Cramer, in the name of "Copenhagen"
Let us now establish the particulars of Cramer's argument in relation to the Copenhagen Interpretation.
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Two Measurement Options:
Take a look at the
diagram. It shows a modification of the Afshar setup in which the wire grid WG has been removed. For this setup, consider the following two measurement options:
(a) Before light can reach the lens, at a screen labeled
sigma1, measure an interference pattern;
(b) After light has passed through the lens, at a screen
labeled
sigma2, measure two distinct, separate images,
situated at 1' and 2'.
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Cramer's Rendition:
Here is what Cramer has to say, in the name of "Copenhagen", regarding these two options (see
diagram):
(C-a) Measure at
sigma1, the interference pattern, giving the
wavelength and the
momentum of the photon;
(C-b) Measure at
sigma2, which slit the particle passed
through, giving its
position.
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Complementarity:
By statements (C-a) and (C-b), Cramer purports that, according to the Copenhagen Interpretation, the following is true:
P1: Options (a) and (b) are experiments which measure
complementary attributes of the quantum system.
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Argument for (C-b):
Cramer's statement (C-b) regarding option (b) is built upon the following type of argument:
P2: A photon arriving at 1' (2') must have passed through slit 1 (2) and not 2 (1). Therefore, a measurement at
sigma2 corresponds to a "determination" of which slit the photon went through.
Since this type of argument serves as a basis for Cramer's statement (C-b) concerning (b), and (C-b) itself is said in the name of "Copenhagen", it must be that the precise sense in which an argument like P2 eventually leads to Cramer's (C-b) is seen by Cramer to be deemed valid by the Copenhagen Interpretation.
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Cramer's Conclusion:
In a final step, the wire grid WG is put back into the arrangement of (b) to give, once again, the Afshar setup. With all of the above in mind, Cramer then concludes - in the name of "Copenhagen" - regarding the Afshar experiment (see
diagram):
The measurement-type forces particle-like
behavior, so there should be no interference, and
no minima ...
This statement makes the intended meaning of Cramer's (C-b) absolutely clear. That intended meaning is equivalent to the following proposition:
P3: In option (b), the measurement performed at
sigma2 is
physically equivalent to a nondemolition measurement which takes place at the site of the slits and determines which slit the photon passes through.
To repeat, according to Cramer, P3 (like the propositions P1 and P2 above) is deemed correct by "Copenhagen".