charge, there is a driving force in the direction of the light beam. This is called radiation Ire or light pressure. Let us determine how strong the radiation pressure is. Evidently it is F= qu B or, since everything is oscillating, it is the time average of this, ( F. From(34. 2 )the strength of the magnetic field is the same as the strength of the electric field divided by c, so we need to find the average of the electric field, times the velocity, times the charge, times 1/c:( F= quE/c. But the charge g times the field E is the electric force on a charge, and the force on the charge times the velocity is the work dw /dt being done on the charge! Therefore the force, the"pushing momentum, " that is delivered per second by the light, is equal to 1/c times the energy absorbed from the light per second! That is a general rule, since we did not say how strong the oscilla- tor was, or whether some of the charges cancel out. In any circumstance where light is being absorbed, there is a pressure. The momentum that the light delivers is al ways equal to the energy that is absorbed, divided by c (F=dw/dt (3424) That light carries energy we already know. We now understand that it als carries momentum, and further, that the momentum carried is always 1/ c times When light is emitted from a source there is a recoil effect: the same thing reverse. If an atom is emitting an energy w in some direction, then there is a recoil momentum p= w/c. If light is reflected normally from a mirror, we get twice the force That is as far as we shall go using the classical theory of light. Of course we particle. The energy of a light-particle is a constant times the frequency. ts like a know that there is a quantum theory, and that in many respects light act (3425) We now appreciate that light also carries a momentum equal to the energy divide by c, so it is also true that these effective particles, these photons, carry a momentum p=W/c=加u/c=掀 The direction of the momentum is, of course, the direction of propagation of the light. So, to put it in vector form, (3427) We also know, of course, that the energy and momentum of a particle should form a four-vector. We have just discovered that w and k form a four-vector. Therefore it is a good thing that (34.27)has the same constant in both cases; it means that the quantum theory and the theory of relativity are mutually consistent Equation (34.27)can be written more elegantly as Pu=hku, a relativistic equation, for a particle associated with a wave. Although we have discussed this only for photons, for which k(the magnitude of k)equals a/c and p=w/c, the elation is much more general. In quantum mechanics all particles, not only photons, exhibit wavelike properties, but the frequency and wave number of the waves is related to the energy and momentum of particles by (34. 27)(called the deBroglie relations)even when p is not equal to w/c In the last chapter we saw that a beam of right or left circularly polarized light also carries angular momentum in an amount proportional to the energy 8 of the wave. In the quantum picture, a beam of circularly polarized light is regarded as a stream of photons, each carrying an angular momentum + h along the direc- tion of propagation. That is what becomes of polarization in the corpuscular point the photons carry angular momentum lik rifle bullets. Bu to discuss these ideas more fully in a later chapter on Quantum Beharo hall have bult” picture is really as incomplete as the“wave”' picture, and we