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**Einsteinıs**

**Theory of Relativity**

(February
3, 1929)

presented to the general public

in terms that the average
person could understand (or
so he thought).

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**The
History of Field Theory**

(³Old and New developements of
Field Theory²)

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**By Albert Einstein **

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While physics
wandered exclusively in the paths prepared by Newton, the following conception
of physical reality prevailed:
Matter is real, and matter undergoes only those changes which we
conceive as movements in space.
Motion, space and also time are real forms. Every attempt to deny the physical reality of space
collapses in face of the law of inertia.
For if acceleration is to be taken as real, then that space must also be
real within which bodies are conceived as accelerated.

Newton saw this with perfect clarity and
consequently he called space "absolute". In his theoretical system, there was a third constituent of
independent reality; the motive force acting between material particles, such
forces being considered to depend only on the position of the particles. These forces between particles were
regarded as unconditionally associated with the particles themselves and as
distributed spatially according to an unchanging law.

The physicists of the nineteenth century
considered that there existed two kinds of such matter, namely, ponderable
matter and electricity. The
particles of ponderable matter were supposed to act on each other by
gravitational forces under Newton's law, the particles of electrical matter by
Coulomb forces also inversely proportional to the square of the distance. No definite views prevailed regarding
the nature of the forces acting between ponderable and electrical particles.

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**The
Old Theory of Space**

Mere empty space was not admitted as a carrier for
physical changes and processes. It was only, one might say, the stage on which
the drama of material happenings was played. Consequently Newton dealt with the fact that light is
propagated in empty space by making the hypothesis that light also consists of
material particles interacting with ponderable matter through special
forces. To this extend Newton's
view of nature involved a third type of material particle, though this
certainly had to have very different properties from the particles of the other
forms of matter. Light particles
had, in fact, to be capable of being formed and of disappearing. Moreover, even in the eighteenth
century it was already clear from experience that light traveled in empty space
with a definite velocity, a fact which obviously fitted badly into Newton's
theoretical system, for why on earth should the light particles not be able to
move through space with any arbitrary velocity?

It need not, therefore, surprise us that this
theoretical system, built up by Newton with his powerful and logical intellect,
should have been overthrown precisely by a theory of light. This was brought about by the
Huygens-Young-Fresnel wave theory of light which the facts of interference and
diffraction forced on stubbornly resisting physicists. The great range of phenomena, which
could be calculated and predicted to the finest detail by using this theory,
delighted physicists and filled many fat and learned books. No wonder then that the learned men
failed to notice the crack which this theory made in the statue of their
eternal goddess. For, in fact,
this theory upset the view that everything real can be conceived as the motion
of particles in space. Light
waves, were, after all, nothing more than undulatory states of empty space, and
space thus gave up its passive role as a mere stage for physical events. The other hypothesis patched up the
crack and made it invisible.

The ether was invented, penetrating everything,
filling the whole of space, and was admitted as a new kind of matter. Thus it was overlooked that by this
procedure space itself had been brought to life. It is clear that this had really happened, since the ether
was considered to be a sort of matter which could nowhere be removed. It was thus to some degree identical
with space itself; that is, something necessarily given with space. Light was thus viewed as a dynamical
process undergone, as it were by space itself. In this way the field theory was born as an illegitimate
child of Newtonian physics, though it was cleverly passed off a first as
legitimate.

To become fully conscious of this change in
outlook was a task for a highly original mind whose insight could go straight
to essentials, a mind that never got stuck in formulas. Faraday was this favored spirit. His instinct revolted at the idea of
forces acting directly at a distance which seemed contrary to every elementary
observation. If one electrified
body attracts or repels a second body, this was for him brought about not by a
direct action from the first body on the second, but through an intermediary
action. The first body brings the
space immediately around it into a certain condition which spreads itself into
more distant parts of space, according to a certain spatio-temporal law of
propagation. This condition of
space was called "the electric field." The second body experiences a force because it lies in the
field of the first, and vice versa.
The "field" thus provided a conceptual apparatus which
rendered unnecessary the idea of action at a distance. Faraday also had the bold idea that
under appropriate circumstances fields might detach themselves from the bodies
producing them and speed away through space as free fields: this was his
interpretation of light.

