Hello John:

You have posed an important question in Cosmology. And you are right, energy conservation in cosmological models is far from clear.

But it is not a problem about radiation alone, it can even be more dramatic for Dark Energy.

The standard Lambda-CDM cosmology assumes that we have a constant Lambda (the cosmological  constant) throughout the entire history of the Universe and this means that the associated vacuum energy increases more and more as the Universe expands.

Moreover, the issue of energy conservation in General Relativity has always been problematic:

it goes back to the fact that conservation laws are derived from a zero divergence, and not from a covariant divergence, as it is given for the stress-energy tensor.  This problem was studied by Landau and Lifshitz who proposed a stress-energy pseudotensor for gravity:

https://en.wikipedia.org/wiki/Stress%E2%80%93energy%E2%80%93momentum_pseudotensor

However, this pseudotensor can be made zero at any point, by coordinate transformations, and it is not a good definition of an energy density for the gravitational field. In standard GR the concept  of localized energy for gravity is meaningless. Anyway, we can define the energy content of a gravitational wave in reference to a Minkowskian asymptotic background with this tool.

In this case, we have a time-invariant Universe.

Landau and Lifshitz proved that (-g) (T(matter)ik+t(gravity)ik) has zero divergence (here g is the determinant of the metric) and they inferred total energy and momentum conservation from this.

But, if you try to do that with an expanding Universe we get strange answers:

(i) For a closed Universe, you get a negative t00 in agreement with a potential energy for a bound system, but it cannot balance the radiation density decrease.

(ii) For a spatially flat Universe (the currently accepted model) we have a zero

t00 and no contribution from gravity in the balance.

You can see the details in the attached notes.

The moral of this story is that perhap we will not understand the energy balance of the Universe as a whole until a good theory of Quantum Gravity is found and the origin and nature of vacuum energy is disclosed.

Look at it the other way. These photons filled the Universe then, as they do now. What has changed is the scale of your ruler! Matter has cooled and contracted. The Hubble Constant tells us that a 1 meter rod in our little corner of the Universe, is contracting at a rate of ~6.8 nanometers per century, and has been for billions of years. Relative to the time when the universe became transparent. The photons haven't changed at all. 

The proper energy of a photon remains the same: zero.

Todd,  Your answer does not tell me where the energy went. I can illustrate the problem with an example. A sodium atom has a resonance absorption at a wavelength of 589 nm which is about 2.1 eV.  Suppose that a sodium atom is moving away from me at a speed roughly 1/4 the speed of light but more specifically, I need to send out a photon with energy of 2.6 eV in order for this photon to be absorbed by the receding sodium atom adjusting for the Doppler shift.  The difference between my emitted photon and the absorbed Doppler shifted photon is 0.5 eV. Was this 0.5 eV lost energy? No! The receding sodium atom also received an increase in momentum when it absorbed the photon. This increased its kinetic energy by 0.5 eV. The total energy is conserved. A Doppler shift does not produce a loss of energy.    

However, the galaxies are not expanding into a pre-existing void. The cosmic redshift is not a Doppler shift. It is usually considered to be an expansion of space itself.   There is no obvious conservation of energy when cosmic expansion is the cause of increasing distance between galaxies.  The photon energy disappeared into the expanding spacetime.  Where did it go? Saying that the wavelength stretched is correct, but this is another way of saying that the energy disappeared into "empty space". The acceleration of the expansion is not a real consideration either.  The acceleration is a small effect compared to the basic expansion itself.  Furthermore, the accelerating expansion of the universe only became noticeable in the second half of the lifetime of the universe. 

John,

As matter cools and contracts to lower and lower ground state energies, it radiates the energy away as heat and light. The CMB photons remain unchanged until they interact with matter. 

 Michael,   You say "Is spacetime expanding or are the galaxies traveling through a stationary spacetime?" If the universe extends far beyond our particle horizon and we do not exist in a favored part of the universe, then it seems that the model of galaxies traveling through stationary spacetime must be rejected.  To make sure that we agree on definitions of terms, I am equating your term "stationary spacetime" with my term "preexisting void" or "preexisting spacetime". If we agree that these terms have the same meaning, and if we agree that we do not live in a special part of the universe, then the universe extends very far beyond our particle horizon, perhaps infinitely far. With this picture of the extended universe, it seems that the galaxies cannot be expanding into a preexisting stationary spacetime because most galaxies would have to be traveling faster than the speed of light.   

There is a mathematical explanation, at least based on the standard cosmological model. But it is somewhat against standard intuition and "common sense".

There is a kinetic energy associated with the expansion rate of the universe itself. Reasonable enough, you should think. But it has the wrong sign! The faster the universe expands, the more negative its kinetic energy is. In fact, in such a way that the total energy of the universe is exactly zero (this is the content of the first Friedman equation).

Consider the universe as consisting only of photons (or more generally only relativistic particles), plus itself. As it expands, the energy of the photons decreases quite rapidly, but its velocity (rate of expansion) also decreases equally rapidly. That makes its kinetic energy less negative.

So, the answer is quite simple: The energy of the photons is converted into kinetic energy of the universe itself, making it expand less rapidly.

