The Principle of Relativity · Albert Einstein
(A)
We remark that this result about the mass hold also for ponderable material mass; for in our sense, a ponderable material point may be made into an electron by the addition of an electrical charge which may be as small as possible. Let us now determine the kinetic energy of the electron. If the electron moves from the origin of co-ordinates of the system K with the initial velocity 0 steadily along the X-axis under the action of an electromotive force X, then it is clear that the energy drawn from the electrostatic field has the value ∫_e_X_dx_. Since the electron is only slowly accelerated, and in consequence, no energy is given out in the form of radiation, therefore the energy drawn from the electro-static field may be put equal to the energy W of motion. Considering the whole process of motion in questions, the first of equations A) holds, we obtain:— $$ W = \int eXdx = \int_0^v m\beta^3 vdv = mc^2 (\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} - 1) $$ For _v_ = _c_, W is infinitely great. As our former result shows, velocities exceeding that of light can have no possibility of existence. In consequence of the arguments mentioned above, this expression for kinetic energy must also hold for ponderable masses. We can now enumerate the characteristics of the motion of the electrons available for experimental verification, which follow from equations A).
1. From the second of equations A), it follows that an electrical force Y, and a magnetic force N produce equal deflexions of an electron moving with the velocity _v_, when Y = N_v_/_c_. Therefore we see that according to our theory, it is possible to obtain the velocity of an electron from the ratio of the magnetic deflexion A_{_m_}, and the electric deflexion A_{_e_}, by applying the law:— $$ \frac{A_{m}}{A_{e}} = \frac{v}{c} $$ This relation can be tested by means of experiments because the velocity of the electron can be directly measured by means of rapidly oscillating electric and magnetic fields. 2. From the value which is deduced for the kinetic energy of the electron, it follows that when the electron falls through a potential difference of P, the velocity _v_ which is acquired is given by the following relation:— $$ P = \int Xdx = \frac{m}{e}c^2 (\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} - 1) $$ 3. We calculate the radius of curvature R of the path, where the only deflecting force is a magnetic force N acting perpendicular to the velocity of projection. From the second of equations A) we obtain: $$ - \frac{d^2y}{dt^2} = \frac{v^2}{R} = \frac{e}{m} \frac{v}{c} N \sqrt{1 - \frac{v^2}{c^2}} $$ or _mv_β_c_ R = ---------- _e_N These three relations are complete expressions for the law of motion of the electron according to the above theory.
Footnote 6: _Vide_ Note 9. Footnote 7: _Vide_ Note 9. Footnote 8: _Vide_ Note 12. ALBRECHT EINSTEIN [_A short biographical note._] The name of Prof. Albrecht Einstein has now spread far beyond the narrow pale of scientific investigators owing to the brilliant confirmation of his predicted deflection of light-rays by the gravitational field of the sun during the total solar eclipse of May 29, 1919. But to the serious student of science, he has been known from the beginning of the current century, and many dark problems in physics has been illuminated with the lustre of his genius, before, owing to the latest sensation just mentioned, he flashes out before public imagination as a scientific star of the first magnitude. Einstein is a Swiss-German of Jewish extraction, and began his scientific career as a privat-dozent in the Swiss University of Zürich about the year 1902. Later on, he migrated to the German University of Prague in Bohemia as ausser-ordentliche (or associate) Professor. In 1914, through the exertions of Prof. M. Planck of the Berlin University, he was appointed a paid member of the Royal (now National) Prussian Academy of Sciences, on a salary of 18,000 marks per year. In this post, he has only to do and guide research work. Another distinguished occupant of the same post was Van’t Hoff, the eminent physical chemist.