Maxwell then discovered the wonderful group of
formulae which seems so simple to us nowadays and which finally build the
bridge between the theory of electro-magnetism and the theory of light. It
appered that light consists of rapidly oscillating electro magnetic fields.

After Hertz, in the '80s of the last century, had
confirmed the existence of the electro-magnetic waves and displayed their
identity with light by means of his wonderful experiments, the great
intellectual revolution in physics gradually became complete. People slowly accustomed themselves to the
idea that the physical states of space itself were the final physical reality,
especially after Lorentz had shown in his penetrating theoretical researches
that even inside ponderable bodies the electro-magnetic fields are not to be
regarded as states of the matter, but essentially as states of the empty space
in which the material atoms are to be considered as loosely distributed.

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**Dissatisfied
With Dual Theory**

At the turn of the century physicists began to be
dissatisfied with the dualism of a theory admitting two kinds of fundamental
physical reality: on the one hand the field and on the other hand the material
particles. It is only natural that
attempts were made to represent the material particles as structures in the
field, that is, as places where the fields were exceptionally
concentrated. Any such
representation of particles on the basis of the field theory would have been a
great achievement, but in spite of all efforts of science it has not been
accomplished. It must even be
admitted that this dualism is today sharper and more troublesome that it was
ten years ago. This fact is
connected with the latest impetus to developments in quantum theory, where the
theory of the continuum (field theory) and the essentially discontinuous
interpretation of the elementary structures and processes are fighting for
supremacy.

We shall not here discuss questions concerning
molecular theory, but shall describe the improvements made in the field theory
during this century.

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**[The Theory of Relativity]**

These all arise from the theory of relativity,
which has in the last six months entered its third stage of development. Let us briefly examine the chief points
of view belonging to these three stages and their relation to field theory.

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** [The
Special Theory of Relativity]**

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**The first stage, the special theory of
relativity**, owes its origin principally to
Maxwell's theory of the electro-magnetic field. From this,
combined with the empirical fact that there does not exist any
physically distinguishable state of motion which may be called "absolute
rest", arose a new theory of
space and time. It is well known
that the theory discarded the absolute character of the conception of the
simultaneity of two spatially separated events. Well known is also the courage of despair with which some
philosophers still defend themselves in a profusion of proud but empty words
against this simple theory.

On the other hand, the services tendered by the
special theory of relativity to its parent, Maxwell theory of the electro-magnetic field, are less adequately recognized. Up to that time the electric field and
the magnetic field were regarded as existing separately even if a close causal
correlation between the two types of field was provided by Maxwell's field
equations. But the special
theory of relativity showed that this causal correlation corresponds to an
essential identity of the two types of field. In fact, the
same condition of space, which in
one coordinate system appears as a pure magnetic field, appears simultaneously in another
coordinate system in relative motion as an electric field, and vice versa. Relationship of this kind displaying an
identity between different conceptions,
which therefore reduce the number of independent hypotheses and concepts
of field theory and heighten its logical selfcontainedness are a characteristic
feature of the theory of relativity.
For instance, the special
theory also indicated the essential identity of the conceptions' inertial mass
and energy. This is all generally
known and is only mentioned here in order to emphasize the unitary tendency
which dominates the whole development of the theory.

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**[The General Theory of Relativity]**

We now turn to **the second stage** in the development of the theory of relativity, the
so-called **general theory of relativity**. This theory also
starts from a fact of experience which till then had received no satisfactory
interpretation; the equality of
inertial and gravitational mass, or,
in other the words, the
fact known since the days of Galileo and Newton that all bodies fall with equal
acceleration in the earth's gravitational field. The theory uses a special theory as its basis and at the
same time modifies it: the recognition that there is no state of motion
whatever which is physically privileged - that is, that not only velocity but
also acceleration are without absolute significance - forms the starting point
of the theory. It then compels a
much more profound modification of the conceptions of space and time than were
involved in the special theory.
For even if the special theory forced us to fuse space and time together
to an invisible four-dimensional continuum, yet the Euclidean character of the
continuum remained essentially intact in this theory. In the general theory of relativity, this hypothesis
regarding the Euclidean character of our space-time continuum had to be
abandoned and the latter given the structure of a so-called Riemannian
space. Before we attempt to understand
what these terms mean, let us recall what this theory accomplished.

