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2. The measurement problem

Paul Budnik paul@mtnmath.com

The formulation of QM describes the deterministic unitary evolution of a wave function. This wave function is never observed experimentally. The wave function allows us to compute the probability that certain macroscopic events will be observed. There are no events and no mechanism for creating events in the mathematical model. It is this dichotomy between the wave function model and observed macroscopic events that is the source of the interpretation issue in QM. In classical physics the mathematical model talks about the things we observe. In QM the mathematical model by itself never produces observations. We must interpret the wave function in order to relate it to experimental observations.

It is important to understand that this is not simply a philosophical question or a rhetorical debate. In QM one often must model systems as the superposition of two or more possible outcomes. Superpositions can produce interference effects and thus are experimentally distinguishable from mixed states. How does a superposition of different possibilities resolve itself into some particular observation? This question (also known as the measurement problem) affects how we analyze some experiments such as tests of Bell's inequality and may raise the question of interpretations from a philosophical debate to an experimentally testable question. So far there is no evidence that it makes any difference. The wave function evolves in such a way that there are no observable effects from macroscopic superpositions. It is only superposition of different possibilities at the microscopic level that leads to experimentally detectable interference effects.

Thus it would seem that there is no criterion for objective events and perhaps no need for such a criterion. However there is at least one small fly in the ointment. In analyzing a test of Bell's inequality one must make some determination as to when an observation was complete, i. e. could not be reversed. These experiments depend on the timing of macroscopic events. The natural assumption is to use classical thermodynamics to compute the probability that a macroscopic event can be reversed. This however implies that there is some objective process that produces the particular observation. Since no such objective process exists in current models this suggests that QM is an incomplete theory. This might be thought of as the Einstein interpretation of QM, i. e., that there are objective physical processes that create observations and we do not yet understand these processes. This is the view of the compiler of this document.

For more information:

Ed. J. Wheeler, W. Zurek, Quantum theory and measurement, Princeton University Press, 1983.

J. S. Bell, Speakable and unspeakable in quantum mechanics, Cambridge University Press, 1987.

R.I.G. Hughes, The Structure and Interpretation of Quantum Mechanics, Harvard University Press, 1989.


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