It is rather difficult to give a detailed, and consistent chronological account of his scientific activities,—they are so variegated, and cover such a wide field. The first work which gained him distinction was an investigation on Brownian Movement. An admirable account will be found in Perrin’s book ‘The Atoms.’ Starting from Boltzmann’s theorem connecting the entropy, and the probability of a state, he deduced a formula on the mean displacement of small particles (colloidal) suspended in a liquid. This formula gives us one of the best methods for finding out a very fundamental number in physics—namely—the number of molecules in one gm. molecule of gas (Avogadro’s number). The formula was shortly afterwards verified by Perrin, Prof. of Chemical Physics in the Sorbonne, Paris. To Einstein is also due the resuscitation of Planck’s quantum theory of energy-emission. This theory has not yet caught the popular imagination to the same extent as the new theory of Time, and Space, but it is none the less iconoclastic in its scope as far as classical concepts are concerned. It was known for a long time that the observed emission of light from a heated black body did not correspond to the formula which could be deduced from the older classical theories of continuous emission and propagation. In the year 1900, Prof. Planck of the Berlin University worked out a formula which was based on the bold assumption that energy was emitted and absorbed by the molecules in multiples of the quantity _h_ν, where _h_ is a constant (which is universal like the constant of gravitation), and ν is the frequency of the light.
The conception was so radically different from all accepted theories that in spite of the great success of Planck’s radiation formula in explaining the observed facts of black-body radiation, it did not meet with much favour from the physicists. In fact, some one remarked jocularly that according to Planck, energy flies out of a radiator like a swarm of gnats. But Einstein found a support for the new-born concept in another direction. It was known that if green or ultraviolet light was allowed to fall on a plate of some alkali metal, the plate lost electrons. The electrons were emitted with all velocities, but there is generally a maximum limit. From the investigations of Lenard and Ladenburg, the curious discovery was made that this maximum velocity of emission did not at all depend upon the intensity of light, but upon its wavelength. The more violet was the light, the greater was the velocity of emission. To account for this fact, Einstein made the bold assumption that the light is propagated in space as a unit pulse (he calls it a Light-cell), and falling upon an individual atom, liberates electrons according to the energy equation 1 _h_ν = --- _mv²_ + A, 2 where (_m_, _v_) are the mass and velocity of the electron. A is a constant characteristic of the metal plate.
There was little material for the confirmation of this law when it was first proposed (1905), and eleven years elapsed before Prof. Millikan established, by a set of experiments scarcely rivalled for the ingenuity, skill, and care displayed, the absolute truth of the law. As results of this confirmation, and other brilliant triumphs, the quantum law is now regarded as a fundamental law of Energetics. In recent years, X-rays have been added to the domain of light, and in this direction also, Einstein’s photo-electric formula has proved to be one of the most fruitful conceptions in Physics. The quantum law was next extended by Einstein to the problems of decrease of specific heat at low temperature, and here also his theory was confirmed in a brilliant manner. We pass over his other contributions to the equation of state, to the problems of null-point energy, and photo-chemical reactions. The recent experimental works of Nernst and Warburg seem to indicate that through Einstein’s genius, we are probably for the first time having a satisfactory theory of photo-chemical action.
In 1915, Einstein made an excursion into Experimental Physics, and here also, in his characteristic way, he tackled one of the most fundamental concepts of Physics. It is well-known that according to Ampere, the magnetisation of iron and iron-like bodies, when placed within a coil carrying an electric current is due to the excitation in the metal of small electrical circuits. But the conception though a very fruitful one, long remained without a trace of experimental proof, though after the discovery of the electron, it was generally believed that these molecular currents may be due to the rotational motion of free electrons within the metal. It is easily seen that if in the process of magnetisation, a number of electrons be set into rotatory motion, then these will impart to the metal itself a turning couple. The experiment is a rather difficult one, and many physicists tried in vain to observe the effect. But in collaboration with de Haas, Einstein planned and successfully carried out this experiment, and proved the essential correctness of Ampere’s views. Einstein’s studies on Relativity were commenced in the year 1905, and has been continued up to the present time. The first paper in the present collection forms Einstein’s first great contribution to the Principle of Special Relativity. We have recounted in the introduction how out of the chaos and disorder into which the electrodynamics and optics of moving bodies had fallen previous to 1895, Lorentz, Einstein and Minkowski have succeeded in building up a consistent, and fruitful new theory of Time and Space.
Ideas discussed in this chapter
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