It furnished an exact field theory of gravitation
and brought the latter into a fully determinate relationship to the metrical
properties of the continuum. The
theory of gravitation, which until then had not advanced beyond Newton, was
thus brought within Faraday's conception of the field in a necessary manner;
that is, without any essential arbitrariness in the selection of the field
laws. At the same time gravitation
and inertia were fused into an essential identity. The confirmation which this theory has received in recent
years through the measurement of the deflection of light rays in a
gravitational field and the spectroscoptic examination of binary stars is well
known.

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**[The Unitary Field Theory]**

The characteristics which especially distinguish
the general theory of relativity and even more the **new third stage** of the theory, **the unitary field theory**, from other physical theories are the degree of
formal speculation, the slender empirical basis, the boldness in theoretical
construction and, finally, the fundamental reliance on the uniformity of the
secrets of natural law and their accessibility to the speculative
intellect. It is this feature
which appears as a weakness to physicists who incline toward realism or
positivism, but is especially attractive, nay, fascinating, to the speculative mathematical mind. Meyerson in his brilliant studies on
the theory of knowledge justly draws a comparison of the intellectual attitude
of the relativity theoretician with that of Descartes, or even of Hegel,
without thereby implying the censure which a physicist would read into
this. However that may be in the
end experience is the only competent judge.

Yet in the meantime one thing may be said in
defense of the theory. Advance in
scientific knowledge must bring about the result that an increase in formal
simplicity can only be won at the cost of an increased distance or gap between
the fundamental hypothesis of the theory on the one hand and the directly
observed facts on the other hand.
Theory is compelled to pass more and more from the inductive to the
deductive method, even though the most important demand to be made of every
scientific theory will always remain: that it must fit the facts.

We now reach the difficult task of giving to the
reader an idea of the methods used in the mathematical construction which led
to the general theory of relativity and to the new unitary field theory.

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**The
Problem Stated**

The general problem is: Which are the simplest formal structures that can be
attributed to a four-dimensional continuum and which are the simplest laws that
may be conceived to govern these structures? We then look for the mathematical expression of the physical
fields in these formal structures and for the field laws of physics - already
known to a certain approximation from earlier researches - in the simplest laws
governing this structure.

The conceptions which are used in this connection
can be explained just as well in a two-dimensional continuum (a surface) as in
the four-dimensional continuum of space and time. Imagine a piece of paper ruled in millimeter squares. What does it mean if I say that the
printed surface is two-dimensional?
If any point *P* is marked on the paper, one can define
its position by using two numbers.
Thus, starting from the bottom left-hand corner, move a pointer toward
the right until the lower end of the vertical through the point *P* is
reached. Suppose that in doing
this one has passed the the lower ends of *X*
vertical (millimeter) lines.
Then move the pointer up to the point *P*
passing *Y* horizontal lines. The point *P* is
then described without ambiguity by the numbers *X Y*
(coordinates). If one had
used, instead of ruled millimeter paper, a piece which had been stretched or
deformed the same determination could still be carried out: but in this case
the lines passed would no longer be horizontals or verticals or even straight
lines. The same point would then,
of course, yield different numbers, but the possibility of determining a point
by means of two numbers (Gaussian coordinates) still remains. Moreover, if *P* and *Q* are
two points which lie very close to one another, then their coordinates differ
only very slightly. When a point
can be described by two numbers in this way, we speak of a two-dimensional
continuum (surface).

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**Riemannian
Metric**

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Now consider two neighboring points** ***P, Q, *

ds2 =
g11dx2 + 2 g11 g22 dx
dy + g22 dy2

Then
it is called a Riemannian metric.
If it is possible to choose the coordinates so that this expression
takes the form:
ds2 = dx2
+ dy2

(Pythagoras's
theorem), then the continuum is Euclidean (a plane).

