Dear Eric Baird,

if you draw the Doppler effect of light from conservation laws (exchange of quantum of light with atoms) you first get the (1+v/c) and (1-v/c) -1 from classical considerations.

This naturally occurs when it is not identifiable in space who is approaching to whom, or it does not make sense to say that the source approaches or departs from the observer, the distance in between simply increases or decreases.

The equality of the two is made possible only by introducing the Lorentz factor, hence (1+v/c)gamma= [gamma(1-v/c)]-1

The gamma factor comes out also because the absorption or emission of the photon is an inelastic scattering.

Dear Eric Bird,

It is well known that Newtonian Optics is a wrong theory because light never can transform using Galileo's transformations at all.

Hi Stefano!

The paper says that with the Newtonian (c-v)/c, plus the principle of relativity ((c-v)/c for recession velocity, for everyone), traditional conservation laws don't work. There's a round-trip energy-loss (and an accompanying bias towards exothermicity), giving an arrow of time. That's a potentially important result that doesn't seem to have been documented by people who've done studies of the "arrow" problem. Everybody seems to say that all forms of classical physics, Einsteinian and and Newtonian, are (or appear to be) completely time-symmetrical. Well, Newtonian physics isn't.

The penultimate section describes how imposing traditional energy conservation then inevitably gives the SR Doppler equations ... but in the process also imposes time-symmetricality, and creates the "arrow of time" problem.

If we now (post-1930s) believe that our universe is expanding, and that Hubble shifts are continually removing energy from radiant EM, then "traditional" energy-conservation is not a feature of our universe, and shouldn't be used as assumed exact behaviour when deriving the laws of nature. You can treat it as a rough guide that's useful for most practical engineering approximations ... you can say, we know that everyday experience tells us that energy is pretty much conserved in most situations, so any violations must be quite small ... but you can't use it as exact foundational Law for exact derivations of fundamental equations.

At least, not if you want the equations to give behaviour that corresponds to how the universe appears to work in practice.

Daniel: "It is well known that Newtonian Optics is a wrong theory ..."

That wasn't what you were being asked.

You were not being asked to like the calculation I provided or to approve of it, or to be happy with what some people might think that it might or might not imply, or even to believe that it might lead to any useful physics.

You are asked to agree that the calculations, as provided, are mathematically correct. And I'm also asking whether anyone happens to know whether this correct (in context) result has ever been pointed out before (in which case, I need to be making sure that I'm giving someone else the appropriate credit and citations).

Daniel: " ... because light never can transform using Galileo's transformations at all. "

From my point of view that's quite irrelevant. Any further extension that I might later base on these arguments will be based on the properties of a relativistic acoustic metric, in which the hoary old "frame-plus-transformation" approach is considered outdated and invalid except as an engineering first approximation.

In an r.a.m., it's assumed that all physical observers have mass (and that "physics" only applies to actual physical entities), and that the presence and relative motion of a physical observer and a massed particle then has a complicating effect on the geometry that also needs to be taken into account.

If we then conduct the same experiment twice, and give our physical observer different relative states of motion to the objects being observed each time, then our two sets of observations will NOT correspond to a single agreed underlying spacetime geometry that is the same in both experimental runs, and we cannot guarantee to be able to map between the two different sets of readings as different views of the same underlying geometry with the help of a handy transform ... because both experimental runs involve physically different geometries and different curvature-transition effects.

In an r.a.m., the observer's relative properties wrt the other masses are written into the shape of the metric, so if the observer has a different relative motion to other bodies, the metric has a different shape ... with the main difference being in the region directly adjacent to the surface of the differently-moving observer, through which they make all their (different) observations.

And that's how you get to observer-dependence and quantum gravity.

The "frame-plus-transformation" approach (on the other hand) is deliberately designed to erase the observer's position and therefore their fields and/or associated associations distortions from the description and from any derivations. It eradicates all velocity-dependent gravitomagnetic effects between masses, and gives a simplified flat (Minkowski) spacetime. "F+t" says that since the equations must also apply to observers with no physical existence, the observer's agreed physical properties and influence on the shape of spacetime must be zero, and therefore, by the principle of relativity, for us to get the same results regardless of whether the ficticious observer or real observee is "moving", it requires the gravitational and gravitomagnetic effects of all "real" observed masses to be zero , too.

"Frame-plus-transformation" only works consistently in a universe in which the presence and motion of masses has zero effect on lightbeam geometry, and in which gravity is effectively illegal. The moment that you allow a particle's massenergy to have any distortional effect on the shape of the metric at all ... meaning that it most have some sort of associated gravitomagnetic distortion if it moves wrt other masses ... the PoR requires our observers to have corresponding distortions and gravitomagnetic effects and the method breaks down.

So if you ever want to look at more sophisticated physics in which the observer and their associated distortions are part of the experiment, and part of the physics ... which you seem to have to do for quantum gravity ... the frame+transformation approach is guaranteed to make you fail.

And that's why the community can't get quantum gravity to work ... they're insisting that it has to build on the results of the oversimplified "frame+transformation" approach, whereas you can't on principle build a working theory of quantum gravity without rejecting "f+t" and embracing mass-field interactions, including the mass-field of the observing body.

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Sorry to veer so much off-topic, but I didn't know how else to answer your point.

So ... can I now assume that everyone here agrees that the math in the paper is technically correct, and that a relativistic application of (c-v)/c leads to round-trip energy-loss, and that (c-v)/c isn't symmetrical wrt time-reversal?

Dear Eric,

let's make the calculations right with relativistic electrodynamics:

at the beginning of my paper which also Prof. Baldomir knows

Article Dynamics of bodies exchanging radiation and the Relativistic...

there is a straightforward calculation about the double application of the Relativistic Doppler effect which brings to the frequency ratio

1-beta/(1+beta).

with the Classical doppler effect only, you would not be able to find such relation

Such double Doppler effect was applied also in the NASA gravity probe A experiment with success for the cancelling system of the first order DE.

I know that it looks misleading. At the very beginning in 2015 I was induced to make your same mistake. You have to apply the same relation twice, as in the figure for example if it is an approaching configuration, it is the same from both sides (1+beta)*gamma.

It corresponds to a double matrix transformation wtih the quadratic form LAL which if A is unitary goes to L2 .

Eventually (in my paper) you can see that the RDE itself consists eventually in a actual variation of the energy of the photons calculated in the IRF of emission.

E’0=nhν'0=hν0(1+β)/(1-β) =E0(1-β)/(1+β)

the energy shift in the IRF0 of emission due to the relative motion of the bodies is

ΔEIRF0 ≡ΔEDD =E'0-E0=-2E0β/(1+β)

hence ΔEIRF0 /E0 = -2β/(1+β)

Stefano: " let's make the calculations right with relativistic electrodynamics: "

Or, we could try to stay on topic, and pause for a moment to think about the implications of the result.

What we have here is a fundamental and famous problem in theoretical physics that's been the subject of intensive study for at least 90 years, and one of the foundational facts of the problem – that all known classical systems of physics are inherently time-symmetric – turns out to be trivially wrong. We only really have two "major" classical reference-systems, and our "fact" turns out to be wrong for one of them.

That's a major result. It's a fundamental change to the landscape of the problem that demands to be documented and publicised, without requiring any further justification. We are obliged to correct and publicise mistakes when we find them, otherwise they propagate and corrupt further work.

In this case, almost all the research that's been done on this subject has been done in the context of faulty initial assumptions, which seem to have persisted, uncorrected, for longer than an average human lifespan. That's not acceptable.

Dear Eric Baird

I stayed on topic and showed you that considering two approaching or departing IRFs and appling twice the LT we get that relation which was used by the way sucessfully during the NASA GPA experiment for the Doppler cancelling system. IN that case there is *no time symmetry* or reversal since what comes out is L2 where L is the transformation matrix, or a quadratic form.