Aram D'Abro

“ We thus reach the remarkable conclusion that the principles of conservation, which in classical science were of an empirical nature and were totally unconnected with the law of gravitation, now appear as immediate and necessary consequences of Einstein’s law of gravitation. In other words, granting the correctness of the law of gravitation, conservation cannot help but exist in this universe. To many thinkers this is one of the most beautiful aspects of Einstein’s theory, showing as it does the wonderful unity and relatedness of nature. ”

“ Does any one really imagine that Newton or Einstein has ever attempted to explain gravitation? To say that gravitation is a property of matter or a property of space-time in the neighbourhood of matter is just as much of an explanation as to say that sweetness is a property of sugar; for in the last analysis, what is matter—what is space-time? If we say that matter is an aggregate of molecules, atoms, electrons, protons, what of it? What are electrons? ”

“ Judging from what we know of physical laws, we may expect the which belongs to it to be distinguished by having simple mathematical properties. Physics, this time as a physics of fields, is again pursuing the object of reducing the totality of natural phenomena to a single physical law: it was believed that this goal was almost within reach once before when Newton’s Principia, founded on the physics of mechanical point-masses, was celebrating its triumphs. But the treasures of knowledge are not like ripe fruits that may be plucked from a tree. ”

“ If Nature was blind, by what marvellous coincidence had all things been so adjusted as to conceal a velocity through the ether? And if Nature was wise, she had surely other subjects to attend to, more worthy of her consideration, and would scarcely be interested in hampering our feeble attempts to philosophise. In Lorentz’s theory, Nature, when we read into her system all these extraordinary adjustments ad hoc, is made to appear mischievous; it was exceedingly difficult to reconcile one’s self to finding such human traits in the universal plan. ”

“ The word “observer” is a very loose term and does not necessarily mean a living human being. We might replace the observer’s eyes by a photographic camera, his computation of time-flow by a clock—in fact, all his senses and measurements by recording instruments of a suitable nature, whose readings any man situated in any frame could check later. The results would still be the same.
Now it might be feared that, with this vanishing of the absoluteness of such fundamental forms of perception as duration and distance, the entire objective world of science would sink to a shadow ”

“ Could we but annihilate all the stars, we should have a means of solving the problem; for in Einstein’s universe the result would be the total disappearance of mass and centrifugal force. In fact, complete chaos would result; for the metrical field of space-time would have vanished, so that light rays and free bodies would no longer know how to move. But as an annihilation of the stars is beyond the range of possibility, we must have recourse to other methods. So we are led to examine the question of stability. Is it true that the stars are in a state of statistical equilibrium? ”

“ In short, if we wish to co-ordinate natural phenomena with simplicity, we must thus conceive the various time-flows and simultaneities defined by Einstein, to represent the times imposed upon us, not by the caprice of a mathematician, not by optical transmissions alone, but by the entire physical world. The times of relativity are therefore those which will govern all physical processes, not merely optical ones; and for this reason we must regard them as representing the real time-flows of the universe. ”

“ But it is obvious that we have no right to assume that Newton’s law or those of mechanics are above all suspicion. The laws of physical science present no a priori inevitableness; and our sole reason for accepting them is because they appear to be borne out to a high degree of approximation when we compare their rational consequences with the results of observation. Approximation is thus all we can aspire to in physical science; and even classical scientists recognised the possibility that more precise observation might prove Newton’s law and those of mechanics to stand in need of correction. ”

“ Our inability to differentiate between a field of inertial forces generated by acceleration and one of gravitation generated by matter is due solely to a miraculous coincidence, that of the equality of the two masses. Again, when, in the elevator falling in the earth’s gravitational field, we experience no feeling of weight, it is not that the gravitational field has vanished; it is solely that the field of gravity has been counteracted by an equal and opposite field of inertia generated by the elevator’s accelerated motion. ”

“ All these spheres of science, from mathematics to psychology, dovetail into one another, as terms like bio-chemistry, psycho-physics and physical chemistry indicate.
It might be urged that the results embodied in the special sciences do not embody all of nature; that there is mind and consciousness, that there are emotions, values in quality, religious instincts, and so on. But here it should be remembered that whatever transcends the sphere of the special sciences transcends it precisely because it is vague and only dimly apprehended. ”

“ We must recognise, therefore, that the common objective world, whether such a thing exists or is a mere convenient fiction, is indispensable to science, if in no other capacity than as a working hypothesis. And neo-realism, as we have said, when pursued consistently, renders a collective view impossible. Furthermore, from the standpoint of science, whether it be classical physics, relativity, physiology or psychology, neo-realism is untenable, for under no circumstances can vision and our knowledge of nature in general be considered a matter of direct apprehension. ”

