, the mass is always zero.

https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation

SDW: By the way, please be kind and tell me, what is the star closest to us, and likely to have developped around itself a solar system like ours?

The Kepler mission and various others are looking for such systems, the indication is that virtually all solitary main sequence stars and some binary systems have planets. However, in most cases they are "the wrong way round". The large gas giants are closest to the star, they are called "hot Jupiters". Look up "exoplanet" for lots more on that topic.

SDW: At which distance from us is there a chance to have appeared intelligent beings?

We have no idea. There are around 300 billion stars in our galaxy so perhaps 100 billion have planetary systems. if we are lucky, maybe one in 10,000 would have an Earth-like planet (temperature and mass). Just looking at the history of Earth, I might think 2/3 of those could have single-celled life and the rest maybe multi-celled (if they are old enough). However, the dinosaurs were around for millions of years and there were a great many species but none ever built a radio telescope. We have absolutely no idea why our species developed the intelligence that lets us build technology so it's impossible to predict the probability for other planets. It might be that there are hundreds of civilisations in the average large galaxy, or it might be one civilisation per hundred galaxies. Until we go out and "meet the neighbours", we won't know.

SDW:But there is somethings which puzzles me: in our Universe do we see black hole exploding?

No. It is possible that the might slowly "evaporate" by glowing like a hot coal and therefore giving off energy, it would appear to arise in a region some way outside the hole, but they cannot explode.

SDW: And if "yes", does the space-time around them expand in addition to the general expansion of the space-time of the Universe? As to the opposite phenomenon, the formatio of a black hole contracts the space-time around itself?

No, the best way to think of a black hole, though it is a bit misleading, is to think of space "flowing" into it and moving faster as it falls. The boundary of the hole, the event horizon, is where the speed exceeds that of light. Anything trying to come out is like a salmon trying to go up a river that is flowing faster than it can swim.

SDW: Sofia (P.S. I ckecked the problem with the ant moving on an extending rubber rod. It is hard to say whether the ant would reach the end of the rod, because it takes an infinite time to reach that end.)

Check again, the time can be finite depending on the rate of expansion. In cosmology, that rate is always reducing which helps too.

https://en.wikipedia.org/wiki/Exoplanet

Here is an expanded version of my last.

 A photon moving upward in a gravitational field does not lose energy: it will be received red shifted because it was red shifted on emission. The red shift is caused by a phenomenon not yet recognized by the physics establishment: - gravitational rest mass reduction. Here is a proof of this important effect.

A direct examination of the gravitational red shift is sufficient to identify its cause. The frequency spectrum emitted by every species of atom is determined by a formula involving species-specific quantum numbers, but in every case the leading factor in the formula is the Rydberg frequency: R =e4me// h3 This formula holds for every location in the field, and the factor by which frequencies are reduced is the same for every species of atom. Thus the gravitational field somehow causes a decrease in the Rydberg frequency. The imagined ‘time dilation effect’ cannot be held responsible, since none of the factors in R is sensitive to the ‘flow of time.” The obvious answer is a simple decrease in the electron rest mass, me, rather than some unimaginable change in the factor e4/ h3..  Frequency reduction implies clock slowing, which Einstein feared would cause the under-valuation of the speed of light.  But the Bohr radius ,a0 = h2 / e2me , increases with the decrease in me, implying the elongation of measuring rods, so that the measure of distance is reduced by the same factor that time is reduced, insuring the invariance of the measured speed of light.  Happily, the idea that the flow of time itself is reduced by gravity may be dropped

John Heighway's interpretation on cosmological redshift has certainly valid reasons that don't have been considered adequately in mainstream physics. Myself did many researches on this issue and I formulated an atomic theory of the cosmological redshift in which this redshift can be explained through a different value of resting mass in the Rydberg constant. In order to allow a widening let me attach two links:

https://www.researchgate.net/publication/211874241_Basic_Principles_of_Deterministic_Quantum_Physics

https://www.researchgate.net/publication/216068842_Not_linear_element_cosmological_redshift_and_deflection_of_light_in_the_gravitational_field

Article Basic Principles of Deterministic Quantum Physics

Article Not linear element, cosmological redshift and deflection of ...

A photon is a quantum of electro-magnetic energy - it does not lose energy, it IS

energy.

A wave, or more correctly, a ray of EM radiation carries the action of a source of

stimulation of the vacuum medium as energy and delivers  quanta of action to

the recipient. Quanta of energy are delivered during the period of the ray,

(1/freq). Each and every  photon delivers 1 Planck quantum of ACTION to the

recipient electron or other EM charged particle during the period of the ray. If the

ray's wavelength and freq have been red or blue shifted then the period is

different to that at the source.  Planck and de Broglie had a better sense of waves

than Maxwell or Einstein.

