IIIA4. The Photoelectric and Compton Effects

1. The Photoelectric Effect (1905). 

The first experiment to suggest that light had particlelike properties was the photoelectric effect.  A beam of light shone on a metal surface gives the electrons ejected from the metal a maximum energy of hc/λ (minus the potential energy necessary to get the electron out of the metal) where λ is the wavelength of the light, h is Planck=s constant, and c is the speed of light.  It gives this energy to the electrons instantaneously, regardless of the intensity of the beam.  In the classical view of waves, in which the energy is spread out over the entire wave, this was inexplicable.  To explain it, Einstein proposed that, embedded within the beam there must be localized particles of light—photons—that had energy hc/λ.  But that interpretation is not warranted, for quantum mechanics alone can explain the result. 

2. The Quantum Explanation of the Photoelectric Effect. 

To see this, note first that the group representation theory of section IIIA2 implies we can assign the energy hc/λ to the lightlike wave function (rather than to a conjectured particle of light).  Now if we ignore multiple scatterings, the light-electron Hamiltonian guarantees that the light wave function will interact separately with each electron wave function.  (This is similar to the localization argument of section IIIA5.) This implies that, if there are N electrons, then the state after the light wave function hits the electrons will be a sum of N terms, with only one electron having collided with the light wave function in each term.  Further, in each collision, the small fraction of the lightlike wave function that hits the electron can, in a completely inelastic collision, give the full energy of the wave function, hc/λ, to the electron.  That is, as is pointed out in the localization section IIIA5, subsection 7, the wave function does not act like a classical wave in this respect.

Each of the N terms, one for each electron, corresponds to a branch of the wave function, and one and only one of the branches will be perceived (IIIA3).  On each branch, the lightlike wave function can give its full energy, hc/λ, to the electronlike wave function.  This implies that quantum mechanics alone, without the conjectured existence of the photon, gives a full explanation of the photoelectric effect.  (Of course, Einstein did not know of the wave function or its nonclassical properties in 1905, so his particle-based explanation seemed necessary then.)  Thus the photoelectric effect cannot be used to argue for the existence of photons because it can be explained by quantum mechanics alone.

3. The Compton Effect (1922). 

The Compton scattering of light (actually x-rays) off electrons was the experiment which finally convinced physicists that light Ais@ a particle.  By careful measurements, it was found that energy and momentum were conserved if one assumed the light consisted of particles of energy hc/λ and momentum h/λ that scattered off particulate electrons.  The presumption was that this particlelike conservation of energy and momentum proved that light—and of course electrons—consisted of particles. 

4. Quantum Explanation of the Compton Effect. 

We can now see, however, that the presumption of underlying particles is not necessary.  For representation theory implies that we can simply say that the conserved energy and momentum belong to the photonlike (charge 0, mass 0, spin 1) and electronlike (charge Be, mass m_e, spin ½) wave functions that scatter off each other in accord with the equations of quantum mechanics.   As in the photoelectric effect, because of the nonclassical nature of the wave function (IIIA5, subsection 7), the light transfers the full complement of energy and momentum to the electronlike wave function even if the lightlike wave function is spread out over a much larger volume than the electronlike wave function.  Thus quantum mechanics give exactly the same result as the assumption that there are particles, so the Compton effect provides no reason to assume particulate photons, or electrons, exist.

Note: The photoelectric effect is really just the Compton effect in a more complicated environment.