The Impossibility of Accurate State Self-Measurements

It is shown that it is impossible for an observer to distinguish all present states of a system in which he or she is contained, irrespective of whether this system is a classical or a quantum mechanical one and irrespective of whether the time evolution is deterministic or stochastic. As a corollary, this implies that it is impossible for an observer to measure the EPR-correlations between himself or herself and an outside system. Implications of the main result are discussed for how we have to conceive of universally valid theories.

[1]  H. Primas,et al.  Foundations of Theoretical Chemistry , 1980 .

[2]  Rolf Herken,et al.  The Universal Turing Machine: A Half-Century Survey , 1992 .

[3]  Asher Peres,et al.  IS QUANTUM THEORY UNIVERSALLY VALID , 1982 .

[4]  A. Tarski Truth and proof. , 1969, Scientific American.

[5]  David Finkelstein,et al.  Finite physics , 1988 .

[6]  H. Stowell The emperor's new mind R. Penrose, Oxford University Press, New York (1989) 466 pp. $24.95 , 1990, Neuroscience.

[7]  E. Schmidt Zur Theorie der linearen und nichtlinearen Integralgleichungen , 1907 .

[8]  Maria Luisa Dalla Chiara,et al.  Logical self reference, set theoretical paradoxes and the measurement problem in quantum mechanics , 1977, J. Philos. Log..

[9]  Michael Barr,et al.  The Emperor's New Mind , 1989 .

[10]  Asher Peres,et al.  On quantum-mechanical automata , 1984 .

[11]  Karl R. Popper,et al.  INDETERMINISM IN QUANTUM PHYSICS AND IN CLASSICAL PHYSICS: PART II* , 1950, The British Journal for the Philosophy of Science.

[12]  Jerome Rothstein,et al.  Thermodynamics and Some Undecidable Physical Questions , 1964, Philosophy of Science.

[13]  A. Komar UNDECIDABILITY OF MACROSCOPICALLY DISTINGUISHABLE STATES IN QUANTUM FIELD THEORY , 1964 .

[14]  David Z. Albert,et al.  A Quantum-Mechanical Automation , 1987, Philosophy of Science.

[15]  Peter Mittelstaedt,et al.  Unsharp particle-wave duality in a photon split-beam experiment , 1987 .

[16]  Paul Busch,et al.  Indeterminacy relations and simultaneous measurements in quantum theory , 1985 .

[17]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .