I Rayleigh scattering and reversibility

[J O Linton]

TL;DR

Is Rayleigh scattering a reversible process?

In many books and websites the elastic (Rayleigh) scattering of low energy photons off an atom is stated as being reversible. It seems to me that it is a mistake to think that all elastic processes are reversible. If a process is reversible it should be possible to calculate the initial state of the system given the final state. This is not the case with RS because the emitted photon can be emitted in any direction at random so there is no way of calculating the direction it was originally moving in.
If RS is an irreversible process then it would provide the ideal candidate for the random element which is required to explain the success of Boltzmann's statistical theory of gases and the Second Law of Thermodynamics. Is there something wrong with this argument?

 

[tech99]

I should have thought that a single scattering particle acts as a dipole re-radiator, so if we know its geometry and orientation, then the characteristics of the scattered wave can be calculated. I am not sure that Rayleigh scattering is necessarily a quantum process as it can occur with long wavelengths and correspondingly large objects - the attenuation between source and detector will be the same in both directions (Rayleigh-Carson law of reciprocity) and so is reversible. Of course, no optical system of source-detector if operated with single photons can be predicted from moment-to-moment and so is non reversible.

 

[J O Linton]

It sounds as if you largely agree with me. The scattering of a single photon off an atom will impart an impulse typically of the order of the momentum of the photon in a random direction.

 

[renormalize]

It sounds as if you largely agree with me. The scattering of a single photon off an atom will impart an impulse typically of the order of the momentum of the photon in a random direction.

OK, but why even bother with Rayleigh scattering? If you simply take an isotropic point-source of light that is sufficiently dim, it will emit detectable individual photons, each in a "random direction". How does that help explain "Boltzmann's statistical theory of gases and the Second Law of Thermodynamics"?

 

[J O Linton]

If gas molecules were perfectly elastic then all the collisions would be reversible and entropy would stay the same. In order to explain the 2nd law there must be some occasional randomness. I am suggesting that it is RS which provides this randomness.

 

[J O Linton]

Sorry - What I meant to say was: since the collisions between gas molecules are perfectly elastic and reversible, then in the absence of any photons, entropy would stay the same etc.

 

[renormalize]

If gas molecules were perfectly elastic then all the collisions would be reversible and entropy would stay the same. In order to explain the 2nd law there must be some occasional randomness. I am suggesting that it is RS which provides this randomness.

I don't follow your reasoning.
An ideal classical gas has only elastic collisions, with no involvement of photons (a quantum concept) or Rayleigh scattering. Yet the entropy of an ideal gas increases when that gas is subjected to an irreversible, out-of-equilibrium process (e.g., adiabatic free expansion).
How is your idea consistent with this fact?

 

[J O Linton]

During adiabatic expansion thermodynamic entropy increases in the sense that there are a lot more ways to put atoms in a large box than a small one. But this assumes that during the expansion all correlation between the motions of the molecules is lost. If the correlation is never lost then reversing the velocities of all the molecules will put them back where they started. (Loschmidts paradox). If the correlations remain the expanded gas may look disordered but it is in fact highly ordered and the entropy would be unaltered. For entropy to increase there must be a random element in the process somewhere and I am proposing that this is provided by RS. Do you have an alternative suggestion?

 

[renormalize]

For entropy to increase there must be a random element in the process somewhere and I am proposing that this is provided by RS. Do you have an alternative suggestion?

No, because I disagree that there must be an additional "random element" to explain entropy increase. My take on "Loschmidt's paradox" aligns with that of @PeterDonis as expressed in this thread:

B

B Thread 'Loschmidt's paradox and free gas expansion'

Dec 19, 2021

Following up on a previous discussion: https://www.physicsforums.com/threa...entum-in-a-closed-system.1009693/post-6570341

An uncontained system of particles interacting only by elastic collision is the same as a gas undergoing free expansion. If, for simplicity, the particles are assumed to be identical with equal mass, then the evolution of the system can be treated as if the particles pass through each other without colliding and can be drawn as just the straight world-lines extending from the initial velocity vectors of each particle (both backward and forward...

• bobdavis
• Expansion Gas Gas expansion Paradox
• Replies: 5
• Forum: Thermodynamics

Loschmidt's paradox suggests that it's paradoxical for an irreversible process to arise from time-symmetric dynamics.

Yes, but we now understand that this is wrong. The time asymmetry does not arise from the dynamics but from the special nature of the initial conditions. You chose initial conditions with the particles all bunched up in a very small region of space, surrounded by emptiness. That is a very, very unlikely condition, and its time evolution will, as you note (though you have the details of the reasoning wrong), cause the system of particles to expand, occupying more and more space as time passes. That is the reason why the time evolution increases entropy: because there are many, many more ways for the particles to occupy a larger region of space than a smaller one, and you chose a special initial condition where they occupied a small space.