“ Here we are living in a world which, theoretically at least, is vastly different from the world of separate space and time, and yet it is only thanks to ultra-refined experiment and to the genius of Einstein and Minkowski that we have finally realised it to be a four-dimensional continuum of events. How is it that ordinary perception is so blind to facts? ”

“ And now let us revert to the common objective world of classical science, to the world of separate space and time in which molecules, atoms and electrons move and vibrate, and in which other types of realities, such as electromagnetic fields, are present. Let us recall once again that this real objective universe is the world as the scientist must assume it to be if he wishes to co-ordinate the complex of his experiences (reducing in the final analysis to sense impressions) in a simple and consistent manner. ”

“ Every new scientific discovery reveals aspects of nature, or even of the mind, as in pure mathematics, which we never suspected before. To-day, both the discoveries of relativity and the quantum hypothesis are case in point. It is precisely because the philosophy of a theory of mathematical physics can only be attained a posteriori, coming as a crowning achievement, that the philosophy which is beginning to disentangle itself from Einstein’s discoveries is still in an embryonic stage. It is not that a scientific philosopher of sufficient scope could not be found ”

“ For inasmuch as we know practically nothing about the intra-atomic occurrences responsible for radiation, we may postulate anything we please with impunity, and as a result make the theory predict any shift we wish, be it vanishing or great. But the purpose of a scientific theory is to give us the power to predict phenomena as yet unknown, and not merely to account for what we already know. It was for this reason that Newton’s law of gravitation was so great an advance over Kepler’s laws of planetary motion or Ptolemy’s crystal spheres. ”

“ When, therefore, we consider the laws of classical science, we shall be able to accept them without modification only provided they happen to satisfy the restrictive condition imposed by the space-time theory.
It must be kept in mind, however, that the space-time tensor test cannot aspire to tell us with certainty what the laws of the real world will be. Its action is merely one of elimination; it tells us what these laws can never be. When it comes to deciding which one of the many possible laws is to be accepted as the true law, experiment must be our guide. ”

“ But when it is considered that Einstein’s theory is based on the relativity of velocity, then that it establishes, in a partial way at least, the relativity of acceleration, it cannot be denied that a logical extension of its triumphs would be for it to succeed in establishing the complete relativity of all motion and of inertia. Although Einstein never conceals his hope that this will be the ultimate outcome, there is no desire on his part to force the issue in defiance of facts. ”

“ Now although length, size and duration are relatives, the theory of relativity has discovered absolutes which transcend the observer, remaining the same for all. They are to be found in the absolute world of space-time; and it is this thought that Minkowski desired to convey when he said: “Henceforth space and time by themselves are mere shadows.” In the absence of some specified observer, space and time become indeterminate, and with them length and duration; that which endures and transcends the observer is a something in space-time, and this is neither a length nor a duration. ”

“ If, with science, we consider that our knowledge of the external universe can be arrived at only by a rational synthesis of facts of experience, we must recognise that substance escapes us completely; all we can hope to approach is structure, or relationships. Of course, a view of this sort presupposes that we are justified in asserting that knowledge can be acquired only by means of rational co-ordinations. If we dispute the legitimacy of this point the entire argument collapses. ”

“ It is for this reason that a theory of mathematical physics, in contradistinction to one of pure mathematics, is constantly subjected to the control of experiment. If, therefore, the Lorentz-Einstein transformations failed to yield the results that would be actually measured, Einstein’s theory as a means of physical discovery, as a co-ordination of physical facts, would be not only useless, but entirely incorrect, and we should have to abandon it. ”

“ It has been one of the triumphs of the relativity theory to disprove this fundamental thesis, and to show that in the real world of experience a continuum of space by itself is but a shadow. Henceforth the continuum of reality is space-time, a four-dimensional continuum of events, and no longer, as in classical science, a three-dimensional one of points, coupled with a one-dimensional continuum of instants. ”

“ Now, as we have remarked previously, when the critic attacks the theory of relativity on the ground that it defines simultaneity by optical methods, it must be presumed that he attributes the strangeness of Einstein’s theory to its exclusive use of light signals. Were this opinion correct, it would certainly appear rather arbitrary to found a theory of the universe on one particular choice of time determinations, when other methods would have yielded our classical results. Why, indeed, define time in terms of light rather than of sound or moving bodies? ”

“ All that we have a right to demand of any theory is that it be in harmony with the existence of an inertial frame with respect to which rotation develops centrifugal forces; for these forces have been detected by experiment. But we have no right to maintain that any experiment performed to this day has ever been sufficiently precise to demonstrate the absolute fixity of the inertial frame, or to deny that the frame may not suffer from a certain measure of indeterminateness when large masses move in its neighbourhood. ”

