TITLE:
Quantum Effects from a Simple Card Game
AUTHORS:
Allen D. Allen
KEYWORDS:
Quantum Mechanics, Hidden Variables, Three Prisoners Problem, Bertrand’s Box Paradox, Monty Hall Problem
JOURNAL NAME:
Journal of Modern Physics,
Vol.5 No.18,
December
4,
2014
ABSTRACT: 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.