4. Classical Physics and Indeterminacy. The various
theses of indeterminacies in physics mentioned so far
have been advanced by philosophers and not by
physicists, the reason being, of course, that classical
physics, since the days of Newton and Laplace, was
the paradigm of a deterministic and predictable sci-
ence. It was also taken for granted that the precision
attainable in measurement is theoretically unlimited;
for although it was admitted that measurements are
always accompanied by statistical errors, it was
claimed that these errors could be made smaller and
smaller with progressive techniques.
The first physicist in modern times to question the
strict determinism of physical laws was probably
Ludwig Boltzmann. In his lectures on gas theory he
declared in 1895: “Since today it is popular to look
forward to the time when our view of nature will have
been completely changed, I will mention the possibility
that the fundamental equations for the motion of indi-
vidual molecules will turn out to be only approximate
formulas which give average values, resulting accord-
ing to the probability calculus from the interactions
of many independent moving entities forming the sur-
rounding medium” (Boltzmann, 1895). Boltzmann's
successor at the University of Vienna, Franz Exner,
proposed in 1919 a statistical interpretation of the
apparent deterministic behavior of macroscopic phe-
nomena which he regarded as resulting from a great
number of probabilistic processes at the sub-
microscopic level.
From a multitude of events... laws can be inferred which
are valid for the average state [Durchschnittszustand] of this
multitude whereas the individual event may remain un-
determined. In this sense the principle of causality holds
for all macroscopic occurrences without being necessarily
valid for the microcosm. It also follows that the laws of
the macrocosm are not absolute laws but rather laws of
probability; whether they hold always and everywhere
remains to be questioned; to predict in physics the outcome
of an individual process is impossible
(Exner, 1919).
In the same year Charles Galton Darwin, influenced
by Henri Poincaré's allusion toward a probabilistic
reformulation of physical laws and his doubts about
the validity of differential equations as reflecting the
true nature of physical laws (H. Poincaré, Dernières
pensées), made the bold statement that it may “prove
necessary to make fundamental changes in our ideas
of time and space, or to abandon the conservation of
matter and electricity, or even in the last resort to
endow electrons with free will” (Charles Galton
Darwin, 1919). The ascription of free will to electrons—
clearly an anthropomorphic metaphorism for a- and
u-indeterminacies—was suggested by certain results in
quantum theory such as the unpredictable and appar-
ently acausal emission of electrons from a radioactive
element or their unpredictable transitions from one
energy level to another in the atom. In the early twen-
ties questions concerning the limitations of the sensi-
tivity of measuring instruments came to the forefront
of physical interest when, with no direct connection
with quantum effects, the disturbing effects of the
Brownian fluctuations were studied in detail (W.
Einthoven, G. Ising, F. Zernike). It became increasingly
clear that Brownian motion, or “noise” as it was called
in the terminology of electronics, puts a definite limit
to the sensitivity of electronic measuring devices and
hence to measurements in general. Classical physics,
it seemed, has to abandon its principle of unlimited
precision and to admit, instead, unavoidable i-indeter-
minacies. It can be shown that this development did
not elicit the establishment of Heisenberg's uncertainty
relations in quantum mechanics (Jammer [1966], p.
331).
