A quantum wave function was originally conceived by Schröedinger as a tangible, physical wave. This viewpoint was quickly threatened both by Born relating the wave function to probabilities, and by the realisation that quantum states could not always be assigned separately to individual systems. Nevertheless most physicists and chemists concerned with pragmatic applications successfully treat the quantum state as a real object encoding all properties of microscopic systems. However, many ... have suggested that the quantum state should properly be viewed as something less than real. For example:
... I incline to the opinion that the wave function does not (completely) describe what is real, but only a (to us) empirically accessible maximal knowledge regarding that which really exists [...] This is what I mean when I advance the view that quantum mechanics gives an incomplete description of the real state of a airs.
The motivation for physicists to take an interest in this question was eloquently stated by Jaynes:
But our present QM formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature - all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we think that the unscrambling is a prerequisite for any further advance in basic physical theory. For, if we cannot separate the subjective and objective aspects of the formalism, we cannot know what we are talking about; it is just that simple.
Some physicists hold that quantum systems do not have physical properties, or that the existence of quantum systems at all is a convenient fiction. In this case, the state vector is a mere calculational device, used to make predictions of the probabilities for macroscopic events. This work, however, proceeds on the assumption that quantum systems - like atoms and photons - exist, and have at least some physical properties. We assume very little about these properties, for example we do not assume that systems have a de nite position or momentum. The statistical view of the quantum state is that it merely encodes an experimenter's information about the properties of a system. We will describe a particular measurement and show that the quantum predictions for this measurement are incompatible with this view.
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