4 V O L . 3 , D O C . 1 0 a B O L T Z M A N N S P R I N C I P L E here, we rather pose this question in the following form: Do we always establish an entirely causal connection between the events to closer approximation, the more exactly we realize the initial state and the more exactly we follow the process in time by measurement? The point of view of physicists toward this problem changed considerably in the last century. If we leave aside for the time being Brownian motion, radioactive fluc- tuations, and a few other phenomena, which came into the focus of scientific inter- est in the past few years, we arrive decidedly at the verdict that according to experience[3] an entirely causal connection in the last sense indicated does exist. Nevertheless, physicists, more specifically, heat theoreticians, managed to deny the entirely causal connection between events, more precisely speaking, between events insofar as they can be the objects of observation. Let us throw a fleeting glance at this development! From the simple idea that gases are composed of mate- rial points (molecules) that essentially only act upon one another mechanically by contact (collision), Clausius was able to derive a relation between the specific heats and the constants of the equations of state of monatomic gases as well as a ratio between thermal conduction, internal friction, and the diffusion of gases, which magnitudes or phenomena, resp., were entirely unrelated without Clausius’s theory.[4] This major success prompted physicists to attribute heat phenomena to irregular motions by molecules. This kinetic theory of heat required, however, that the laws of conduction, etc., be taken as only approximately valid laws according to this theory a precisely valid law of conduction is absolutely impossible, being instead just a law of averages. That deviations from these averaging laws must nor- mally be very small is unimportant in principle. The kinetic theory so broadly supported by experience is not just incompatible with the presumption that observable occurrences be related precisely completely causally, however. The analyses carried out by Cla Maxwell, Boltzmann, and Gibbs[5] also show that randomly large deviations from those averaging laws would have to occur within the range of observation, even though this happens so rarely in most groups of phenomena accessible to observation systems according to the theory that we are not really able to detect such deviations. The following well-known consideration shows most concisely that the laws of conduction, just as all other laws concerning irreversible processes, cannot be pre- cise. According to the kinetic theory of heat the reversal in time of any process of molecular motion is likewise a possible process of motion hence no such thermal process exists that could not also run in [the] opposite direction. Therefore, from the point of view of the molecular theory of heat, it has to be regarded as possible that by mere thermal conduction heat would flow from a colder body into a warmer [p. 3] [p. 4]
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