The vacuum medium cannot be 'empty' - it must be an active vacuum  - the

quantum vacuum or active vacuum - to carry transient energy.  At greater than

the Compton wavelength of the electron, a ray can carry many electrons, limited

by the cube of the half-wavelength.  It would be more helpful to regard variable

'c' than the time dilation and the fixed 'c' of GRT.

Regarding Rydberg, please see our formula for the measured value of alpha, the

fine structure constant of space, correcting Arnold Sommerfeld's original

derivation in 1916 with second and third order corrections. Applying a Lorentz-

FitzGerald contraction (aka Einstein-Lorentz transformation)  to the H atom

obtained the same peculiar velocity of the Solar system that George Smoot

determined experimentally in 1978 and eventually earned him a Nobel Prize.

(Read his Nobel Lecture of 2006).

In confirmation of this formula for alpha please note that during the period of

the 10.2eV UV-ray emitted when the 2s electron of the H-atom (-3.4eV) collapses

to the 1s ground state (-13.6eV, Lyman alpha decay ) the proton simultaneously

moves across the difference of the two radii at that same peculiar velocity,

391km/s.

 The significance of this fact has not yet been acknowledged by modern physics.  

Speed of c/760  would not normally be regarded as a significant 'relativistic'

velocity.

The epola model of the vacuum by Simhony (1973) recognised that increasing

speed above that on Earth by 600km/s will add (or require) 1eV to the binding

every electron of an atom. (p.89, The Electron-Positron Lattice Space (1990).

The energy of any object in a spacetime that's curved requires particular care to define properly. The reason is that time translation invariance, the symmetry that expresses the fact that energy is conserved, isn't a global symmetry, but a local symmetry. The conclusion is that the question, as stated, doesn't make sense-it, simply, expresses a  misunderstanding, due to trying to transfer intuition valid in flat spacetime to curved spacetime. There isn't any way to define ``energy loss'', in an invariant way,  if certain conditions aren't met. In general it will depend on the details of how energy is being measured.

Similarly, the statement that a photon is massless only makes sense when Lorentz invariance is a global symmetry.

There isn't any way to define ``energy loss'', in an invariant way,  if certain conditions aren't met. In general it will depend on the details of how energy is being measured.

Then would not be a big problem to admit also that bodies free rise in a gravitational field, but seems they don't. The energy loss is  in the RF of the emitter. Gravitation in a steady state is conservative regardless of what GR can bring forth, unless somebody can set up an experiment from which can be shown that a  body rises  in a gravitational field.

Dear Stefano ~

A photon does not "lose (or gain) energy". That's not the correct to think about frequency shifts! According to Relativity (SR or GR) energy (and frequency) are not scalars, they are observer-dependent. They are components of four-vectors. The emitter of a photon and the receiver are not in the same (local) inertial frame and the emitted and received 4-vectors are related by a Lorentz transformation. This fully accounts for frequency (and energy) shifts, whether we are talking about the gravitational red shift or a Doppler shift.

 I seem to remember we've had this conversation before, Stefano. So I'm surprised to see it's still regarded by many people as a puzzle, and surprised to see so many answers here making a complicated controversy out of something so simple

 (For many weeks I've been away from RG because, mysteriously, "notifications" about the threads I used to follow ceased...)

Eric,

first of all welcome back, it is always a pleasure to interact with you.

For photons you are right and as you know I always sustained such point of view, not in agreement with the 1911 paper of Einstein. Not in general though, otherwise we would contradict the main tenets of Physics, and that was the subject I was counterreacting to.

https://www.researchgate.net/post/The_gravitational_redshift_is_a_phenomenon_based_on_gravitational_time_dilation_dont_we_want_to_exclude_definitely_any_loss_of_energy_of_photons/56

The energy lost by the photon goes into the energy of the vacuum. There where vacuum energy becomes large, new particles are born. Micro-particles decay over their life-time. Thus, there's a steady balance of energy structured matter (particles) and unstructured matter (physical vacuum) in the Universe.

--

Энергия, потерянная фотоном, переходит в энергию вакуума. Там, где энергия вакуума становится велика, происходит рождение новых микрочастиц. Микрочастицы со временем распадаются. Таким образом, сушествует устойчивое равновесие энергии структурированной материи (частицы) и неструктурированной (физический вакуум) во Вселенной.

In order to answer to this thread:

What happens to the energy lost by photons as they become red-shifted by gravity or cosmic expansion?

Static Gravitation does not alter the energy content of photons referred to the emitter.

The effects of a variable gravitation on photons have never been measured in one experiment, so it is difficult to talk about consequences. 

