This reprints an essay written ca. 1983, "'What Song the Syrens
Sang': How Did Einstein Discover Special Relativity?" in John
Stachel, Einstein
from "B" to "Z".
If you have read Edgar
Allen Poe's "The Murders in the Rue Morgue," perhaps you remember
the epigraph that Poe chose for this pioneer detective story:
What song the Syrens sang, or what name Achilles assumed when
he hid himself among women, though puzzling questions, are not
beyond all conjecture.1
I believe that the problem of how Einstein discovered the special
theory of relativity (SRT) falls into this category of "puzzling
questions," that "are not beyond
all conjecture."
2
Let me begin by explaining why.
When I started work on the Einstein Papers, there was already a
large literature on the origins of SRT compared, say, to the rather
scanty amount published on the origins of the general theory of
relativity (GRT). So I assumed that the development of SRT must
be fairly clear. However, I soon learned that the amount of work
published on the origin of SRT and GRT are just about inversely
proportional to the available primary source material. For GRT,
we have a series of Einstein's papers from 1907 to 1915, capturing
the successive steps of his search for the final version of the
theory. In addition, there is extensive contemporary correspondence
on the subject, several research notebooks, records of lectures
given by Einstein during this period, not to mention a number of
later reminiscences and historical remarks by Einstein.
3
For SRT we have the paper
On the Electrodynamics of Moving
Bodies, in which the theory was first set forth in 1905
in its finished form, indeed a rather polished form (which is
not to say that it bears no traces of its gestation process).
The only earlier documentary evidence consists of literally
a couple of sentences to be found in the handful of preserved
early Einstein letters (I will quote both sentences later).
We do have a number of later historical remarks by Einstein
himself, sometimes transmitted by others (Wertheimer, Reiser-Kayser,
Shankland, Ishiwara, for example), which raise many problems
of authenticity and accuracy; and some very late Einstein letters,
answering questions such as whether he had prior knowledge of
the Michelson-Morley experiment, what works by Lorentz he had
read, the influence of Poincaré, Mach, Hume, etc., on
his ideas; Einstein's replies are not always self-consistent,
it must be noted.
4
Yet the urge to provide an answer to the question of the discovery
of SRT has proven irresistible to many scholars. It is not hard
to see why: A twenty-six year old patent expert (third class),
largely self-taught in physics, who had never seen a theoretical
physicist (as he later put it), let alone worked with one, author
of several competent but not particularly distinguished papers,
Einstein produced four extraordinary works in the year 1905,
only one of which (not the relativity paper) seemed obviously
related to his earlier papers. These works exerted the most
profound influence on the development of physics in the 20th
Century. How did Einstein do it? Small wonder that Tetu Hirosige,
Gerald Holton, Arthur I. Miller, Abraham Pais, John Earman,
Clark Glymour, Stanley Goldberg, Robert Rynasiewicz, Roberto
Torretti,
et al., have been moved to study this question.
I shall not try to record my debts to and differences with each
of these scholars, lest this survey become even longer and more
tedious than it is already; but must at least acknowledge the
influence of their work on my own.
5
I resisted the urge to conjecture for some years, but have finally
succumbed, so I can well understand the temptation.
Contrary to my original, naive expectation,
no general consensus has emerged from all this work. Given the nature
of the available documentation and the difficulty of understanding
any creative process-let alone that of a genius-this really is not
surprising. I now believe that the most one can hope to do in discussing
the discovery of SRT is to construct a plausible conjecture. Such
a conjecture will be based upon a certain weighting of the scanty
evidence we possess, based upon certain methodological hypotheses,
as well as the imagination of the conjecturer.
6
There are bound to be differences of opinion in these matters. All
one can demand is that it be made clear on what methodological hypotheses
a conjecture is based, and a demonstration that the conjecture is
in accord with the available evidence when the latter is weighted
in accord with these hypotheses.
Let me emphasize that no such account can hope to encompass
those elements of the creative process that Einstein referred
to as "the irrational, the inconsistent, the droll, even the
insane, which nature, inexhaustibly operative, implants into
the individual, seemingly for her own amusement," for "These
things are singled out only in the crucible of one's own mind."
Yet one may draw courage for the type of conjecture I have in
mind from another remark of Einstein:
"A new idea comes suddenly and in a rather intuitive way. That
means it is not reached by conscious logical conclusions. But, thinking
it through afterwards, you can always discover the reasons which
have led you unconsciously to your guess and you will find a logical
way to justify it. Intuition is nothing but the outcome of earlier
intellectual experience."
