Poincaré and the Special Theory of Relativity

GENERAL ⎜ ARTICLE
Poincaré and the Special Theory of Relativity
Supurna Sinha
The special theory of relativity is one of the cornerstones of
Supurna Sinha received
physics. When we learn this theory in our college years we focus
her PhD in condensed
on the subject in its finished form, rather than on the history of
matter physics from
Syracuse University in
its evolution. It is often not appreciated that it took many great
1992. She did
minds to finally attain the point of view that is now called ‘the
postdoctoral research in
special theory of relativity’. In this article we focus on the
theoretical physics at
contribution of the French mathematician Henri Poincaré in
Indian Institute of
Science and Raman
the development of this theory. While it is true that Einstein’s
Research Institute,
unique and radical point of view established the universal valid-
Bangalore. Her interests
ity of the principle of relativity, many great physicists and
include writing popular
mathematicians, Poincaré in particular, came very close to an-
physics articles and
making picture books for
ticipating this.
children.
In the mid to late 1800s, several experiments were conducted to
detect the motion of the Earth through the ether. (In fact there
were ingenious schemes proposed for converting this motion
into useful work!) In 1887 the American scientists A A Michelson
and E W Morley tried to detect this motion with an interferom-
eter. They were, however, unable to detect any relative motion
between the Earth and the ether. In order to explain the null
result of this experiment, the Dutch physicist H A Lorentz and
independently the Irish physicist G F Fitzgerald proposed that
the arm of the interferometer in the direction of the motion
contracts and exactly compensates the effect of the Earth’s
motion. Lorentz and others came up with separate hypotheses to
account for the null result in each such experiment.
In 1895, Poincaré expressed his dissatisfaction with such ad hoc
hypotheses and emphasized the need for a more general point of
view. He stated : “Experiment has revealed a multitude of facts
which can be summed up in the following statement: it is
impossible to detect the absolute motion of matter, or rather the
relative motion of ponderable matter with respect to the ether;
all that one can exhibit is the motion of ponderable matter with
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GENERAL ⎜ ARTICLE
respect to ponderable matter.” In 1904 his ideas crystallized
Poincaré again
further and he stated his “Principle of Relative Motion” as one
stated his unease
of the six general principles of physics: “The principle of relativ-
with the ad hoc
ity, according to which the laws of physical phenomena should
hypotheses
be the same, whether for an observer fixed, or for an observer
proposed by
carried along in a uniform movement of translation; so that we
Lorentz to explain
have not and could not have any means of discerning whether or
the null result of
not we are carried along in such a motion”. Poincaré again stated
the experiments
his unease with the ad hoc hypotheses proposed by Lorentz to
probing the motion
explain the null result of the experiments probing the motion of
of the earth relative
the earth relative to the ether. He was, however, very apprecia-
to the ether.
tive of one of these hypotheses: the notion of a local time.
Lorentz had introduced this notion in order to simplify the
theoretical study of electromagnetic processes in a frame mov-
ing with a velocity v relative to the ether. The difference be-
tween the ‘local time’ and the ‘true time’ was vx'/c2 for each point
on the x' axis of the moving system, with c the speed of light in
vacuum. Poincaré recognized the importance of this notion in
the context of the principle of relativity. He showed that the
concept of a local time introduced by Lorentz could be given a
simple physical interpretation in the following manner. He
considered an operation by which observers at various points
along the axis x' of the moving system synchronize their respec-
tive clocks by exchanging light signals with an observer at the
origin. Assuming that the velocity of light is independent of the
motion of its source, the difference between the local and the
true times would give a measure of the extent to which each
clock has been thrown out of ‘true synchrony’. He went on to
stress that although the time in a moving frame would differ
from the true time in a fixed system, such a difference would not
Poincaré showed
be inconsistent with the principle of relativity. The observer in
that the concept of
the moving frame would not be able to detect the absolute
a local time
motion of the frame since he would be unaware of the fact that
introduced by
the clocks in his frame were out of synchrony with those in the
Lorentz could be
fixed frame. Thus we see that a crucial ingredient in Einstein’s
given a simple
theory of relativity, namely the notion of relativity of simultane-
physical
ity, was already anticipated by Poincaré. It is remarkable that
interpretation.
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GENERAL ⎜ ARTICLE
Suggested Reading
Poincaré, the mathematician, realized the importance of attach-
ing an operational and physical meaning to the concept of a local
[1] Charles Scribner, Am-
time whereas Lorentz, the physicist, considered local time to be
erican Journal of Phys-
ics, 32, 672, 1964.
a mere mathematical trick to simplify the electrodynamic
[2] Sir Edmund Whittaker,
equations!