The initial Hagedorn temperature of the thermal equilibrium generated very powerful photons according to the theory of the Big Bang. That these photons were altered during their path in free space, is quite difficult to accept in order to explain that they cooled down. We find the cosmic background radiation at that low frequency now, this though should due mostly to "relativistic" reasons.

``The effects of a variable gravitation on photons have never been measured in one experiment, so it is difficult to talk about consequences.'' This statement is incorrect: that's the content of the experiment by Pound and Rebka. Cf. also http://relativity.livingreviews.org/Articles/lrr-2006-3/download/lrr-2006-3BW.pdf for more details. 

It is, indeed, clear that the gravitational redshift can't be explained by a Lorentz transformation. The reason is that a Lorentz transformation relates two inertial reference frames, whereas the gravitational redshift pertains to two reference frames that aren't both inertial-that's what the term ``gravitational'' means.  The gravitational redshift can be consistently described within general relativity. 

``The effects of a variable gravitation on photons have never been measured in one experiment, so it is difficult to talk about consequences.'' This statement is incorrect: that's the content of the experiment by Pound and Rebka. Cf. also http://relativity.livingreviews.org/Articles/lrr-2006-3/download/lrr-2006-3BW.pdf for more details. 

It is obvious that it was not space variable but time variable gravitation which I meant.

 The difference is whether the metric admits a time-like Killing vector, or not. How to describe this situation is known. This is how the expansion and the accelerated expansion of the Universe are described. 

In fact the subject of the gravitational redshift is nothing more and nothing less than the illustration of the so-called twin paradox in special relativity. The photons are the twins and the spacetime curvature implies that the paths taken can't be equivalent.

So it suffices to do the calculation for the metric one is interested in. There's no need to speculate about it.

It's not a question of nomenclature, but of meaning: if the spacetime metric has certain properties, then two photons propagating from points A and B and detected at point C, will have frequencies, measured at C, in a relation that can be calculated and measured. Conversely, by measuring this relation, conclusions about the properties of spacetime can be reached. What matters is that the points are in spacetime, not space. The reason is that, in curved spacetime, physical properties depend on the path taken-which is what ``spacetime curvature'' means. Indeed, the metric of our Universe, seems to be spatially flat-but the spacetime is, nevertheless, curved. It is described by the so-called Friedmann-Robertson-Walker-Lemaître metric, with flat spatial slices. It isn't the Minkowski metric.

Dear friends,

As one not specialized in cosmology, I have a question. I saw in the literature on the Big-bang, that immediately after the explosion the Universe expanded extremely much in an extremely short time. I don't remember numerical values.

Now, doesn't this model seem ad hoc?

From what I learnt from George (and thanks!) about the "cosmological principle", there is a certain uniformity of the evolution of the Universe in space and time, on large scale. Then why should have been such a non-uniformity in the beginning?

Saying otherwise, if we admit a dilatating space-time metric, why do we need a Big-Bang? If we reverse in time this dilatation, what we get? How would have looked like the early Universe, before the beginning of the thermo-nuclear reactions that generate the elements?

Yes-that's called ``inflation'' (this is just a name, of course) and, of course, it is ad hoc-while its consequences can be tested with known physics, the details depend on the theory of quantum gravity, which isn't known at the moment.  

There isn't any issue of non-uniformity ``at the beginning''-the sentence doesn't mean anything. While general relativity implies the generic existence of singularities, of which the Big Bang singularity is an example, (cf. the paper by Hawking and Penrose, http://rspa.royalsocietypublishing.org/content/314/1519/529 ), the point is that, assuming an inflationary period, implies many testable consequences, that have been confirmed by observation-most recently by the Planck satellite, e.g. https://arxiv.org/abs/1502.02114

The resolution of gravitational  singularities depends on a theory of quantum gravity, as does the ``microscopic'' mechanism, whose ``field-theoretic manifestation'' would be the action of the inflaton field, that describes inflation.  

Of course, the Friedmann-Robertson-Walker-Lemaître metric was studied in the 1920s and 1930s, long before inflation was proposed and describes post-inflationary cosmology. It simply depends on the value of the Hubble parameter and the value of the cosmological constant.

Re. Singularities:

In my paper The Fundamental Nature of Gravity (available on Research Gate) I show that the singularity associated with a black hole, and, In cosmology, the 'Big Bang' singularity are in each case illusions associated with a poor choice of metrics..  

To answer the original question "What happens to the energy lost by photons as they become red-shifted by gravity or cosmic expansion?", it should first be noted that the answer is slightly different in the cases "gravity" and "cosmic expansion" (although strictly speaking the first case encompasses the second - but usually the statement refers to a particular case, one where we have a time-like Killing field and hence, energy conservation can be formulated globally).

