BOMBAY CALCUTTA MADRAS
quantum
theory.
four-dimensional
of the
monographs.
Within
these
restrictions
Professor I. N. Srieddon
curvature
tensor
of
the
space-time
metric
Also
the
validity
'absolute
space',
reference
and
therefore
are
in
no
causal
relationship
with
the
physical
properties
of
other
terrestrial
systems.
It
was
just
this
difference
I,
2
the
following
consequences
this
ether.
Relative
to
Ft,
a
plane
monochromatic
light
a
constant
velocity
v
in
the
direction
the vvavo
From
equations
(15)
we
get
at
once
tan
QL
of
of
departure
velocity
of
the
light
signal
is
equal
of
Michelson
's
experiments
in
a
later
section
dragged
phase
velocity
elementary
waves
in
a
direction
parallel
to
the
light
motion
of
the
earth.
An
experiment
ether,
such
an
arrange-
ment
would
give
We shall
a much
simpler way
from the
magnitude
telescope
T.
Analogously,
the
ray
2
is
reflected
by
a
to
S
t
and
back
again
we
first
obtain
an
experiment
indicating
that
the
principle
of
relativity
experiments
mentioned
above
cannot
be
explained
on
theory,
even
if
the
contraction
hypothesis
is
added
to
it;
for
the
formula
(22)
the
3
X
10
10
cm.
/sec.
in
every
system
emission
of
the
that
places
of
sent
on
to
the
point
0,
its
system
also
the
concept
of
velocity
assumes
an
exact
meaning
and,
especially
time t
primary
task
will
be
to
find
the
connexion
ratio
K
can,
however,
only
depend
according
to
the
equation
light
signal
in
velocity
(x,
y,
z,
t)
which
then
to
where
corresponding
inverse
rotation
ofthe
image
vectors
x
and
v,
while
occurring
From
placed parallel
to the
end-points
the ether.
for
the
in
v,
respectively.
Since
the
length
of
metre stick
In this
coordinate
x'
x\
(Fig.
8).
When
the
clock
C'
records
the
time
compared
with
is at
per
->
absurd
results.
Let
velocities
larger
than
r.
By
differentiation
of
(25)
and
(25')
we
be
given
by
8
transition from S' to
(59)
and
(59')
W
by
(64)
repre-
sents
t-}-dt
in
frequency
way
by
interchanging
the
primed
given by
at the
distance
vt
during
this
18,
it
is
necessary
to
change
Newton
's
fundamental
equations
of
mechanics
in
treated
on
the
same
footing,
so
that
any
systems
of
inertia
with
the
relative
velocity
v,
and
consider
\
are at
more
general
Lorentz
transformation
u'
mass
given
by
(22).
Introducing
this
into
(39
a)
we
get
the
equations
mass
a
material
particle
of the
zero
energy
measured
in
S
and
equal
magnitude
but
opposite
in
energy
conserva-
energy.
a whole with
8 has a
-*-*
determine
spectrograph,
which
permits
a
.very
precise
determination
of
the
ing
to
(87)
this
mass
defect
quantum
of
action
cannot
(la).
An
arbitrary
the
functions
is
a
straight
line.
end-points
of
a
measuring-rod
at
rest
on
the
ar'-axis,
the
rest
be
equal
to
the
difference
immedi-
following
chapters,
tensor form.
With Dirac's
in which
particle.
The
proper
B
t
A
If
we
consider
another
arbitrary
time
track
N
stationary
value,
viz.
a
maximum,
com-
pared
with
all
other
possible
motions
connecting
the
same
plane
wave.
In
24,
Chapter
II,
and
energy
four-momentum vectors
time,
ro
in
(3+
l)-space
components
in
8
are
equal
to
S,
A
rank zero has
three axes
law
t\
k
pseudo-tensors
of
the
pseudo-tensor
with
a
rank
equal
axial vector
with
a
without
rotation
the
co-
efficients
oL
lk
follow
from
(II.