I shall discuss only this intellectual, logical side of Einstein's
struggles. Before trying to reconstruct these struggles, it is well
to note that his outward existence was far from tranquil during
the period when he was developing SRT. While attending the Polytechnic
at Zurich, thanks to the support of maternal relatives, he was plagued
by the thought that he was unable to help his family, which was
in dire financial straits due to constant business reverses. He
was the only graduate in his section (VIA) not to get an academic
post, and lived a hand-to-mouth existence for almost two years,
until he got a job at the Swiss Patent Office thanks to help from
a friend's father. During this period he was under severe family
pressure to break with his fiancee, whom he only married in 1903
after his father's death. His first child was born in 1904, and
he had to support wife and child on his modest income from the Patent
Office, while his mother found work as a housekeeper. So one must
not think of Einstein as a tranquil academic, brooding at leisure
on weighty intellectual problems. Rather one must imagine him fitting
his intellectual work into the interstices of a professional career
and personal life that might have overwhelmed someone with a different
nature.
The main methodological hypothesis
guiding my conjecture was stated by Hans Reichenbach some time ago:
"...the logical schema of the theory of relativity corresponds surprisingly
with the program which controlled its discovery." To put it in more
hifalutin' terms, also due to Reichenbach, I believe that "the context
of justification" of SRT used by Einstein can shed light on "the
context of its discovery."
7
This hypothesis suggests that we can learn a good deal about the
development of the theory by paying close attention to the logical
structure of its initial presentation in 1905, and to the many accounts
of the theory that Einstein gave afterwards. Of course, I have tried
not to neglect any scrap of evidence known to me, including the
pitifully small amount of contemporary documentation and the later
reminiscences. But I have given special weight to Einstein's early
papers, letters, and lectures, in which he sought to justify the
theory to his contemporaries. Intellectually, Einstein was an exceedingly
self-absorbed person, willing to go over and over the grounds for
the theory again and again. These accounts, given over a number
of years, are remarkably self-consistent. They provide evidence
for a number of conjectures about the course of development of his
own ideas, and occasionally even include explicit statements about
it. I assume that by and large memory tends to deteriorate with
time, and (worse) that pseudo "memories" tend to develop and even
displace correct recollections. So, a second methodological hypothesis
which I shall adopt is that, in case of discrepancies between such
accounts, earlier ones are to be given greater weight than later
ones. Explicit remarks that Einstein makes about the discovery of
SRT in the course of his later expositions must always be given
great weight, but the earlier he made them the greater the weight
I give to them. Of course, if some feature of Einstein's accounts
remains unchanged over many years, I take this as evidence for giving
such a point the most weight.
8
It follows from these methodological assumptions that I must preface
my conjectures with a brief resume of the "logical schema of
the theory of relativity" as it was first published in the 1905
paper. In this paper, as in almost all subsequent accounts,
Einstein bases SRT on two fundamental principles: the principle
of relativity and the principle of the constancy of the velocity
of light. The principle of relativity originated in Galilean-Newtonian
mechanics: Any frame of reference in which Newton's law of inertia
holds (for some period of time) is now called an inertial frame
of reference. From the laws of mechanics it follows that, if
one such inertial frame exists, then an infinity of them must:
All frames of reference (and only such frames) moving with constant
velocity with respect to a given inertial frame are also inertial
frames. All mechanical experiments and observations proved to
be in accord with the (mechanical) principle of relativity:
the laws of mechanics take the same form in any of these inertial
frames. The principle of relativity, as Einstein stated it in
1905, asserts that
all the laws of physics take the
same form in any inertial frame-in particular, the laws of electricity,
magnetism, and optics in addition to those of mechanics.
The second of Einstein's principles
is based on an important consequence of Maxwell's laws of electricity,
magnetism, and optics, as interpreted by H. A. Lorentz near the
end of the nineteenth century. Maxwell had unified optics with electricity
and magnetism in a single theory, in which light is just one type
of electromagnetic wave. It was then believed that any wave must
propagate through some mechanical medium. Since light waves easily
propagate through the vacuum of interstellar space, it was assumed
that any vacuum, though empty of ordinary, ponderable matter, was
actually filled by such a medium, to which our senses did not respond:
the ether. The question then arose, how does this medium behave
when ordinary matter is present? In particular, is it dragged along
by the motion of matter? Various possible answers were considered
in the course of the nineteenth century, but finally only one view
seemed compatible with (almost) all the known experimental results,
that of H. A. Lorentz: The ether is present everywhere. Ordinary
matter is made up of electrically charged particles, which can move
through the ether, which is basically immobile. These charged particles,
then called "electrons" or "ions", produce all electric and magnetic
fields (including the electromagnetic waves we perceive as light),
which are nothing but certain excited states of the immovable ether.