[Note added: If you don't think you need energy to slow down a large body, you should go visit a farm far north, in late spring when they let loose the cows for the first time that season. Then try to stop the motion of these cows, so they don't damage themselves or their surroundings.]

And this is not something I dreamed up a Saturday night; this is what can be read out of the Friedman equations, which describes the universe quite accurately.

Robert> Why do you think that energy is conserved in an expanding universe? Energy conservation has to do with time translation symmetry, and an expanding universe does not have this symmetry.

The (Lagrangian) model for the universe is time translation invariant. It is the solution which is not invariant. And it is the corresponding Noether conserved quantity E which is the energy I wrote about above. The requirement that E=0 is an additional consequence of the Einstein equations.

It boils down to the definition of energy.

What Caroll refers to as energy is the matter contribution, i.e. what you calculate from the energy-momentum tensor of matter. I.e., the covariantly conserved quantity you usually find on the right hand side of the Einstein equations. This leads to a conserved total energy if there is a timelike Killing vector present.

However, if you consider the complete matter-gravity action, it has a lot of invariances, in particular under time and space translations. That leads, by the standard Noether procedure, to conserved currents (which contain contributions from the pure-gravity part of the action also). In many cases, like Friedman cosmology, this can be used to define globally conserved quantities. This is the quantity I was referring to. Its various contributions are useful for understanding where the energy of the matter system disappears, as is the question of this thread. It does not just disappear into a fuzzy fog; it ends up in the purely gravitational part of the balance sheet, as I explained. And it has nothing to do with fuzzy philosophy, it is all clearly visible in the mathematical equations.

So, if you want to generate some extra (matter) energy, just make space expand a little faster! Maybe one should patent that, contrary to the suggestion discussed here: https://www.researchgate.net/post/What_would_be_the_consequences_if_We_could_create_or_destroy_Energy#view=57dd59cc615e272b2f0889c1

In the end it depends on what can be usefully exploited. As long as nobody can make use of the pure-gravity part you can live happy in your camp.

Note added: After sleeping on it, I have come to realize that you should not live completely happy. About a year ago, a dramatic event was (claimed) observed, where 3 solar masses worth of energy had disappeared into thin air. Or, rather, from the right hand side of the Einstein equations into the energy of gravitational waves. The latter is a pure-gravity quantity (with some notoriety of description).  Do you classify it as energy or not?

Robert> And there is no way of getting this total energy by integrating an energy density which includes the gravitational contribution (which I'd like to see in the balance sheet)

It is! It is in fact extremely easy. The balance sheet of course looks simpler in cases of high symmetry. In the Friedman model (in Robertson-Walker coordinates), the contribution is  -C*[(a'/a)^2 +kc^2/a^2], where C is positive constant inversely proportional to the gravity constant, a is the scale factor, and k = -1, 0, 1.

What I do in the case of the Friedman model, is to interpret the full Einstein tensor as the pure-gravity energy momentum tensor (up to a negative constant of proportionality). That leads to an energy density which is exactly zero, hence easy to integrate. Of course, such a definition does not lead to many useful results. But it can sometimes have some value for interpreting the balance sheet.

Now, in the absence of matter, the Einstein tensor vanishes. So it seems useless interpreting it as the energy momentum tensor for gravitational waves. Instead, one has come up with the pseudo-tensor, which divides the balance sheet into finer (but alas somewhat coordinate dependent) details. I also don't quite understand the issue of the latter. I am unhappy with it, but I attribute that to missing investment of work. What are the physical consequences of the coordinate dependence, if any? Does it really lead to different predictions for how much gravitational-wave energy is transported between two physical objects, dependent on coordinate systems?

Note added: After a more careful check, I have come to the (in retrospect completely obvious) realization that my offered explanation and addition to the energy balance sheet is exactly the Landau and Lifshitz pseudo-tensor, which differs from the Einstein tensor only by a term which is automatically conserved, and whose main purpose seems to be to make the pseudotensor free of second order derivatives (of the metric tensor).

In fact, the whole description looks quite natural and respectable, starting with a partial integration of the Hilbert-Einstein action integral, so that the integrand becomes free of higher order derivative (than the first).  

Let's assume now after some 14 billion years, that the curvature of spacetime is well beyond the Weyl (twist) tensor and is now governed by Ricci (spherical) curvature.  So the total energy density (photons + matter) from the decay of the Hawking-Turok pea instanton, over the course of cosmological time, is now occupying a hugely expanded spherical volume.  I'd be inclined to say, of necessity, that the photons emitted from distant galaxies must shift red, to keep the total energy density of the universe constant; i.e. namely ZERO.  

The answer (my opinion) to Cosmological Red shift, is that it not due to Doppler shift.

It is due to slow dissipation of energy in the cosmic Complex Tension Filed (CTF) that supports the perpetual propagation of EM field. Directly relevant paper #2013.5, can be down loaded from: 

http://www.natureoflight.org/CP/

I am of the opinion that Einstein correctly confessed that even after fifty years of brooding, "What are light quanta?" (Letter to his friend Besso), he did not gather any satisfactory answer. If the originator of the concept of "photon" as a "light quanta" remained doubtful about his original proposal; then it behooves upon us to keep on exploring the concept of "indivisible light quanta", until we find some better and more realistic answer. A la Newton, let us "stand on the shoulder of the giants" to increase our knowledge horizon; instead of lowering the horizon by bowing down to their feet!