27):
V
y
(125)
even
if
ot
ik
f
to
S
was
supposed
t'
ik
defined
in
(129).
AS ,
the
equation
U
l
U
l
the
spatial
axes
of
the axis
perpendicular
to
point
in
which
vector
in
the
we
can
Ch
se
cte
t
motion of
SI
7
at
the
place
x
and
at
the
time /.
The
situated inside
impressed
forces,
however,
are
assumed
to
be
volume
forces
^
'
drop
this
assumption
we
have,
in
the
general
energy-
momentum
tensor.
f
(223)
can
thus
be
written
f^
Introducing
the
angular
momentum
density
charge
particle
is
accelerated
until
it
S.
Since
the
charge
define
four
quantities
A
l
in
every
system
of
inertia
by
A-MA,^),
(20)
be
put
equal
perform
the
integration
over
the
space
coordinates
and,
since
s
t
is
zero
everywhere
but
at
the
points
satisfying
(47),
we
have,
according
to
(3)
and
(IV.
39),
Si
choose
a
vector
x
corresponds
electrically charged
system
^o
point.
The
com-
ponents
of
s
i
in
this
system
tion
on
a
definite
infinitesimal
piece
integral
by
a
variation
form of
of
V
by
the
electromagnetic
forces.
For
i
is
zero
and
(1
17)
is
then
exactly
Maxwell's
expression
for
t
LK
is
zero.
momentum we have
thus to assume
velocity
w
defined
by
(120)
the
components
divergence
material
the
components,
i
h
physical
reasons.
In
the
trivial
case
of
a
system
consisting
of
incoherent
matter
without
any
external
forces,
for
instance,
the
proper
and
we
are
of
element
experiences
triangle
abc,
the
area
of
the
triangles
pbc,
yea,
and
pab
are
stress
tensor
a
is
now
equal
to
density
and
explicit
expression
extra
transport
of
energy
due
to
angular
momentum
requires
T
IK
defined
by
(56)
simple
calculation
foiu
-force
density
- -
=
-
~
investigation
shows,
however, ]*
that
the
representative
point
is
not
uniquely
defined
by
this
condition.
In
fact,
even
of
points
which
at
any
time
equation
are
gravitational
forces,
expressions
(VT.
87)
also be
sphere.
where
p
Q
elementary
particles
can
probably
Besides
components
pu
we
have
curl(uxB)
D,
and
case of
electromagnetic
forces
can
be
regarded
as
small.
small.
J.
the
charge
and
current
four-force
density
in
the
electron
theory
is
in
the
rest
system
is
pE
because
unit test
body placed
side of
a
complicatedway
The
four-force
density
get
the
ray,
i
e
the
eneigy,
into
the
telescope
rest
system
are
perpendicular
to
vector
n,
ray
velocity
as
defined
the
system
by
the
process,
=
considered
we
then
have,
according
to
(125),
Here,
d(s
8V)
/dt
is
E
Q
is
equal
to
gas
to
systems
of
reference
instead
of
regarding
them
as
an
expression
of
a
difference
in
principle
between
the
fundamental
equations
in
are
kind of
had been considered
gravitational
forces
is
corroborated
decisively
by
inertial and
particular
interest
in a
system
of
reference,
viz.
by
a
system
the sun
fixed
points
on
the
rotating
inertial
systems.
If
the
measuring-rods
in
one
way
or
contracted
special
theory
of
rela-
tivity,
was
regarded
as
an
indispensable
foundation
of
all
description
of
space.
This
also
has
the
consequence
(cf.
87)
that
system
rate
of
rotating
disk,
for
example,
geometry,
the
cos
g
lk
For
the
area
RELATIVITY 229
curve the
curve
connecting
by
(30)
and
(31)
also
satisfy
the
Euler
equations
(24)
with
ordinates x'
holds
the
co-
form
(37).
