complex; and the scientific method is to analyse them into
simpler elements. Theories and laws of behaviour of these
simpler constituents are studied; and from these it becomes
possibleto predict and explain phenomena. It seems a natural
procedure to expl

for space, time, and velocity.But again the laws of
nature must be the same in all c.s. moving uniformly,
relative to each other. The laws of nature must be
invariant, not, as before,with respect to the classical
transformation,but with respect to a new t

those near the velocityof light.The number expressing
the velocityof lightappears explicitly in the Lorentz
transformation,and plays the role of a limitingcase,
like the infinite velocityin classical mechanics. This
more general theory does not contradict

FIELD, RELATIVITY 205
complicatedone appears. From our new pointof view
classical mechanics is simple because in nearly all
observations we deal with velocities much smaller than
that of light.
A body at rest has a definite mass, called the rest mass.
We

is given as a function of time, then our set of points
becomes a continuous line. Our next drawing therefore
represents not justa fragmentas before,but a complete
knowledge of the motion.
Feet
Seconds
Time axis
The motion along the rigid rod (the tower),

imagine ourselves once more on board an ocean steamer
so perfectly constructed that it travels without rolling
or pitching, and with straight course and uniform
velocity. We shall suppose there is a whinjsical rich
old gentleman on board, who says :
" I'U

gravitationalmasses are equivalent.A beam of light
will bend in a gravitationalfield exactlyas a body
would ifthrown horizontallywith a velocityequalto that
of light.If the inside observer had reasoned correctly
and had taken into account the bending of l

better solution of our difficultiescould have been found.
We have had to forsake the description of individual
cases as objectivehappenings in space and time; we
have had to introduce laws of a statisticalnature. These
are the chief characteristics of mod

Expressingthe same fact in the field language,
FIELD, RELATIVITY 14!
we can say: an electrostatic field does not influence a
magnetostaticone and vice versa. The words "static
field" mean a field that does not change with time.
The magnets and chargeswoul

we find the point of conflict that gave rise to the origin
of the theory of relativity. Theoretical considerations
seemed to indicate that the principle of relativity can
have no validity for optical phenomena, whereas emexnpetriteaches
us that it has. In

132 THE EVOLUTION OF PHYSICS
speed of the actions along the lines of force must be
assumed as infinitely great ! The force between two
bodies, according to Newton's law, depends only on
distance ; time does not enter the picture.The force has
to pass from

near the wire through which a current flows. We may
remark in passingthat this property enables us to csotnr-uct
sensitive apparatus for detectingthe existence of
a current. Once havinglearned how to read the charac136
THE EVOLUTION OF PHYSICS
ter of the

about the observer on the disc? From the pointof view
of classical physicsand also the specialrelativittyheory,
his c.s. is a forbidden one. But if we intend to find new
forms for physicallaws,valid in any c.s., then we must
treat the observer on the disc

streets and avenues, though these are no longer
straightand equidistant.Similarly,on our earth,
longitudeand latitude denote the positionsof points,
althoughthere is no "American town" construction.
0. But I stillsee a difficultYyo.u are forced to use
you

events; they do not connect the happenings here with
FIELD, RELATIVITY 153
the conditions there. The field here and now depends
on the field in the immediate neighbourhoodat a time
justpast. The equationsallow us to predictwhat will
happen a littlefarther

sent lightwaves. We should catch them in a
reverse order to that in which they were sent, and the
train of happenings on our earth would appear like a
film shown backward, beginningwith a happy ending.
These conclusions all follow from the assumption that

plane, no
spherical,109
standing,288
theoryof light,no
transverse, 108, 121
velocity,106
Weightless substances, 43,
79
X-rays, 284-286
Young, 118
CAMBRIDGE : PRINTED BY
W. LEWIS, M.A.
AT THE UNIVERSITY PRESS
THE
IDEAS OF EINSTEIN'S THEORY
THE IDEAS OF
EIN

initial one, is also an inertial c.s.
Let us consider the case of two c.s. startingfrom a
known positionand moving uniformly,one relative
to the other, with a known velocity.One who prefers
concrete picturescan safelythink of a ship or a train
moving rela

Our starting-pointis a classical example having
nothing to do with modern physics.We take in our
hand the end of a very long flexible rubber tube, or a
very long spring,and try to move it rhythmicallyup
and down, so that the end oscillates.Then, as we hav

transformation. We could try, as we did so successfully
with the laws of motion, to generalizethe gravitational
law, to make it fit the specialrelativity theory,or, in
other words, to formulate it so that itwould be invariant
with respect to the Lorentz a

which appears as a small segment. The tangent is its
prolongation.Thus the vector drawn represents the
velocityat a given instant. The velocityvector lies on
the tangent. Its lengthrepresents the magnitude of the
velocity, or the speed as indicated,for in

is usually made, not by determining what matter is, but by
what certain combinations of matter do. Hence the interval is
at once identified with something familiar to experience,namely
the thing that a scale and a clock measure. However atadgvaeno-us
that

it is an arrow. Velocity may be representedby an
arrow or, brieflyspeaking,by a vector whose length
in some chosen scale of units is a measure of the speed,
and whose direction is that of the motion.
If four cars divergewith equal speed from a traffic
rou

arbitrary choice of gauge-system. The electromagnetic forces
on the other hand are independent of the gauge-system, which
is eliminated by "curling."]
It thus appears that the four new quantities appearing in our
extended geometry may actually be the four

118; theory of, 107,207
Density, effect of motion on, 62
Displacement of spectral lines, 129; in
nebulae, 161; in stars, 135
Displacement of star-images, 112, 115
Double stars and Einstein effect, 133
Duration, not inherent in external
world, 34
216 INDEX

the riddles of nature have been solved,althoughmany
of the solutions have proved temporary and superficial
in the lightof further research.
A most fundamental problem, for thousands of years
wholly obscured by its complications,is that of motion.
All thos

mechanical operationabove mentioned?
Is it furnished by the metallic chipswhich are separated
by the borer from the solid mass of metal?
If this were the case, then, according to the modern
doctrines of latent Heat, and of caloric,the capacityought
not on

* There must be some absolute track, and if absolute significancecan only
be associated with hurdle-counts and not with distances in the field, the path
of fewest hurdles is the only track capable of absolute definition.
108 THE NEW LAW OF GRAVITATION [ch

at one point of space and the appearance of an apparently
identical particleat a neighbouring point. This manifestation
of motion can be deduced mathematically from the identifying
definition here adopted. Remembering that in physicaltheory
it is necessar

dimension. But the four-dimensional world is no mere itillonu;strait
is the real world of physics,arrived at in the recognised
way by which physics has always (rightlyor wrongly) sought for
reality.
I hold a certain object before me, and see an outline of