308
DOC.
31
ON THE RELATIVITY PROBLEM
2.
The
spatial
distance between the locations
in
which
two events
occur
simultaneously
is
independent
of the choice of the reference
system.
Since the Maxwell-Lorentz
theory
as
well
as
the
relativity principle
are
supported
to
a
great
extent by
experience, one
will have
to
decide
to
let
go
of the
two
just–
mentioned
arbitrary assumptions,
the
apparent
evidence for which
rests
solely
on
the
fact that
light gives
us
evidence of
events
occurring
in distant
places
in
an
apparently
instantaneous
way,
and that the velocities of bodies with which
we
have
to do in
our
everyday
experience are
small
compared
with
c.
By
giving up
these
arbitrary assumptions,
one
obtains the
compatibility
of the
principle
of the
constancy
of the
velocity
of
light
that results from Maxwell-Lorentz
electrodynamics
with the
relativity principle.
One
can
retain the
assumption
that
one
and the
same
light
ray
in
vacuum
propagates
with
velocity
c
not
only
relative
to
a
reference
system K,
but also relative
to
every
reference
system
K' in uniform
translational motion with
respect
to K.
One has
only
to
make
a
suitable choice of the
transformation
equations
that hold between the
tempero-spatial
coordinates
(x,
y,
z, t)
with
respect
to
K
to
those
(x',
y', z', t')
with
respect
to
K';
the
system
of
transforma-
tion
equations
for these four
quantities
to
which
one
is
thus led
is
called "Lorentz
transformation." This Lorentz transformation has
to
take the
place
of the
correspond-
ing
transformation
equations
that
were
considered the
only
ones
conceivable before
the
theory
of
relativity was
established,
but
were
based
on
the above
assumptions (1)
and
(2).
The heuristic value of the
theory
of
relativity
consists
in
the fact that
it
provides
a
condition that
all
systems
of
equations
that
express general
laws of
nature must
satisfy. Every
such
system
of
equations
must
be constructed in
such
a manner
that
with the
application
of
a
Lorentz transformation
it
goes
over
into
an
equation system
of the
same
form
(covariance
with
respect
to
Lorentz
transformations).
Minkowski
presented a simple
mathematical schema
to
which
equation systems
must
be reducible
[4]
if
they are
to
behave
covariantly
with
respect
to
Lorentz
transformations;
he achieved
thereby
the
advantage
that
it is not at all
necessary actually
to
perform
a
Lorentz
transformation
on
those
systems
in
order
to
accomodate these
systems
of
equations
to
the condition indicated above.
The
foregoing
clearly implies
that the
theory
of
relativity
in
no
way
provides us
with
a
tool for
deducing
previously
unknown laws of
nature
from
nothing.
It
only
provides
an
always applicable
criterion that restricts the number of
possibilities;
in
this
respect
it is
comparable
to
the
energy principle
or
the second law of
thermody-
namics.
[5]
A
careful
inspection
of the
most
general
laws of
theoretical
physics
has shown
that Newtonian mechanics
must
be modified
in
order
to
have it
correspond
to
the
criterion of
the
theory
of
relativity.
These modified mechanical
equations
have
proved