My re-discovery and its generalization as Non-Interaction of Waves (NIW), is profoundly simple; and yet profoundly important. It helps remove most of the un-necessary non-causal and mystical postulates behind modern physics. Systematic application of NIW reveals that the formalism of QM has more realities built into it than the Copenhagen Interpretation has allowed us to extract out it.

NIW conclusively tells us that there cannot be any "single photon interference". We have been fooling ourselves by assigning the real quantum-ness in the binding energy of the photo electron on to the EM waves. Superposition Effect is observable as a released photo electron, but only after a frequency resonant quantum dipole carries out the square modulus operation on all the superposed waves. Superposition Principle, the mathematical summation of the superposed amplitudes, in the absence of any detcetor, is not an observable phenomenon. Please, try to appreciate this point. The entire mysticism behind the interpretation of QM will vanish and the real successes of QM will become more appreciable.

Please, Google Amazon for my book, "Causal Physics: Photon Model by Non-Interaction of Waves", Taylor & Francis, 2014. The book is based upon my publications, most of which can be found and downloaded from the same website:

http://www.natureoflight.org/CP/

NIW is built into Huygens-Fresnel (HF) diffraction integral; without which the entire classical optical science and engineering will simply collapse.

Since the HF integral is a summation of spherical harmonic waves; it is necessarily a solution of the Maxwell's wave equation. This, the so called "infallible" Maxwell' equation also incorporates NIW.

Then Planck in his book on the derivation of his famous Black body, explicitly recognizes that the innumerable wave packets, emitted by the Blackbody surface molecules, keep on diffractively evolving inside the cavity crossing through each other without interacting with each other.

Bose's so called pure math (quantum mechanical) derivation of Planck's equation required him accept that the "photon number" inside his phase-space box remains constant, implying no interactions.

After Dirac quantized the EM field, he was forced conclude that "different photons never interfere".

Finally, let us acknowledge that several "working" laser fusion labs in the current world never finds any any particle production out of the immensely dense focused laser "photons", whenever their microscopic Deuterium sphere misses the focus-spot. 

I rest my case. Let us get over with the mystical "Indivisible light quanta" or the "photon" concept; and learn to appreciate the universal NIW-property, and start re-building our physics founded on the realities that are already available to us. 

Dear John Macken,

On my opinion, a lack of understanding of the Big Bang hypothesis purely was shown in your main question of the topic. The fact is that  almost all do not pay attention to the acceleration of the pace of time in BB-hypothesis. Since the photons are emitted under conditions of slow pace of time, and now they occur at a great pace time, the red shift is obtained at 100% only due to this difference in the pace of time and loss of photon energy cannot be in this hypothesis.  In addition, all decrease of energy density in Universe is due to the increased pace of time and increased three-dimensional distances, which, however, does not lead to the movement of objects in space, because the speed of the objects in this space is purely peculiar.

Since the objects remain almost stationary in space, the cosmological Doppler effect does not occur. This effect occurs only when the motion of bodies in space.

Thus, in the hypothesis of the Big Bang there is nor the Doppler effect, and nor the loss of energy by photons, and the disappearance of energy in empty space.  And given the fact that the Big Bang hypothesis not found a single confirmation, and there are only contradictions ( the distribution of the number of objects depending on distance, the distribution of the average of the radii of elliptical galaxies, the dependence of the luminosity per distance, etc.), then this hypothesis should be thrown out of scientific consideration. And with it the GR should be thrown out, the postulates of which are performed only in the infinitely small volume, and obviously are not performed in the final volume, i.e., the Einstein equations obviously cannot be integrated, consequently, GR is not applicable to the whole space of the Universe!

It remains to consider only stationary metric of the Universe. In such a Universe the photons must lose energy, and this energy is converted into vacuum energy.

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На мой взгляд, в вашем основном вопросе темы показано отсутствие понимания гипотезы Большого Взрыва. Дело в том, что в ней почти все дружно не обращают внимания на ускорение темпа времени. Поскольку раньше фотоны излучались в условиях медленного темпа времени, а теперь они наблюдаются при большом темпе времени, то красное смещение получается на все 100% только за счет этой разницы темпов времени, и НИКАКОЙ потери энергии фотонов в этой гипотезе не может быть. К тому же, всё уменьшение плотности энергии во Вселенной происходит за счет увеличения темпа времени и расширения трехмерных расстояний, которое, однако, не приводит к движению объектов в пространстве, поскольку скорость объектов в этом пространстве является чисто пекулярной.

Раз объекты остаются практически неподвижны в пространстве, то космологический эффект Доплера не возникает. Этот эффект возникает только при движении тел в пространстве.

Таким образом, в гипотезе Большого Взрыва отсутствует и эффект Доплера, и потеря энергии фотонами, и  исчезновение энергии в пустоте пространства.

