popper-logic-scientific-discovery

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new appendices
of insuperable barriers to the precision of our measurements; (b) the disturbance of the
measured object by the process of measurement, whether of position or of
momentum; and (c) the impossibility of testing the spatio-temporal ‘path’ of the
particle. I believe that Heisenberg’s arguments tending to establish these
points are all clearly invalid, whatever the merits of the three points in
themselves may be. The reason is that Heisenberg’s discussion fails to
establish that measurements of position and of momentum are symmetrical; symmetrical,
that is, with respect to the disturbance of the measured object
by the process of measurement. For Heisenberg does show with the help
of his experiment that in order to measure the position of the electron we
should have to use light of a high frequency, that is to say, high energy
photons, which means that we transfer an unknown momentum to the
electron and thus disturb it, by giving it a severe knock, as it were. But
Heisenberg does not show that the situation is analogous if we wish to
measure the momentum of the electron, rather than its position. For in
this case, Heisenberg says, we must observe it with a low frequency
light—so low that we may assume that we do not disturb the electron’s
momentum by our observation. The resulting observation (though revealing
the momentum) will fail to reveal the electron’s position, which will
thus remain indeterminate.
Now consider this last argument. There is no assertion here that we
have disturbed (or ‘smeared’) the electron’s position. For Heisenberg
merely asserts that we have failed to disclose it. In fact, his argument
implies that we have not disturbed the system at all (or only so slightly
that we can neglect the disturbance): we have used photons of so low
an energy level that there simply was not enough energy available to
disturb the electron. Thus the two cases—the measurement of position and that of
momentum—are far from analogous or symmetrical, according to Heisenberg’s
argument. This fact is veiled, however, by the customary talk (positivist
or operationalist or instrumentalist talk) about the ‘results of measurement’
whose uncertainty is admittedly symmetrical with respect to position
and momentum. Yet in countless discussions of the experiment,
beginning with Heisenberg’s own, it is always assumed that his argument
establishes the symmetry of the disturbances. (In the formalism, the
symmetry between position and momentum is complete, of course,
but this does not mean that it is accounted for by Heisenberg’s imaginary
experiment.) Thus it is assumed—quite wrongly—that we disturb the