By introducing a new concept called Entropy, defined as the ratio of a quantity of heat to a temperature, Clausius was able to give a more general form to this principle. It then became the Principle of Entropy, according to which, in any irreversible change, the entropy of a system was increased; only in the case of a reversible change would it remain constant. Under no circumstances, however, would the total entropy decrease. Thus all natural processes involve an increase of entropy since none are ideally reversible.
Now when we consider the principle of entropy in its bearing on the concept of energy, we find that it implies a continual loss of potentiality in the energy of the system. The energy is thus constantly dissipated, or, more properly speaking, degraded into that lowest of forms, namely, disorderly molecular agitation, i.e., heat; whence the name, Principle of the Degradation of Energy, under which it is often referred to.
The principle is of such extreme importance that it has been named the Second Principle of Thermodynamics; the appellation First Principle of Thermodynamics being reserved for the principle of the conservation of energy. It is important to note that these two principles, that of degradation and that of conservation, do not conflict. In quantity the energy is conserved; it is solely in quality, or in potentiality, or in its ability to perform work, that it is degraded.
We now come to Boltzmann’s contributions. Entropy as defined by Clausius was an exceedingly abstruse thermodynamical concept. Boltzmann, by basing his deductions on the kinetic theory of gases, succeeded in giving a more concrete representation of entropy, defining it as the logarithm of a probability. Thus, if we admit the correctness of the kinetic theory, the principle of entropy becomes one of maximum probability, losing thereby its status of absolute validity and assuming a statistical significance. The representation of entropy in terms of probability permits an easy application of the principle to the problems of molecular physics and to atomistic physics in general. We may note that it was by following this method, or rather by combining the two definitions of entropy, that Planck established his quantum radiation formula, and was thus led to his quantum theory. Needless to say, the principle holds only when exceedingly large numbers are considered. In other words, it is a principle governing the chaos, or, again, it is a statistical principle.
It will be seen that the principle of entropy, by stating that the world is ever passing from states of lesser to states of greater probability, indicates that when the state of maximum probability or entropy is reached, no further change can take place. There will then be silent immobility or death. Under the circumstances it might appear that the principle was inconsistent with the existence of an original state of minimum probability. But here it should be remembered that the principles of science do not aspire to any absolute measure of value. All we can demand is that they be satisfied in the very restricted domain which science can explore. In the case of the principle of entropy, however, there is no reason to fear any conflict with the possibility of rebirth or re-creation. For instance, when shaking the powders, we saw that a uniform grey mixture would be the outcome; but were we to go on shaking the bottle for trillions of centuries, at some time or other the black and white separation would reoccur, and the cycle begin all over again. In short, the entropy would continually increase, but once every trillion years it might suddenly decrease, and then start to increase once more. We may mention that although there is no reason to assume that vital phenomena are in any wise inconsistent with the principle of entropy, it is safer to restrict the principle to the physical world. With biological phenomena, questions of probability are far too complex to be treated with any measure of assurance in the present state of our knowledge. Only in certain special cases, such as those connected with Mendel’s observations, have probability considerations been introduced with any profit.[70]
Now the two points we wish to stress are as follows: First, the uni-directional progress of time is imposed by common experience. Secondly, the principle of entropy is suggested both by experience and by arguments of a rational order. We do not assert thereby that the principle of entropy, even when reduced to the rank of a statistical principle, can be claimed with assurance to be of universal validity. It is far from impossible that in certain phenomena, of which as yet nothing is known, some counterbalancing activity may be at work. Nevertheless, it may be pointed out that a denial of the principle of entropy, at least as regulating those physical phenomena with which science deals, would arrest further progress.
For instance, we can readily understand in what an embarrassing situation we should be placed were a reversal of time to occur. Quite aside from such trivial examples as that of a hen becoming a chick and disappearing into an egg, or from effects becoming causes, a number of more scientific considerations must be mentioned. Phenomena would now pass from states of maximum probability to those of minimum probability; we could not merely interchange the meanings of the words “maximum” and “minimum,” for these are given by purely numerical considerations, which are quite irrelevant to the direction of the time-flow. Hence phenomena would pass from the homogeneous to the heterogeneous. But whereas a homogeneous state is unique, and can be predetermined, a heterogeneous one is more or less arbitrary, and baffles prevision. Thus, in the case of the two powders, the homogeneous state is a uniform grey mixture; whereas a heterogeneous state might be a succession of alternate layers, or only two layers, or a juxtaposition of black and white cubes. In fine, prevision would become well-nigh impossible.
From this we may readily anticipate that should Einstein’s theory render the direction of time’s progress indeterminate, should past and future be interchangeable according to our circumstances of motion, the utmost chaos would ensue. However, we need have no fear on this score, for as we shall see, the theory of relativity leads to no reversal of causality. Let us now consider the space-time theory in greater detail.
When we consider the four-dimensional space-time continuum, where space and time are on the same footing, there is nothing to suggest either a flowing of time or a privileged direction for this flow. In order to conform the theory to the facts of experience, it is therefore necessary to postulate that our consciousness rises along the world-line of our body through space-time, discovering the events on its course. Obviously, we might reverse the presentation by assuming that it was space-time that was moving past our consciousness; we might also claim that the very texture of space-time possessed dynamic properties urging our consciousness along time directions. But in view of the vagueness of the subject, not much is to be gained by speculating on this score.
Now when, along the world-lines which each one of us follows, a common direction from past to future has been specified, we find that an absolute past and an absolute future (though not an absolute present) are demanded by the theory of relativity. To be more explicit, we find that whereas, according to the nature of our relative motions, certain events may appear as simultaneous, or as antecedent and consequent, or as consequent and antecedent, others will invariably present themselves in the same order of temporal sequence regardless of our motion.