1 8 6 D O C U M E N T 2 9 8 N O V E M B E R 1 9 2 1
3. Let a homogeneous beam of parallel rays of light have the energy E per unit
volume. Then the Poynting energy current is ( ) cE, also the momentum per unit
volume ( ) ; on a plane perpendicular to the direction of propagation there is a
Maxwell pressure . All this stems from the light quanta. If their number (mean
over a longer period) per unit volume is N, then . ( ) is here the energy
transported by the quanta, ( ) the transported momentum; ( ) the momentum of the
quanta per unit volume.
4. In a ponderable transparent medium—to be precise, so as to take a direct look
at the most general case—in a double refractive body with dispersion, the quanta
move in the direction of the ray, at the group velocities u of the bundle of rays. Thus
a quantum always remains in the train of waves to which it belongs.
The quantity of a quantum still is . Now, however, the momentum is
.
5. From the principles of the special theory of relativity one can derive how the
various quantities change when one moves by familiar transformation to a new sys-
tem of coordinates . One can also transform the interference radiation
independent of it. It becomes apparent that even in the new system of coordinates
the quantum moves in the direction of the Poynting vector (light-ray) and that the
new energy changes in the same ratio as the frequency of the interference radiation,
so also holds in the new system. The same is obtained for the new mo-
mentum for the quantum,
.
6. A quantum can only really disappear as such in absorption. If the intensity of
a beam of light changes by reflection off a moving mirror, the number of quanta
remains unchanged, but a change takes place in the quantity of energy of the indi-
vidual quanta, namely, exactly in the same ratio as the change in frequency of the
light. (This is correlated with [no.] 5.) The pressure on the moving mirror and the
work of this pressure are calculated from the change that the momentum and the
quantity of energy of the quanta suffer upon reflection.
7. Earlier I once raised doubts about assuming that quanta were concentrated
radiant energy, in that one could not understand the advantage of a large lens for
resolving power as a single quantum cannot fill the lens’s entire surface.[7]
This
reservation no longer stands. The influence of the large aperture would already be
1E
c
-- -
E
N
E
---- - =
h =
u
c2
--------
x y z t
h =
u
c2
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