Einstein Explained
BY PROFESSOR JAMES RICE.
[During the visit of Professor Einstein to London this week, we are here publishing an exposition of the Einstein theory of relativity (by Professor James Rice, of Liverpool University, author of Relativity (Ben's Sixpenny Library), in place of Professor William McDougall's contribution to our series of "Science Yesterday and To-Day." The article on " Psychology " by Professor McDougall will appear next week.] WILL you, the reader, imagine that you arc in a car travelling quite smoothly and uniformly along a straight road ? Another car passes by going in the same direction. The police on the roadway are measuring, and they find that your speed is twenty miles per hour and that the other car is travelling at thirty miles per hour. The police would say quite correctly that the other ear is getting away from you at a speed of ten miles per hour, and that if it were coming towards you instead of over- taking you its speed relative to you would be fifty miles per hour. If this occurrence were taking place at cross- roads so that you passed by on one road and the second ear on the other, they could work out the relative speed by a rather more complicated calculation. You will probably have had some acquaintance with the " Paral- lelogram of Velocities " in your school days. As the writer cannot appeal to mathematical formulae, you must not be surprised at this unusual curiosity about relative speed on the part of the police. You must not even be surprised to find that you also have suddenly developed an insatiable curiosity about the speed of that car relative to yourself. You scorn to stop and obtain from the police the necessary information ; for you have thoughtfully installed in the car all the necessary clocks and rulers and
sighting instruments for the purpose. So you make your own measurements, never concerning yourself with the road or any observers on it. Later you compare your result with that of the police and find that they agree. You expect this agreement ; it is common sense.
Now will the reader pause a moment to reflect on a hypothesis which has intruded in taking this agreement for granted ? Obviously your instruments arc not quite in the same situation as those of the police ; their in- struments are at rest on the roadway ; yours arc not. So you have obviously assumed that simple, steady motion produces no difference in the measurements of your apparatus as compared with that of the police, Nevertheless, the result of assuming that this hypothesis is absolutely valid for any speeds however great, and that relative velocities could be calculated in this manner in all circumstances led physicists into difficulties at the end of last century. Out of these difficulties Einstein extricated them in 1905 by the " Principle of Relativity."
The first difficulty arose in the decade 1880-90. Phy- sicists had, as it were, made space substantial by con- ceiving it to be filled with the ether, the medium for carrying the waves of light. All heavenly bodies were drifting through this immense ocean, and naturally the physicist sought to measure the rate of the earth's drift through it. The idea underlying the suggested experi- ment resembled the fanciful illustration just given, the ether being the roadway, the earth your car, and waves of light taking the place of the other car. A skilful American physicist, Michelson, designed the necessary apparatus with wonderful ingenuity and made the observations. To everyone's surprise he found that the earth's speed through the ether was always just nothing, No one questioned the accuracy of his observations and certainly no one thought of questioning the validity of the calculations based on them ; for they made use of the simple law of relative motion illustrated above. If, for example, the earth were drifting at the moment towards some celestial body which we shall call " A," then light going towards " A " would travel through terrestrial instruments slower than through the ether, while light travelling in the opposite direction would travel faster relative to appliances on the earth. Indeed, the speed of light in any direction should as measured on the earth vary with the direction. Michelson found no such variation. Repetitions of the experiment have consistently supported him.
Naturally physicists sought for explanations of this awkward fact. They simply could not believe that the earth was the one body fixed absolutely in the ether, or in " absolute space " as they would have said in those clays ; such a belief was too violently at variance with the accepted cosmology. So they explained things by assuming that motion through the ether produced minute contractions in the drifting earth and in all things on it, and that these contractions in our apparatus were just of such amount as to prevent us measuring this ether drift. However, no one pretended that this was altogether a satisfactory state of affairs. Added to that, the opening of this century was witnessing the birth of the electrical theory of matter, and the newly discovered electron, endowed in general with speeds enormously great com- pared with anything we had previously experienced except in the case of light, was not behaving itself under forces as Newton's laws of motion predicted. This was significant, for the law of relative motion in common use was also a part of the Newtonian scheme of things. Yet not only light but high-speed electrons, with speeds from one tenth to nine tenths of the speed of light, were somehow at variance with the accepted mechanical principles.
