772 
mw TURE 
[JUNE 9, 1923 

proofs make use of exact conservation, and fail if it 
is denied ; so the denial makes it far more possible 
to believe in the continuity of Nature. In the course 
of various discussions it has been suggested to me 
that it would be more satisfactory to suppose that 
energy was exactly conserved, but could become 
latent. It is difficult to see what advantages such an 
idea can have; but, at any rate, there is an essential 
difference in it, for it would imply that the total 
apparent energy of an enclosed system will fluctuate 
about a fixed average value, whereas in the case of a 
statistical balance it may slowly wander away from 
the initial value and will exhibit no tendency to return 
to it. Of course the wave equations possess an energy 
integral, and so acceptance of the wave theory implies 
conservation of energy in free space; it is for inter- 
action with matter that it need not hold. 
The principal point which I wish here to make is 
that a mere acceptance of the wave theory implies 
certain important consequences, which must follow 
no matter what is the nature of the reaction between 
waves and matter—consequences which have perhaps 
not always been fully appreciated. The starting- 
point is that when a light wave acts on matter there 
is certainly a reaction on the light and that it is 
inconceivable that this should be anything but a 
spherical wave issuing from the matter. Now con- 
sider what happens when light is absorbed. Evi- 
dently the molecules must give out waves of such a 
type that the transmitted light is reduced in intensity, 
and the diminution can only arise through the inter- 
ference pattern composed by the plane and the 
spherical waves round about the produced direction 
of the incident beam. Moreover, the reduction is 
only possible if there is some phase relation between the 
incident and the emitted light. Examined from any 
other direction there will be no interference and the 
matter will appear to emit light—in other words, 
there must certainly be a scattered wave. It can be 
shown without more specific hypothesis that its 
magnitude is related to the optical constants of the 
matter in much the same way as it is in the classical 
theory. To any one accustomed to thinking only in 
terms of the electromagnetic theory there will be 
nothing remarkable in all this, though it is worth 
noting how much more general it is than the electro- 
magnetic theory; but I have never seen the point 
mentioned in connexion with the quantum theory, 
and it appears to me that this scattered wave, having 
a phase relation with the incident and determining 
the balance of energy, is one of the most essential 
features to be watched in any attempt to work out a 
quantum theory of absorption. 
In my former letter a similar argument led to the 
dispersion formula. Dispersion is more or less ade- 
quately described by the classical theory, provided 
that the electrons are supposed to be retained with 
such forces that in a free vibration they would emit 
light of frequency corresponding to some spectrum 
line. On the other hand, this line can only be 
described in terms of the quantum theory by the 
difference between the energies of two stationary 
states. Now the most striking merit of the Bohr 
theory was that it gave a simple physical meaning to 
the “terms” of the spectrum line, and the meaning 
ought also to apply for refraction. For this reason 
I tried the idea that an atom could only give out a 
standard type of wave, intending it to be the same wave 
as in a free emission, and was much surprised to find 
how easily this led to the ordinary dispersion formula. 
In a private letter Prof. Bohr pointed out to me an 
objection which makes it impossible to maintain the 
hypothesis in this simple form, because if the standard 
wave were as large as is indicated: by the quantum 
NO. 2797, VOL. 111] 

theory, it would not explain the refraction of very 
faint lights. He has since published the same 
criticism in Zs. f. Ph., vol. 13, 3, p. 117. I had over- 
looked this important point, but after writing the 
letter I came across another result which suggested 
the need for modification. This was that the 
intensity of scattering of hard y-rays would be 
proportional not to the intensity, but to the amplitude 
of the incident rays. This seemed a very improbable 
result, but not quite inconceivable in view of the 
well-known difficulties about the scattering of y-rays. 
In the course of a visit which I paid to Montreal, 
Dr. J. A. Gray, of McGill University, who is familiar 
with such work, very kindly agreed to examine the 
question experimentally, and has since informed me 
that he has verified that the scattered intensity is 
proportional to the incident intensity.1 In the 
meanwhile it was evident that a simple modification 
of the hypothesis would meet the difficulty, and it 
also meets Prof. Bohr’s objection. It was before 
assumed that the scattered light depended on the 
product of two factors. One of these was the prob- 
ability of excitation, proportional to the rate of 
change of the incident electric force; this I called 
A,(5E/ét)dt. The other was the amplitude a, of the 
standard wave. It is only necessary to alter the 
assumptions by taking A,dt as the probability and 
a,(6E/ét) as the amplitude of the scattered wave for 
both objections to disappear. The excited wave is 
still characteristic of the atom in frequency and 
phase, but its amplitude is proportional to the 
incident wave. This is the form of the theory with 
which I have since been working. But the failure 
of the standard wave is a very severe blow to 
accepted ideas of the quantum theory. It is not 
possible to suppose that the atom goes right into its 
upper quantum state; but instead we are forced to. 
believe that the atom, so to speak, knows what the 
upper state is like without going there, and the 
exact opposite of this is one of the greatest merits of 
the Bohr theory. We must now believe (and the 
same conclusion can be drawn from the views of 
Bohr in the paper already cited) that the two 
stationary states associated with a spectrum line have 
a much more intimate connexion than is suggested 
by the theory of emission, a connexion of which 
their dynamical formulation gives no hint ; and once 
this is admitted it becomes very questionable exactly 
what the physical nature of the states may be, and 
how much further we may depend on the simple 
ideas hitherto in vogue. 
The necessary abandonment of the standard wave 
destroyed the strongest argument for my hypothesis, 
as it could no longer unite the classical theory with 
the simple form of the quantum theory. Neverthe- 
less it seemed well worth while to follow it up, for it 
explains interference while departing very widely 
from the difficulties in which the classical theory is 
involved. In the course of later work it has appeared 
that all the ordinary phenomena of optics are given 
quite satisfactorily, including dispersion, metallic 
reflection, optical activity, X-ray reflection, and 
scattering as exemplified in the light of the sky. 
The theory gives a straightforward interpretation of 
one of the two effects recently discovered by Clark 
and Duane (Proc. Nat. Acad., oe te 126 and p. 131). 
For the “ X-peak’’ I know of explanation, but 
the other effect strongly suggests that white X-rays 
can excite the characteristic radiations of the atoms 
of a crystal in phase. In this instance I think my 
hypothesis has very distinct advantages over the 
classical theory, but it would be premature to discuss 
1 The test consisted in varying the distance of the source—changing its 
amount would not have done. 
