Relativity - The Special and General Theory | Page 2

who, from a general scientific and philosophical point of view,
are interested in the theory, but who are not conversant with the mathematical apparatus
of theoretical physics. The work presumes a standard of education corresponding to that
of a university matriculation examination, and, despite the shortness of the book, a fair
amount of patience and force of will on the part of the reader. The author has spared
himself no pains in his endeavour to present the main ideas in the simplest and most
intelligible form, and on the whole, in the sequence and connection in which they actually
originated. In the interest of clearness, it appeared to me inevitable that I should repeat

myself frequently, without paying the slightest attention to the elegance of the
presentation. I adhered scrupulously to the precept of that brilliant theoretical physicist L.
Boltzmann, according to whom matters of elegance ought to be left to the tailor and to
the cobbler. I make no pretence of having withheld from the reader difficulties which are
inherent to the subject. On the other hand, I have purposely treated the empirical physical
foundations of the theory in a "step-motherly" fashion, so that readers unfamiliar with
physics may not feel like the wanderer who was unable to see the forest for the trees.
May the book bring some one a few happy hours of suggestive thought!
December, 1916 A. EINSTEIN

PART I
THE SPECIAL THEORY OF RELATIVITY
PHYSICAL MEANING OF GEOMETRICAL PROPOSITIONS
In your schooldays most of you who read this book made acquaintance with the noble
building of Euclid's geometry, and you remember -- perhaps with more respect than love
-- the magnificent structure, on the lofty staircase of which you were chased about for
uncounted hours by conscientious teachers. By reason of our past experience, you would
certainly regard everyone with disdain who should pronounce even the most
out-of-the-way proposition of this science to be untrue. But perhaps this feeling of proud
certainty would leave you immediately if some one were to ask you: "What, then, do you
mean by the assertion that these propositions are true?" Let us proceed to give this
question a little consideration.
Geometry sets out form certain conceptions such as "plane," "point," and "straight line,"
with which we are able to associate more or less definite ideas, and from certain simple
propositions (axioms) which, in virtue of these ideas, we are inclined to accept as "true."
Then, on the basis of a logical process, the justification of which we feel ourselves
compelled to admit, all remaining propositions are shown to follow from those axioms,
i.e. they are proven. A proposition is then correct ("true") when it has been derived in the
recognised manner from the axioms. The question of "truth" of the individual geometrical
propositions is thus reduced to one of the "truth" of the axioms. Now it has long been
known that the last question is not only unanswerable by the methods of geometry, but
that it is in itself entirely without meaning. We cannot ask whether it is true that only one
straight line goes through two points. We can only say that Euclidean geometry deals
with things called "straight lines," to each of which is ascribed the property of being
uniquely determined by two points situated on it. The concept "true" does not tally with
the assertions of pure geometry, because by the word "true" we are eventually in the habit
of designating always the correspondence with a "real" object; geometry, however, is not

concerned with the relation of the ideas involved in it to objects of experience, but only
with the logical connection of these ideas among themselves.
It is not difficult to understand why, in spite of this, we feel constrained to call the
propositions of geometry "true." Geometrical ideas correspond to more or less exact
objects in nature, and these last are undoubtedly the exclusive cause of the genesis of
those ideas. Geometry ought to refrain from such a course, in order to give to its structure
the largest possible logical unity. The practice, for example, of seeing in a "distance" two
marked positions on a practically rigid body is something which is lodged deeply in our
habit of thought. We are accustomed further to regard three points as being situated on a
straight line, if their apparent positions can be made to coincide for observation with one
eye, under suitable choice of our place of observation.
If, in pursuance of our habit of thought, we now supplement the propositions of
Euclidean geometry by the single proposition that two points on a practically rigid body
always correspond to the same distance (line-interval), independently of any changes in
position to which we may subject the body, the propositions of Euclidean geometry then
resolve themselves into propositions on the possible