Thus it is clear that the Euclidean continuum is a
special case of the Riemannian.
Inversely, the Riemannian continuum is a metric continuum which is
Euclidean in infinitely small regions,
but not in finite regions.
The quantities g11, g12, and g22 describe the metrical
properties of the surface; that is, the metrical field.

By making use of empirically known properties of
space, especially the law of the propagation of light; it is possible to show that the space -
time continuum has a Riemannian metric.
The quantities g11, g12, and g22 , appertaining to
it, determine not only the metric
of the continuum, but also the
gravitational field. The law governing
the gravitational field is found in answer to the question: Which are the
simplest mathematical laws to which the metric (that is the g11, g12, and g22) can be subjected? The answer was given by the discovery of the field laws of
gravitation, which have proved themselves more accurate than the Newtonian
law. This rough outline is
intended only to give a general idea of the sense in which I have spoken of the
"speculative" methods of the general theory of relativity.

**Expanding
the Theory.**

This theory having brought together the metric and
gravitation would have been completely satisfactory of the world had only
gravitational fields and no electro-magnetic fields. Not it is true that the latter can be included within the
general theory of relativity by taking over and appropriately modifying
Maxwell's equations of the electro-magnetic field, but they do not then appear
like the gravitational fields as structural properties of the space - time
continuum, but as logically independent constructions. The two types of field are causally
linked in this theory, but still not fused to an identity. It can, however, scarcely be imagined
that empty space has conditions or states of two essentially different kinds,
and it is natural to suspect that this only appears to be so because the
structure of the physical continuum is not completely described by the
Riemannian metric.

The new unitary field theory removes this fault by
displaying both types of field as manifestations of one comprehensive type of
spatial structure in the space-time continuum. The stimulus to the new theory arose from the discovery that
there exists a structure between the Riemannian space structure and the
Euclidean, which is richer in formal relationships than the former but poorer
than the latter. Consider a
two-dimension Riemannian space in the form of the surface of a hen's egg. Since this surface is embedded in our
(accurately enough) Euclidean space, it possesses a Riemannian metric. In fact, it has a perfectly definite
meaning to speak of the distance of two neighboring points P, Q on the
surface. Similarly it has, of
course, a meaning to say of two such pairs of points (PQ) (P'Q'), at separate
parts of the surface of the egg, that the distance PQ is equal to the distance
P'Q'. On the other hand, it is
impossible now to compare the direction PQ with the direction P'Q'. In particular it is meaningless to
demand that P'Q' shall be chosen parallel to PQ. In the corresponding Euclidean geometry of two dimensions,
the Euclidean geometry of the plan, directions can be compared and the
relationship of parallelism can exist between lines in regions of the plane at
any distance from one another (distant parallelism). To this extend the Euclidean continuum is richer in
relationships than the Riemannian.

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**A
Mathematical Discovery**

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The new unitary field theory is based on the
following mathematical discovery:
There are continua with a Riemannian metric and distant parallelism
which nevertheless are not Euclidean.
It is easy to show, for instance, in the case of three-dimensional
space, how such a continuum differs from a Euclidean.

First of all, in such a continuum there are lines
whose elements are parallel to one another. We shall call those "straight
lines". It also has a
definite meaning to speak of two parallel straight lines as in the Euclidean
case. Now choose two such
parallels E1L1 and E2L2 and mark on each a point P1, P2.

On E1L1
choose in addition a point Q1. If we now draw through Q1 a straight line Q1-R parallel to the straight line P1, P2,
then in Euclidean geometry this will cut the straight line E2L2 ;
in the geometry now used the line Q1-R
and the line do
not in general cut one another. To
this extent the geometry now used is not only a specialization of the
Riemannian but also a generalization of the Euclidean geometry. My opinion is that our space-time
continuum has a structure of the kind here outlined.

The mathematical problem whose solution, in my
view, leads to the correct field laws is to be formulated thus: which are the
simplest and most natural conditions to which a continuum of this kind can be
subjected? The answer to this
question which I have attempted to give in a new paper yields unitary field
laws for gravitation and electro-magnetism.

