Re: Von Neumann's Blunder

Omega (
Mon, 27 Jan 1997 02:22:38 -0800

John K Clark,

Interesting review of history we have gotten into here by recounting the
somewhat varying perspectives of different authors.

> 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.

Thanks for the tidbit, this almost gives new meaning to the word scandal.

> >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.

Supposedly both Bell and Mermin have used the word silly in describing von
Neumann's proof and the assumptions that went into it. I will grant that
they may be overly harsh in hind-sight, but I'm not sure we want to start
ascribing the type of infallibility to von Neumann that, ahem, certain other
people ascribe to say someone like Paul.

I also point out that your counter example is only mathematically correct if
the values of the individual members are actually known. That this is true
is not at all clear in this quantum mechanics business. This quite likely
could be related to what Grete Hermann was complaining about. Since Victor
J Stenger contradicts both Bell and Mermim (and presumably Hermann too) about
the lack of mathematical error in von Neumann's work, getting to the bottom
of this will probably take some digging.

> 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.

This is incongruous too. I thought that Dirac had proven the equivalence
of these many years earlier. Perhaps von Neumann simplified it or made
the presentation of Dirac's proof more elegant in some way.

> >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.

Technically I would agree, BUT such a statement amounts to a sweeping and
profound metaphysical statement. I might even be inclined to agree, but
I don't feel logic should be dismissed before we've exhausted the pos-
sibilities of using it. Specifically, I feel it should be applied to the
puzzles of advanced-action now that the "action" seems to be there.

> >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
> >bridge
> 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.

It's really doesn't stretch the meaning so much as we may first think. The
reason is that when we talk about:

> 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.

we are already in deep shit with just Maxwells equations. Einstein went a long
way toward fixing this when he developed special relativity, but it introduced
(or perhaps failed to fix) the paradox that when causality manifests itself
through forces that propagate on lightlike vectors such as the EM force (and
presumably gravity also) that it automatically entangles the causal sequence of
reality in conflicting definitions of A causes B unless exactly the amount of
advance action that Cramer talks about is added to the picture.

With hindsight QM might have been anticipated through timely appreciation of
this paradox, but then again hindsight is always so much clearer.

> This would certainly have horrified Einstein, he didn't much like a nondeter-
> ministic universe but a non-local one bothered him far more.

Actually Cramer's transactional interpretation does not necessarily imply non-
locality so much as the fact that local causal principles propagate (on the
microcausal level) symmetrically bidirectionally through time. I agree in
advance that Einstein might well be rolling over in his grave, but philosopher
Huw Price in his book 'Time's Arrow and Archimedes Point' also makes the point
that the temporally symmetrical bidirectional causality on the microcausal
level could also have been anticipated by some of the problems Boltzmann was
having with his work; both arguments are compelling IMO, although Price's
arguments are somewhat dense.

The big question in my mind, and area of greatest interest, is what the
f... is going on in macrocausality. As far as I can see, many assumptions
that we have long been comfortable with are lined up like dominoes.

In the Ecstatic Service of Life -- Omega