Albert Einstein: Equivalence of Mass and Energy
These pages explore Albert Einstein's life, work
and philosophy. Albert Einstein was above all a great physicist and mathematician. Because the ideas involved in
his professional work were generally obscure especially in the first part of the 20th century, the public was not aware
that many other physicists had been working on the same problems, nor were they in a position to understand the unique
contribution of Albert Einstein in each case, which is never quite as it is explained in popular science books.
Albert Einstein's work, like all scientific work, reflected advances of others and ideas that were in the air. He did
not give proper references in many cases because he worked in a patent office, and had no access to proper libraries at
the time he derived these theories. However, he was aware of the physical principles involved. This circumstance,
together with the great publicity that was suddenly accorded to Physics beginning in 1920, to has given rise,
among those who understand only popular science accounts, to three different types of misconceptions. First, many
attribute to Albert Einstein ideas that really belonged to others, but were popularized when his own work became known.
Second, others, having discovered this fact, insist that Einstein was a plagiarist. Third, many attribute to Einstein's
scientific theories various philosophical, ethical or moral concepts, which they do not predict or relate to in any way,
as Einstein would be the first to acknowledge, and in fact pointed out.
Concepts and predictions that preceded Albert Einstein and accusations of plagiarism
include the notion of relativity, first used by Galileo and, in the 19th century by Poincaré, thought experiments
about synchronization of clocks, which Poincaré had also used, changes in mass and in size of objects at
different velocities, which arise from the equations of Poincaré and Lorentz, and the equivalence of mass and
energy, derived in 1902 by Poincaré, and by the Italian
Olinto De Pretto, and in the speculations of the 19th century eccentric S. Toliver Preston. The recognition afforded to
Einstein was not based on these particular conclusions, but on the ways in which he derived them and the elimination of
the need to postulate a " luminiferous Aether," a construct on which all previous derivations depended. Preston, in
particular, had expatiated on the properties of this Aether, which he decided was filled with a gas of particles moving
at the speed of light, and for which he thought he could even derive the gas pressure.
Einstein did not invent the idea that heavy bodies bend light, either. It is a consequence of Newtonian physics.
However, Einstein's General Theory of Relativity predicted twice the value of deflect that Newton's theory did.
A theory is not worth much if some of the different predictions of that theory are not true. Newton's greatness was not
that he observed that bodies fall or that bullets move, but rather in developing a theory and a mathematical methodology
for describing all these phenomena. Einstein's greatness, like that of most scientists including Newton, lies in
producing theories that tied together the observed phenomena and predictions of others. Poincaré,
Lorentz, de Pretto, Newton and even Preston each had different pieces of the puzzle. Einstein put the puzzle
Those who accuse Einstein of plagiarism must consider that his work was reviewed by his peers and accepted for
publication. Notably, Max Planck was on the review board of the Annalen der Physik that published his papers, and was a
big enthusiast of Einstein's theory of special relativity. As for Lorentz and Poincaré, had they thought
that Einstein plagiarized their work, they would surely have protested! On the contrary, Lorentz was one of those who
recommended Einstein for a Nobel prize.
The popular misconception about the paper before us, is that Einstein formulated the equation E= mc2,
demonstrating that mass could be turned into a large quantity of energy, and thereby created the basis of nuclear energy and the atomic bomb.
Einstein's equation, given in this paper, is equivalent to E= mc2. This particular expression
however, was apparently not used until the 1920s. Einstein himself did not believe that this relation could be used for
practical purposes, though he did suggest using radium salts to test his theory. Becquerel had already found that
radioactive elements lose weight when they decay, and in fact, nuclear physics proceeded for the most part in parallel
to relativity theory and the equivalence of mass and energy played only a small part.
The scientific importance of Einstein's derivation of the equivalence of mass and energy was, apparently:
- The equivalence relation was derived from the
special theory of relativity and did not rely on the "luminiferous Aether."
- The equivalence was meant as a real world prediction, and not as a hypothetical case, as in the earlier paper of Poincaré.
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 based 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, these alterations of state
are referred (principle of relativity).
With these 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), possess 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 --possesses
where c denotes the velocity of light. We shall make use of this result in what follows.
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.
Let this body send 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 to 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
By subtraction we obtain from these 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 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
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 sense
by L/9 × 1020, the energy being measured in ergs, and the mass in grammes.
It is not impossible that with bodies whose 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.
principle of the constancy of the velocity of light is of course contained in Maxwell's equations.
About this Edition
This edition of Einstein's Does the Inertia of a Body Depend upon its
Energy-Content? is based on the English translation of his original 1905 German-language paper (published as
Ist die Trägheit eines Körpers von seinem 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 these 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,
The footnote is as it appeared in the 1923 edition. The 1923 English
translation modified the notation used in Einstein's 1905 paper to conform to that in use by the 1920's; for example,
c denotes the speed of light, as opposed the V used by Einstein in 1905. In this paper Einstein uses L to
denote energy; the italicised sentence 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.
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