Re: Super Copenhagen Interpretation (Consistent Histories)

Oh No wrote:

Probability theory itself is not these days given a frequentist
interpretation based on ensembles, and, with a Bayesian approach, may
be quite legitimately used on a single throw of a die.

It may be that in the big industry of philosophy about probability
theory there are other interpretations than the frequentist one, but so
far I could not make out what that means in practice. Physics is an
empirical sience after all, i.e., you have to do experiments and find
out what's really going on. If you like to apply other interpretations
of probability theory, you have to define, how to check a simple result
like: "The probability for finding a particle, prepared in states |psi>
in the state |phi> is |<phi|psi>|^2." How do you check this within a
non-frequentist interpretation? In my opinion, you need to prepare
sufficiently many identically prepared systems (i.e., an ensemble of
systems) to check probabilistic statements of this kind with a certain
statistical certainty, and you cannot find out whether this statement
is correct (within the given error).

The same is true for "classical systems" like a die. Throwing it once
does not tell you whether the probability for a "6" is 1/6 or not.
Again you have to repeat the experiment sufficiently many times to get
the probability for getting a "6" verified (or falsified) within a
given level of accuracy.

You ignore the fact that if the particles are identically prepared
they are a pure state in which the wave function of each one is
identical, so the wave function can be said to describe a single
particle.

This, I don't ignore, but I say that, since the knowledge of the quantum
state (in some cases wave functions are a convenient representation for
a state) is probabilistic, you need an ensemble to verify the
predictions about the behavior of the system (as I detailed above).

--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:hees@xxxxxxxxxxxxx

.

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