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MOST IMPORTANT SCIENTIFIC DISCOVERIES
Ash-theorem. History and essence of scientific discovery
Directory / The most important scientific discoveries Ludwig Boltzmann, the author of the "ash-theorem", without a doubt, was the greatest scientist and thinker that Austria gave to the world. Even during his lifetime, Boltzmann, despite the position of an outcast in scientific circles, was recognized as a great scientist, he was invited to lecture in many countries. And yet, some of his ideas remain a mystery even today. Boltzmann himself wrote about himself: "The idea that fills my mind and activity is the development of theory." And Max Laue later clarified this idea as follows: "His ideal was to combine all physical theories in a single picture of the world."Ludwig Eduard Boltzmann was born in Vienna on February 20, 1844. Ludwig studied brilliantly, and his mother encouraged his diverse interests, giving him a comprehensive education. In 1863, Boltzmann entered the University of Vienna, where he studied mathematics and physics. Then Maxwellian electrodynamics was the latest achievement of theoretical physics. It is not surprising that Ludwig's first article was also devoted to electrodynamics. However, already in his second work, published in 1866 in the article "On the mechanical significance of the second law of thermodynamics", where he showed that the temperature corresponds to the average kinetic energy of gas molecules, Boltzmann's scientific interests were determined. In the autumn of 1866, two months before receiving his doctorate, Boltzmann was admitted to the Institute of Physics as an assistant professor. In 1868, Boltzmann was granted the right to lecture at universities, and a year later he became an ordinary professor of mathematical physics at the University of Graz. During this period, in addition to developing his theoretical ideas, he was also engaged in experimental studies of the relationship between the dielectric constant and the refractive index in order to obtain confirmation of Maxwell's unified theory of electrodynamics and optics. For his experiments, he twice took short leave from the university to work in the laboratories of Bunsen and Königsberger in Heidelberg and Helmholtz and Kirchhoff in Berlin. The results of these studies were published in 1873–1874. Boltzmann also took an active part in the planning of the new Physics Laboratory in Graz, of which he became director in 1876. As early as 1871, Boltzmann pointed out that the second law of thermodynamics could only be derived from classical mechanics using the theory of probability. In 1877, Boltzmann's famous article on the relationship between entropy and the probability of a thermodynamic state appeared in the Vienna Communications on Physics. The scientist showed that the entropy of a thermodynamic state is proportional to the probability of this state and that the probabilities of states can be calculated on the basis of the ratio between the numerical characteristics of the distributions of molecules corresponding to these states. Irreversible processes in nature, according to Boltzmann, are processes of transition from a less probable state to a more probable one. Reversible transitions are not possible, but unlikely. Therefore, the entropy must also be related to the probability of a given state of the system. This connection was established by Boltzmann in his so-called H-theorem. "Ash-theorem" became the pinnacle of Boltzmann's doctrine of the universe. The formula of this beginning was later carved as an epitaph on the monument above his grave. This formula is very similar in essence to the law of natural selection. Charles Darwin. Only Boltzmann's "Ash-theorem" shows how the "life" of the Universe itself is born and proceeds. “Just as differential equations represent only a mathematical method of calculation and their true meaning,” writes Boltzmann, “can only be understood with the help of representations based on a large finite number of elements, along with general thermodynamics, and without detracting from its importance, which never cannot be shaken, the development of mechanical representations, which make it visual, contributes to the deepening of our knowledge of nature, and not in spite of, but precisely because they do not coincide in all points with general thermodynamics, they open up the possibility of new points of view. These new points of view are that the transitions of the system from one state to another obey the laws of probability theory. "The introduction of probability theory into the consideration of mechanical systems (and the particles of the body in Boltzmann's theory obey the laws of mechanics)," P.S. Kudryavtsev writes in his book, "seems to be a contradiction. The dynamic pattern that mechanics deals with seemed so definite that it Laplace believed that if the mind had access to the knowledge of the location of all the particles of the Universe at a given moment and the forces acting between them, then, if it had the ability to mathematically process these data, it would be able to predict the future of the Universe with certainty, as well as see its past. How do the laws of mechanics in kinetic theory lead to statistics? Boltzmann answers this question: the cause of statistics lies in mechanics itself, in