370 DOC.
375
AUGUST
1917
(Tik
energy
tensor,
Aik
gravitational
tensor).
I
acknowledge
the
importance of
your objection
that
in this
way
the
energy principle
completely
loses its heuristic
value,
in that it
does not
a
priori
exclude
any
(or
almost
any) physical processes
because it
would
suffice
to
modify
the
ds2
in the
appropriate
way.
You
point
out
that
in
abandoning (1),
or
rather their
interpretation,
the
energy
contributed
by
the
field
can
be
understood
as
something
dependent
on
the
form
of
ds2,
analogous
to
what
is
done
concerning
the
concept
of
field
strength.
If
one
writes
the
equations of motion in
the
form
d
Xi ^\
j
j
l\
1
dxj
dxk
ds2
jk
l
*
)
ds ds
(2)
and
carries out
the
necessary verification,
the
analogy
between
the
right-hand
side
(which
defines
neither
a
covariant
system
nor a
contravariant
one)
and the
ordinary
concept
of
force
is
made
explicit;
in
your
view,
your
tov's
(which
do not
constitute
a tensor)
should be dealt with in
the
same way.
I have
no
objections
to
your
view; on
the
contrary,
I
am
inclined
to
assume
that
it
is
sound,
as
is
always
the
case
with the intuition
of
a
genius.
But
I
would need to
see,
in
appropriately
explicated step-by-step reasoning, how,
starting
from
(2),
one
actually
arrives at
the
ordinary concept
of force
(or
at least how
one
should
go
about
it).
I
shall
give
the
matter
more
thought
when circumstance
(or
inspiration)
is
favorable,
but
it
is
from
you
in the first
place
that
I
expect
a
solution.
As I
am
for
now
in
this
state of cautious
reserve, I
would
like
to defend
my
tensor
Aik,
at
least with
respect
to
its
logical
soundness.
Thus,
I point out
that
no
contradiction
such
as
you
believe
to
find,
exists
in the
example
of
a
pendulum
clock,[5]
considered in
two
different
systems
K and
K',
of which the
first
is stationary
(in
the
Newtonian
sense
of
the
word)
and
the
second
moves
with
constant
acceleration. You
say:
a)
with
respect
to K,
the
energy
tensor
is
zero,
because the
guv’s are
constant;
b)
but this
is not
the
case
with
respect
to
K';
on
the
contrary,
the
physical process
shows
a
transformation of
energy
into
heat.
c)
Given
the invariant
character
of
a
vanishing tensor,
the
simultaneous
occur-
rence
of
(a)
and
(b)
implies
that the
premises
are
flawed.
I object
to
(a),
because
we can
very
well
argue
that the
guv's
are
constant
outside of bodies
but
not
inside
your pendulum
clock.
Concerning
the
final
point
of
your
letter
(response 4),
it
is
not linked
to
the
particular
form of
your
tov,
if
I
understand
correctly,
but
holds
just
as
well
for
my
Aik.
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