DOCUMENT 375 AUGUST
1917
509
my
heart,
and
for
your very flattering
and favorable
opinion
of
the
mathematical consider-
ations in
my
latest
papers:
in
any case,
the main
credit
goes
to
you
for
opening up such
wide horizons in natural
philosophy
these
new
fields
of
research.
Now to
our
amicable
controversy.
As I believe
I
also indicated in
a
note I wrote
a
few
months
ago
to
my colleague
Grossmann,[3] I
understand
very
well
your
reluctance to
occu-
py
yourself
with the
not
very
fruitful
solution
represented
by
the
equations[4]
(1)
rik
+
Aik =
0
(i,k
=
0,1,2,3)
(Tik energy
tensor,
Aik
gravitational
tensor).
I
acknowledge
the
importance
of
your objec-
tion 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 process
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
contribut-
ed
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
mo-
tion in the form
(2)
d2x¡
ds2
dxjdxk
ds ds
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
tav
(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
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
the
vanishing
of
a
tensor, the simultaneous occurrence
of
a) and b) implies that the premises are flawed.
I object
to
a),
because
we can very
well
argue
that
the
guv
are
constant outside
of
pon-
derable
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
tav,
if
I
understand
correctly,
but holds
just as
well for
my Aik.
In
fact,
it
seems
to
me
that
one can
also obtain from
(1)
the behavior at
°°,
by
making use
of
the fact
that
the