摘要
A well-known, classical conundrum, which is related to conditional probability, has heretofore only been used for games and puzzles. It is shown here, both empirically and formally, that the counterintuitive phenomenon in question has consequences that are far more profound, especially for physics. A simple card game the reader can play at home demonstrates the counterintuitive phenomenon, and shows how it gives rise to hidden variables. These variables are “hidden” in the sense that they belong to the past and no longer exist. A formal proof shows that the results are due to the duration of what can be thought of as a gambler’s bet, without loss of generalization. The bet is over when it is won or lost, analogous to the collapse of a wave function. In the meantime, new and empowering information does not change the original probabilities. A related thought experiment involving a pregnant woman demonstrates that macroscopic systems do not always have states that are completely intrinsic. Rather, the state of a macroscopic system may depend upon how the experiment is set up and how the system is measured even though no wave functions are involved. This obviously mitigates the chasm between the quantum mechanical and the classical.
A well-known, classical conundrum, which is related to conditional probability, has heretofore only been used for games and puzzles. It is shown here, both empirically and formally, that the counterintuitive phenomenon in question has consequences that are far more profound, especially for physics. A simple card game the reader can play at home demonstrates the counterintuitive phenomenon, and shows how it gives rise to hidden variables. These variables are “hidden” in the sense that they belong to the past and no longer exist. A formal proof shows that the results are due to the duration of what can be thought of as a gambler’s bet, without loss of generalization. The bet is over when it is won or lost, analogous to the collapse of a wave function. In the meantime, new and empowering information does not change the original probabilities. A related thought experiment involving a pregnant woman demonstrates that macroscopic systems do not always have states that are completely intrinsic. Rather, the state of a macroscopic system may depend upon how the experiment is set up and how the system is measured even though no wave functions are involved. This obviously mitigates the chasm between the quantum mechanical and the classical.