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**Glossary of Terms**

Some
of the terms employed by Dr. Einstein in his article on this page will be
recognized by those who recall their elementary physics: others will not be
understood except by students of higher mathematics. For the convenience of all readers, the following glossary
has been compiled of important terms, names and theories mentioned by Dr.
Einstein.

**Continuum** - A line, straight or curved, is a one-dimension
continuum. A surface, flat or
curved, is a two-dimension continuum.
Space is a three-dimension continuum. Einstein's space time is a four-dimension continuum.

**Coulomb
Forces** - Coulomb, a French physicist
(1736-1806), found that two electrified particles attract or repel each other
with a force which is directly proportional to the product of their charges and
inversely proportional to the square of the distance between them. Such forces are called Coulomb forces.

**Deductive
Method** - Establishing particular facts
from general principles or truths.

**Diffraction** - A deviation of the rays of light from a straight
line when they are partially cut off by an obstacle or when they pass near the
edges of an opening.

**Electro-Magnetic
Field** - A portion of space in which
electric and magnetic forces exist.

**Ether** - In physics, ether is a supposed medium which fills
all space and through which radiant energy of all kinds - including radio
waves, light waves, X rays, cosmic rays is propagated.

**Euclid** - A Greek mathematician (about 350-300 B.C.) called
the "father of geometry".

**Faraday** - English physicist (1791-1861) and discoverer of
electromagnetic induction.

**Fourth
Dimension** - Fourth dimension of space
is an assumed dimension whose relation to the recognized dimensions - length,
breadth and thickness is analogous to that borne by any one of them to the
other two.

**Galileo** - An Italian physicist and astronomer (1564-1642)
inventor of the telescope and discoverer of the moons of Jupiter and the laws
of falling bodies.

**Gaussian
Coordinates **- Gauss, a German mathematician
(1777-1855). In studying the
properties of curved surfaces he used coordinates to latitude and longitude on
the surface of a sphere. Such
coordinates are called Gaussian coordinates.

**Gravitational
Field** - a portion of space across
which heavy bodies attract each other.

**Hegel** - A German philosopher (1770-1831)

**Hertz** - A German physicist (1857-1894) who discovered the
propagation of electromagnetic waves.

**Huygens
- Young - Fresnel Wave Theory of Light**
- Huygens, a Dutch mathematician (1629-1695); Young, an English physicist
(1773-1829), and Fresnel, a French physicist (1788-1827), founded the theory
that light is propagated by waves.

**Inductive
Method** - The scientific method which
attempts to obtain general laws from particular cases.

**Inertia** - In physics, inertia is that property of matter by
virtue of which it persists in its state of rest or of uniform motion, in a
straight line, unless some force changes that state.

**Interference** - In physics, interference is the term used to
describe the effect of waves in neutralizing or in reinforcing each other.

**Lorentz** - A Dutch physicist who developed the theory of
electrons.

**Maxwell's
Field Equations** - Maxwell, a Scottish
physicist (1831-1879), laid down the electromagnetic theory of light. This theory predicted the effects
afterward observed by Hertz. The
equations of Maxwell's theory are called the Maxwell field equations.

**Metric** - A term used to describe a mathematical system of
measurement.

**Newton's
Law** - Newton's law of universal
gravitation asserts that every particle of matter attracts every other particle
of matter with a force which is directly proportional to their masses and
inversely proportional to the square of the distance between them.

**Ponderable
Matter** - Matter that has weight.

**Quantum
Theory - **In Atomic Physics, the Quantum theory was founded in 1900
by Planck, A German mathematical
Physicist. This theory may be
briefly characterized by saying that it considers Atomic phenomena as
essentially discontinuous phenomena.

**Riemmanian
Space and Riemannian Metric** - If the
properties of two-dimensional space can be described by the formula given in
the article, viz:

ds2 = g11dx2 + 2 g11 g22 dx dy + g22 dy2

The
space is said to be a Riemannian space and to have a Riemannian metric. If the two-dimensional space, however,
can be described by the simple formula
ds2 = dx2 + dy2, it is said to be a Euclidean space and
to possess Euclidean metric.
Riemann was a German mathematician (1836-1876).