DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT?
By A. Einstein
September 27, 1905
The results of the previous investigation lead to a very interesting conclusion, which is here to be deduced.
I bad that investigation on the Maxwell-Hertz equations for empty space, together with the Maxwellian expression for the electromagnetic energy of space, and in addition the principle that:—
The laws by which the states of physical systems alter are independent of the alternative, to which of two systems of coordinates, in uniform motion of parallel translation relatively to each other, the alterations of state are referred (principle of relativity).
With the principles* as my basis I deduced inter alia the following result (§ 8):—
Let a system of plane waves of light, referred to the system of co-ordinates (x, y, z), posss the energy l; let the direction of the ray (the wave-normal) make an angle with the axis of x of
the system. If we introduce a new system of co-ordinates () moving in uniform parallel translation with respect to the system (x, y, z), and having its origin of co-ordinates in motion along the axis of x with the velocity v, then this quantity of light—measured in the system
()—posss the energy
where c denotes the velocity of light. We shall make u of this result in what follows.
货币收藏价格Let there be a stationary body in the system (x, y, z), and let its energy—referred to the system
(x, y, z) be E0. Let the energy of the body relative to the system () moving as above with the velocity v, be H0.
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Let this body nd out, in a direction making an angle with the axis of x, plane waves of light, of energy ½L measured relatively to (x, y, z), and simultaneously an equal quantity of light in the opposite direction. Meanwhile the body remains at rest with respect to the system (x, y, z). The principle of energy must apply to this process, and in fact (by the principle of relativity) with respect t
o both systems of co-ordinates. If we call the energy of the body after the emission of
light E1 or H1 respectively, measured relatively to the system (x, y, z) or () respectively, then by employing the relation given above we obtain
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q币怎么转给别人By subtraction we obtain from the equations
The two differences of the form H − E occurring in this expression have simple physical significations. H and E are energy values of the same body referred to two systems of co-ordinates
皓月集团which are in motion relatively to each other, the body being at rest in one of the two systems (system (x, y, z)). Thus it is clear that the difference H − E can differ from the kinetic energy K of the body, with respect to the other system (), only by an additive constant C, which depends on the choice of the arbitrary additive constants of the energies H and E. Thus we may place
since C does not change during the emission of light. So we have
The kinetic energy of the body with respect to () diminishes as a result of the emission of light, and the amount of diminution is independent of the properties of the body. Moreover, the difference K0− K1, like the kinetic energy of the electron (§ 10), depends on the velocity.
Neglecting magnitudes of fourth and higher orders we may place
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From this equation it directly follows that:—
If a body gives off the energy L in the form of radiation, its mass diminishes by L/c². The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that
The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same n by L/9 × 1020, the energy being measured in ergs, and the mass in grammes.
It is not impossible that with bodies who energy-content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test.
If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies.
Footnotes
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*The principle of the constancy of the velocity of light is of cour contained in Maxwell's equations.
About this Edition
牵张反射This edition of Einstein's
Does
the Inertia of a Body Depend upon its Energy-Content? is bad on the English translation of his original 1905 German-language paper (published as Ist die Trägheit eines Körpers von inem Energiegehalt abhängig?, in Annalen der Physik . 18:639, 1905) which appeared in the book The Principle of Relativity , published in 1923 by Methuen and Company, Ltd. of London. Most of the papers in that collection are English translations by W. Perrett and G.B. Jeffery from the German Das Relativatsprinzip , 4th ed., published by in 1922 by Tuebner. All of the sources are now in the public domain; this document, derived from them, remains in the public domain and may be reproduced in any manner or medium without permission, restriction, attribution, or compensation.
The footnote is as it appeared in the 1923 edition. The 1923 English translation modified the notation ud in Einstein's 1905 paper to conform to that in u by the 1920's; for example, c denotes the speed of light, as oppod the V ud by Einstein in 1905. In this paper Einstein us L to denote energy; the italicid ntence in the conclusion may be written as the equation "m = L/c²" which, using the more modern E instead of L to denote energy, may be trivially rewritten as "E = mc²".
This electronic edition was prepared by John Walker in March 2001. You can download a ready-to-print PostScript file of this document or the LaTeX source code ud to create it from this site; both are supplied as Zip ped archives. An Adobe Acrobat PDF edition of this document is also available.
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