the initial conditions. The negligible roughness of the walls of the vessel, against which the molecules of the gas collide, are sufficient to introduce chaos into the original order, if it were to take place. The laws of conservation in the collision of two molecules leave full scope for the directions of velocities after the impact. All this leads to the fact that it is precisely due to the mechanical interactions of molecules that their ordered movement becomes improbable, and the chaotic most probable. The development of this line of thought led Boltzmann to a new point of view on the second law of thermodynamics. Boltzmann formulates this law as follows: "When an arbitrary system of bodies is left to itself and is not subject to the action of other bodies, then the direction in which each change of state will occur can always be indicated." This direction can be characterized by a change in some function of the state - entropy, which changes with the change in the state of the system in the direction of increase. Hence the conclusion, "that any closed system of bodies tends to a certain final state, for which the entropy will be maximum!" How to reconcile this orientation with the reversibility of the equations of mechanics? Is nature really approaching its natural end - "thermal death" with inexorable fate? Boltzmann was the first to give a statistical interpretation of the second law and revealed its probabilistic nature. There is no contradiction between the reversibility of the equations of mechanics and the irreversibility of processes in a closed mechanical system. Imagine a drum filled with half white and half black balls, one on top of the other. If the drum is brought into rotation, then, due to mechanical laws, the balls will mix and, in the end, the white and black balls will mix evenly, giving the same “variegation” throughout the volume. The collection of balls has moved from a less probable state to a more probable one. The German physicist Clausius drew conclusions from the second law of thermodynamics about the inevitability of heat death. These thoughts were adopted not only by many physicists, but mainly by philosophers who received powerful, seemingly undeniable arguments in favor of idealistic concepts of the beginning and end of the world, including in favor of empirio-criticism, the teachings of E. Mach and the "energetic "the teachings of W. Ostwald. The indomitable Ludwig Boltzmann declared with his Ash-theorem: “Heat death is a bluff. No end of the world is foreseen. energies, as the Ostwaldians believe, but from atoms and molecules, and the second law of thermodynamics should be applied not to some kind of "ether", spirit or energy substance, but to specific atoms and molecules. Around the "Ash-theorem" by Ludwig Boltzmann, discussions instantly flared up no less in intensity than on heat death. "Ash-theorema" and the fluctuation hypothesis put forward on its basis were dissected with all care and scrupulousness and, as expected, they found gaping, unforgivable, it would seem, flaws for such a great scientist as Boltzmann. It turned out that if we accept the Boltzmann hypothesis as true, then we must accept for faith such a monstrous assumption that does not fit into any framework of common sense: sooner or later, or rather already now, somewhere in the Universe there must be processes in the opposite direction to the second law direction, that is, heat must move from colder bodies to hotter ones! Isn't that absurd. Boltzmann defended this "absurdity", he was deeply convinced that such a course of development of the Universe is the most natural, for it is an inevitable consequence of its atomic structure. It is unlikely that the "Ash-theorem" would have received such fame if it had been put forward by some other scientist. But it was put forward by Boltzmann, who was able not only to see the world hidden from others behind the curtain, but who knew how to defend it with all the passion of a genius armed with fundamental knowledge of both physics and philosophy. The culmination of the dramatic events between the materialist physicist and the Machists must apparently be considered the congress of natural scientists in Lübeck in 1895, where Ludwig Boltzmann gave his friend-enemies a pitched battle. He won, but as a result, after the congress, he felt an even greater emptiness around him. In 1896, Boltzmann wrote an article "On the inevitability of atomistics in the physical sciences", where he raised mathematical objections to Ostwald's energyism. Until 1910, the very existence of atomistics was constantly under threat. Boltzmann fought alone and was afraid that his life's work would be forgotten. In the end, Boltzmann could not stand the colossal stress, fell into a deep depression and on September 5, 1906 committed suicide. It is very regrettable that he did not live to see the resurrection of atomism and died with the thought that everyone had forgotten about the kinetic theory. However, many of Boltzmann's ideas have already found their solution in such amazing discoveries as the ultramicroscope, the Doppler effect, gas turbine engines, and the release of the energy of the atomic nucleus. And these are all just individual consequences of the atomic structure of the world. Author: Samin D.K.
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