Restricting to the case of a stationary gravitational situation, the "gravity" part has two answers, depending on the frame of reference chosen. If we take as frame of reference the global frame, in which the metric is described as stationary, then the photon does not change frequency (measured in terms of the global time) and hence its energy is constant. Its frequency is measured to be different by the emitter and the receiver, because those two observers have clocks running at different rates, due to time dilation. If the emitter's clock is running more slowly, he will perceive the photon at a higher frequency, so the receiver will see a photon redshifted w.r.t. the emission frequency. If the receiver is "below" the emitter in the gravitational field, the emitter's clock will be running faster, so the receiver will perceive the photon to be blueshifted. But in this picture, there is no energy loss. The energy difference is due to energy being measured in different local frames.

If energy conservation is to be described in a frame that is composed of the local frames of observers stationary in the metric, the first problem is that in such a frame time, being the local proper time of observers, is not homogeneous. Energy conservation is a consequence of the homogeneity of time, or in relativity parlance, the existence of a time-like Killing field (which is translational invariance w.r.t. time). Of course, we can reformulate energy conservation also in our composite frame patched up from local frames, because we were able to formulate it in the global frame. All we have to do is to introduce a gravitational potential leading to potential energy (which is absent in the global frame). Then the picture becomes that the photon gains potential energy when rising in a gravitational field and loses kinetic energy, which is the energy given by h f , where f is its frequency. So again the photon does not lose energy, but since we can measure its kinetic energy only, inferrable from its frequency, it looks as if it loses energy. Or else we might say, it loses energy, if by its energy we mean its kinetic energy. Nevertheless, to account for the energy, we have to put part of it in the potential.

General relativists typically prefer the first point of view, some to the extent of calling the second wrong.

The case of cosmological expansion is different in that the metric does change with time. However, due to symmetries (homogeneity and isotropy), it is possible to formulate a global law of energy conservation. For matter and radiation in a coexpanding volume V(t) of space this takes the form d(μ V) = -p dV, where μ is the energy density and p the pressure. This is similar to the first law of thermodynamics. If the pressure is zero, it means that the energy density in a volume decreases inversely proportional to the volume (μ V=const.). For radiation, i.e. photons, we have p=μ/3, and hence the energy density in a volume decreases as V-4/3 as the volume increases. Therefore, for energy conservation to hold, the decrease in photon density following from the volume increase is insufficient, they must lose energy in addition, i.e. redshift. That energy goes into the work needed to expand the volume, which is necessary at nonzero pressure.

Sofia, what is called "inflation" is just a faster version of the subsequent "expansion" and it was also uniform throughout space. None of it is uniform through time, the rate of expansion at first was very fast, then suddenly dropped to a much lower level, then fell slowly and is now rising. The rate is driven by physical changes (matter density drops as volume increases for example) and the maths works out. We have to believe what we see even if it is a bit surprising.

No: whereas the cosmological accelerated expansion can be described by the Friedmann-Robertson-Walker-Lemaître metric, inflation can't-it's another mechanism. 

In fact just what physical  mechanism leads from inflation to the cosmological accelerated expansion isn't known and finding it  is an open problem. A major issue, of course, is data: it's very hard to measure the relevant processes to discovery precision and some of the reasons are that the chemical composition of the interstellar dust medium isn't known so well as to remove its electromagnetic properties as background. 

This, however, doesn't matter for describing processes of post-inflationary cosmology.

Stam, I understood that it could be described in similar fashion to the effect of dark energy, i.e. as exponential expansion but still uniform through space. How does it differ?

In the following way: http://lesgourg.web.cern.ch/lesgourg/Inflation_EPFL.pdf (in particular p. 6 and following).

While a cosmological constant does lead to accelerated expansion, similar to inflation, the expansion, it describes, doesn't stop, while inflation did stop. So just a cosmological constant is, either, too little, or too much and additional fields are required-for the moment it seems that a scalar field is sufficient for describing inflation and the cosmological constant is sufficient for describing the current state of accelerating expansion.

Inflationary models make definite predictions, that have been subject to tests from observation, cf. the link to the Planck satellite data-and they pertain to classical gravitational effects-the matter fields, of which the inflaton is one, are treated as quantized fields, since, at this stage, gravitational backreaction can be neglected, but quantum effects of matter can't.  This is consistent with general relativity, since the matter content changes, not how it is coupled to the metric-the description is always invariant under general coordinate transformations. One needs a quantum theory of gravity, from which to deduce inflation-or whatever mechanism does its job-not to describe its consequences; as mentioned, a quantum scalar field does the job. 

