Re: Book about mathematical sloppiness by physicists?

"Arnold Neumaier" <Arnold.Neumaier@xxxxxxxxxxxx> wrote
Salviati wrote

Was John v. Neumann sloppy when he introduced Hilbert space just a few
years before he in 1935 admitted that he did no longer believe in it?

Some months ago I posted here where Schroedinger was sloppy in 1926. His
dramatised cat was not based on sloppy use of mathematics but ...

.. but at least your use of dates is very sloppy.

Schroedinger invented his equation in 1926, but his cat only in 1935.

In case of 1926 I referred to Quantisation as Eigenwertproblem, 4th
Communication, Ann. Phys. 81(4), 109-139 where Schroedinger wrote

"... one may consider the real part of psi as the real wave function, if
necessary." He returned from complex domain into the real one just by
multiplying psi with its complex conjugate psi*. "

This quite common method was formally flawless from the perspective of
those who sloppily concluded from their belief and from the symmetry of
differential equations that the difference between past and "future has
merely the meaning of an albeit obstinate illusion". However, it is
insufficient if one is ready to accept the argument by Ritz that future
events cannot influence the past.

At the end of the same paper Schroedinger wrote:

"If the use of a complex wave function was in principle inevitable and
not just a mere advantage in calculation, then this would imply that
there are in principle two wave functions which only together give
information about the state of the system."

Such sloppy illusions gave rise to the EPR paper, the cat, and v.
Neumann's letter to Garret Birkhoff, dated Nov. 13: "I would like to
make a confession, which may seem immoral. I do not believe absolutely
in Hilbert-space any more." They also gave rise to naive hope for
quantum computing in the far far future. Do already announced quantum
computers work as the sellers are claiming? I was told the opposite.

The same man who was mocking about the battle between frogs and mice in
the ongoing fundamental crisis of mathematics but nonetheless reproached
Hilbert's behaviour towards Brouwer, the same man agreed with
Schroedinger on: "... two physical quantities described by non-commuting
operators, the knowledge of one precludes the knowledge of the other"
and "The psi-function must not describe a sort of blend of not yet
exploded and exploded systems."

Salviati


Arnold Neumaier


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