Undecidable Classical Properties of Observers |
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Authors: | Email author" target="_blank">Sven?AertsEmail author |
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Institution: | (1) Center Leo Apostel for Interdisciplinary Studies (CLEA) and Foundations of the Exact Sciences (FUND), Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium |
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Abstract: | A property of a system is called actual, if the observation of the outcome of the test that pertains to that property yields
an affirmation with certainty. We formalize the act of observation by assuming the outcome itself is an actual property of
the state of the observer after the act of observation and correlates with the state of the system. For an actual property
this correlation needs to be perfect. A property is called classical if either the property or its negation is actual. We
show by a diagonal argument that there exist classical properties of an observer that he cannot observe perfectly. Because
states are identified with the collection of properties that are actual for that state, it follows no observer can perfectly
observe his own state. Implications for the quantum measurement problem are briefly discussed.
PACS: 02.10-v, 03.65.Ta |
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Keywords: | undecidability observation self-reference quantum measurement problem |
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