Now it is, of course, not excluded, that it may be possible to parametrize the effects of the inflaton by other fields-however the question is, whether this is just a reparametrization or not. In any case, such a reparametrization, once more, makes sense at the level of quantum fields, on a classical gravitational background. 

Words don't matter, equations do. It is possible to describe what's called inflation quantitatively and test this description against measurements. So the statement that it doesn't make valid predictions is, easily, checked to be wrong. 

Words that can't be set to precise equations, whose results can be then tested by measurements are meaningless. They're rhetoric, to impress, not to inform, since they don't support any quantitative description.

So it is possible to understand that certain predictions of inflation, namely primordial gravitational waves,  can't be tested by detecting the electromagnetic waves they produce, because these electromagnetic waves can't be distinguished, to discovery precision, from the electromagnetic waves generated by the dust grains of the interstellar medium. The reason has to do with astrophysics-the chemical composition of the dust  isn't known sufficiently well. Other predictions, however, can be and have. It must be stressed that this electromagnetic background doesn't affect inflation, only, but any other model, that describes primordial gravitational signals, that could be detected by electromagnetic avatars.

So there's no point in writing sentences with ambiguous words. It suffices to write the equations and work out the consequences. However the statement about there not being any position, thus any expansion or horizon is wrong. So that must be formulated correctly. Observables in gravitational theories require care.

But whatever the particular mechanism is, it, inevitably, involves quantum fields on a classical gravitational background, because that's what's under control for the moment.

So there's no point in talking vaguely about ``quantum theory''-the inflaton is a quantum scalar field. Cf. the lectures linked to in a previous message, for reference.

More precisely: the current state of the Universe can be described by a Friedmann-Lemaître-Robertson-Walker metric, as regards gravity and the Standard Model as regards known matter. Dark matter can be, for the moment, described by an equation of state, rather than by its particle content, that's not known, yet.  The accelerated expansion can be described by the cosmological constant. This description is consistent, since gravitational backreaction can be neglected. 

One can ask, whether this description breaks down, when gravitational backreaction becomes significant, or before it does so-and the answer is the latter: the description breaks down, while gravity can, still,  be described classically.  That's the situation that inflation and all other afferent proposals address and that the measurements from the Planck satellite have started to test. 

The Universe has been-quantitatively-described, in equations  https://arxiv.org/abs/1103.2271

http://www.damtp.cam.ac.uk/user/db275/Cosmology/Lectures.pdf

and

 http://ocw.mit.edu/courses/physics/8-286-the-early-universe-fall-2013/ 

and observations: http://sci.esa.int/planck/31074-publications/?farchive_objecttypeid=15&farchive_objectid=30995&fareaid_2=17

That's what counts. If the words are just story-telling, without leading to quantitative differences, they don't matter. If the quantitative differences aren't supported by calibrated observations, they're not good enough. It's surprising, that, with so much scope for work in cosmology, people are not taking advantage of the resources available.

I don't see any publications-with equations, not words-that support the ``alternative'' viewpoint, but I do understand the equations-and observations-that support the standard cosmology. Regarding Big Bang nucleosynthesis, cf. https://arxiv.org/abs/1505.01076 (which, also, alas, relies on the Friedmann-Robertson-Walker-Lemaître metric). Cf. also http://lss.fnal.gov/archive/2008/pub/fermilab-pub-08-216-a.pdf

These imply, among other things, that no ``release of thermonuclear energy'' *could* take place at all, that would be relevant to the discussion.

So what *are* these ``flat contradictions to observation''? The accelerated expansion of the Universe is described by the cosmological constant, which (a) is consistent with general relativity and (b) is sufficient to describe-quantitatively-the measurements,

http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/

 that lead to it and do rely on standard Big Bang cosmology-unless, of course, they, too, have erred, which is, of course, not impossible, but, if the only report of this is to be found on a discussion forum on ResearchGate, one wonders about whether its importance is appreciated at all, particularly by those that propound it.  Shouldn't there have been, at least, a preprint, explaining, in quantitative detail, not words, how everything we thought understood is, in fact, wrong and just how this comes about? Incidentally, ``dark energy'', for now, at least, is perfectly well described by the cosmological constant. 

Once more: the *current* state of the Universe, ca. 13  billion years after the Big Bang, is quantitatively described, in the large, by a Friedmann-Robertson-Walker-Lemaître metric, with the cosmological constant describing the accelerated expansion-i.e. ``dark energy'' and cold dark matter describing non-baryonic matter. In the *past*, this seems to require additional effects, when gravity was, already, described by general relativity, however.  There are many ways to describe this situation, the inflaton being one of them. (There are, also, many ways to describe dark matter effects,  massive gravity, http://arxiv.org/abs/1401.4173  being another way of describing dark matter.)