The important experimental problem then arose of detecting the motion
of ponderable matter-the earth in particular-through the ether.
No other theory came remotely close to Lorentz's in accounting
for so many electromagnetic and especially optical phenomena.
This is not just my view of Lorentz's theory, it was Einstein's
view. In particular, he again and again cites the abberration
of starlight and the results of Fizeau's experiment on the velocity
of light in flowing water as
decisive evidence in favor
of Lorentz's interpretation of Maxwell's equations.
A direct consequence of Lorentz's conception of the stationary
ether is that the velocity of light with respect to the ether is
a constant, independent of the motion of the source of light (or
its frequency, amplitude, or direction of propagation in the ether,
etc.).
Einstein adopted a slightly-but crucially-modified version of this
conclusion as his second principle: There is an
inertial frame
in which the speed of light is a constant, independent of the velocity
of its source. A Lorentzian ether theorist could agree at once to
this statement, since it was always tacitly assumed that the ether
rest frame is an inertial frame of reference and Einstein had "only"
substituted "inertial frame" for "ether." But Einstein's omission
of the ether was deliberate and crucial: by the time he formulated
SRT he did not believe in its existence. For Einstein a principle
was just that: a principle-a starting point for a process of deduction,
not a deduction from any (ether) theory. (I am here getting ahead
of my story and will return to this point later.) The Lorentzian
ether theorist would add that there can only be
one inertial
frame in which the light principle holds. If the speed of light
is a constant in the ether frame, it must be non-constant in every
other inertial frame, as follows from the (Newtonian) law of addition
of velocities. The light principle hence
seems to be incompatible
with the relativity principle. For, according to the relativity
principle,
all the laws of physics must be the same in
any inertial frame. So, if the speed of light is constant in one
inertial frame, and that frame is not physically singled out by
being the rest frame of some medium (the ether), then the speed
of light
must be the same (universal) constant in every
other inertial frame (otherwise the democracy of inertial frames
is violated). As Einstein put it in 1905, his two principles are
"apparently incompatible." Of course, if they really were incompatible
logically or physically, that would be the end of SRT.
9
Einstein showed that they are not only logically compatible, but
compatible with the results of all optical and other experiments
performed up to 1905 (and since, we may add). He was able to show
their logical compatibility by an analysis of the concepts of time,
simultaneity, and length, which demonstrated that the speed of light
really could have the privileged status, implied by his two principles,
of being a universal speed, the same in every inertial frame of
reference.
10
Now I shall begin my conjecture
about Einstein's discovery of SRT. In a 1921 lecture, Einstein stated
that SRT originated from his interest in the problem of the optics
of moving bodies. He seems to have been fascinated from an early
age by the nature of light, a fascination that persisted throughout
his life. From an essay he wrote in 1895, (at age 16), we know that
he then believed in the ether, and had heard of Hertz's experiments
on the propagation of electromagnetic waves; but he does not show
any knowledge of Maxwell's theory. In much later reminiscences,
he reports that during the following year (1895-1896) he conceived
of a thought experiment: what would happen if an observer tried
to chase a light wave? Could s/he catch up with it? If so, s/he
ought to see a non-moving light wave form, which somehow seemed
strange to him. In retrospect, he called this "the first childish
thought-experiment that was related to the special theory of relativity."
Reliable accounts inform us that during his second year (1897-98)
at the Swiss Federal Technical Institute, or Poly as it was then
called, he tried to design an experiment to measure the velocity
of the earth through the ether, being then unacquainted with either
the theoretical work on this problem by Lorentz or the experiment
of Michelson and Morley (M-M). A precious bit of contemporary documentary
evidence reinforces this later account. In a letter to his schoolmate
and friend Marcel Grossmann, written in the summer of 1901 (by then
both had graduated from the Poly), Einstein wrote:
A considerably simpler method for the investigation of the relative
motion of matter with respect to the light ether has again
occurred to me, which is based on ordinary interference experiments.
If only inexorable destiny gives me the time and peace necessary
to carry it out.
At first sight, it would seem remarkable for Einstein to have written
these words (which also show that he had not yet abandoned the concept
of the ether), if he knew about the M-M experiment at this time.
However, while still at the Poly (i.e., before 1901) he appears
to have studied Maxwell's theory (not covered in his school lectures)
on his own, perhaps from the new textbook of August Föppl (which,
in various reincarnations, such as Föppl-Abraham, Abraham-Becker,
Becker-Sauter, has stayed in print to this day). Föppl discusses
a problem which evidently made a strong and lasting impression on
Einstein, since he opens the 1905 paper with a discussion of it.
