Why physical understanding should precede the mathematical formalism - Conditional quantum probabilities as a case-study

Yakir Aharonov, Eliahu Cohen, David H. Oaknin

Research output: Contribution to journalArticlepeer-review

Abstract

Conditional probabilities in quantum systems which have both initial and final boundary conditions are commonly evaluated using the Aharonov-Bergmann-Lebowitz rule. In this short note, we present a seemingly disturbing paradox that appears when applying the rule to systems with slightly broken degeneracies. In these cases, we encounter a singular limit - the probability "jumps" when going from perfect degeneracy to negligibly broken one. We trace the origin of the paradox and solve it from both traditional and modern perspectives in order to highlight the physics behind it: the necessity to take into account the finite resolution of the measuring device. As a practical example, we study the application of the rule to the Zeeman effect. The analysis presented here may stress the general need to first consider the governing physical principles before heading to the mathematical formalism, in particular, when exploring puzzling quantum phenomena.

Original languageEnglish
Pages (from-to)668-673
Number of pages6
JournalAmerican Journal of Physics
Volume87
Issue number8
DOIs
StatePublished - 1 Aug 2019

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