“ We thus understand the significance of a theory of mathematical physics. Its utility is to allow us to foresee and to foretell physical phenomena. In this way it suggests precise experiments which might never have been thought of, and permits us to anticipate new relationships and new laws and to discover new facts. From a philosophical point of view, by establishing a rational connection between seemingly unconnected phenomena, it enables us to detect the harmony and unity of nature which lie concealed under an outward appearance of chaos. ”

“ Having established the solidarity of the evolution of all physical phenomena at rest in the same Galilean frame as an inevitable consequence of the relativity of Galilean motion, we must now enquire whether this general solidarity should be assumed to extend to vital phenomena and to our consciousness of the flight of time. Of course we cannot deny that aging is accompanied by a physiological alteration of our bodies; hence, on this ground alone, there can be no doubt that physiological aging will proceed in terms of the general solidarity of all physical phenomena. ”

“ Yet they are not, properly speaking, great mathematicians. Mathematics, for the theoretical physicists, constitutes but a tool, a means of arriving at a co-ordination of the physical facts. These men have never entered into the study of mathematics as an art in itself; they have never forged new mathematical instruments, never made mathematical discoveries. Thus, they cannot be classed with mathematicians of the calibre of Lagrange, Gauss, Riemann or Poincaré, to whom modern mathematics owes its existence. ”

“ When we realise the important rôle played by space-time in our attempts to avoid a belief in absolute rotation, we can well understand that the doctrine of the relativity of all motion would have been absurd in Newton’s day. In fact, any thinker prior to, say, the year 1900 could never have anticipated the discovery of space-time, for its sole justification arose from the negative experiments in optics and electrodynamics attempted at about that time. ”

“ The verdict of scientists is that the atomicity of action entails a gigantic revolution in our understanding of nature. In the first place, the laws of mechanics, whether those of classical science or those of relativity, issue in a principle of action; so that by tampering with action, we are tampering with the basic laws of mechanics. Hence, it would appear that our insight into the laws of nature, even in spite of the great advance due to relativity, was still far too crude. ”

“ Its aim and its raison d’être are not solely to construct the rational scheme of some possible world, but to construct that particular rational scheme of the particular real world in which we live and breathe. ”

“ Now the criticism has often been raised that there is nothing in Einstein’s space-time model which enables us to explain the reason for that most fundamental fact of consciousness, our awareness of the flowing of time. It is difficult to see why a criticism of this sort should be directed with any greater justification against space-time than against the classical theory. The fact that in classical science space and time were separate did not allow us to explain the phenomenon of the flowing of time any better than does the space-time theory. ”

“ Consider a train moving with constant speed along a straight course; obviously there is no trace of acceleration in the train’s motion, since no forces of inertia are felt in its interior. In common practice, we should speak of the train as having a definite speed of so many miles per second. But if we reflect we shall see that this constant speed is computed with respect to the earth’s surface, considered as defining a Galilean frame of reference. Were the earth suddenly to become invisible, we should have no physical means of determining the exact speed of the train through space. ”

“ Of course, in everyday life, the distinctions the scientist is compelled to consider are very often of scant importance. When, for instance, we bark both our shins and are conscious of a psychological simultaneity of painful impressions, we are perfectly justified in practice in assuming that we have barked our shins simultaneously. It is only when we subject an example of this sort to the rigorous logic of scientific thought that the crude view becomes untenable in theory though of course still permissible as an approximation. ”

“ But, once again, for a given observer it is as physically real as a chair or a table. Only when we consider the contraction from an impersonal standpoint, from that of space-time, without mentioning the conditions of observation, is the contraction not an illusion, but downright meaningless. It is, as we see, the concept of spatial magnitude, of primary qualities, which is at stake, in a form entirely different from anything science or philosophy had ever dreamed. ”

“ For even if it should appear that the universe of ideas cannot be deduced from experience by logical means but is in a sense a creation of the human mind without which no science is possible, nevertheless this universe of ideas is just as little independent of the nature of our experiences as clothes are of the form of the human body. This is particularly true of our concepts of time and space which physicists have been obliged by the facts to bring down from the Olympus of the a priori in order to adjust them and put them in a serviceable condition. ”

“ If with Einstein we follow this line of argument, we must assume that the large number of negative experiments prove conclusively that velocity through the stagnant ether or through space is physically meaningless, not only from a purely mechanical point of view, as was the belief of classical science, but from every point of view. If we accept this relativity of the ether and space for Galilean motion as a fundamental fact of nature, holding for all manner of experiments, our past difficulties are seen to be of our own making. ”

“ A coincidence for one would no longer be a coincidence for the other. Coincidence would thus cease to be absolute, and it is doubtful whether any science could exist, since all unity in nature would be lacking. Furthermore, the coexistence of two conflicting species of space and time transformations appears very improbable when we remember that it is impossible to establish a clear-cut distinction between mechanics and electrodynamics, since matter seems to be in large part an electromagnetic phenomenon. ”