This is the problem of the relative motion of a magnet and a conducting
wire loop. If the loop is at rest in the ether and the magnet is
moved with a given velocity, a certain electric current is induced
in the loop. If the magnet is at rest, and the loop moves with the
same relative velocity, a current of the same magnitude
and direction is induced in the loop. However, the ether theory
gives a different explanation for the origin of this current in
the two cases. In the first case an electric field is supposed to
be created in the ether by the motion of the magnet relative to
it (Faraday's law of induction). In the second case, no such electric
field is supposed to be present since the magnet is at rest in the
ether, but the current results from the motion of the loop through
the magnetic field (Lorentz force law). This asymmetry of explanation,
not reflected in any difference in the phenomena observed, must
already have been troubling to Einstein. Even more troubling was
the knowledge, when he acquired it, that all attempts to detect
the motion of ponderable matter through the ether had failed. This
was an "intolerable" (his word, about 1920) situation. Observable
electromagnetic phenomena depend only on the
relative motions
of ponderable matter; their explanations differ, however, depending
on the presumed state of motion of that matter relative to the hypothetical
ether; yet all attempts to detect this presumed motion of ordinary
matter relative to the ether end in failure! He later (c. 1920)
recalled that the phenomenon of electromagnetic induction compelled
him to adopt the relativity principle.
In 1938 he wrote "The empirically suggested non-existence of such
an [ether wind] is the main starting point [point of departure]
for the special theory of relativity."
11
It is not clear when the significance of the failure of all attempts
to detect the motion of ordinary matter through the ether first
struck him. The letter quoted above suggests that it was after the
summer of 1901. We know from a letter to another friend, Michele
Besso, dating from early 1903, that he had decided to "carry out
comprehensive studies in electron theory." No later than that, and
quite possibly earlier, he read Lorentz's 1895 book, "Attempt at
a Theory of Electrical and Optical Phenomena in Moving Bodies."
Einstein surely learned about, the many such failures by reading
this book, since one of its main purposes was to show that such
failures were compatible with Lorentz's stationary ether theory.
His later comments suggest that study of this book (Einstein says
this is the only work by Lorentz he read before 1905) convinced
him of the essential superiority of Lorentz' approach to the optics
of moving bodies; yet it also convinced him that the Lorentz theory
was still not fully satisfactory. Lorentz could explain away the
failure to detect motion of matter relative to the ether convincingly
to Einstein in all cases but one: the M-M experiment. To explain
this, Lorentz had to introduce a special hypothesis, which to Einstein
seemed completely unconnected with the rest of the theory: the famous
Lorentz contraction. To Einstein, such an approach was not a satisfactory
way out of the "intolerable dilemma." It seemed preferable to him
to accept at face value the failure of the M-M and all similar experiments
to detect motion of matter relative to the ether. Taken by themselves,
these negative results suggested to Einstein that the relativity
principle applied to electromagnetism, while the ether should be
dropped as superfluous. There has been some confusion on this important
point, so I shall expand on it. Sometimes the case is presented
in such a way as to suggest that it was the "philosophical concept"
of the relativity of all motion, as Einstein once called it, which
was the key step in his rejection of the ether. But the concept
of a stationary ether, as well as of a moving ether, is quite compatible
with this philosophical concept of the relativity of motion: one
need only assume that motions relative to the ether in the first
case, as well as relative motions of the parts of the ether in the
second, have physical efficacy. The leading advocates of both the
dragged-along and the immovable ether concepts, Hertz and Lorentz,
respectively, both understood this and both were read by Einstein.
12
By the time he gave up the ether
concept, Einstein most likely took this philosophical conception
of the relativity of all motion for granted, presumably under the
influence of his early reading of Mach's
Mechanics (around
1897). What bothered him now was that no phenomenon existed that
could be interpreted as empirical evidence for the physical efficacy
of the motion of ordinary matter relative to the ether, in spite
of repeated efforts to find one. Yet the best available theory-
Lorentz's theory-could only attempt to explain away such failures.
These explanations were satisfactory, within the framework of Lorentz'
theory, in almost all known cases (i.e., for all experiments sensitive
only to order
v/c), and Einstein even seems to have been
tempted to give up what we may call his physical relativity principle
(with no ether needed). But Lorentz's explanation of the M-M experiment
seemed to Einstein so artificial that he resisted this temptation,
opting for the physical relativity principle. After eliminating
the ether from the story altogether, one can simply take the results
of the M-M and similar experiments as empirical evidence for the
equivalence of all inertial frames for the laws of electricity,
magnetism and optics as well as those of mechanics. I believe Einstein
gave up the ether concept and definitely opted for the physical
relativity principle at least a couple of years before the final
formulation of SRT, perhaps even earlier. At any rate, at some point
well before the 1905 formulation of the theory, he made this choice
and adhered to it thereafter.
