98
What
does
it mean?
the
momentum
of
the box.
How
docs this affect the weighing?
The
uncontrollable
transfer
of
momentum
to
the box causes
it
to
jump
about
unpredictably.
Although
we can
fix
the box's instantaneous position
against
the scale, the sizeable interaction during the act
of
measurement
means that the box
will
not
stay in
that
position. Bohr argued that
we
can
increase the precision
of
measurement
of
the average position by
allowing ourselves a long lime interval in
which
to
perform the whole
balancing procedure.
This
will give
uS
the necessary precision in the
weight
of
the box. Since we
can
antidpate
the need for this, we can set
the
dock
mechanism so
that
it
opens
the shutter after the balancing
procedure has been completed.
Now
comes Bohr's
coup
de grace. According to Einstein's general
theory
of
relativity, the rate
of
a clock moving
in
a gravitational field
changes,
and
so the very act
of
weighing a clock effectively changes the
way
it keeps time. This
phenomenon
is
responsible for the red shift in the
frequency
of
radiation emitted
from
the sun
and
stars. Because the box
is
jumping
about
unpredictably in a gravitational field (owing
to
the act
of
measuring the position
of
the pointer), the rate
of
the clock
is
changed
in a similarly unpredictable
manner.
This introduces an uncertainty in
the exact timing
of
the opening
of
the shutter which depends on the
length
of
time needed
to
weigh
the
box.
The
longer
we
make the balanc-
ing
procedure (rhe greater the ultimate precision
in
the measurement
of
the energy
of
the
photon),
the greater the uncertainty in its exact moment
of
release. Bohr was able
to
show
that
the
relationShip between the uncer-
tainties
of
energy
and
time is in accord with the uncertainty principle.
This
response was hailed as a triumph for Bohr and for the Copenhagen
interpretation
of
quantum
theory. Einstein's own general theory
of
relativity had been used against him.
However,
Einstein remained stubbornly uneonvinct'd, although he
did change the
nature
of
his attacks
on
the theory. Instead
of
arguing
that
the theory
is
inconsistent, he began
to
develo~.!.L!.tI1!'!·-
~~
behe~<:.<!...~ons~
its
inconjjjJifien~
When discussing the
photon
hox experlment. Einstein conceded
that
it now appeared to be
'free
of
contradictions',
but
in·
his view it still contained
'3
certain
unreasonableness' .
We should
not
leave the
photon
box experiment without noting
that
many physicists, including Bohr, have since examined it over again in
considerable
detail. Some have rejected Bohr's response completely,
denying that the uncertainty principle can be 'saved'
in the way Bohr
maintained.
Others have rejected Bohr's response but have given alter-
native reasons why the uncertainty principle
is
not invalidated. DespIte
these counterproposals, the prevailing view
in
the physics community at
the
lime appears to be that
Bohr
won this particular round in his debate