Magnetohydrodynamics of the early Universe has, of course, been studied, e.g. http://arxiv.org/abs/astro-ph/9712083 Cf. also http://www.leif.org/EOS/0009061-Cosmic-Magnetic-Fields.pdf

There are observational constraints for primordial magnetic fields, too: http://arxiv.org/abs/1502.01594

So any alternative proposal has to be, at least,  consistent with Planck measurements, http://planck.caltech.edu/publications2015Results.html , unless the statement is that these measurements, too, are affected-but why and how?

There are many challenging issues to be understood in cosmology, e.g.http://arxiv.org/pdf/1305.0974v1.pdf or http://arxiv.org/abs/1010.4492 pertaining to turbulent flows, but they don't involve declaring that everything known to date is wrong and the correct approach doesn't have anything in common with what was known till now. Especially, since the claims are words, not equations.  

As several people mentioned, energy conservation is related to time translation invariance by Noether's (first) theorem.  But it is the time translation invariance of the ACTION (hence the laws), not the time translation invariance of the metric (a time-like Killing vector field), that counts.  See the distinction between objects varied in the action and objects that aren't varied in Andrzej Trautman, "The General Theory of Relativity," _Soviet Physics Uspekhi_ 89 (1966), pp. 319-339.  The GR Lagrangian density (pick one---Hilbert, Einstein, Rosen, Moller, Dirac....) does not depend explicitly on t, so there is energy conservation.  

In GR the action is invariant under uncountably infinitely many notions of time translation invariance (as many as there are vector fields), so there are infinitely many conserved quantities.  See Peter Bergmann, "Conservation Laws in General Relativity as the Generators of Coordinate Transformations," _ Physical Review_ 112 (1958) pp. 287-289.  These are pseudotensorial (weird transformation properties) but they are real continuity equations, that is, with a partial divergence, the kind that can be integrated to give total stuff = constant if the boundary term can be ignored.  Covariant divergences (that aren't also partial divergences) don't give the conservation of anything.  Hence there are, if anything, too many conservation laws in GR, rather than too few.  

Not everyone likes pseudotensors, partly because of the tacit assumption that there should be only 4 energy-momenta rather than as many  as there are symmetries (which is infinite) as Noether's theorem implies.  I make a case for liking pseudotensors well enough in "Gauge-Invariant Localization of Infinitely Many Gravitational Energies from All Possible Auxiliary Structures,"  _General Relativity and Gravitation_ 42 (2010) pp. 601-622, 0902.1288 [gr-qc].  It also gives references to responses to someone, Gentry, who took the supposed non-conservation of energy due to photon redshifting as a good argument against GR.  Dealing with such claims got me into the topic of gravitational energy and made clear to me the importance of making as much sense as possible of conservation laws in GR.    

 By the way, statements above (such as about fields) are generally intended to apply in large neighborhoods, not necessarily globally.  

In general relativity, it is true that energy and momentum are locally conserved (which is established from  $ T^{\mu \nu} ; \nu = 0 $), but in general there is no global conservation of energy and momentum (unless there exists a time-like Killing vector).

Since for an expanding universe  there is no time-like Killing vector, the energy and momentum of a photon (or any other test particle) keeps decreasing with time. In fact, the decrease in the temperature of matter and radiation with the expansion is essentially due to the fact that momentum of particles decrease as 1/a(t) where a(t) is the scale factor.

So, where does this energy go? One way to think of this is as follows: 

Universe is an isolated system, and therefore, its expansion is adiabatic leading to decrease in random kinetic energy of matter and radiation at the expense of increase in the gravitational potential energy. Since distance between particles increases with time, the gravitational potential energy keeps increasing. 

That's a good way to look at it but isn't it difficult to define gravitational potential in the FLRW metric?

A simple way out would be to acknowledge the fact that Cosmos might be an open system. When talking about the beginning and the end of our Universe we employ the concept of life times, which are fundamental to all physical processes associated with evolution. Resonance states characterized by time scales do impart open systems and dissipative dynamics, with the result that energy and entropy, in contrast to closed systems, are not constant. One implication would be that redshifted photons loose energy to the gravitational field which originates in a possible distant black hole singularity responsible for the cosmic expansion.

It is quite easy to devise such a Zero Energy Universe Scenario, see enclosed article.

@Pitts:

"As several people mentioned, energy conservation is related to time translation invariance by Noether's (first) theorem. But it is the time translation invariance of the ACTION (hence the laws), not the time translation invariance of the metric (a time-like Killing vector field), that counts."