There was a related motive for his skepticism with regard to the
ether, which I shall now mention. Not only was Einstein working
on problems of the optics of moving bodies, he was also working
on problems related to the emission and absorption of light by matter
and of the equilibrium behavior of electromagnetic radiation confined
in a cavity-the so-called black body radiation problem. He was using
Maxwell's and Boltzmann's statistical methods, which he had redeveloped
and refined in several earlier papers, to analyze this problem.
This was itself a daring step, since these methods had been developed
to help understand the behavior of ordinary matter while Einstein
was applying them to the apparently quite different field of electromagnetic
radiation.
13
The "revolutionary" conclusion to which he came was that, in certain
respects, electromagnetic radiation behaved more like a collection
of particles than like a wave. He announced this result in a paper
published in 1905, three months before his SRT paper. The idea that
a light beam consisted of a stream of particles had been espoused
by Newton and maintained its popularity into the middle of the 19th
century. It was called the "emission theory" of light, a phrase
I shall use. The need to explain the phenomena of interference,
diffraction and polarization of light gradually led physicists to
abandon the emission theory in favor of the competing wave theory,
previously its less-favored rival. Maxwell's explanation of light
as a type of electromagnetic wave seemed to end the controversy
with a definitive victory of the wave theory. However, if Einstein
was right (as events slowly proved he was) the story must be much
more complicated. Einstein was aware of the difficulties with Maxwell's
theory-and of the need for what we now call a quantum theory of
electromagnetic radiation-well before publishing his SRT paper.
He regarded Maxwell's equations as some sort of statistical average-of
what he did not know, of course-which worked very well to explain
many optical phenomena, but could not be used to explain all the
interactions of light and matter. A notable feature of his first
light quantum paper is that it almost completely avoids mention
of the ether, even in discussing Maxwell's theory. Giving up the
ether concept allowed Einstein to envisage the possibility that
a beam of light was "an independent structure," as he put it a few
years later, "which is radiated by the light source, just as in
Newton's emission theory of light."
So abandonment of the concept of the ether was a most important
act of liberation for Einstein's thought in two respects: It
allowed Einstein to speculate more boldly on the nature of light
and it opened the way for adoption of his relativity principle
as a fundamental criterion for all physical laws. I must add
a word about Einstein's use of such principles as a guide to
further research. In 1919 he explicitly formulated a broad distinction
between constructive theories and theories of principle. Constructive
theories attempt to explain some limited group of phenomena
by means of some model, some set of postulated theoretical entities.
For example, many aspects of the behavior of a gas could be
explained by assuming that it was composed of an immense number
of constantly colliding molecules. Theories of principle formulate
broad regularities, presumably obeyed by all physical phenomena,
making these principles criteria ("rules of the game") that
any constructive theory must satisfy. For example, the principles
of thermodynamics are presumed to govern all macroscopic phenomena.
They say nothing about the, micro-structure or detailed behavior
of any particular gas, but do constitute limitations on any
acceptable constructive theory of such a gas. Any theory not
conserving the energy of the gas, for example, would be immediately
rejected. Since the turn of the century, Einstein had been searching
for a constructive theory of light, capable of explaining all
of its properties on the basis of some model, and was to continue
the search to the end of his days. But, "Despair[ing] of the
possibility of discovering the true answer by constructive efforts,"
as he later put it, he decided that the only possible way of
making progress in the absence of such a constructive theory
was to find some set of principles that could serve to limit
and guide the search for a constructive theory.
14
There is no contemporary evidence showing when Einstein adopted
this point of view (he first indicated it in print as early
as 1907). I believe he had done so by 1905. The structure of
the 1905 SRT paper is certainly compatible with his having done
so. It is based on the statement of two such principles, deduction
of various kinematic consequences from them, and their application
to Maxwell's electrical and optical theory.
To return to the main thread
of my conjecture, I believe that Einstein dropped the ether
hypothesis and adopted his relativity principle by 1903 or 1904
at the latest. This is by no means the end of the story. It
seemed that he must then drop Lorentz's version of Maxwell's
theory, based as it was on the ether hypothesis. With what was
he to replace it? There is good evidence suggesting he spent
a great deal of effort trying to replace it with an emission
theory of light-the sort of theory suggested by his concurrent
researches into the quantum nature of light.
15
An emission theory is perfectly compatible with the relativity
principle. Thus, the M-M experiment presented no problem; nor
is stellar abberration difficult to explain on this basis.
