RS>> You wrote about the correspondence between physical measurements and
RS>> the real numbers
> Gordon Fisher:
GF> If this is what at issue, I note that for one, Erwin Schro"dinger
GF> questioned whether or not real numbers were suitable for use by
GF> physicists to represent physical phenomena, presumably on account
GF> of his thoughts about quanta. If I recall correctly, he suggested
GF> that perhaps people had taken a wrong turn in ancient Greece when
GF> they went the way of Eudoxus as found in Euclid, and eventually
GF> came up with what we call the real numbers.
GF> He evidently had hopes that some of the puzzles of quantum theory
GF> would be relieved by the introduction of some new kind of numbers
GF> for use in physical measurement. A number of physicists tried to
GF> do something along these lines.
Indeed, the problem on "The correspondence between physical measurements
and the real numbers" had been discussed in the frames of operational
approach. See, for example,
Berka K. (1983) Measurement. Its concepts, theories and problem (Boston
studies in the philosophy. Vol. 72). Boston: Kluwer.
Bridgeman P.W. (1937) The nature of physical theory. Princeton.
Brillouin L. (1964) Scientific uncertainty and Information. New York -
London: Academic Press.
The modern approach to solving this problem supposes the introduction
of a measurement function g into the postulated model. More detailed
information can be found in my book (with Vladimir Shmagin) Regression
data analysis for physicists and chemists. St.-Petersburg: St.-Petersburg
State University Press, 1998 (written in English).
Professor of St-Petersburg
Technical University,
Dr. Yu. V. Chebrakov
Nevsky Ave., Bldg.3, Apt. 11
191186, St-Petersburg, Russia
e-mail: chebra@phdeg.hop.stu.neva.ru