When we are dealing with particles in a gravitational field, the action is given by an integral over the metric. Essentially, the geodesic equations follow from the Lagrangian sqrt(gμν \dot(xμ) \dot(xν)), so I do not see what your remark wants to say. The Lagrangian for gravtiational interaction is time translation invariant, whenever the metric is. And conservation laws à la Noether follow from invariances of the Lagrangian. In GR, the action is the integral of the Lagrangian over proper time.

Dissipation of energy increases the entropy but it isn't true to say that the energy is "stored" that way because you can't get the energy back by decreasing the entropy.

Kassner: And conservation laws à la Noether follow from invariances of the Lagrangian. In GR, the action is the integral of the Lagrangian over proper time.

Doesn't that impart that the "proper" lifetime of the Universe is infinite?

Why the Graviton smaller 10^42 times than a Photon, can not travel faster than the speed of light?

Because you were brainwashed by your professors for 100 years, that nothing can travel faster than light!

 “I am the first who understood and explained Gravitation with high speed gravitons v = 1.001762 × 10^17 m/s, with Negative Momentum, Negative Mass and Negative Energy” Adrian Ferent

https://www.researchgate.net/publication/299135595_Ferent_Gravitation_theory

Article Ferent Gravitation theory

I have a research about this problem. Please see:

https://www.researchgate.net/publication/301682815_Method_to_detect_gravitational_field_and_graviton

Experiment Findings Method to detect gravitational field and graviton

VZ: What you say is true for the standard model of big bang in which irreversible expansion is assumed.

What I said is valid unless you violate the 2nd Law of Thermodynamics. Even if the universe started to collapse towards a big crunch, entropy would continue to increase.

VZ: .. sum of the entropy changes in the universe is always equal to zero.

That is possible in ideal conditions, but then if there is no change, there is no stored energy in that form. If you think the energy can be in the form of kinetic, then that might be recoverable, but it isn't entropy.

Spatial homogeneity implies momentum conservation (Noether) .  In the case of photons, energy = c times momentum, so photon energy is also conserved.  Unfortunately, currently accepted cosmologies do not attempt to conserve momentum.  The only way momentum can be conserved involves allowing for variable rest mass. Please see my paper The Fundamental Nature of Gravity, available on Research Gate. 

George,

The fluid (Spirit) out of which the universe is created in my model is a perfect fluid, which is perfectly motionless. The reversible process described by my equations changes its direction without increasing any entropy. This happens when the total amount kinetic energy and total amount of potential energy in the universe crosses a critical point. Universe begins in my theory with 100% pure kinetic energy in the form of particle anti-particle pairs of Savitons. Savitons are particles associated with electro-nuclear force. As these particles collide with each other their velocities drop and their kinetic energy gets converted into mass (potential energy). And this keeps going till most of the kinetic energy is exhausted. Now the potential energy becomes dominant and this reverses the velocity vector without change in entropy. So all the matter in the universe starts falling towards each other and again potential energy starts getting converted into kinetic energy but the process is now reversed. At the end of this reversed cycle, you end up with 100% pure kinetic energy of Savitons. And particle anti-particle fall towards each other and disappear into the perfect fluid. This is when the gravity unites with the electro-nuclear force. So the stored energy in my theory is in the form of potential energy. Not in the form of kinetic energy or the entropy.

Increse in the potential energy of the system is proportional to the increse in the entropy of the system and decrese in the potential energy of the system is proportional to decrese in the enetropy of the system. Since this cycle happens over a very long period of time, the process is perfect reversible. So stored in the form of potential energy is meant when I said, stored in the form of entropy. So there is no violation of second law of thermodynamics.

VZ: ... perfectly motionless ... 100% pure kinetic energy

"Motionless" means the particles must have non-zero mass and zero kinetic energy. Your post is riddled with such contradictions.

VZ: .. this reverses the velocity vector without change in entropy

Collisions randomise the direction of the vector. That increases the entropy and the process will stop when the system reaches dynamic equilibrium and maximum entropy.

VZ: So stored in the form of potential energy is meant when I said, stored in the form of entropy.

That's a completely different thing. I think you need to start learning the meaning of these basic terms.

JH: Spatial homogeneity implies momentum conservation (Noether).

It does but you also require time translation symmetry to conserve energy.

JH: In the case of photons, energy = c times momentum, so photon energy is also conserved.

No, time translation symmetry does not apply in the FLRW metric. In fact a photon is described by an energy-momentum 4-vector where the energy and magnitude of momentum must always be equal (as you said) and conservation applies to the 4-vectors so the absence of time translation symmetry means simple conservation in the usual sense doesn't work.

Do you think that the absence of time translation symmetry invalidates the equation  e=cp for photons?  

