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Rejecting the Blurriness Criticism
by Louis Marmet  2023 June 20
The “blurriness criticism of tiredlight” assumes a single interaction that satisfies conservation of energy and momentum in nonexpanding space, and a resulting photon propagating in the same direction as the initial photon. It is applicable to Compton scattering and other tiredlight models.
Rejecting the Blurriness Criticism
By Louis Marmet  2023 June 20
Work in progress.
The “blurriness criticism of tiredlight” assumes a single interaction that satisfies conservation of energy and momentum in nonexpanding space, and a resulting photon propagating in the same direction as the initial photon. It is applicable to Compton scattering and other tiredlight models. The argument debunks increasingly complex tiredlight mechanisms as follows:
1) Photon losing energy on its own
The energy of the photon is E = h f. After the interaction, the photon is redshifted to frequency f’ and the energy of the system is E’ = h f’. Conservation of energy demands: h f = h f’.
Therefore f = f’ and this mechanism cannot produce a redshift. (Mechanisms labeled “Inherent” are all debunked with this argument.)
2a) Photon interacting with a massless particle
 An incoming photon interacts with a massless particle (say another photon or graviton), the energy of the photonparticle system is E = h f + h f2.
 After the interaction, the photon is redshifted to frequency f’ and the massless particle is blueshifted to f2’. The energy of the system is E’ = h f’ + h f2’.
Conservation of energy demands: h f + h f2 = h f’ + h f2’.
A frequency shift from f to f’ of any size is possible in this mechanism, therefore the mechanism predicts that every redshift values are possible. Since we don’t see all those possible frequency shifts but only the specific redshift given by Hubble’s relation, this interaction does not happen.
Therefore, the simple mechanism photonmassless particle interaction is not the explanation for the cosmological redshift. (“LightLight” and “LightGravity” mechanisms are debunked.)
2b) Photon interacting with a massive particle

Starting with a particle of mass m at rest (say an electron), the energy of the photonelectron system is E = h f + mv^2/2 = h f (photon frequency f, particle velocity v = 0).

After the interaction, the photon is redshifted to frequency f’ and the particle is moving at velocity v’. The energy of the system is E’ = h f’ + mv’^2/2.
Conservation of energy demands: h f = h f’ + mv’^2/2.
Similarly, the momentum of the system is p = h f/c and p’ = h f’/c + mv’, before and after the interaction, respectively.
Conservation of momentum demands: h f/c = h f’/c + mv’, or h f = h f’ + mv’c.
Energy and momentum can only be conserved if v’ = 0 and f = f’, i.e. no frequency shift. (The other mathematical solution v’ = 2c is not physical).
Therefore, the simple mechanism photonparticleinteraction cannot produce a redshift. (Compton/Thompson redshift and most “LightElectron” mechanisms are readily debunked, and no Nobel will be awarded for any of those.)
2c) Photon interacting with many massless particles
This slightly more complex interaction involves a photon interacting with a massless particle and producing one or more extra massless particles.
 The energy of the photonparticle system is E = h f1 + h f2.
 After the interaction, the photon is redshifted to frequency f1’ and the massless particles give a total energy E’ = h f1’ + h f2’ + h f3’ + …
Conservation of energy demands: h f1 + h f2 = h f1’ + h f2’ + h f3’ + … Here, the new massless particles can be produced in any directions, as long as the redshifted photon is reemitted in the direction of the original photon. In this equation, h f1’, h f2’, etc. represent the energy (or momentum) of the direction component parallel to the direction of photon 1.
Again, any frequency shift f1 to f1’ is possible in this mechanism. As in 2a) above, the photonmassless particle mechanism is not the explanation for the cosmological resdhift. (“LightLight” and “LightGravity” mechanisms are debunked altogether.)
2d) Photon interacting with a massive particle and other particles
For example, a photon interacts with an electron. The resulting photon is redshifted, the electron takes some energy and momentum, and other photons are emitted to satisfy energymomentum conservation.
As in case 2a), the redshift can take any value. That is not observed, therefore the mechanism photonparticlesinteraction is not the explanation for the cosmological resdhift. (This debunks the rest of the “LightElectron” mechanisms.)
3) Photon interacting with particles with internal structure (and internal energy)
When the particle present in the interaction can absorb quanta of energy (such as a hydrogen atom), different interactions are possible.
 Starting with a particle of mass m at rest and in the ground state (say an atom), the energy of the photonatom system is E = h f + mv^2/2 = h f (photon frequency f, atom velocity v = 0).
 After the interaction, the photon is redshifted to frequency f’ and the atom is moving at velocity v’ with an excitation energy A’. The energy of the system is E’ = h f’ + mv’^2/2 + A’. Conservation of energy demands: h f = h f’ + mv’^2/2 + A’.
Similarly, the momentum of the system is p = h f/c and p’ = h f’/c + mv’, before and after the interaction, respectively. Conservation of momentum demands: h f/c = h f’/c + mv’, or h f = h f’ + mv’c.
In this case, a frequency shift f  f’ close to A’/h is not excluded by energymomentum conservation. However, the mechanism produces a constant frequency shift f  f’ = A’/h, but not the wavelength independent redshift z = (f  f’)/f’ that is observed.
Therefore all photonatom redshift mechanisms are also debunked (listed under “LightHydrogen” mechanisms).
Adding other particles to this kind of interaction does not solve the wavelength dependence of this type of mechanism and adds a continuum of solutions as in cases 2a, 2c and 2d.
4) Photon interacting with a bulk medium
When a photon interacts with a bulk medium (such as dust, glass, a crystal, any solid, a grid, aether, etc.) it can lose any amount of energy since the medium has an energy continuum.
It is possible to have a medium that is structured in a way that would absorb an amount of energy proportional to the energy of the photon. As a result the redshift could mimic the cosmological redshift, or Doppler redshift.
However, such a mediun would interact with light to produce a rich variety of phenomena that are not observed. For a medium to mimic a Doppler redshift implies a very high absorption of the medium^{1}: no light could reach us from galaxies at distances of Gpc. But since nobody seems to know about this important property, I will give another description of the problem.
When light propagates in a medium that has a varying index of refraction, partial reflection occurs. For example, we see some 4% reflection of light on the surface of a transparent window. If any medium redshifts light between a galaxy and our telescope, its index of refraction must vary in a specific manner to produce the redshift. This would inevitably reflect the light of a distant galaxy and make it invisible to us.
Therefore all photonmedium redshift mechanisms are also debunked (listed under “LightDust” and “LightAether” mechanisms).
The “blurriness criticism of tiredlight” does not discredit tiredlight. However it eliminates almost every redshift mechanisms ever published so far.
Other types of redshift mechanisms are possible, but to be valid it must reproduce the Doppler effect without unobserved side effects.
2022822
© 2020–2024 Louis Marmet

Based on the KramersKronig relations, which are a different way to express conservation of energy and momentum. ↩