16
Einstein seems to have wrestled with the problems of an emission
theory of light for some time, looking for a set of differential
equations describing such a theory that could replace the Maxwell-Lorentz
equations; and trying to explain a number of optical experiments,
notably the Fizeau experiment, based on some version of the emission
theory. He could not find any such equations, and his attempt to
explain the Fizeau experiment led him to more and more bizarre assumptions
to avoid an outright contradiction. So he more-or-less abandoned
this approach (you will soon see why I say more-or-less), after
perhaps a year or more of effort, and returned to a reconsideration
of the Maxwell-Lorentz equations. Perhaps there was a way of making
these equations compatible with the relativity principle once one
abandoned Lorentz's interpretation via the ether concept.
But here he ran into the most blatant-seeming contradiction, which
I mentioned earlier when first discussing the two principles. As
noted then, the Maxwell-Lorentz equations imply that there exists
(at least) one inertial frame in which the speed of light is a constant
regardless of the motion of the light source. Einstein's version
of the relativity principle (minus the ether) requires that, if
this is true for one inertial frame, it must be true for all inertial
frames. But this seems to be nonsense. How can it happen that the
speed of light relative to an observer cannot be increased or decreased
if that observer moves towards or away from a light beam? Einstein
states that he wrestled with this problem over a lengthy period
of time, to the point of despair. We have no details of this struggle,
unfortunately.
Finally, after a day spent wrestling
once more with the problem in the company of his friend and patent
office colleague Michele Besso, the only person thanked in the 1905
SRT paper, there came a moment of crucial insight. In all of his
struggles with the emission theory as well as with Lorentz's theory,
he had been assuming that the ordinary Newtonian law of addition
of velocities was unproblematic. It is this law of addition of velocities
that allows one to "prove" that, if the velocity of light is constant
with respect to one inertial frame, it cannot be constant with respect
to any other inertial frame moving with respect to the first. It
suddenly dawned on Einstein that this "obvious" law was based on
certain assumptions about the nature of time always tacitly made.
In particular, the concept of the velocity of an object with respect
to an inertial frame depends on time readings made at two different
places in that inertial frame. (He later referred to this moment
of illumination as "the step.")
17
How do we know that time readings at two such distant places are
properly correlated? Ultimately this boils down to the question:
how do we decide when events at two different places in the same
frame of reference occur at the same time, i.e., simultaneously?
Isn't universal simultaneity an intuitively obvious property of
time? Here, I believe, Einstein was really helped by his philosophical
readings. He undoubtedly got some help from his readings of Mach
and Poincaré, but we know that he was engaged in a careful
reading of Hume at about this time; and his later reminiscences
attribute great significance to his reading of Hume's
Treatise
on Human Nature. What could he have gotten from Hume? I think
it was a relational-as opposed to an absolute-concept of time and
space. This is the view that time and space are not to be regarded
as self-subsistent entities; rather one should speak of the temporal
and spatial aspects of physical processes; "The doctrine," as Hume
puts it, "that time is nothing but the manner, in which some real
object exists." I believe the adoption of such a relational concept
of time was a crucial step in freeing Einstein's outlook, enabling
him to consider critically the tacit assumptions about time going
into the usual arguments for the "obvious" velocity addition law.
This was the second great moment of liberation of his thought.
I shall not rehearse Einstein's arguments here, but it led to the
radically novel idea that, once one physically defines simultaneity
of two distant events relative to one inertial frame of reference,
it by no means follows that these two events will be simultaneous
when the
same definition is used relative to another inertial
frame moving with respect to the first. It is not logically excluded
that they
are simultaneous relative to all inertial frames.
If we make that assumption, we are led back to Newtonian kinematics
and the usual velocity addition law, which is logically quite consistent.
However, if we adopt the two Einstein principles, then we are led
to a new kinematics of time and space, in which the velocity of
light is a universal constant, while simultaneity is different with
respect to different inertial frames; this is also logically quite
consistent. The usual velocity addition law is then replaced by
a new one, in which the velocity of light "added" to any other velocity
("added" in a new sense-it would be better to say "compounded with")
does not increase, but stays the same! The Maxwell-Lorentz equations,
when examined with the aid of this new kinematics, prove to take
the same form in every inertial frame. They are, therefore, quite
compatible with the relativity principle, which demands that the
laws of electricity, magnetism and optics have this property. The
presence or absence of an electric or magnetic field, is then also
found to be relative to an inertial frame, allowing a completely
satisfactory relativistic analysis of the example of the conducting
wire loop and magnet in relative motion. Within six weeks of taking
"the step," Einstein later recalled, he had worked out all of these
consequences and submitted the 1905 SRT paper to
Annalen der
Physik.
This does not imply that Lorentz's equations are adequate to explain
all the features of light, of course. Einstein already knew they
did not always correctly do so-in particular in the processes of
its emission, absorption and its behavior in black body radiation.