No, it doesn't invalidate it, and that's the point. Since energy isn't conserved and E=cp still holds, momentum isn't conserved either.

Imagine light from a galaxy hitting a solar sail. Close to the galaxy, it will exert a higher force than farther away because of the cosmological redshift. Conservation is a tricky subject, depending on how you deal with the change of rest frame.

But spatial homogeneity, by Noether's theorem, implies momentum conservation.

In this situation, energy is not generally conserved: while the  momentum of particles of non-zero mass is conserved, their energy is not.

JH: In this situation, energy is not generally conserved: while the momentum of particles of non-zero mass is conserved, their energy is not.

It would appear that way at first sight but as you said, E=pc still holds. To solve it we would need to go into more detail. This is a long-standing question and doesn't have a trivial answer as I understand. I believe you can only maintain conservation if you use pseudo-tensors, but that's beyond my level of knowledge.

Going back to the original question, I just found the linked paper. The early part is exactly what I was saying some time ago about the Pound-Rebka analysis using the Equivalence Principle.

http://arxiv.org/abs/1605.08634

George,

I have nothing to add or retract.  

Best regards,

Jack   

George,

If you are determined not to understand, then you will never understand what is explained. The meanings of the basic terms are alright. Keep your mindset aside and think deep and you will understand the meaning. Instead of making vain arguments, first study the article and references therein which you have not even read. After reading the article if you don't understand then this article is not meant for you. Don't waste your time on it.

Vikram,

Your long post did not address my question.  Please stop using this tread to promote your theory of nonsense.  Real physicists are trying to have an intelligent discussion.

Jeremy,

I got your point. I have removed my theory from your thread.

Although photons are red shifted when ascending a G field, the total energy flux at ANY height is conserved. There is no energy lost to the field. Imagine a transverse wave traveling on a stretched rope. Suppose the single rope splits into two ropes; half th energy to each rope. The initial energy now "red shifted" into two waves of lower energy; total energy conserved. Space changes photons in a similar manner when ascending a G field.  

Goffrey,

in principle you are right. But when you compute according to the known phenomena of redshift and clock retardation, the flux per unit time per unit surface it comes out shifted to the power 2.

Geoffrey is not correct Stefano, the number of photons emitted and received in a finite burst of light does not change, and the rate received is in fact less than that emitted due to time dilation.

“…imagine a transverse wave traveling on a stretched rope. Suppose the single rope splits into two ropes; half the energy to each rope. The initial energy now "red shifted" into two waves of lower energy…”

there isn’t so. There  are  simpler analogues of these “two ropes” case above – for example a pointlike wave source on a water surface. The energy flow per waves front element  indeed evidently decreases when waves spread through the surface “splitting” along the front circle line, but at that there is no “red shift”. The waves frequency remains be the same and the energy flux decreases  because of that the waves’ amplitude decreases.

Though in the gravity fields photons are red/blue shifted  [when the GR postulates that photons don’t change their energy at traveling along geodesics, when they travel so always], but not because of  that “Space changes photons” [as that could be claimed in the GR]. Space by definition cannot impact on any material object, including photons. On the another hand any material object cannot impact/transform on/of space/time/spacetime by some magic way also; there is no any “active spacetime curvatures that force by some magic way bodies to move along geodesics”.

Correspondingly  photons indeed change their energy in the gravity fields, but that is an quite natural result of purely material impact on photons of 4-the fundamental Nature force “Gravity”, which, unlike any of the rest 3-th fundamental forces [EM, weak, strong] is universal – every material object has a gravity charge that creates a gravity field and interacts with external gravity field.

Cheers

During cosmic expansion (in BB) photon doesn't loss its energy because this effect is  fully due to time dilation of old time

Sorry to be slow responding. Been traveling. Let's approach from a different perspective. If a red shifted photon losses energy, where does the energy go? In financial matter, we say follow the money. In physics, follow the energy. Ok we all agree, you simply CAN'T say red shift energy loss is mysteriously absorbed into the field. Can'y buy that at face value. Please, show me where the lost energy resides.

On a personal note, of all the great things Einstein studied, he never touched the "mechanism of gravity." Never. It is truly a perplexing phenomenon. The only way we will ever come to understand is through conversations like this. I really wish we invested more in theoretical physics discussions, rather than forever spending billions of $$ smashing protons into increasingly smaller pieces. 

Sergey, the water drop is good analogy. As the water wave radiates away from the  center, indeed the "waves frequency" remains the same. However, the waves energy is redistributed into an increasing amount of water mass as it propagates. Same is true of red shifted photons as they divide into increasingly smaller photons while ascending G field. The fact that the water wave frequency remains constant while red shifted photon frequency diminishes is due to the method of propagation. Which introduces a whole different subject.