3 ms·

The wave-function as a true ensemble

1 points by kgwgk 5y ago

kgwgk 5y ago
I must confess once I found the following fragment in the first page I just skimmed over the rest (emphasis mine): "We will begin by explaining what exactly we mean by the wave-function being an ensemble. We do not mean the En- semble, or Statistical, Interpretation of quantum mechanics [7], according to which the wave-function describes an ensemble of identically prepared states in identical experiments. It arguably does, but if the states are indeed identical, that’s not much of an ensemble. WE MEAN INSTEAD THAT THE SUPPOSEDLY IDENTICALLY PREPARED STATES IN SUPPOSEDLY IDENTICAL EXPERIMENTS ARE IN FACT DIFFERENT: they have different hidden variables and this is the reason why the measurement outcomes can be different for identical wave-functions. We will refer to this interpretation of the wave-function as the ψ-ensemble interpretation." [7] Leslie E Ballentine. The statistical interpretation of quantum mechanics. Reviews of Modern Physics, 42(4):358, 1970. This is the abstract of that reference: "The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of considering the QUANTUM STATE DESCRIPTION TO APPLY ONLY TO AN ENSEMBLE OF SIMILARILY PREPARED SYSTEMS, RATHER THAN SUPPOSING, AS IS OFTEN DONE, THAT IT EXHAUSTIVELY REPRESENTS AN INDIVIDUAL PHYSICAL SYSTEM. Most of the problems associated with the quantum theory of measurement are artifacts of the attempt to maintain the latter interpretation. The introduction of hidden variables to determine the outcome of individual events is fully compatible with the statistical predictions of quantum theory. However, a theorem due to Bell seems to require that any such hidden-variable theory which reproduces all of quantum mechanics exactly (i.e., not merely in some limiting case) must possess a rather pathological character with respect to correlated, but spacially separated, systems." The conclusions start: "The central theme connecting all of the topics in this paper has been the superiority of a purely statistical interpretation of quantum theory, in which A STATE VECTOR REPRESENTS AN ENSEMBLE OF SIMILARLY PREPARED SYSTEMS, AS OPPOSED TO THE STRONGER ASSUMPTION THAT A STATE VECTOR PROVIDES A COMPLETE DESCRIPTION OF AN INDIVIDUAL SYSTEM." I'd say that Ballentine also meant that supposedly identically prepared states in supposedly identical experiments are in fact different.

1 points by kgwgk 5y ago

I must confess once I found the following fragment in the first page I just skimmed over the rest (emphasis mine): "We will begin by explaining what exactly we mean by the wave-function being an ensemble. We do not mean the En- semble, or Statistical, Interpretation of quantum mechanics [7], according to which the wave-function describes an ensemble of identically prepared states in identical experiments. It arguably does, but if the states are indeed identical, that’s not much of an ensemble. WE MEAN INSTEAD THAT THE SUPPOSEDLY IDENTICALLY PREPARED STATES IN SUPPOSEDLY IDENTICAL EXPERIMENTS ARE IN FACT DIFFERENT: they have different hidden variables and this is the reason why the measurement outcomes can be different for identical wave-functions. We will refer to this interpretation of the wave-function as the ψ-ensemble interpretation." [7] Leslie E Ballentine. The statistical interpretation of quantum mechanics. Reviews of Modern Physics, 42(4):358, 1970. This is the abstract of that reference: "The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of considering the QUANTUM STATE DESCRIPTION TO APPLY ONLY TO AN ENSEMBLE OF SIMILARILY PREPARED SYSTEMS, RATHER THAN SUPPOSING, AS IS OFTEN DONE, THAT IT EXHAUSTIVELY REPRESENTS AN INDIVIDUAL PHYSICAL SYSTEM. Most of the problems associated with the quantum theory of measurement are artifacts of the attempt to maintain the latter interpretation. The introduction of hidden variables to determine the outcome of individual events is fully compatible with the statistical predictions of quantum theory. However, a theorem due to Bell seems to require that any such hidden-variable theory which reproduces all of quantum mechanics exactly (i.e., not merely in some limiting case) must possess a rather pathological character with respect to correlated, but spacially separated, systems." The conclusions start: "The central theme connecting all of the topics in this paper has been the superiority of a purely statistical interpretation of quantum theory, in which A STATE VECTOR REPRESENTS AN ENSEMBLE OF SIMILARLY PREPARED SYSTEMS, AS OPPOSED TO THE STRONGER ASSUMPTION THAT A STATE VECTOR PROVIDES A COMPLETE DESCRIPTION OF AN INDIVIDUAL SYSTEM." I'd say that Ballentine also meant that supposedly identically prepared states in supposedly identical experiments are in fact different.