Part 3
In other words, after admitting the principle of relativity in a mechanical sense, practically as stated in Einstein’s first postulate, Newton then denied or at least overlooked that principle when it touched the subject of the propagation of light. Take, for instance, the case of light rays reaching us from certain distant stars. We cannot surely know whether the source of light is traveling toward us, or whether we are moving toward the source of light. Newton would say that the velocity of light would be unaffected in the first instance, but increased in the second. Einstein says it makes no real difference which way it is, because the principle of relativity is universal, all motion is relative, and the universe is so constructed that the velocity of light always appears constant to all observers irrespective of their motion or of the motion of the source of light relative to them.
If, however, we were traveling away from a given source of light at a greater velocity than light itself can travel it would certainly not be true that light, under such a condition, would register a constant velocity. But such a rate of motion is manifestly impossible of physical attainment, light being considered to possess the maximum velocity greater than which no material body can travel. In other words, 186,300 miles a second is the limiting velocity beyond which physical phenomena does not reach, because all matter would evidently suffer complete dissolution, being reduced to the state of free electrons, by the time such a velocity would be attained. Light is matter in the free electronic state, and the velocity of such a form of matter is known to be 186,300 miles a second, as has been stated.
Light, being a form of matter, is acted upon by gravitation. This was first demonstrated during the solar eclipse of May 29, 1919, when photographs were taken of various stars whose light at that season had to pass very near the sun in order to reach us. Three months later photographs were taken of these same stars after they had moved from their former positions. Their normal relative motion being known, it was easy to determine from the two sets of photographs whether their displacement was entirely due to that motion. It was found that their displacement was considerably less than it would have been under normal conditions, thereby indicating that the light from these stars had been deflected as it passed near the sun’s rim, making it appear to the observer that these stars then occupied positions which they did not occupy. See Fig. 3.
=Electronic Structure of Matter=
Light and electricity both travel at the same velocity, and in the final analysis they are the same form of matter. All ponderable matter is made up of molecules, and molecules consist of atoms of varying elements, except where the substance is elementary throughout, in which case the molecules are made up of a certain number of atoms of the same element. An atom is an aggregation of negatively charged particles of electricity, called electrons, which revolve and vibrate at enormous rates around a central nucleus of “protons” carrying a positive charge. If we conceive of a handful of sand as whirling around and around at such an enormous velocity as to appear as a globe several feet in diameter we have a visualization of the ultra microscopic atom and its comparative dimension to that of the individual electrons and protons which compose it.
Electrons and protons are manifestly identical in all form of matter, but all atoms do not contain the same number of them. An atom of hydrogen contains only one electron and one proton, while atoms of heavier matter contain a vast number. It is the _number of electrons and protons per atom_, together with their respective vibratory rates, that constitute the difference between elements. Hence every known form of matter, if reduced to the electronic state, would be found to consist of the same original stuff. Light, therefore, may be termed _free electrons_, i. e., electrons which are not bound into atoms, and consequently glide off in every direction at the highest possible velocity of which matter is capable, viz., 186,300 miles per second.
Thus it may be seen that all other forms of matter, since they consist of electrons in the atomic or “bound” state, could not possess a velocity equal to that of _free_ electrons. But electrons do not become “free” simply by reason of matter undergoing a change of form. Water, for instance, may be changed into a solid (ice) or into gas (steam), but the electrons continue to revolve around their nucleus in true atomic order, and the atoms continue to hold together in the molecular state, the only change being in their rate of vibration which affects the degree of elasticity between the molecules and between the atoms. Hence whether water be in the solid, liquid or gaseous state, the molecules thereof will be found intact, each consisting of two atoms of hydrogen and one atom of oxygen (H₂O).
When matter is being burned up, producing a flame or a glow of light, this phenomenon indicates that some of the electrons have been freed from their atomic condition and have started off on their journey in the form of light rays, while another portion of them remain bound as atoms but undergo a change of form, becoming either gas or ashes.
=Michelson-Morley Experiment=
Returning now to Einstein’s second postulate, that the velocity of unobstructed light rays appears to be constant to all observers irrespective of the relative velocity between the observer and the source of light. The evidence on which this theory is based was first produced by Michelson and Morley in 1887 who at that time undertook an experiment to ascertain if possible the velocity of the earth relative to the ether. The experiment revealed that light registers a constant velocity, whether it travels in the direction of the earth’s rotation, or against the rotation, or at right angles thereto. The experiment was repeated many times with different apparatus and under various conditions, but always with the same result.
