Quantum-Mechanical Self-Measurement

Abstract

The idea of self-measurement by a quantum-mechancal automaton is presented, and the conclusions that are typically reached about what we can come to know from doing self-measurements are shown to be mistaken. Specifically, it is shown that, while we are capable of predicting and measuring the values of two incompatible observables, we are incapable of knowing both these values simultaneously. This is an example of the interesting limitations quantum mechanics places on knowledge.

For helpful comments on previous versions of this paper, I would like to thank Jeff Barrett, Jeff Bub, Rob Clifton, Dennis Dieks, Tim Maudlin, Chad Mohler, Jitendra Subramanyam, Bas van Fraassen, Pieter Vermaas, and Bob Weingard. I would also like to thank David Albert for inspiring me to think about self-measurement. This material is based upon work supported under a National Science Foundation Graduate Research Fellowship.