Indeed, his new velocity addition law is also compatible with an
emission theory of light, just
because the speed
of light compounded with any lesser velocity still yields the same
value. If we model a beam of light as a stream of particles, the
two principles can still be obeyed. A few years later (1909), Einstein
first publicly expressed the view that an adequate future theory
of light would have to be some sort of fusion of the wave and emission
theories. This is an example of how the special theory of relativity
functioned as a theory of principle, limiting but not fixing the
choice of a constructive theory of light.
Here I shall end my conjectures
on how Einstein arrived at SRT. To briefly recapitulate, I believe
that the first principle, the relativity principle, recapitulates
his struggles with the mechanical ether concept which led finally
to the first crucial liberation of his thought-the abandonment of
the ether. The second principle, the principle of the constancy
of the speed of light, recapitulates his struggle, once he had definitely
opted for the relativity principle, first to evade the Maxwell-Lorentz
theory by an emission theory; then to isolate what was still valid
in the Maxwell Lorentz theory after giving up the ether concept
and abandoning absolute faith in the wave theory of light. The struggle
to reconcile the two principles could only end successfully after
the second great liberation of his thought: the relativisation of
the concept of time. The resulting theory did not force him to choose
between wave and emission theories of light, but rather led him
to look forward to a synthesis of the two. This synthesis was finally
achieved, over twenty years later, in the quantum theory of fields,
to the satisfaction of most physicists, but ironically, never to
that of Einstein.
I cannot ask you to accept my conjectures after all of my warnings
at the outset of this paper, but will be content if you say
"Si non è vero, è ben trovato," "If it isn't true,
it's well contrived."
You can
EXIT
to Einstein's own words on "Ether and the Theory of Relativity"
(1920 address)
Notes
1. Poe is quoting Sir Thomas Browne's
Hydrotaphia.
BACK
2. A preliminary question is raised
by my use of the word "discovery." Is it better to speak of the
"discovery" or the "creation" of a theory like SRT? "Discovery"
suggests the finding of some pre-existent, objective structure,
as when we say "Columbus discovered America." "Creation" suggests
an individual, subjective act, as when we say "Tolstoy created
Anne
Karenina." Neither word seems really appropriate to describe
what goes on in the scientific endeavor. Einstein apparently preferred
the word "Erfindung" (invention) to describe how scientific theories
come into being. Speaking of Mach, Einstein says: "Er meinte gewissermassen,
dass Theorien durch
Entdeckung und nicht durch
Erfindung
entstehen." (
Einstein-Besso Correspondence (Hermann, Paris
1972), p. 191, dated January 6, 1948.
BACK
3. In the study of the discovery
of GRT, therefore, one may hope to formulate conjectures which can
be either confirmed or refuted. For example: A study of Einstein's
published papers and private correspondence between 1912-1915 convinced
me that the standard explanation for his failure to arrive at the
correct gravitational field equations until the end of this period-namely,
his presumed lack of understanding of the meaning of freedom of
coordinate transformations in a generally covariant theory and the
ability to impose coordinate conditions that this freedom implied-could
not be correct (see "Einstein's Search for General Covariance, 1912-1915,"
presented at the Ninth International Conference on General Relativity
and Gravitation, July 17, 1980, in Stachel
Einstein from "B"
to "Z", pp. 301338). On the basis of his study of a research
notebook of Einstein from the early part of this period, John Norton
was able to prove that Einstein already was aware of the possibility
of imposing coordinate conditions on a set of field equations, and
indeed had used the harmonic coordinate conditions (see John Norton,
"How Einstein found his field equations: 1912-1915,"
Historical
Studies in the Physical Sciences 14, 253 (1984). For reasons
discussed in the text, one cannot hope to confirm or disconfirm
most conjectures about the origins of SRT.
BACK
4. For a survey of this material
for the period up to 1923, see J. Stachel, "Einstein and Michelson:
The Context of Discovery and the Context of Justification," Astron.
Nachricht.
303, 47 (1982). Unless otherwise noted,
quotations from Einstein are cited from this paper, which gives
the full references. [See Stachel,
Einstein from "B" to "Z",
pp. 177-190].
BACK
5. See Arthur I. Miller,
Albert
Einstein's Special Theory of Relativity (Addison-Wesley, Reading
1981), which contains references to his earlier papers as well as
those of Holton, Hirosige and many others; Abraham Pais, 'Subtle
is the Lord. . .'
