I Photon Frequency: Can a Photon Change Color?

[gmalcolm77]

Can a photon ever change frequency? What I mean is, can say a photon of red light ever become a photon of green or yellow light?

 

[vanhees71]

There are many ways that photons can change frequency. The most simple example is Compton scattering, where a photon is hitting a charged particle. In this process it changes its energy and thus its frequency according to the laws of energy-momentum conservation.

https://en.wikipedia.org/wiki/Compton_scattering#Derivation_of_the_scattering_formula

 

[gmalcolm77]

The most simple example is Compton scattering, where a photon is hitting a charged particle. In this process it changes its energy and thus its frequency according to the laws of energy-momentum conservation.

So the energy of a photon may be absorbed a little here and a little there?

 

[PeterDonis]

So the energy of a photon may be absorbed a little here and a little there?

No. A photon is not a little billiard ball, and neither is the electron that is Compton scattering it. They don't have particular trajectories that can be tracked, and they don't exchange energy a little at a time the way a pair of classical particles would do.

 

[tech99]

No. A photon is not a little billiard ball, and neither is the electron that is Compton scattering it. They don't have particular trajectories that can be tracked, and they don't exchange energy a little at a time the way a pair of classical particles would do.

I was wondering if the motion of a free electron is quantised?

 

[jtbell]

I was wondering if the motion of a free electron is quantised?

What kind of quantization are you thinking of?

 

[tech99]

What kind of quantization are you thinking of?

I was wondering if the coupling between electron and photon means that the electron can only have certain values of acceleration or certain values of velocity.

 

[Nugatory]

I was wondering if the coupling between electron and photon means that the electron can only have certain values of acceleration or certain values of velocity.

A free particle has a continuous energy spectrum, so no, any values are good (as long as we're respecting conservation of energy, momentum, and the like).

 

[gmalcolm77]

A free particle has a continuous energy spectrum, so no, any values are good (as long as we're respecting conservation of energy, momentum, and the like).

That sounds like a little here and a little there doesn't it? Or what am I missing?

 

[PeterDonis]

That sounds like a little here and a little there doesn't it?

No. Please take some time to learn how QM actually models objects like photons and electrons. The words "continuous energy spectrum" don't mean what you think they mean.

 

[Zafa Pi]

So the energy of a photon may be absorbed a little here and a little there?

From the above cited Wiki article:
Compton derived the mathematical relationship between the shift in wavelength and the scattering angle of the X-rays by assuming that each scattered X-ray photon interacted with only one electron. His paper concludes by reporting on experiments which verified his derived relation:

Thus the frequency change can be as small as you like.

Mind you, how does one know if the original photon changed frequency, or the original was absorbed and a new one emitted?

 

[PeterDonis]

the frequency change can be as small as you like

Yes, but that is still not the same as saying that the energy of the photon "may be absorbed a little here and a little there". In any given instance of Compton scattering, the energy transfer occurs all at once. More precisely, we can only observe the full transfer of energy, in one lump; we can't observe any gradual in between states while the transfer is in progress.

 

[Zafa Pi]

Yes, but that is still not the same as saying that the energy of the photon "may be absorbed a little here and a little there".

I wasn't sure what the OP meant by "a little here and a little there", so I provided something that may help him (or not) rather than merely tell him to learn QM.

More precisely, we can only observe the full transfer of energy, in one lump; we can't observe any gradual in between states while the transfer is in progress.

Agreed. And perhaps this helps him as well.

 

[vanhees71]

I was wondering if the motion of a free electron is quantised?

According to our contemporary best working theory, relativistic quantum field theory, everything obeys the rules of quantum theory from the tiniest elementary particle (like electrons) to the macroscopic matter and the electromagnetic fields of everyday life. The only thing we don't yet fully understand is the the gravitational interaction within the framework of quantum theory.

It is important to note that subatomic "particles" and "photons" are not well understood as miniature billiard balls in the sense of classical mechanics, which holds true for macroscopic objects, because we cannot resolve the microscopic degrees of freedom of all the particles making them up but only "relevant degrees of freedom" are sufficient to describe their behavior in the macroscopic realm, i.e., also this classical behavior is understood from quantum theory.

Photons are the least like classical particles under all circumstances, because they have a vanishing mass. E.g., there's no way to define a position for a photon. They are never localized at a point. Particularly you cannot localize them in the direction of their momentum. Indeed photons are certain states of the quantized electromagnetic field, the socalled one-photon Fock states. These states are rather defined by modes of the electromagnetic field. Any single-photon state can be described as the superposition of e.g. transverse plane-wave electromagnetic field modes, which are formally states with definite momentum and helicity, where helicity is the projection of the total angular momentum to the direction of momentum.

That's why almost always a better intuitive picture for photons is to think in terms of electromagnetic waves, interacting with charged particles, which themselves are also described by fields (e.g., the electron as a Dirac field, describing quanta of spin 1/2). Since electrons have a non-vanishing mass they are closer to classical particles and also have a position observable, but also here one must be careful and keep in mind that after all electrons as elementary particles also obey the rules of quantum theory rather than classical mechanics.

The description I've given about the Compton effect above was thus pretty brief. It's a kind of slang particle physicists use although it's strictly speaking not accurate, but you have to obey the rules of quantum (field) theory, and what I said above has to be understood in the sense of the rules of QFT either. The Feynman diagrams of quantum electrodynamics depicting electrons (and positrons) as straight lines with arrows on it (the arrow giving the flow of electric charge) and the photons by wiggly lines (without an arrow on it, because photons do not carry any kind of charge) also have an intuitive meaning only to a certain extent. First of all they imply the "kinematics" of energy-momentum conservation, and the external lines stand for free quanta like electrons and photons, i.e., the momenta associated with these external legs must also be "on the mass shell", i.e., obey the energy-momentum relation $E=\sqrt{\vec{p}^2+m^2}$, where I'm using the natural system of units, where $c$ and $\hbar$ are set to 1. Second, and most importantly, the Feynman diagrams should not be taken to litterally as space-time diagrams of processes ongoing with the field quanta, but seen as ingenious notations for mathematical expressions, helping us to calculate the socalled S-matrix (S=scattering) elements. The scattering matrix describes processes like Compton scattering or electron-electron scattering in a typical quantum theoretical way: The modules squared of an S-matrix element gives the probability rate for the process of some (asymptotic free) particles (usually two particles, as two protons in the LHC at CERN) in the initial state to undergo to some other asymptotic free final state (usually consisting of many particles).