 А с учетом того, что гипотезе Большого Взрыва не найдено ни единого подтверждения, а есть только противоречия ( распределение числа объектов в зависимости от расстояния, распределение средних радиусов эллиптических галактик, зависимость светимости от расстояния и т.п.), то эту гипотезу давно следует выбросить из научного рассмотрения. А вместе с ней и общую теорию относительности, постулаты которой выполняются только в бесконечно малых объемах, и заведомо не выполняются в конечных объемах , то есть, уравнения Эйнштейна заведомо нельзя интегрировать, следовательно, к пространству Вселенной GR не применима!

Остается рассматривать только стационарную метрику Вселенной. В такой Вселенной фотоны обязаны терять энергию, и эта энергия переходит в энергию вакуума.

In red shift , gravity does negative work on the photon and In blue shift , gravity does positive work on the photon.

See our new papers about Particle Physics.You will find all of your questions in these fields.

https://www.researchgate.net/post/What_are_the_new_advancements_in_recognition_of_Photon_and_its_related_technologies

Dear John Macken,

About the last part of Your initial question:

"Big Bang" is nonsense! Such opinion was of the author of this term,  in which he  expressed the relation to this hypothesis ("Bang" means not with a Burst but a Christmas cracker, cracker, joke!). And you are right that in the hypothesis of "Big Bang" there is no conservation of energy.

Friedman proposed a model based on the system of Einstein's equations which cannot be integrated! Moreover, the assumption of Friedman about the unsustainability of the location of a substance applies only to the finite volume of the Universe! An infinite volume requires an infinite time of interaction, and so such interaction never occurs, and there is a global contraction of matter. Local ones are, we see them in the cellular structure of the Universe! 

So, seriously, there is no obstacle to the existence of the Universe, infinite in time and space. In this model, there cannot be Big Bang, no beginning or end of the Universe, there is no expansion of space and global stretching of time.

In particular, in full accordance with the law of conservation of energy, the photons lose energy, leaving it in the form of a supplement to the vacuum energy, which in case of exceeding a certain density generates the substance. A substance, of course, has the property of attraction, but when exceeding the critical concentration, matter gives rise to stars, they begins to emit matter and energy, and thus reduces its density. Thus, the Universe maintains a balance between vacuum energy and matter.

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О последней части Вашего начального вопроса:

«Big Bang» - это чушь! Примерно так автор этого термина выразил свое отношение к этой гипотезе («Bang» означает не взрыв, а елочная хлопушка, шутиха, шутка!). И вы правы, что в гипотезе «Big Bang» нет сохранения энергии.

Предложенная Фридманом модель основана на системе уравнений Эйнштейна, которые нельзя интегрировать! Более того, само предположение Фридмана о неустойчивости расположения вещества относится только к конечному объему Вселенной! Бесконечный объем требует бесконечного времени взаимодействия, и значит, такого  взаимодействия никогда не происходит, и нет глобального стягивания материи. Локальное – есть, его мы видим в ячеистой структуре Вселенной!

Таким образом, если серьезно, то нет препятствию существованию Вселенной, бесконечной во времени и пространстве. В такой модели не может быть «Big Bang», нет начала или конца Вселенной, нет расширения пространства и глобального растяжения времени.

В частности, в  полном соответствии с законом сохранения энергии,  фотоны теряют энергию, оставляя ее в виде добавки к энергии вакуума, которая, в случае превышения некоторой плотности, порождает материю. А материя, естественно, имеет свойство притяжения, но, при превышении критической концентрации, материя  порождает звезды, начинает активно излучать материю и энергию, и этим уменьшает свою плотность.  Таким образом, во Вселенной поддерживается баланс между энергией вакуума и материей.

The answer is, in my opinion, simple: The energy is still in the space which is continuously enlarging its volume so it captures more and more of electromagnetic energy.

 Dear Dr Hamed Daei Kasmaei 

Tsiolkovsky invented the Formula F=dP/dt = v dm/dt+ m dv/dt more than 100 years ago. Since then, all rockets operate on this formula.

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К. Циолковский придумал Формулу F=dP/dt = v dm/dt+ m dv/dt больше 100 лет назад. С той поры все ракеты действуют на этой формуле.

Dear Chandra Roychoudhuri,

I agree with you that there is no cosmological Doppler effect, since the galaxies aren't receding from us in space.

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Я согласен с вами, что не существует космологического эффекта Доплера, так как галактики не удаляются от нас в пространстве.

Thank you, Chepick.

John, photons are bosons which can occupy the same place in space and act like a single particle. So the photons that existed 380,000 years ago can split into multiple low energy photons that we see today. So the energy of photon today x number of photons today = energy of photon at earlier epoch x number of photons at earlier epoch. Therefore there is no violation of conservation of energy.

Standard model does not have a quantum gravity theory therefore you can talk about photons having a planck energy. But in Periodic quantum gravity and cosmology theory (PQG), photons cannot exist before 10^(-26) sec. after the big bang. (see data no. 21 in the table). PQG equations cannot generate the photon parameters before this time. This means that this is the point of symmetry breaking which resulted in separation of electromagnetic force from the electroweak force. Prior to this time photons did not have an independent existence. So the maximum energy that a photon can have at 10^(-26) sec. is about 3.466 x 10^(-3) Gev which is much less than the Planck energy.

