Von Neumann's Blunder

John K Clark (johnkc@well.com)
Sun, 26 Jan 1997 13:11:57 -0800 (PST)


On Sun, 26 Jan 1997 Omega <omega@pacific.net> Wrote:

>isn't the application of a set average to the individual members
>of a set flawed on purely mathematical grounds?

No. If for example every member of a set has a value of 10.2 then the entire
set certainly has a average value of 10.2. Von Neumann wasn't such a fool
that he didn't realize that there are other ways the average could end up
being that number, but he didn't think they were physically reasonable.
He was wrong about that.

Speaking of blunders, Bell actually wrote his paper in 1964 and sent it off
to Reviews of Modern Physics, they promptly misfiled it someplace in their
vast office. Two years later they finely found it and published it in 1966.
To treat such a vastly important paper in such a way is a scandal, Reviews of
Modern Physics is no longer in operation.

>Supposedly the proof was shown to be flawed in 1935 by Grete Hermann
>on purely mathematical grounds.

I've never heard of Grete Hermann, but he must have pointed out that Von
Neumann's assumptions were too restrictive, Hermann couldn't have pointed to
a mathematical flaw because there are none. I quote from "The Unconscious
Quantum" by Victor J Stenger:

"Von Neumann's proof was eventually rejected, not because it did not follow
from its assumptions but because those assumptions were not all-inclusive."
[...] the proofs [ in his book] were mathematically correct, insofar as they
followed from their assumptions, but the assumptions were too restrictive."

This was only a small part of Von Neumann's 1932 book and it is still
considered a masterpiece. For example, in it he proved that although they
look very different, Schrodinger's and Heisenberg's versions of Quantum
Mechanics are logically equivalent.

>You say that "There would be nothing illogical about a world that
>worked that way" (referring to one that followed von Neumann's proof)
>but such a world is one in which microcausality is hopelessly lost,
>which for me, is about as illogical as we can get.

I know of no law of logic the demands that every event have a cause.

>With the modern understanding that advanced-action can reduce all of
>the puzzling phenomena of quantum physics down to one concise
>deterministic explanation, I would say that it's all water under the

Some say John Cramer's Transactional interpretation of Quantum Mechanics is
deterministic, but to do so one must stretch the meaning of "deterministic",
perhaps to the breaking point, it has little to do with our everyday use of
the word. In everything EXCEPT Quantum Mechanics when we say "A causes B" we
mean that whenever you find A you can be certain to find B further along the
time sequence; this is NOT at all what Cramer means when he talks about
causes and determinism. This would certainly have horrified Einstein,
he didn't much like a nondeterministic universe but a non-local one bothered
him far more.

John K Clark johnkc@well.com

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