popper-logic-scientific-discovery

some observations on quantum theory 231
this section to an imaginary experiment proposed by Einstein 7 and
called by Jeans 8 ‘one of the most difficult parts of the new quantum
theory’; though I think that our interpretation makes it perfectly clear,
if not trivial.* 4
Imagine a semi-translucent mirror, i.e. a mirror which reflects part of
the light, and lets part of it through. The formally singular probability
that one given photon (or light quantum) passes through the mirror,
αP k(β), may be taken to be equal to the probability that it will be
reflected; we therefore have
αP k(β) = αP k(β - ) = 1 2.
This probability estimate, as we know, is defined by objective statistical
probabilities; that is to say, it is equivalent to the hypothesis that one
half of a given class α of light quanta will pass through the mirror
whilst the other half will be reflected. Now let a photon k fall upon the
mirror; and let it next be experimentally ascertained that this photon
has been reflected: then the probabilities seem to change suddenly, as it
were, and discontinuously. It is as though before the experiment they
had both been equal to 1 2, while after the fact of the reflection became
known, they had suddenly turned into 0 and to 1, respectively. It is
plain that this example is really the same as that given in section 71.* 5
And it hardly helps to clarify the situation if this experiment is
described, as by Heisenberg, 9 in such terms as the following: ‘By the
experiment [i.e. the measurement by which we find the reflected
7 Cf. Heisenberg, Physikalische Prinzipien, p. 29 (English translation by C. Eckart and
F. C. Hoyt: The Physical Principles of the Quantum Theory, Chicago, 1930, p. 39).
8 Jeans, The New Background of Science (1933, p. 242; 2nd edition, p. 246).
* 4 The problem following here has since become famous under the name ‘The problem
of the (discontinuous) reduction of the wave packet’. Some leading physicists told me in 1934
that they agreed with my trivial solution, yet the problem still plays a most bewildering
role in the discussion of the quantum theory, after more than twenty years. I have
discussed it again at length in sections *100 and *115 of the Postscript.
* 5 That is to say, the probabilities ‘change’ only in so far as α is replaced by β - . Thus αP(β)
remains unchanged 1 2; but β -P(β), of course, equals 0, just as β -P(β - ) equals 1.
9 Heisenberg, Physikalische Prinzipien, p. 29 (English translation: The Physical Principles of
the Quantum Theory, Chicago, 1930, p. 39). Von Laue, on the other hand, in Korpuskularund
Wellentheorie, Handbuch d. Radiologie 6 (2nd edition, p. 79 of the offprint) says quite
rightly: ‘But perhaps it is altogether quite mistaken to correlate a wave with one single