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The Counterfactual Meaning of the ABL Rule

Quantum Physics 2007-05-23 v2

Abstract

The Aharonov-Bergmann-Lebowitz rule assigns probabilities to quantum measurement results at time t on the condition that the system is prepared in a given way at t_1 < t and found in a given state at t_2 > t. The question whether the rule can also be applied counterfactually to the case where no measurement is performed at the intermediate time t has recently been the subject of controversy. I argue that the counterfactual meaning may be understood in terms of the true value of an observable at t. Such a value cannot be empirically determined for, by stipulation, the measurement that would yield it is not performed. Nevertheless, it may or may not be well-defined depending on one's proposed interpretation of quantum mechanics. Various examples are discussed illustrating what can be asserted at the intermediate time without running into contradictions.

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Cite

@article{arxiv.quant-ph/0307082,
  title  = {The Counterfactual Meaning of the ABL Rule},
  author = {Louis Marchildon},
  journal= {arXiv preprint arXiv:quant-ph/0307082},
  year   = {2007}
}

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