A History of the Theories
of Aether and Electric-
Poincaré was the first one to take the bold step of advocating the
ity: The Modern Theo-
importance of formulating a general principle embracing all
ries 1900–1926(Philo-
physical laws. He repeatedly questioned the value of ad hoc
sophical Library, New
York, 1954), p 40.
hypotheses. In this respect his philosophy was close to that of
[3] Sir Edmund Whittaker,
Einstein’s. However, a closer analysis shows that he could not
From Euclid To Edding-
formulate a proper theory of relativity because of some views
ton (Cambridge At The
which, in retrospect, appear conservative. While he adhered to
University Press, 1949).
[4] Jeremy J Gray, Math-
the principle of relativity, he believed that this principle might
ematical Intelligencer,
be deducible from a suitably revised version of electrodynamics.
Vol.17, No.1, p.65, 1995.
Consequently, he was not ready to take the important step of
eliminating the ether. This concept was in conflict with the
spirit of the principle of relativity which is supposed to treat all
frames on an equal footing. Poincaré was also troubled by the
fact that gravitational phenomena seemed to be inconsistent
with the principle of relativity. In this respect Poincaré was, in
fact, handicapped by having too large a canvas. He would per-
haps have been able to go further with special relativity if he had
restricted his attention to electrodynamic phenomena. The
time was not right for including gravity. It would be many years
Box 1. The Postulates
and many efforts later that gravity was finally encompassed in
of Special Relativity.
the framework of relativity.
1. The laws of physics are
the same in all inertial
Poincaré’s principle of relativity can be viewed as a transitional
frames. No preferred in-
stage between traditional electrodynamics and the fully relativ-
ertial frame exists. (The
istic theory formulated by Einstein. Einstein’s radical and
Principle of Relativity.)
unique perspective helped in building an inherently relativistic
2. The speed of light in
theory. Unlike Poincaré, Einstein did not try to account for this
free space has the same
principle in terms of other physical phenomena like electrody-
value c in all inertial
namics. He transformed Lorentz’s notion of ‘local time’ (retain-
frames. (The Principle of
ing the physical interpretation given by Poincaré) into a stan-
the Constancy of the
Speed of Light.)
dard definition of time valid for all of physics without any
reference to any preferred frame. Einstein’s main contribution
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GENERAL ⎜ ARTICLE
Box 2. Lorentz Transformation.
It is interesting to note that, unknown to Einstein, Lorentz had come up with the transformation equations
(connecting two inertial reference frames) almost in identical form a year before Einstein’s paper
appeared. In 1895, motivated by Poincaré’s belief in the need for a principle of relativity valid for all
physical laws and his rejection of ad hoc assumptions for explaining the results of experiments probing
motion relative to the ether, Lorentz demonstrated the invariance of Maxwell’s equations in two inertial
frames, using a set of transformation equations, which were correct to order v/c. Later on he tried to write
down the exact transformation equations. However, he was unable to shed the burden of the ether and he
continued to refer to motion relative to the ether. Furthermore, he continued to make a difference between
the effect of contraction of moving bodies along the direction of relative motion and the idea of relativity
of simultaneity which follows from the notion of a local time. He attached physical meaning to the first
effect while dismissing the second one as a mere mathematical artifice. While he was able to write down
the transformation equations for the spatial coordinates, he failed to write down the right transformation
equations for the time coordinate. Thus he was unable to establish perfect symmetry between two inertial
frames moving relative to each other.
to the principle of relativity was to recognize that there is no
essential difference between a ‘stationary’ and a ‘moving’ frame
of reference. In other words he was the first one to give up the
idea of singling out a reference frame at rest relative to the ether.
This helped him in constructing a simple logical structure based
on the two postulates (see Box 1). Consequently, he was the first
one to arrive at the exact transformation equations relating two
inertial frames of reference (See Box 2).
The British writer Edmund Whittaker takes the point of view
that Einstein’s role in formulating the special theory of relativ-
ity was limited to elaborating on the theoretical insights of
others like Poincaré and Lorentz. He believed that Einstein had
little to contribute in terms of original ideas in this field. This is
clearly an extreme point of view and it is in sharp contrast to the
viewpoint that we are exposed to in our college years that the
special theory of relativity is the product of Einstein’s fresh and
unique perspective on space and time. The truth perhaps lies
somewhere between these two extreme points of view. Although
Address for Correspondence
Poincaré was the first one to put forward a general principle
Supurna Sinha
307, Sampige Road
embracing all physical laws one cannot ignore the fact that it was
Malleswaram
Einstein who finally constructed a fully relativistic theory by
Bangalore 560003, India.
giving up the ‘ether’.
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