It is interesting to note the details of this experiment. Light is known to travel in waves, because rays coming against each other from opposite directions can be made to “interfere” in precisely the same manner as waves in water. If waves in the ocean come together from different directions, one of two things will happen; they will either unite and produce a larger wave, or else they will strike in a manner to measurably kill off both waves. If the crests of the two waves coincide they reinforce each other, but if they strike at right angles, the destruction of the wave motion results. This is called “interference.”
Light rays conduct themselves in the same manner, thereby revealing their wave-like nature. This is not contradictory to the idea that light rays really consist of individual electrons, freed from atomic attraction. Possibly each separate electron which goes to make up a ray of light vibrates in a wave-like manner, possessing a wave motion within itself. Waves of light are exceedingly minute and we do not ordinarily witness any reinforcement or interference of light rays about us, because there is no occasion for them to “pile up.” However, in laboratory experiments, interference of light waves has been produced, and to whatever extent the interference kills off the wave motion, to that extent darkness ensues irrespective of the brightness of the light at its source.
Michelson and Morley worked on the theory that if they sent rays of light from west to east (the direction of the earth’s rotation) and then reflected them back over their course it should take longer to make the eastward trip than the westward, because in the first instance the earth is carrying the objective point away from the light while in the latter instance it would be rushing to meet the oncoming reflected rays. Under this condition there should be a noticeable _interference_ of the light waves due to the difference in distance and time involved in making the two halves of the round trip. But to the amazement of all there was no interference whatever, notwithstanding the fact that the apparatus was ten times larger than it needed to be to reveal such interference of the waves had it really occurred.
The conclusion reached by Einstein as a result of this experiment is that since light rays consist of matter in its basic or electronic state, freed from atomic attraction, they therefore possess the limiting velocity of which matter is capable. Hence they could not travel more rapidly than 186,300 miles a second even if given a quick send-off, nor would our traveling toward the light affect its apparent velocity to us--unless it were possible for us to be traveling forward more rapidly than light itself can travel. This would undoubtedly be impossible, inasmuch as any physical body would necessarily consist of electrons in the atomic or “bound” state and therefore could not possess the mobility that free electrons would enjoy. The universe, then, being a four-dimensional continuum, is so constructed that the velocity of light always appears constant to all observers within it.
This is what Einstein means when he postulates that light _in vacuuo_ (i. e., unobstructed) possesses a constant velocity irrespective of the relative velocity of observer and source of light. That is, it is constant so far as the observer is concerned. Thus if a flash should occur on any heavenly body and we were moving toward the flash at say 40,000 miles a second and another observer were moving away from it at say 60,000 miles a second, the experiment of each observer would indicate that the light has reached him at exactly 186,300 miles a second, although according to Euclid’s conception of space the light has been obliged to travel 100,000 miles a second faster to reach the one observer than the other. But Euclid’s conception is faulty, as will be seen shortly.
How, then, would it be possible for the light rays to possess the same apparent velocity per second for the two observers? It would not be possible if “time” and “distance” are absolute quantities having the same meaning for all observers. But if “seconds” and “miles” mean one thing to observer “A” and a totally different thing to observer “B,” then the apparent contradiction of facts becomes harmonious. This is the essence of the doctrine of relativity. Observer “A” himself does not use the terms “seconds” and “miles” consistently, i. e., as unvarying quantities, nor does anyone. They mean one thing today and something else tomorrow, depending upon what we are measuring and the relative velocity between the observer and the object. The observer is not aware of this inconsistency. To him there is no inconsistency whatever. Nevertheless, only by acknowledging the varying quantities of time and of space, and admitting the geometry which combines the two into one unit, can the Michelson-Morley experiment and other similar observations be understood and explained.
=Simultaneity a Meaningless Term=
We have been taught that the true length of a moving body is “the distance between _simultaneous_ positions of its end points”--a very good definition, but impossible of application for the reason that we cannot determine the _simultaneous_ positions of any two points in the universe. Simultaneity is a meaningless term so long as the absolute velocity of the observer and the absolute velocity of the object being measured are unknown. We may know the _relative_ velocity between them, but that is not sufficient. The two may be relatively at rest--but for all we know the entire universe may be speeding through space at thousands of miles a second in either one direction or another.
