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§ 9 -- ABSOLUTE MOTION
Translated (1980) from
Recherches critiques sur l'Électrodynamique Générale,
Annales de Chimie et de Physique, Vol. 13, p. 145, 1908.
In placing the hypothesis of ether at the base of electrodynamics and optics
we of necessity introduce, at least for the propagation of light and electric
actions, a system of coordinates, independent of ordinary matter. We should
therefore expect, and we have indeed long expected, an influence of absolute
motion with respect to the assumed ether. We know that the experiments
have always been negative. Lorentz's theory gives this result when we
consider first order terms; but the experiments (Oeuvres 361) of Michelson
and Morley, Trouton and Noble, and Lord Rayleigh, which should have
shown second order effects, have, contrary to the theory, also given negative
results. Lorentz and FitzGerald have therefore assumed that all bodies
experience a contraction of the relation in the direction of their velocity v. We thus
account for the observed negative results.(1) To explain this contraction,
Lorentz calls to mind that, according to his theory, for a system of electric
charges S, at rest, in equilibrium, this same system, when
(1) M. Planck has shown that if we assume that the density of the ether at the
earth's surface is less than 50,000 times greater than that in the
interplanetary medium, without any appreciable change in its properties
resulting, we may possibly reconcile the aberration theory with the hypothesis
that the ether is entrained in the earth's motion (see LORENTZ,
Enzyklop. math. Wiss., vol 5, art. 133, p. 104). This would be a very
strange property of the ether.
assumed to be animated by a uniform translational motion v, will
still be in equilibrium if we modify its dimensions by the indicated ratio. Therefore,
if the molecular actions obey the law of electrostatic actions, and if we can exclude
the molecular motion, the molecules of a solid body should of necessity take the
position of equilibrium, the accepted contraction will take place.
It is evident that this hypothesis confuses our notions of solids. The invariability
of certain bodies, when we transfer them from one place to another, when we
change their direction or their speed, gives us the experimental definition of
distance and of other geometric magnitudes. The bodies that we use, necessarily
participating in the motion of the earth, will always have an infinity of movements
and rotations. which change their dimensions and since we don't have any way to
precisely determine the absolute motion which comes into play here. These
deformations remain absolutely unknown. How do you physically define the true
length of a body? Does the assertion of the reality of this contraction
have any sense? It results, from the researches of Einstein, to which we return
later on, that the answer is negative.
The question of stability brings forth a second objection. (Oeuvres 362) A system
of electric charges, subject only to electrostatic forces, is never in
stable equilibrium. This is evident when the sole restriction imposed is the
conservation of electricity. In changing all the dimensions of the system by the
ratio of 1 to 1+ , the charges of
elements of corresponding volume being equal, we will have performed a
deformation compatible with the conditions of the system. The energy will fall to
of its original value.
The equilibrium, therefore, is not stable. The sphere, for example, is for a
deformable electron a shape of unstable equilibrium, and its the same if we
suppose, with Bucherer and Langevin, that its volume is invariable(1) a
fortiori, whereas in Lorentz's hypothesis this restriction doesn't exist. To
obtain a solid body, we therefore need to add forces of a very different
character from those of electrostatic forces, or of liaisons other than
incompressibility, or finally of whirling motions giving a dynamic equilibrium.
But in all of these cases, Lorentz's explanation no longer applies so this
explanation doesn't seem acceptable.
Poincaré has finally objected to the hypothesis as being incomplete. New
experiments could bring new terms into evidence and we would require new
hypotheses if, as expected, results are negative. The question of the complete
elimination of absolute motion was therefore posed and was addressed by
Lorentz(2), Poincaré(3), and Einstein(4).
It is no longer permissible to overlook the difference between "local time"
and "true time", which was an essential point when we were content to
explain the negative results observed up until now and a few others
analogous. For us to render a full account, lets consider two points A and B
which move with a constant absolute velocity v in the direction AB.
A luminous wave, starting from A at instant t, will arrive
(Oeuvres 363) at B at instant t'. It will have to travel
(1) This is what Ehrenfest pointed out ( Physik. Zeitschr., vol. 7, 1906,
p. 302): for gravitation the equilibrium would be stable; but in changing the
attractions into repulsions, the energy changes sign and the equilibrium
(2) Amsterdam Proceedings, 1903-1904, p. 809.
(3) Comptes rendus, vol.. CXL, 1905, p. 1504.
(4) Ann. der Physik, vol. XVII, 1905, p. 891.
the distance AB + (t - t')v: with the speed c we have then
[That's probably AB + (t'- t)v.]
The duration of transmission will depend on v, and its changes include
a first order term -AB v/c, the correction (including higher order
terms) being precisely the one we have to apply to the true time to get the
local time. Lorentz(1) showed that for terrestrial phenomena, this
correction is without influence. In particular, to determine the speed of light directly,
we are obliged to make it cover a closed path which brings it back to its starting point;
thus eliminating the first order terms. So, in the example considered, if the wave
emitted at A is reflected at B, it will arrive at A after a time
But it will be otherwise for astronomical Phenomena. In the determination of
the speed of light by the occultations of satellites, we don't use a closed path, thus,
the perturbation, that the hypothesis of a translation of the solar system with respect
to the ether would cause in the observed retardation, would be of a first order and
of observable magnitude.
