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By Gert Roepstorff
The current textual content is designed to introduce graduate scholars to the practical integration process in modern physics as painlessly as attainable. the writer concentrates at the conceptual difficulties inherent within the direction critical formalism. The notable interaction among stochastic approaches, statistical physics and quantum mechanics involves the fore. The reader will locate all of the equipment of basic curiosity amply illustrated by means of vital actual examples.
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30 Complementarity, Epistemology, and Quantum Mechanics as an Information Theory The situation just described, sometimes also known as the quantum measurement paradox, is remarkable. Other standard locutions include strange, puzzling, mysterious (and sometimes mystical), and incomprehensible. The reason for this reaction is that, if one speaks in terms of particles themselves, in the interference picture the behavior of each particle appears to be “influenced” by the location of the slits. Or, even more radically, individually or (which is hardly less troubling) collectively, particles appear somehow to “know” whether both slits are or are not open, or whether there are or are not counting devices installed.
As Bohr says: This point is of great logical consequence, since it is only the circumstance that we are presented with a choice of either tracing the path of a particle or observing interference effects, which allows us to escape from the paradoxical necessity of concluding that the behavior of an electron or a photon should depend on the presence of a slit in a diaphragm through which it could be proved not to pass. We have here to do with a typical example of how the complementary phenomena appear under mutually exclusive experimental arrangements … and are just faced with the impossibility, in the analysis of quantum effects, of drawing any sharp separation between an independent behavior of atomic objects and their interaction with the measuring instruments which serve to define the conditions under which the phenomena occur.
Indeed, as a result, the statistical nature of quantum mechanics appears to be irreducible (PWNB 2, p. 34). It is itself an aspect of “the peculiar individuality of quantum effects,” the concept to be discussed in more detail in Chapter 3. In other words, we do not know and, in Bohr’s view, ultimately cannot know why certain probability rules, say, those of Planck’s law or Born’s square moduli rule for calculating quantum-mechanical probabilities in fact apply, but they do. Whenever the interference pattern is found, one cannot assign probabilities to the two alternative “histories” of a “particle” passing through either one slit or another on its way to the screen.