We may _see_ two events occur at the same instant, but that does not prove that they actually _occurred_ simultaneously. Before we could compute the exact time of the occurrence of either of the events we must know the direction in which, and the velocity at which the universe as a whole is moving, together with any and all velocities of the observer at the moment. This knowledge we do not possess. Until the _absolute_ velocity of bodies can be determined the question of simultaneity must remain unsolved.
=The General Principle of Relativity=
When in 1905 Einstein published the foregoing postulates which are limited to uniform, rectilinear motion he may have considered that it would be expecting too much to look for a general principle of relativity such as would hold good for all kinds of rotating and irregular motions and by which observers of different and variable velocities might agree as to the reality of things under their observation. Concluding, however, that the universe must surely be constructed in a consistent manner he finally set out to find some rule or principle by means of which an observer in one region would be seen to possess no advantage over an observer in any other region of the great expanse in arriving at accurate conclusions.
Of course Einstein hardly expects to go to the Pleiades or to Betelguese and from there take measurements and make calculations; he is doubtless content to make all his observations from this earth. But how may he be sure that observations made from a reference frame located in this particular region of the universe will be true to the reality since it is manifest that observers located elsewhere and using different reference frames must necessarily reach conclusions different from ours if they employed our accustomed laws? Maybe they would be much nearer the reality than we! What right have _we_ to assume a monopoly on truth! None whatever until we can formulate nature’s laws in a manner that will hold good for every part of the universe alike.
Until we are able to do this our science must be like the vain efforts of the unskilled fisherman who harpoons for fish. Ignorant of the trick that water plays on the line of sight he strikes directly at the spot where he “sees” the fish and always misses his prey. The skilled harpooner, on the contrary, understands the law of refraction of light rays in water, and knows how to allow for this refraction; hence he strikes a little this side of where the fish appears to be and is rewarded with success. He is guided by a proven law and thereby ascertains the true location of the fish, whereas the other man follows “blind” observation which is quite frequently deceptive.
Einstein’s “General Principle of Relativity” is not, in fact, a mere generalization of the Special Theory in the sense that it simply enlarges upon the two postulates which we have already considered. On the contrary it handles the subject of Relativity from quite a new standpoint, and therefore might be said to belong to an entirely different school of thought. It does not lend itself to visualization as readily as does the Special Theory, and is consequently more difficult of explanation and comprehension. However, what we have already learned concerning Relativity will materially aid us in understanding what follows, for the two theories are, after all, dealing with the same general subject matter. We shall therefore endeavor to link the two phases of the subject in a logical and consistent manner.
We know, as a matter of fact, that “uniform, straight-ahead motion” which Einstein in his original theory assumed to exist, is an ideality that does not appear in nature, because all motion with which we are familiar is to some extent irregular, nor does any material object move in a perfectly straight line. But realizing the necessity for a standard from which to proceed, Einstein properly enough assumed a standard of absolute perfection and absolute simplicity of motion, even though it does not actually exist anywhere around us. In exactly the same manner Euclidean geometry assumes and deals with theoretical points, lines and planes which have no material existence in fact.
As set forth in Einstein’s first postulate of the Special Theory, an observer on a uniformly moving system could not possibly detect the motion of his system without making reference to some outside object. In the case of bodies or systems moving irregularly (i. e., with acceleration) however, an observer thereon would detect “forces” acting upon himself and upon all other objects on his system, due, of course, to the acceleration. Recalling the illustration of the moving train: so long as it is moving with perfect uniformity an observer thereon would not know he is in motion at all until he made a comparison with some outside object. But if the train suddenly slows down he is thrown forward in his seat; if it speeds up he is thrown backward. This force is called _inertia_. Now if we had never experienced it before and were put aboard a noiseless and uniformly moving car from which we could not see out we would be unable to interpret these strange “forces” that we would feel as the motion of the car became accelerated. We would probably attempt to explain them as some sort of magnetic attraction, exactly as we are accustomed to explain the “force” of gravity.
