0

Parent question here: Do photons lose energy after radiation pressure is applied to a perfect reflector?

So I have been told that radiation pressure that sets a mirror in motion (e.g. in outer space) translates to a photon's wavelength getting longer.

I cannot see why such a process could not go on and on as long as the photon finds a mirror on its way. So is the photon going to get a lower and lower frequency? And ultimately, can all its energy be converted into kinetic energy of the mirrors encountered?

I would add a bonus question here, how does this end? With the complete disappearance of the photon?

Deschele Schilder
  • 1
Winston
  • 3,226
  • Note: some answers here https://physics.stackexchange.com/questions/575788/is-there-a-way-to-convert-directly-most-electromagnetic-radiation-to-kinetic-ene – Winston Aug 26 '20 at 23:15

3 Answers3

1

These are consecutive scatterings of the individual photon ( an elementary particle) with the residual field of the atoms and molecules of the mirror.

The Feynman diagram would look something like this:

enter image description here

where the $e$ can be thought as a surface electron in the mirror.

Generally, the scattering can be elastic, or inelastic. If inelastic as the linked answer says there will be a small loss of the momentum of the photon and thus its wavelength will get incrementally smaller. BUT, since it is a mirror, the photon's direction will change and it will go backward with respect to the momentum direction of the mirror.

Consecutive mirrors have to be put in a random walk (quantum mechanical scattering is probabilistic as far as angles of scattering go) in space for the individual photon followed. If this can be done consecutively the photon will keep losing momentum/energy until it energy falls to the infrared level where it can be absorbed by raising the lattice of the mirror to a higher energy level, and the energy of the final photon ( it is a moot point whether the derivative photon is the same as the incoming, as we just have the four-vectors and the spin)will be part of the black body radiation of the last mirror.

Deschele Schilder
  • 1
anna v
  • 233,453
  • What if we adapt consecutive mirrors to the lowering of frequencies, i.e. providing a reflective surface to infrared frequencies once necessary? – Winston Aug 28 '20 at 00:54
  • at some number of reflections the energy levels of the matter composing the mirror will be the same as the energy of the reflected photons , and then they will be absorbed.as discussed in the answer. – anna v Aug 28 '20 at 03:41
  • I read your answer, but you wrote about infrared and I thought there are mirrors able to reflect infrared. And faraday cages can reflect radio waves as well. – Winston Aug 28 '20 at 19:32
  • Sure, but you are asking for a sequenial loss of energy, so when it hits the energy level of the material of the mirror, there is no more reflection. Infrared produced in another way with energy of photons below or above the mirror's lattice energy levels, will be reflected. It is the specific mirror, and in some point in your imaginary experiment the specific frequency will be hit. If you make a more elaborate experiment, checking for the frequency the mirror absorbs the infrared and using an immune one, then the photn wil be degraded in energy untilt te merge with CMB cosmic microwave – anna v Aug 29 '20 at 04:17
  • background https://en.wikipedia.org/wiki/Cosmic_microwave_background at the infrared tail of the distribution – anna v Aug 29 '20 at 05:40
1

Suppose we put two mirrors opposite each other. We let a gamma photon emerge somewhere between the mirrors (consider them infinite in extent). What happens?

I think that not so hard to imagine. A part of the photon's four-momentum will be transferred to the mirror. There are energy transfer and momentum transfer. When the 3-momentum of the photon is reversed, the energy transfer will be maximal (elastic collision). And of course, there will be in-between cases.
The gamma photon will eventually reach such a low frequency that it's able to excite some internal state of the mirror, which can be transformed into heat and the once so powerful gamma photon will have lost power, while the mirrors (to be considered to have a mass, even though infinite in extent) will have gained (opposite) momenta and a minimal warming up.

Deschele Schilder
  • 1
  • 1
    "The gamma photon will eventually reach such a low frequency that it's able to excite some internal state of the mirror" Good point. – Winston Aug 28 '20 at 00:50
0

There are basically three types of interactions between the mirror's atoms and the photon possible:

  1. elastic scattering, the photon keeps its energy and phase and changes angle

  2. inelastic scattering, the photon gives part of its energy to the atom/molecule and changes angle

  3. absorption, the photon gives all its energy to the atom/electron and ceases to exist

In your case, for solar sails, all three happens. It is just the ratio of these that is different. Most photons get elastically scattered, few get inelastically scattered, and very few absorbed.

Many people believe that spacecraft using solar sails are pushed by the Solar winds just as sailboats and sailing ships are pushed by the winds across the waters on Earth.[13] But Solar radiation exerts a pressure on the sail due to reflection and a small fraction that is absorbed.

https://en.wikipedia.org/wiki/Solar_sail

The momentum of the photon is a vector, and its energy is a scalar. But the two are connected, the magnitude of the momentum vector and the amount of energy. When the photon gets elastically scattered from the mirror, its momentum vector changes. This is then transferred to the mirror.

enter image description here

In the case of mirror reflection, you are correct, the photons are able to transfer part of their momenta to the mirror and thus give momentum to the mirror (move the mirror).

each photon loses a very small amount of energy when it reflects from a perfect reflector that can move. The reflected photons will have slightly longer wavelengths than their incident counterparts.

Do photons lose energy after radiation pressure is applied to a perfect reflector?

So basically, elastic scattering, inelastic scattering, and even absorption can give the atoms/molecules in the mirror a recoil. Yes, even absorption gives the atom/molecule a recoil. It is very important to understand that the in the case of absorption the energy and momentum of the photon gets transferred in part to the energy of the electron, and in part to the kinetic energy of the whole atom/molecule.

The transfer of momentum gets included properly when one incorporates the motion centre-of-mass R of the atom as a dynamical variable. In a quantized-field picture, the first, positive-frequency term becomes an annihilation operator which subtracts one photon from the field and adds ℏk momentum to the centre-of-mass motion, and the second term becomes a creation operator which emits one photon while eliminating ℏk momentum from the atom's motion.

How does one account for the momentum of an absorbed photon?

OK, but why do we need the solar sail to be shiny then? Because radiation pressure in the case of solar sails is dominated by elastic scattering. This is how most of the momentum is transferred, and only a little of the momentum is transferred through inelastic scattering and absorption. Now it is very important to understand that solar sails do work, because mirrors, made of shiny metals, have a very specific ability. The surface atoms/molecules in the mirror have available energy gaps that do not correspond to certain wavelength photons' energies. That is, only certain wavelength photons can get absorbed.

In terms of energy, sunlight at Earth's surface is around 52 to 55 percent infrared (above 700 nm), 42 to 43 percent visible (400 to 700 nm), and 3 to 5 percent ultraviolet (below 400 nm).[6]

https://en.wikipedia.org/wiki/Sunlight

In your question, it is very important to understand that solar sails, and mirrors have this specific ability in the emission spectra of the sun, infrared, visible and UV range for example. The mirror reflects (elastically scatters) these wavelength photons, and does not (or does only with very little probability) inelastically scatter or absorb them.

You are asking is it possible to transfer all the momentum of a photon through multiple reflection. The answer is that the final interaction of the photon will be a absorption always, and that is when the total (that is left over) energy and momentum of the photon will be transferred to the atom/molecule. During the reflections, only part of the photon's momentum is transferred, but as long as the photon exists, it will always have some momentum left. Only absorption can make the photon cease to exist, that is when all its momentum gets transferred.

Árpád Szendrei
  • 28,452