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Is the Copenhagen interpretation of quantum mechanics explicitly inconsistent?
While offering a version of the decoherence interpretation of quantum mechanics, Gregory Mulhauser says:
"The Copenhagen interpretation of quantum mechanics is explicitly inconsistent because it treats the (apparently nonvanishing!) off-diagonal terms as if they did not exist." [Mulhauser, G. (1998) Mind Out of Matter: Topics in the Physical Foundations of Consciousness and Cognition, p.160]
I believe the "off-diagonal" terms refer to Heisenberg's matrix formulation, but what would a supporter of the Copenhagen interpretation say about the off-diagonal terms? What are they? and why can't we treat them as if the don't exist? Can anyone here explain what Mulhauser is getting at?
3 Answers
- 1 decade agoFavorite Answer
Looking at page 160 on Google books, it seems that the author is working in the Schroedinger picture (not Heisenberg) and referring to the off-diagonal elements of the density matrix of the quantum state when it is represented in the basis of the eigenstates of the observable operator in question (this operator is A in the example given there).
The density matrix is a mathematical representation of a quantum state that can describe both quantum superposition and classical, statistical uncertainty about the state of the system. If the density matrix can be diagonalized in a basis corresponding to some observable quantity, then the system can be thought of as having a definite, but as-yet-unknown, value for the observable before the measurement is ever performed. If there are off-diagonal elements, though, then there is quantum superposition and the probabilities of having different observable values interfere with one another in a distinctly non-classical way.
I think the author is pointing out that in the Copenhagen interpretation when we calculate the expectation value of a measurement we only take into account the diagonal elements of the density matrix (and the post-measurement state is diagonal as well), so it seems we assume that the off-diagonal elements have gone away.
Where I think he's headed is to show that, with the presence of an environment interacting with the system, you can show that the off-diagonal terms will naturally become very small, due to interaction with the environment, using only Schroedinger's equation without recourse to any special assumptions; however, many experts on decoherence would not agree that this removes the need for the Copenhagen interpretation (or solves the "measurement problem"), because there is still such an assumption involved in interpreting what the reduced density matrix means physically.
Source(s): http://books.google.com/books?id=4baUwJys0bAC&pg=P... http://books.google.com/books?id=6eTHcxeNxdUC - Anonymous1 decade ago
Sorry, can't help. But the standard formulation says that the wave function is All there is about a system until it collapses. Just when/where that happens is NOT part of QM. If that ain't inconsistent, then I don't understand the word.
Now? - no, no now
Now? - no, stop asking me!
But when will we get there? - trust me, I'll let you know.
Here? - No not here....
- ?Lv 45 years ago
in no way. forget approximately this crap with regard to the privileged place of Observers. Any classical rely can crumple wavefunctions. A proton will do it. the actual difficulty is *holding* superpositions from decohering.