Where is this energy today?

This energy is distributed into larger number of low energy photons today. These photons do create gravity and contribute to critical density of the universe. But the contribution is very low. It is accounted as the radiation density. So the energy did not disappear into empty space but got distributed into large number of low energy photons. And there is no violation of conservation of energy.

Article Periodic quantum gravity and cosmology

VZ: So the energy of photon today x number of photons today = energy of photon at earlier epoch x number of photons at earlier epoch. Therefore there is no violation of conservation of energy.

The increased number of photons would however mean that the intensity would be much larger than a black body radiator of the same temperature. The FIRAS instrument on COBE ruled that out.

Einstein equations are an identity,in the sense that left and right side have zero

divergence, and are so equated to each other.;  the left side as defined by Bianchi

identity is arbitrary up to multiple of metric tensor (cosmological term-so called);

so is the right arbitrary up to a multiple of metric term to be defined according to

our concepts of matter'. So there is always some ill definition of energy-except

 locally.  Conformal tensor is analogue of  (2,0)+(0,2) representation of the

 Lorentz group; so its double divergence gives a measure of change in

material energy.  This change is also tracked by projective change of

 connection  (leaves system of geodesics unchanged)by gauge fields

which represent matter. . In the present state of knowledge we do not

 know how to write the right side in terms of classical fields. But an

 spontaneous projective does change the left side to what matter is

created or absorbed in the metric structure. Energy change also is

measured by tetrads- rather their ' co-homology' content- a measure

of non-integrable energy content as Temperature x Entropy-change.

Daniel> For instance, the very same photon maybe have enough energy to knock off an electron producing the photoelectric effect in one frame of reference, but not even enough to be absorbed by a comparable electron in another.

This is a misunderstanding (or at best a misrepresentation). Physical processes do not depend on the frames from which they are observed. But if you keep the photon source fixed, and change the velocity of the sample on which the light shines, then you may change the physical situation such that electron emission becomes possible (from impossible).

Since the discussion has turned to photons having quantized energy, I thought that it is appropriate to quote a part of my paper titled "Energetic Spacetime: The New Aether" available on my RG home page.  

"It is often said that photons possess quantized energy of E = ħω. However, we will examine the limits of this quantization.  Suppose that we make an analogy to the equivalence principle having a “strong” and a “weak” definition. Similarly, the proposal is made that there is a “strong” and “weak” definition of quantization. A strong definition of quantization would imply that only integer multiples of the fundamental unit are allowed. For example, if energy met the strong definition of quantization, then energy would only came in discrete units such as integer multiples of 1 eV. Photons would only come in discrete frequencies which would be integer multiples of the universal fundamental frequency associated with the universal unit of quantized energy. Obviously energy and frequency are not quantized according to the “strong” definition. Instead, a photon’s energy is only weakly quantized. All of a photon’s energy is transferred when it is absorbed, but a photon can possess any energy up to Planck energy. The same photon has different energy when viewed from different frames of reference.

 Compare this to angular momentum which meets the definition of strong quantization. Angular momentum only comes in discrete units. All angular momentum in the universe only comes in integer multiples of ½ ħ. This is obvious with fermions and bosons, but a more revealing example can be made using a carbon monoxide molecule (CO) isolated in a vacuum. An isolated CO molecule can only possess integer multiples of ħ angular momentum. This translates into the CO molecule only being able to rotate at discrete frequencies which are integer multiples of its fundamental rotational frequency of 115 GHz. This meets the definition of strong quantization. For another example, take a photon that is part of the cosmic microwave background.  Over the age of the universe this photon has lost most of its energy. However, the photon has kept 100% of its angular momentum. Angular momentum has strong quantization; energy has weak quantization.

 It is proposed that all quantization in the universe is ultimately traceable to angular momentum being strongly quantized. When a photon is absorbed by an atom, it transfers 100% of its angular momentum to the atom. All the photon’s energy is also transferred to the atom, but that is just a byproduct of transferring its ħ unit of quantized angular momentum. The amount of energy transferred from the photon to the atom depends on the frame of reference of the atom. However, the angular momentum transferred is independent of the frame of reference."

Daniel> Imagine...

What is there to imagine? Physics is like that!

Haven't you read about Lorentz transformations?  Haven't you heard that energy is but one component of a Lorentz transforming 4-vector, hence a frame dependent quantity? Haven't you observed and read about the Doppler effect(s)? Haven't you read about the Pound-Rebka experiment, with its clever use of a moving target?

What is there to imagine?

John> It is proposed that all quantization in the universe is ultimately traceable to angular momentum being strongly quantized.

I don't believe this will be possible. Theoretical calculations do account for consequences of angular momentum conservation, but that is not enough to f.i. calculate the hydrogen spectrum (whose discrete part is nevertheless fully determined by symmetries). So, the hydrogen atom is already a counterexample to your proposal.

DLB: Changing the speed of the target, if the model I use is correct, does not change the energy of the photon.

If someone throws a brick at you it hurts and the faster they throw it, the more it hurts. You get the same effect if you hang a brick from a tree, the faster you run into it, the more it hurts!

Fire a target at a photon and the energy at the interaction is increased compared to the same photon hitting a stationary target.

