Richard C. Tolman
(1881-1948)
Richard C. Tolman was a physical chemist and a mathematical physicist at the California Institute of Technology (Caltech) who made important contributions to statistical mechanics and theoretical cosmology.
In the 1920's Tolman applied the new quantum mechanics to statistical mechanics and
Albert Einstein's general relativity to cosmology.
In the
Proceedings of the National Academy of Sciences in 1925 Tolman described a new postulate circulating among physical chemists concerning the "detailed balancing" of chemical reactions. He called it
the principle of microscopic reversibility.
In recent years increasing use has been made of a new postulate which
perhaps cannot yet be stated in its final form, but which requires in a
general way in the case of a system in thermodynamic equilibrium not only
that the total number of molecules leaving a given state in unit time shall
on the average equal the number arriving in that state in unit time, but
also that the number leaving by any particular path shall on the average
be equal to the number arriving by the reverse of that particular path,
thus excluding any cyclical maintenance of the equilibrium state. The
writer has ventured to name this postulate the principle of microscopic
reversibility.
"The principle of microscopic reversibility." Proceedings of the National Academy of Sciences of the United States of America 11.7 (1925): 436.
Tolman cited Irving Langmuir's remark in 1916,
"Since evaporation and condensation are in general thermodynamically
reversible phenomena, the mechanism of evaporation must be the exact reverse
of that of condensation, even down to the smallest detail."
ibid.,
He also saw Einstein's 1917 analysis of the absorption and emissions of photons as examples of balancing microscopic processes with their reverse process.
In 1917, Einstein, as a necessary step in his famous deduction of the
Planck radiation law, considered a molecule capable of existing in different
quantum states in equilibrium with radiation, - and taking a given pair of
the quantum states Sm and Sn (ϵν > ϵm), equated the number of molecules passing from state Sm to state Sν by the absorption of a quantum
hv = ϵν - ϵm with the number passing in the reverse direction through
the emission of a quantum of the same frequency. He thus used the
principle of microscopic reversibility without, however, making any explicit
statement of it.
ibid., p.437
But Tolman apparently did not notice that Einstein's analysis had concluded that the quantum emission process is not time-reversible. Or perhaps for chemical reaction detailed balancing, it is enough that every individual absorption is balanced by an emission? Tolman was not claiming that chemical reactions are time reversible, as modern physicists are mistakenly claiming while using Tolman's original
principle of microscopic reversibility.
Tolman's microscopic reversibility for a physical chemist is just the detailed balance at the level of chemical processes and not the specific photon emission processes in which Einstein discovered ontological chance and time
irreversibility that can explain
Ludwig Boltzmann's "molecular disorder" assumption.
Just a year after Tolman's work,
Erwin Schrödinger developed his equation for the quantum wave function and showed that the probability amplitude wave function evolves time reversibly and deterministically.
That has led several theorists to claim that quantum statistical mechanics is just as time reversible as classical statistical mechanics, notably in the quantum mechanics textbooks of David Bohm, Albert Messiah, and Landau and Lifshitz.
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