In
between
the
points
x
l
and
x
l
-\-dx
l
geometry
obtained
by
measurements
with
(d.^
From
the
relations
reciprocal
to
(42)
must have
distance
the
the
proper
247
This
is,
for
instance,
the
case
RELATIVITY 251
is
system
of
the
positive
velocity
v,
& T
equations
of
motion
(86)
with
g
the
gravitational
field
in
an
arbitrary
system
and
tensors
to
general
curvilinear
space-time
coordinates,
the
geometry
of
4-space
being
system
of
coordinates
Jby
flat
space
have O
components
general
Biemannian
space.
According
to
( 16)
and
tensors
of
rank
n
we
get
a
new
tensor
ofrank
n,
and
by
direct
multiplica-
tion of two tensors of the ranks n and m we
get
a
by
2.
By
con-
2
(29)
dx
l
the
point
(x
1
+dx
l
zero.
space.
This
is
in
pseudo-Euclidean
space
of
the
special
theory
of
relativity,
we
speak
general
Ricmannian
space
if
a
tensor
(or
pseudo-tensor)
quantities
0.
Since
the
scalar
product
space,
6
motion,
r
being
the
proper
time
of
the
particle
measured
by
a
presence
of
a
gravitational
field
with
the
dynamical
potentials
(yt
particle
surface in
particle
is
of
the
type
discussed
on
p.
293.
If
the
initial
velocity
of
the
particle
is
zero,
we
see
system
motion
of
a
freely
falling
particle
f
The
the
gravita-
tional
/
equal
to
i are
curve
connecting
A
and
 ^\-o
general
field
equations
2
depending
tensor is ofthe form
li
tk
a
general
weak
field,
we
first
remark
order,
will
lk
as the
=
masses,
Apart
again
centrifugal
and
on the
consideration
of
points
(x,
y,
z)
whose
(x'
1
functions
of
the
space-time
dt
2
ordinate
clocks
lk
is
practically
incom-
pressible.
The
proper
mass
the surface of the
Newtonian mass
electrons as
If
we
multiply
(123)
by
^(~g)g
lk
we
get,
using
(IX.
integral
over
of
energy
and
momentum
In
115
(
isolated
system
lk
 
obvious
in
a
gravitational
field
at
rest
at
the
point
p
r
The
number
The
frequency
have,
according
to
(XI.
83,
88),
me
2
kM
where
M
we
get
the
distance
the
body
(the
sun)
described
by
Schwarzschild's
the
planet.
The
square
particle
is
The
equations
m the
equation
is
very
small
compared
with
the
term
p
2
and,
if
we
neglect
it
approximate
equation.
The
maximum
positive
in
2-77
(49)
This will
then
get,
by
means
of
a
long
timef
that
Newton's
gravitational
theory
meets
with
for
the
possible
regular
/
possible
/lc
2
special
theory
of
relativity,
which
is
experimentally
interpretation
as
regards
the
geometry
whole.
If
with
the
Cartesian
coordinates
Defining
polar
coordinates
J/T,
6,
<f>
on
the
sphere
(82)
by
2/
variables
(0,
9,
of
course
always
approximately
valid.
The
equations
of
-f<x>-
With these
Any
reference
point
(x'
,y'
,z')
 
the
particle
the
light
is,
according
to
(104)
and
(122),
I
the
value
(7
1
It is
nebula.
Thus
we
the direction
group
transformations
play
the
same
role
in
the
de
the
ideal
fluid
filling
our
model,
a
value
of
p
of
corresponds
an
to
the
rotating
system.
While
the
non-permanent
gravitational
fields
can
be
explained
along
to
which
the
projection
a
whore
tin*
boundary
surface
cr
is
not
convex,
in
which
case
a
straight
line
parallel
in S'.
of
the
new
pseudo
-scalar
F
space
symmetrical
in
k
is
then
OJnL
weak fields and
columns
by
(ii)
In
the
same
way
may
therefore
204,
205.
Adams,
W
46, 49, 82, 139,