Beginning with a round-up of questions from the previous section, we offer some answers, choose an interpretational strategy, and draw some conclusions.
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A harvest of questions |
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Contextuality |
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Try to fill in the following table in such a way that each cell contains either a +1 or a –1, that the product of the three X components equals –1, and that the product of every pair of Y components equals the remaining X component.
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Bohm's story |
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In this article we learned that if there is nothing — no event, no state of affairs, anywhere, anytime — from which the slit taken by an electron can be inferred, then the following statements cannot both be true:
- Each electron goes through a single slit — either L or R.
- The behavior of an electron going through, say, the left slit does not depend on whether the right slit is open or shut.
According to one attempt to make sense of the quantum formalism, originally due to David Bohm, it is the latter assumption that is false. Bohmians believe that each electron is a well-behaved classical particle, in the sense that it follows a mathematically precise path — its position at any moment is given by three real numbers (coordinates).
- Then how does the condition of the right slit (open or shut) affect the behavior of an electron that goes through the left slit?
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Meaning of "both" |
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In rejecting Bohm's story, we reject the first of two assumptions that, together, are inconsistent with both quantum mechanics and the empirical data. (Bohmians reject the second.) Under the conditions stipulated by Rule B, it is not the case that each electron goes through a single slit — either L or R. In some sense, each electron goes through both slits.
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Interpretational strategy: meaning of "meaningless" |
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In rejecting Bohm's story, and with it all cryptodeterministic interpretations of the quantum-mechanical laws, we are in fact adopting the following interpretational strategy:
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Probability 1 — not sufficient for "is" or "has" |
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It has often been asserted (not least by Einstein) that if quantum mechanics assigns probability 1 to a possible outcome of a measurement of an observable, then the corresponding value is possessed by this observable even if the measurement is not actually made. Probability 1 is sufficient for "is" or "has". Why is this wrong?
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To be is to be measured |
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If probability 1 is not sufficient for "is" or "has," then what is?
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The relative reality of our distinctions |
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