I am quoting this post:
There are two ways to show that photo-absorption by an electron is impossible.

• The simplest is energy momentum conservation. The electron can absorb the momentum, but in doing so it can only account for 0.00024% of the energy. I used this method here.
  
• Another way is the inconsistency of momentum conservation with impulse directions. By conservation of momentum, the impulse to the electron must be along the direction of the photon motion. But by consideration of the wave, the impulse must be perpendicular to the photon direction. The two requirements cannot be reconciled in an alleged absorption of a photon by an electron, and this is another reason it is impossible.

It is Lyndon's error... not anyone else's.... to fail to account for the inevitable transverse impulse and consequent scatter that always arises in photon-electron interactions. In real physics, there is always a transverse component, and therefore always a scatter angle for the photon.

Many BABB contributors are inclined to think these discussions are a waste of time. I don't agree. The point is not to teach Lyndon anything... that is plainly impossible. But looking into each new error and distraction is a chance to learn something, even if Lyndon himself never avails himself of the opportunity.

So how does photo-absorption occur in real physics? Don't physicists speak of electrons absorbing photons? Can't the objections I am raising carry over to photo-absorption or electron-photon interactions proposed in text books?

• In real physics, the absorption of a photon is never with an electron a meter away from other particles. It is with an electron in very close association with a positive nucleus; an atom. In this case, the fields push the electron one way, and the nucleus the other, and these transverse momentum contributions cancel. The two particles are given an increased separation, which corresponds to an increase in potential energy. In quantum physics the electron jumps to an outer orbital which means that the atom is in an excited state.
  
• In interactions between a photon and an electron considered classically as a wave interaction, motion of the particle sets up new fields that combine with fields of the incident wave. The end result is a new direction for the photon. This is essential to conserve momentum, and it also feeds back into motions of the particle while the interaction proceeds. Lyndon's unquantified comments about the wave neglect to consider direction change in the wave itself.
  
• In interaction with an electromagnetic wave, the particle is initially accelerated perpendicular to the photon's line of motion. Given this motion, the particle is then able to interact also with the magnetic fields associated with a photon, and this acts perpendicular to the field, and perpendicular to the particle motion, to contribute a further force parallel to the photon's line of motion. The effect is small, but it exists; but Lyndon has ignored magnetic fields entirely.

This serves to demonstrate that in real physics, you should get the same answer, even if you apply different kinds of analysis to the problem. No matter which way you look at it, Lyndon's interaction is impossible.

• It violates conservation of energy/momentum.
• It ignores the transverse impulse that scatters the photon.
• It uses photo-absorption calculations for particles that don't absorb photons.
• It uses unquantified hand waving to transfer most the incoming energy into the plasma; in conflict with the maximum possible transfer through the calculated forces.
• It brings all that energy back from the plasma, by means unexplained, to power re-emission of a redshifted photon.
• It confuses oscillatory motions of a particle with density waves in billions of randomly moving particles.
• It uses the wrong cross section. No published source; no set of tabulated results, no discussion or theoretical calculation, ever uses a cross section of 2rλ.

ROFL!

This oscillation only occurs while the electron is still interacting with the photon's electromagnetic fields. Once the photon is gone (either absorbed or emitted) this oscillation is over, and all that is left is a small residual impulse on the electron. Lyndon proposes that a photon is absorbed. So where does the energy go? He can't appeal to the oscillations that occur while the photon is still involved. It's gone mate, by his own description.

Lyndon should use his own figures. What I actually say is that 99.99976% of the energy is unaccounted for. Lyndon can try and put that into oscillations if he likes; but it is deliberately dishonest to pretend that I say the energy goes into oscillations. Oscillations are physically unable to get that much energy from a 500 nm photon; and I have backed that up by quantified consideration of the available forces.

If you want to involve other particles a meter or more away, be my guest, but quantify the forces involved. If the energy ends up in motions of any other particles, then you also have to get it all back to power the emission of a redshifted photon!

Here is Lyndon's attempt to manage the energy momentum budget. I have highlighted in blue one particularly reprehensible bit of deliberate dishonesty; and I shall show some trivial errors that make this unacceptable even for high school level.

What is this "according to Sylas" nonsense? I don't use oscillations. I point out that you CAN'T get oscillations that have the requisite energy. I point out that the ACTUAL energy of any subsequent oscillation for the electron is the kinetic energy it gets in the collision, which is more than five orders of magnitude LESS than what Lyndon quotes here. I've done this repeatedly, in post after post after post, and suddenly Lyndon pops up with an oscillation in which the kinetic energy is that of the photon; NOT the energy of the electron.

This is dishonest.

The above still fails to be an energy-momentum budget, because it never mentions the momentum!
Momentum of electron = sqrt(2Em) = 8.51e-25 kg m/s.
Initial momentum of the 500 nm photon = 1.33e-27 kg m/s.
Now the momentum does not balance. The magnitudes differ by a factor of 642!

In his own paper, Lyndon calculates kinetic energy for the electron as 9.65e-25, using conservation of momentum. [[See formula Q^2/2mc^2 on the bottom of page 3, and plug in the numbers.]] That is the energy for the electron that belongs in the above picture.

A high school physics student should be able to figure out how to give a quantified energy momentum budget. You have to calculate numbers for energy, and numbers for momentum, and show that they balance. Lyndon has never done this.

Cheers -- Sylas

PS. I had not heard of the Mössbauer Effect before reading Lyndon's stuff. Initially I accepted his description of straight line transmission with no scatter, and repeated it myself in some posts. I now suspect this is wrong, and that photons can be scatted in all directions. The distinguishing feature is not a lack of scatter, but negligible recoil in the atom, and hence negligible change in wavelength. I'll be checking this further to confirm or retract; whether I'm right or wrong I'll have learned something.

[[Edit to fix a typo in one formula; numbers unchanged.]]