> Lorentz transformation are pretty useless.

Good to know.

The running time t is not a physical parameter. No physical object in this universe has shown the propensity of keeping track of the running-time as one of its physically measurable parameter.

What we directly measure is the frequency of some kind of oscillation, wave or mechanical. Then we invert the frequency to obtain a DERIVED new parameter, we call PERIOD, or a time interval. So, the frequency or the period, being a physical parameter of physical oscillators, can be influenced by changing its physical environment.

So, let us seriously re-think what  physical realities are really contained behind the Space-Time model of the universe!

DLB: I essentially agree with what you are saying, except that I make a distinction between the energy and momentum of a photon, the two being distinct properties.

We have no argument there, I addressed only the question of energy as that was the context.

DLB: The energy of the photon would be unaffected by the motion of the target, but the momentum the photon imparts the target would be different depending on the speed of the target

If you run towards a light source holding a solar sail, you'll feel a greater force on the sail than if you were standing still, the momentum of each photon is increased. If you run towards a light source holding a bolometer, it will register a higher power level because the energy of each photon is also increased.

Bear in mind that, in units where c=1, the invariant mass is given by:

m2 = E2 - |p|2

Since the mass of a photon is zero, it must be the case that E=|p| so both must change (and by the same amount).

DLB: .. relative to the speed and direction of the photon (but independent from the speed of the source).

Unfortunately, "relative to .. the photon" is meaningless but I understand what you are saying, we are comparing like-for-like photons and just considering the motion of the observer, that's not a point of contention.

Chandra Roychoudhuri, Space-time model in reality is the wavelength-period model as discussed in the following article.

Article Periodic relativity: Basic framework of the theory

First it must be considered what photons are. The current idea about photons as EM waves fit for radio waves, but not for photons. Both radio waves and photons are constituted of solutions of homogeneous second order partial differential equations. However, spherical waves quickly loose their amplitude and thus their energy with increasing distance of the emitting source and EM fields do not fit as carrier for this immense range of billions of light years. The EM field requires the nearby existence of electric charges and that fails in empty or near to empty space. The  homogeneous second order partial differential equation offers more solutions than just waves. For odd numbers of participating dimensions these equations also offer solutions that are shape keeping fronts. The spherical types also quickly loose  their amplitude with increasing distance, but the one dimensional shape keeping fronts not only keep their shape, they also keep their amplitude. Thus they can travel billions of light years on a suitable carrier without losing their integrity. The nasty thing is that they do not feature a frequency. If the emitter sends these fronts in equidistant instants, then this establishes a frequency and if these strings all have the same length, and each front carries a bit of energy, then the relation E=h v is also established. What redshift means is determined at the absorber side of the trajectory. If red shift means lower frequency and the length of the string stays the same, then indeed the string carries less energy, because part of the fronts have vanished. Another possibility is that the shape of the fronts has changed, such that each front carries less energy. A third possibility is that the time aperture of the absorption process at the absorption location is shorter than the emission aperture at the emission location. This means that the absorber misses some of the fronts and the corresponding energy bits. If a calorimeter is used at the absorber side, then this instrument will catch all energy bits. An atomic absorber will see a lower frequency and capture a lower energy.

John  --  This effect is just the reverse of the gain in energy when a photon drops in a gravity field. The point is that energy is conserved when you take into account both fields. So in your example the photons left in a strong gravity field and are now measured in a much weaker gravity. The energy "lost" went into the gravitational potential.

There is no lost energy!!! According to my theory the radiation power is invariant. The perceived frequency changes because of the gravitational time dilation (clock retardation), no radiant energy gets “stored”in the gravitational field while travelling.

http://www.ingentaconnect.com/contentone/pe/pe/2016/00000029/00000003/art00018

Azzam  --  Since dilation only decreases that fails to explain the observed gain in energy when a photon moves in the direction of increasing gravity field.

Dear James Langworthy,

You said "Azzam  --  Since dilation only decreases that fails to explain the observed gain in energy when a photon moves in the direction of increasing gravity field."

According to my theory, that is not true!!! That is according to LT and the equivalence principle of Einstein's relativity. But according to my transformation depending on the Copenhagen school and my equivalence principle everything is deferent. The light speed is locally constant and equals to the speed of light in vacuum, but globally it is vacuum energy dependent depending the gravitational potential. 

You said "The energy "lost" went into the gravitational potential."

There is no lost energy went into the gravitational potential!!! Only the perceived frequency changes because of the gravitational time dilation (clock retardation). Radiation power invariant across gravitational potentials according to my transformation and my equivalence principle. Please review the relativistic quantized force in my theory depending on dp/dt.

Hans, you say that "spherical waves quickly lose their amplitude and thus their energy".  This is not correct.  The intensity decreases as the square of the distance, but the area over which the wave spreads increases as the square of the distance, so the total energy remains constant. 

 Dear Daniel L. Burnstein,

According to my transformation  the explanation of Sagnac effect is the same result of explaining Sagnac effect within the framework of ether theory, but instead of the ether theory it is vacuum energy dependent. According to my transformation there are two pictures for the moving train separated in space and time and entangled with each others by the invariance of energy momentum four vectors. In this case my transformation is vacuum energy dependent (gauge), and it is a transformation of acceleration by the vacuum fluctuations, and the vacuum fluctuations the uncertainty plays the rule. It is QFT now. 

