popper-logic-scientific-discovery

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new appendices
with, its co-ordinates may become smeared by the smearing of the
frame of reference.
(4) Bohr’s reply seems to me unacceptable for at least three
different reasons.
First, prior to the proposed imaginary experiment of Einstein,
Podolsky, and Rosen, the reason given for the smearing of the position
or momentum of a system was that by measuring it, we had interfered
with the system. It seems to me that Bohr, surreptitiously, dropped this
argument, and replaced it by saying (more or less clearly) that the
reason is that we interfere with our frame of reference, or with the
system of co-ordinates, rather than with the physical system. This is too
big a change to be allowed to pass unnoticed. It would have to be
explicitly acknowledged that the older position was refuted by the
imaginary experiment; and it would have to be shown why this does
not destroy the principle on which it was built.
We must not forget, in this connection, what the imaginary experiment
of Einstein, Podolsky, and Rosen, was intended to show. It was
intended merely to refute certain interpretations of the indeterminacy formulae;
it was certainly not intended to refute these formulae. In a sense,
Bohr’s reply, though not explicitly, acknowledged that the imaginary
experiment succeeded in its purpose, for Bohr merely tried to defend
the indeterminacy relations as such: he gave up the view that the measurement
would interfere with the system A which it was supposed to
smear. Moreover, the argument of Einstein, Podolsky, and Rosen could
be carried a little further by the assumption that we measure the position
A (accidentally) at the same instant of time at which we measure
the momentum of B. We then obtain, for that instant of time, positions and
momenta of both A and B. (Admittedly, the momentum of A and the
position of B will have been destroyed or smeared by these measurements.)
But this is sufficient to establish the point which Einstein,
Podolsky, and Rosen wanted to make: that it is incorrect to interpret
the indeterminacy formulae as asserting that the system cannot have
both a sharp position and a sharp momentum at the same time—even
though it must be admitted that we cannot predict both at the same time.
(For an interpretation which takes account of all this, see my Postscript.)
Secondly, Bohr’s argument that we have ‘cut ourselves off’ from the
other frame of reference seems to be ad hoc. For it is clearly possible to