=Gravitation and Inertia=
In the General Principle of Relativity Einstein deals with these forces (inertial and gravitational) and attributes them to a common cause, viz., acceleration of motion, and has put the matter upon a consistent mathematical basis which at once accounts for certain discrepancies long observed in Euclidean geometry and in Newton’s laws. It is obvious enough that where there is no acceleration of motion there could be no centrifugal or inertial force exhibited: but we have been accustomed to looking upon gravitation as something entirely different--as a mysterious drawing power or attractive force that is somehow inherent in matter. But gravitation is non-existent if we fall with the proper acceleration. To use Einstein’s own illustration: if we were in a closed room poised somewhere in gravitational space, and began to fall with the acceleration common to that field, there would be no gravitational effects to be observed. Objects released by our hand would not fall but would remain where they are, and we could raise ourselves from the floor and stand midway between the floor and the ceiling as easily as upon the floor itself.
Again assume we are in a closed room poised in space, in a region remote from any gravitational field whatsoever. Then suppose we began to rise with a constant acceleration. Forthwith we would feel our feet pressing against the floor. Objects released from our hand would strike the floor by reason of the floor rising up to meet them, and in all respects the effects would be identical with that of gravitation. In other words we would have created an artificial gravitational field, and it would be due to our accelerated motion.
The characteristics of gravitation and inertia are identical. No amount of insulation or screening will diminish the “pull” of gravity on anything. Furthermore, gravity acts on every kind and quantity of matter alike, so that if a feather weighing less than an ounce and a pig of lead weighing a ton were held side by side at the top of a great vacuum tube and allowed to drop at the same instant, the feather would reach bottom within the same time as the lead, each falling at an acceleration of approximately 32 feet per second. It is the resistance of the air that retards the fall of light materials, such as a feather, but in a vacuum there is no resistance and gravity is found to act on all matter to the same degree under such conditions. The same is true of inertia _in vacuuo_.
When this relationship between the two forces is recognized we are prepared to believe Einstein when he states that inertial force and gravitational force are due to a common cause, viz., acceleration. This does not mean that our earth, for instance, is being accelerated in all directions at once, expanding out to meet “falling” objects such as in the case of the artificial gravitational field mentioned in the above paragraph. It does mean, however, that the falling objects themselves are accelerated, but as will be presently seen this acceleration is not due to any attractive force exerted by a “center of gravity” but rather to a warped condition of space which surrounds all bodies of matter.
Neither Newton nor Einstein have attempted to analyze the structure of matter and on this basis explain the phenomenon of gravitation. Newton evidently believed, however, that every particle of matter exerts a drawing force upon every other particle of matter, hence he formulated his law which specifies this attraction between bodies as being directly proportional to the product of their mass and inversely proportional to the square of the distance between them. But he did not attempt to make clear what that “drawing force” is, or _why_ it is inherent in all matter, nor did he explain how or through what medium or mechanism it operates.
Newton contented himself with merely dealing with the phenomenon of gravitation in the abstract. So does Einstein, but with this difference: the latter denies the existence of any mechanism whatever in connection with gravitational force so far as any attractive power from within is concerned, and accounts for it on purely geometrical grounds. This is the most difficult phase of the Einstein theory for the layman to grasp, for the reason that it involves the whole structure of non-Euclidean geometry with which the public is generally unfamiliar.
=Non-Euclidean Geometry=
Euclid, the famous Greek mathematician, in the third century B. C. published the first systematic treatise on geometry (the science of space and its measurement), and his axioms and theorems are generally taught in our high schools and colleges today. Euclid proceeded upon the simple theory that all space consists of points, lines and planes. He defined a _point_ as that which has position but not size; a _line_ (continuity of points) as possessing length but no breadth or thickness; and a _plane_ (continuity of lines) as having length and breadth, but no thickness. They are simply abstract terms having no physical existence in nature, except as they exist in our minds. Nevertheless they have proved themselves convenient in measurement and calculation.
But when mathematicians, after centuries of earnest effort, were unable to prove Euclid’s postulate concerning parallel lines, it occurred to some of them that possibly the whole Euclidean system rests upon a faulty foundation. Then it was that Saccheri in Italy, Legendre in France, Gauss in Germany, Bolyai in Hungary and Lobatschewsky in Russia, all masters of Euclidean geometry, conceived of other methods of decomposing space than that proposed in Euclid’s _Elements_.
Thus it was that early in the nineteenth century, almost simultaneously in many countries, did many non-Euclidean geometric works come to be published. These were of the same general character or form, commonly called Hyperbolic geometry. Each of them is as consistent in itself as is the geometry of Euclid. But to Riemann belongs the credit of formulating a geometry which in the light of Einstein is seen to approach much nearer to the reality of nature than does the Euclidean or any other system.