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S. H. Burbury
S. H. Burburyl was one of a number of British scientists who criticized the
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H-Theorem of Ludwig Boltzmann, which was widely believed to have shown that the entropy in an isolated system can only increase to a maximum. Boltzmann's quantity H is the opposite of entropy (in modern terms it is the negentropy or information).
Boltzmann at first (1872) claimed to have shown that his "minimum function"
Already in the 1870's William Thomson (Lord Kelvin) and Josef Loschmidt had criticized this dynamical derivation on the grounds that if all the velocities of the particle were reversed the
S = k logW
The proportionality factor Scientists at the 1894 meeting of the British Association for the Advancement of Science (which was attended by Boltzmann) argued that there must be something causing "molecular disorder" or chaos that is introducing the irreversibility. Edward Culverwell suggested molecular disorder might be caused by the ether that was the presumed medium for electromagnetic waves. In 1890 he wrote: We know that by means of the aether, bodies at a distance and wholly prevented from acting on each other molecularly, come to exactly the same temperature-equilibrium without any assistance from their collisions. Hence there is every reason to suppose that it is by the molecules interacting through the aether that the temperature-equilibrium is determined. Then in 1894 he argued that something must be preventing the reversibility, since a dynamical analysis leads to perfect reversibility. The remarkable differences of opinion as to what the H-theorem S. H. Burbury used the terms "haphazard" and "chaos" to describe what is needed. The objection that I understand to be made is that if you reverse all the velocities after collisions, the system will retrace its course with H increasing - which is supposed to be contrary to the thing proved...Sir James Jeans in 1903 agreed with Culverwell and Burbury that interaction with radiation could be dissipative and change the physics of Boltzmann's conservative dynamical system. In the first place the distribution of energy which is given by Boltzmann's Theorem is the only distribution which is permanentBoltzmann largely ignored the suggestions of the British physicists, ignoring the idea of randomizing radiation interactions, arguing instead that the mean free paths of particles in a dilute gas would allow the molecules to escape to distant parts of the gas, leaving behind any correlations (molecular order) with recent collisions. For Boltzmann, molecular disorder is a statistical condition, not a dynamic process whereby molecular paths are made haphazard and thus irreversible. If the mean free path in a gas is large compared to the mean distance of two neighboring molecules, then in a short time, completely different molecules than before will be nearest neighbors to each other. A molecular-ordered but molar-disordered distribution will most probably be transformed into a molecular-disordered one in a short time. Each molecule flies from one collision to another one so far away that one can consider the occurrence of another molecule, at the place where it collides the second time, with a definite state of motion, as being an event completely independent (for statistical calculations) of the place from which the first molecule came (and similarly for the state of motion of the first molecule). However, if we choose the initial configuration on the basis of a previous calculation of the path of each molecule, so as to violate intentionally the laws of probability, then of course we can construct a persistent regularity or an almost molecular-disordered distribution which will become an molecular-ordered at a particular time. Kirchhoff also makes the assumption that the state is molecular-disordered in his definition of the probability concept. Boltzmann was confident that probability played the major role and he prophetically described a future physics of "average values," eerily anticipating the "expectation values" of probabilistic indeterministic quantum physics. 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 individual molecules will turn out to be only approximate formulas which give average values, resulting according to the probability calculus from the interactions of many independent moving entities forming the surrounding medium - as for example in meteorology the laws are valid only for average values obtained by long series of observations using the probability calculus. These entities must of course be so numerous and must act so rapidly that the correct average values are attained in millionths of a second. |