#### A. Neumaier

Science Advisor

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Frequentist arguments are about ensembles modeled in the probability spaceIn the typical presentation the friend models the system as being in the state ##\frac{1}{2}\left(|\uparrow\rangle + |\downarrow\rangle\right)## upon measurement and obtaining the ##\uparrow## outcome he models later experiments with the state ##|\uparrow\rangle##. In an ensemble view he could consider the original preparation and his measurement as a single new preparation.

However Wigner uses the superposed state I mentioned above.

Both of these assignments are from using the textbook treatment of QM.

You're saying if you are a frequentist something is wrong with this. What is it? Wigner's state assignment or the friends or both?

**for the maximal domain of discourse**fixed once and for all. Conditional probabilities are derived statements about well-specified subensembles.

**There are no assignments**in the frequentist's description, except arbitrary subjective approximations to the objective but unattainable truth.

But there is much more wrong with the Wigner's friend setting, and even with von Neumann's original simpler discussion of measurement:

1. Quantum mechanics as defined in the textbooks is a theory about a

**single**time-dependent state, (for a quantum system, an ensemble of similarly prepared quantum systems, or the knowledge about a quantum system, depending on the interpretation). But unlike in frequentist probability theory, the traditional foundations

**make no claims at all about how the state of a subsystem is related to the state of the full system**. This introduces a crucial element of ambiguity into the discussion of everything where a system together with a subsystem is considered in terms of their states. In this sense, the standard foundations (no matter in which description) of quantum mechanics (not the practice of quantum mechanics itself) is obviously

**incomplete**.

2. Projective measurements are realistic only for states of very tiny systems, not for systems containing a detector. As long as the state remains in the microscopic domain where projective measurements may be realistic, Wigner friend arguments apply but prove nothing about the measurement situation. Therefore, Wigner's friend in the 2/3-state setting mentioned here is an irrelevant caricature.

But I better refrain from further discussing in detail interpretations which I don't think to be valid. I only get into a state where my mind is spinning - as in the time about 20 years ago when I seriously tried to make sense of other interpretation. At that time I failed because there were too many simplifications of things I deemed essential for understanding, and because the interpretations were at crucial points too vague to say clearly what they imply in a given context, so that each author used the interpretation in a different way. This experience of a few years fruitless, intense effort taught me to stay away from poorly defined interpretations.

**A good interpretation must be able to spell out exactly what its terms mean**(in the context of a sufficiently rich mathematical model) and how the terms may and may not be applied. That none of the traditional interpretations meets this criterion is the reason for the continued multitude of competing interpretations and modifications thereof. I hope that the thermal interpretation that I developed in response to the above insights will fare better in this respect. Everything is defined in sufficient precision to allow a precisely mathematical analysis, though the latter may be complex. At least there is no ambiguity about what the interpretation claims (apart from the undefined notion of uncertainty which however is familiar from all our knowledge).