The Science end the Life of Albert Einstein
(Oxford U.P., New York 1982); Stanley Goldberg,
Understanding
Relativity (Birkhauser, Boston 1984); Roberto Torretti,
Relativity
end Geometry (Pergamon, Oxford 1983). Earman, Glymour and Rynasiewicz
have not yet published a full account of their views; I thank them
for making available copies of several preprints on this subject.
BACK
6. A popular epigram among historians
runs: "God is omnipotent, but even He cannot change the past. That
is why He created historians."
BACK
7.See the reference in
footnote 4 for the source of the citations from Reichenbach. If
my thesis here is correct, this argues against the still widely
held view that these two contexts should be rigorously separated.
But in this paper I shall not elaborate on the wider issue.
BACK
8. For example, Einstein's
statements of the second principle of SRT, the light principle,
remained remarkably consistent throughout his lifetime (see the
discussion of this principle below). Indeed, an apparent exception
in the printed text of his article "What is the Theory of Relativity?,"
published originally in English translation in the
Times
of London in 1919, proved to be based upon an incorrect transcription
of his manuscript.
BACK
9. Much of the anti-relativity
literature, which still continues to grow in volume if not in weight,
is based on attempts to show that the two principles are indeed
logically incompatible.
BACK
10. Sometimes
(e.g., by Pais and Goldberg), this consequence of Einstein's two
principles is asserted to be his second principle. This is incorrect
factually (Einstein's account of the second principle is one of
the most consistent features of his discussions of SRT over the
years-see footnote 8), and disturbing for several reasons: a) it
makes it impossible to explain why Einstein refers to the two principles
as apparently contradictory. There is no contradiction apparent
between the relativity principle and this deduction from it; b)
it is logically defective, since the two principles would no longer
be logically independent, as they are in Einstein's formulation;
c) most important for present purposes, this formulation deprives
us of important clues to Einstein's reasoning that led to the development
of SRT.
BACK
11. Einstein to Max Talmey,
June 6, 1938. The German text reads: "Die empirisch suggerierte
Nichtexistenz einer solchen bevorzugten 'Wind-Richtung' ist der
Haupt-Ausgangspunkt der speziellen Relativitatstheorie."
BACK
12. Hertz
said: "... the absolute motion of a rigid system of bodies has no
effect upon any internal electromagnetic processes whatever in it,
provided that all the bodies under consideration, including the
ether as well, actually share the motion." (
Electromagnetic
Waves, p. 246). Lorentz said:
That one cannot speak of the absolute rest of the ether, is
self-evident indeed; the expression wouldn't even have any meaning.
If I say for short, the ether is at rest, this only means that
one part of this medium is not displaced with respect to the others
and that all perceptible movements of the heavenly bodies are
relative movements with respect to the ether. [Versuch,
p. 4 (1895).] BACK
13. He was not alone
in transferring statistical methods from ordinary matter to radiation.
Planck had already done so, but Einstein did not see the relation
of his work to Planck's until after publishing his first paper on
the subject.
BACK
14. See Albert Einstein,
Autobiographical Notes (Open Court, LaSalle 1979), pp.
48 (German text) and 49 (English translation).
BACK
15. One such piece of
evidence, not cited in my earlier paper (see footnote 4), has only
recently come to light. It occurs in the most complete review of
SRT that Einstein ever wrote. It was prepared in 1912 but never
published, and is still in private hands. Luckily, a copy has come
into the possession of the Einstein Archive. In it, Einstein explains
at some length the difficulties that are encountered (and presumably
these are the ones he had encountered), if one tries to explain
the results of the Fizeau experiment on the basis of an emission
theory of light combined with the relativity principle and Galilei-Newtonian
kinematics. [See The
Collected Papers of Albert Einstein,
vol. 4.
The Swiss Years: Writings 1912-1914 (Princeton
University Press, Princeton 1995), Doc. 1, "Manuscript on the Special
Theory of Relativity," pp. 32-36].
BACK
16. Indeed,
the earliest explanation of stellar abberation had been based on
the emission theory.
BACK
17. Abraham Pais has
mentioned this in describing his conversations with Einstein.
BACK
This is the text of "'What Song the Syrens Sang':
How Did Einstein Discover Special Relativity?" as printed in John
Stachel,
Einstein
from "B" to "Z" (Boston : Birkhäuser, 2002), pp. 157-169.
It is an English text of "Quale canzone cantarono le sirene: come
scopro Einstein la teoria speciale della relatività?" published
in
L'Opera di Einstein (1989), pp. 21-37. Copyright ©
1989, 2002 by John Stachel.
John Stachel is Professor of Physics
Emeritus and Director of the Center of Einstein Studies at Boston
University. He has written a variety of articles on aspects of the
history of both special and general relativity and other topics, and
has edited or co-edited a number of books dealing with Einstein and
relativity.
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