Indeed, the delay of an occultation can reach d/c (where d
is the diameter of the terrestrial orbit), or about 1000 seconds. An absolute speed of
the solar system (having no connection with the system's motion with respect to the
closer fixed stars)
(1) Versuche einer Theorie, etc., p. 82 and following,
equal to 30 km per second in the plane of the ecliptic would bring about a
correction of about second for the
maximum observed delay, a correction which would change sign according to the
relative position of the Earth and the satellite in relation to the direction of
translation The systematic differences for a (Oeuvres 364) long system of
observations can then reach 0.2 second, a quantity which is on the order of
those which we observe in astronomy
If, therefore, we do not wish to admit that the speed of light depends on that of
the bodies emitting it and is purely relative, like all speeds (and the ether
concept, alone, prevents drawing out of the relativity principle this so natural
consequence), we will have to modify the definition of time.
Lorentz has enunciated the hypotheses which would allow giving to the equations
for an entrained system, as well as for the axes of coordinates, in a uniform motion
of translation v parallel to the x axis, the same form as for
the case of rest. He admits that all the masses are functions of velocity, thus
abandoning the principle of the conservation of mass(2). We must also, as we
formerly revealed, suppress the notion of solid bodies and
(1) Supposing that the laws of gravitation are modified by motion as the laws of
electrodynamics are, the corrections would be only of the second order and could
not cancel the first order term,
(2) The word mass, in the theories of Lorentz, Poincaré, and Einstein, has no precise
meaning anymore. The number representing it depends on the motion of the system
of coordinates, the motion being absolutely arbitrary. But the force depends also on
this motion and it is not the second member of the equation
but (it is) their relation that alone remains invariable when we change this motion.
introduce a new definition of time. It will be the variable
which will play the role of time in the equations.
Time, thus defined doesn't satisfy almost any of the axioms assigned to the notion
of time in the ordinary sense. Two events, simultaneous for an observer A, but
taking place at different points, are not simultaneous anymore for a second
observer B [who is] in motion with respect to the first. Simultaneity becomes
a relative notion.
Two equal times for observer A will not be so for B.
The parallelogram rule for velocities is only approximated: thus for
v and v' being the speeds of two bodies which are moving
in opposite directions in relation to a primary system of coordinates, the relative
speed of the first body with respect to the second, i.e., the velocity that an observer
traveling along with the second body would observe, is not v - v', but
and it will remain steadfastly inferior to the speed of light. For two beta
rays emitted in opposite directions by a grain of radium, each with a speed of 250,000
km per second, the relative speed will not be 500,000 km per second, but 294,000
km per second. The words "speed", "time", etc., have therefore acquired a
significance very different from that which they normally have, and now have only
a relative sense.
The ether in this new Kinematics will not play any role because it no
longer furnishes a system of absolute coordinates. But this concept will oblige us
to replace the simple axioms of the conservation of mass, the invariability of solids,
the parallelogram of velocities, etc., axioms which we should abandon only as a
last resort, with complicated relationships presenting considerable difficulties to
the imagination (similar to those of curved space in three dimensions), and which
we generally can't treat rigorously, except by analytical considerations.
We must add that this theory was presented by Lorentz with all reservations.
Einstein ( loc. cit.) has presented the same results in a different form. He
admits, a priori, for the speed of light, a law which by its nature
involves a large amount of arbitrariness; the comparison with that which we
will adopt in the Second Part of this work will demonstrate this sufficiently. It leads,
with the principle of relativity, to a definition of the simultaneity of two
events at two different points, of which he makes a relative notion, and more
generally leads to the new Kinematics which has just been discussed. The
simultaneity included in the (Oeuvres 366) definition of the length of a body in
motion in relation to the fixed marks of a standard measure (since it will be a matter
of pointing simultaneously to the two extremities of the body. otherwise
the body would move during the interval) this body will appear to be of
a different length to an observer at rest, according to its more or less large speed
(although its true length remains invariable). We therefore avoid the contractions
admitted by Lorentz, or rather we see that their reality is only a question
Einstein verifies that Lorentz's equations are
thus made Independent of absolute motion, and that the law admitted by him for
the propagation of light is in accordance with the equations. These then, in the
measure that they express this law of propagation, become superfluous; moreover,
the reasoning does not demonstrate at all, as some authors have believed, that
these transformations are the only group which leaves Lorentz's equations
invariable. This problem has rather to do with Poincaré's methods (loc. cit.).
Bucherer(1) was led, by considerations on the relativity of motions to abandon the
notion of ether. Lorentz's equations should always be applied by assuming that the
system of coordinates is at rest with respect to the point P whose motion we study.
Bucherer only considers the case of uniform motions; the action on an electron
propelled with a relative velocity u = v' - v in relation to P, according to
formula (13) (where we set v' = u, v = 0), will be given by the formula
For two closed currents, we verify easily ( see the Second Part) that
only the terms proportional to vv' play a role, with the accelerations
excluded, which we haven't taken into consideration, and terms in
. It is moreover what should happen
if the intensity of the force is proportional to the product of the intensities of the
currents. The action of two elements of current on each other will from then on be
The hypotheses of Ampere are verified. The action is
(1) Physik. Zeitschr., vol. 7, 1906, p. 553.
parallel to the line of junction
of the elements; but the parenthesis should be
Bucherer's hypothesis is therefore irreconcilable with the laws of closed
This is because the notion of field ceases to be applicable there.
We are therefore brought back to the complicated hypotheses which were set forth.
We must say, in closing, that these complications occur not only at great speeds,
but also in Fizeau's experiment on the entrainment of waves, for example. In
effect, according to the principle of relativity, an observer carried along in the
translational movement of a transparent body will find, for the speed of propagation
of waves in this environment, the same value as if he were at rest (supposing the
period to be the same, or the dispersion negligible). We would conclude that, in
ordinary kinematics, the waves are totally carried along by the substance. There is
nothing to it. The term velocityhas a new meaning, and in reality,
Lorentz's proof continues to be applicable; we come back to Fresnel's coefficient.
Copyright © 1980, 2000 Robert S. Fritzius
Installed September 16, 2000