In this situation of doubt Einstein did the simple, obvious thing. The genius always does that. There were at least a dozen physicists of the first rank then living, skilful mathematicians and experimenters, who were struggling to explain away this awkward fact. Einstein said, " Don't explain it away ; accept it as a fundamental, experimental fact and begin your explana- tions from it as a starting point."
So Einstein started from the statement that the speed of light is exactly the same for two observers " X " and " Y," even if " Y " is in motion relative to " X," and even if " Y's " relative motion were much greater than would be humanly possible in our planet. He then proceeded to work out the conclusions deducible from such a statement of theoretic equality. He found that the first things to be affected were our ideas as to measure- ments in space and time. The implicit assumption pointed out above that relative motion does not affect instruments measuring length and time was found to be untenable, and mathematical formulae indicating exactly how the modifications of the instrumental indications depend on the value of the relative speed were worked out.
Such results naturally involved a modification of the accepted laws of motion as originally stated by Newton, the main change being that the same force produces a smaller acceleration in the speed of a body the greater that speed is, until at the speed of light no acceleration is produced at all ; this obviously implies an increase of mass in the body with increasing speed, thus doing away with invariability of mass. This was all very startling, but it was found to be in excellent agreement with the behaviour of fast travelling electrons. For the relatively slow moving things of our ordinary life or even for the heavenly bodies, the changes are so small as to be undetectable in a direct fashion by our instruments, so that naturally we never conceived such possibilities previously.
But this was not all. We had to conceive a Universe whose phenomena of movement could be observed from different standpoints by intelligences resident in different stars. Owing to the relative motions of the stars, the numerical data of events in space and time would not agree as between observers in different stellar observa- tories. How could these be fitted to give a consistent mathematical statement ? There was no question of singling out one body as an " absolute fixture in space." The whole meaning of such a phrase had evaporated. No such privilege could be accorded to any one celestial body. Einstein showed how this articulation of ap- parently inconsistent data into a consistent whole could be effected. He not only pointed the way but he blazed the trail. His new statements of physical laws were found to be in beautiful accord with the electrical theory of matter ; his results illumined in a most unexpected way the internal behaviour of atoms. Macrocosm and microcosm alike came within the ambit of this new principle.
Only one phenomenon seemed to stand out—Gravita- tion. The clever mathematicians wrestled with ingenious modifications of Newton's law of gravitational force so as to bring it into the relativistic scheme of things, but again it was the genius who took the physicist out of the rut and discovered the true solution, and in the most unexpected quarter. There is a familiar similarity between the effects of gravitation and the effects expe- rienced in a starting or stopping carriage. The ordinary man often describes himself as being " under a force " in the latter situation. The physicist would say that there is no " real " force at all. Einstein, however, found in the similarity a fact of tremendous significance and pointed out that the differences between the " real " forces of gravitation and " imaginary " forces such as occur in a carriage whose speed is changing are, so far as the laws of Physics are concerned, not at all easy to formulate in mathematical terms. (To this extent the instinct of the ordinary man was justified.) He did, however, succeed in doing so and in a manner naturally consistent with his own principle of Relativity. This mathematical formula- tion of the difference between real gravitational forces and influences ascribable to the " acceleration of a frame of reference " is his law of gravitation. In reality it takes gravitation out of the category of force and describes it as the result of a modification in the measurement of space and time due to the presence of matter. The law has predicted an important series of astronomical pheno- mena, which have been successfully observed.
In conclusion, the reader should realize that Rela- tivity is nowadays not a new principle struggling for acceptance. Within a quarter of a century it has esta- blished itself as an absolutely indispensable, almost commonplace, member of the group of laws by whose aid the scientist sets out to conquer new worlds.
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