My transformation

x=R2(x'-vt') t=R2(t'-vx'/c2) y=Ry' and z=Rz' R is the Lorentz factor

Take the time term of my transformation

t=R2(t'-vx'/c2) and from that t+=R2(t'+vx'/c2) and t-=R2(t'-vx'/c2) and from that delta (t)=R2(2vx'/c2) and since space is invariant, thus x=x'=L and from that

delta (t)=R2(2vL/c2) which is the same result of explaining Sagnac effect within the framework of ether theory, but instead of the ether it is vacuum energy dependent. My theory in this case is gauge theory and by the equivalence principle gravity is gauge theory. 

Read these papers about Sagnac effect  http://arxiv.org/pdf/1404.4075v1.pdf

and 

http://www.ingentaconnect.com/contentone/pe/pe/2016/00000029/00000003/art00026

In the experiment of the Sagnac effect on a rotating plate, the speed of light is also shown to be anisotropic which agrees with my transformation  and that explains the CMB anisotropy according to my transformation. 

Ramzi,

You are right. However, spreading the energy is as bad as losing energy. The energy does not reach the detector, which must catch enough energy in order to be triggered.

I invite who down-voting to discussing instead of down-voting.

Radiation power is invariant across gravitational potentials. Only the perceived frequency changes due to the gravitational time dilation (clock retardation), no radiant energy gets “stored”in the gravitational field while travelling. 

Is not F=Δp/Δt=I(area)/c and I=ΔU/(area)Δt 

Now what about the relativistic quantized force???

And what about the measured speed of light locally and globally. Local and global in SRT are independent. Local versions of the (special) principle of relativity say that if the same type of experiment is conducted in two isolated, unaccelerated laboratories, then the outcomes of those experiments must be the same. Global versions of the principle say that if you take a physically possible world and boost the entire material content of that world, you get another physically possible world. Local and global are independent. 

So I wish instead of down-voting discussing!!! I solved all of these problems in my paper.

There are two different effects which risk being confused here. If light is emitted from an isotropic source, the flux (power per unit area) decreases as the square of the distance from the source. Similarly the photon rate per unit area also falls as the square of the distance, the energy per photon is constant and proportional to the frequency which also remains constant.

However there are a variety of reasons why the frequency can change, notably (but not exclusively) Doppler shift,  gravitational time dilation and cosmological redshift. All of these change the observed frequency and consequently the energy (and momentum) per photon. Total energy is conserved for the Doppler effect in Minkowski spacetime and for the gravitational shift in the Schwarzschild Metric but the situation is more complicated for cosmological redshift.

George Dishman,

You said "but the situation is more complicated for cosmological redshift."

The problem is not complicated if we understood the real interpretation of Sagnac effect. As in this paper http://arxiv.org/pdf/1404.4075v1.pdf

Calculating the ensuing travel times of light round the interferometer we find that the LT – due to its linear term x v/c2 – does not predict any Sagnac Effect, but results in c = const also in a rotating system as it does in an inertial system. This explains then why Ashby [6], e.g., uses the Newtonian or Galilean time transformation t’ = t rather than t’ = γ (t - x v/c2) when he calculates the Sagnac Effect in the GPS-System. This was also observed by Carroll Alley in a comment at the end of an engineering presentation on GPS and Relativity. 

In this case if we want to understand Sagnac effect by proposing time dilation in SRT, in this case we must understand what is the meaning t'=t0 at x'=x0 and t=t0 at x=x0. In this case we t=t'=t0 at x=x'=x0, and by considering the time dilation in this case, there must be two pictures for the moving train. These two picture must be separated in space and time, but entangled by the invariance of the energy-momentum four vectors.  In this case time dilation is resulted from the clock retardation.

In this case Sagnac effect can't be explained by LT. It is explained by my transformation. According to that  the CMB rest frame in which IvCMB appear a perfect blackbody at TCMB ≈ 2.7 K and according to my transformation the decrease in the speed of light globally depending on the gravitational potential must be anisotropic by the vacuum fluctuations according to the uncertainty principle. If the Earth were moving relativistically the spectrum would still be exactly thermal in any given direction. The relative velocity of the each will no affect on the physical calculations. That is because according to my theory all the reference frames are truly equivalent. 

According to that Radiation power is invariant across gravitational potentials. Only the perceived frequency changes due to the gravitational time dilation (clock retardation), no radiant energy gets “stored”in the gravitational field while travelling. Space must be invariant in this case, and the relativistic quantized force must be defined according to the radiation exchange and F=Δp/Δt=I(area)/c and I=ΔU/(area)Δt . My exact solution of the Pioneer anomaly is good prove for that. The decrease in the deceleration which caused the blueshift is exponential as in my paper  http://vixra.org/pdf/1109.0058v1.pdf depending on the gravitational potential depending on the distance from the Sun. And this term which is responsible for the Pioneer anomaly 10/11 depending on the distance from the Sun is the same term for the Mercury precession. According to that we can understand the Hubble law.  According to my solution, there are two terms of decelerations that controls the Pioneer anomaly. The first is produced by moving the Pioneer spacecraft through the gravitational field of the Sun, which causes the velocity of the spacecraft to be decreased according to the Schwarzschild Geometry of freely infalling particle. This deceleration is responsible for varying behaviour of the Pioneer anomaly in Turyshev. The second term is produced by the Hubble’s law which is constant and equals to the Hubble’s constant multiplied by the speed of light in vacuum. 

Daniel  --  The difference in  gravitational potential between, say, a satellite in orbit and a measurement at the same orbit but stationary is minuscule compared to the difference of that between the epoch when photons were freed from the universal plasma and the current epoch. Typically measurement of the shift in energy gained by falling some part of a hundred feet near earth's surface is done using Mossbauer effect with accuracies near 10^(-9) if memory serves.

Hello John:

You have posed an important question in Cosmology. And you are right, energy conservation in cosmological models is far from clear.

But it is not a problem about radiation alone, it can even be more dramatic for Dark Energy.

The standard Lambda-CDM cosmology assumes that we have a constant Lambda (the cosmological  constant) throughout the entire history of the Universe and this means that the associated vacuum energy increases more and more as the Universe expands.

Moreover, the issue of energy conservation in General Relativity has always been problematic:

it goes back to the fact that conservation laws are derived from a zero divergence, and not from a covariant divergence, as it is given for the stress-energy tensor.  This problem was studied by Landau and Lifshitz who proposed a stress-energy pseudotensor for gravity:

https://en.wikipedia.org/wiki/Stress%E2%80%93energy%E2%80%93momentum_pseudotensor

However, this pseudotensor can be made zero at any point, by coordinate transformations, and it is not a good definition of an energy density for the gravitational field. In standard GR the concept  of localized energy for gravity is meaningless. Anyway, we can define the energy content of a gravitational wave in reference to a Minkowskian asymptotic background with this tool.

In this case, we have a time-invariant Universe.

Landau and Lifshitz proved that (-g) (T(matter)ik+t(gravity)ik) has zero divergence (here g is the determinant of the metric) and they inferred total energy and momentum conservation from this.

But, if you try to do that with an expanding Universe we get strange answers:

(i) For a closed Universe, you get a negative t00 in agreement with a potential energy for a bound system, but it cannot balance the radiation density decrease.

(ii) For a spatially flat Universe (the currently accepted model) we have a zero

t00 and no contribution from gravity in the balance.

You can see the details in the attached notes.

The moral of this story is that perhap we will not understand the energy balance of the Universe as a whole until a good theory of Quantum Gravity is found and the origin and nature of vacuum energy is disclosed.

The red shifted photon loses energy to the field that red shifted it. A departing photon increases the gravity potential of the field it escapes from.

This means that something must change the energy of the photon into mass and something must carry that mass. Fields do not carry mass. However, spherical shock fronts temporarily carry mass and they spread this mass over the field by expanding the field. Photons are constituted by one-dimensional shock fronts.

Where is the mystery here? Why isn't it the same as a charged particle leaving an opposite charge center. Viewed externally (as if the observer were at an infinite distance) the particle's energy is always kinetic plus potential but when it's a photon, it can't slow down so it looses energy by shifting red.

The "lost" energy is in reality contained in the increasing volume of space fulfiled by photons, so it is not realy lost.

If the radiation is red-shifted, then you cannot apply the same kind of atoms to absorb the radiation as the kind of atom that emitted the radiation.

Hans: Indeed.

Start with a box with perfectly-reflecting walls and place an electron and an anti-electron in it. Eventually the two particles meet and mutually annihilate in a burst of gamma radiation. The radiation bounces around the box and eventually refocuses to recreate the original particle-pair. The system is time-symmetric and has no overall "arrow of time".

But if the box slowly expands, the gamma radiation will lose a little energy each time it reflects, and when it finally refocuses, it won't have enough energy to be able to recreate the initial particles.

The same goes for other processes within the expanding box: if they convert massenergy into radiant energy and back again, the losses in the radiant energy mean that when the reactions attempt to achieve equilibrium, they have a bias towards exothermic reactions rather than endothermic ones.

The expansion of the box creates a box-scale ("cosomological"-scale) "arrow of time".

Eric,

In the mathematical model, the positron can be interpreted as a time reversed electron. So, nothing is created or annihilated. Only a single object switches its time direction. Observers cannot follow this. They must follow the time window. Thus they only see the creation and annihilation events.

Elementary particles are very complicated constructs. That is why in the mathematical model they never die and are only created before the begin of time. Instead they can zigzag through the time domain. The model has two views; the mathematical view and the observers view. Observers can only perceive events that for them have a historical time stamp. Before the start of time the math model archives all dynamic geometrical data in a read-only repository that consists of a series of separable quaternionic Hilbert spaces. The math model applies stochastic processes to fill the read-only repository before it is used by any reader. With other words, all observers are fooled by the creator of the model.

The math model explains far more than observers can ever comprehend. It can simply explain absorption as time reversed emission, while observers might comprehend emission, but cannot explain the incredible aiming precision that is involved in absorption.