Biology Reference
In-Depth Information
of perception. We learn that these forms of perception are idealizations, the suitability of
which for reducing our ordinary sense impressions to order depends upon the practically
infinite velocity of light and upon the smallness of the quantum of action.
(2.40)
Of the five complementary pairs listed in Table
2.9
(Murdoch 1987, pp. 58-66;
Bohr 1934, pp. 19, 61, 623), the first two are the consequences of the smallness of
the quantum of action, h
10
34
¼
6.63
J s, and the third results from the
10
10
cm/s, as already indicated. What is
common to the first two (if not all) of the five complementarities may be the
dichotomy of
continuity
vs.
discontinuity
as described by Murdoch (1987, p. 46):
Bohr's view now was that when
continuity
obtains, the standard models are applicable, i.e.,
matter may be conceived of as corpuscular and radiation as undulatory; when, however,
discontinuity
prevails, the standard models break down, since they presuppose continuity,
and the nonstandard models then suggest themselves
...
. (2.41)
It is interesting to note that the
quantum of action
is implicated only in the two
margins of Table
2.9
, in the form of Inequalities
2.38
and
2.39
, but not in the
diagonal boxes. This suggests that HUP and BCP belong to two different logical
classes; i.e., one is about
measurement
(or results of measurements) and the other
about
measurability
(or measuring conditions). To understand the difference
between these two terms, it is necessary to return to Heisenberg's original explana-
tion for his uncertainty relation, Inequality
2.38
, based on his thought experiments
with the “gamma-ray microscope.”
Heisenberg describes his experiment thus (Murdoch 1987, p. 48):
At the moment of the position determination, when the light-quantum is diffracted by
the electron, the momentum of the electron is changed discontinuously. The shorter the
wavelength of the light, i.e., the more accurate the position measurement, the greater
the change in the momentum. At the moment the position of the electron is ascertained, its
momentum can be known only within a magnitude that corresponds to this discontinuous
change
constancy of the speed of light,
c
¼
3
. (2.42)
In short, Heisenberg originally thought that the reason for his uncertainty
principle resided in the discontinuous change in the trajectory of the electron due
to collision with the light-quantum. But Bohr claimed, according to Murdoch
(1987, p. 49), that:
...
[W]hat precludes the measurement of the momentum of the electron in the “gamma-ray
microscope” experiment is not the discontinuity of the momentum change as such but
rather the impossibility of
measuring
the change. What prevents measurement of the
momentum change is the indispensability of the wave model for the interpretation of this
experiment. The Compton-Simon experiment shows that the discontinuous change in
momentum can be accurately determined provided the angle of scatter of the incident
photon can be precisely determined. In the gamma-ray microscope' experiment, however,
the angle of scatter cannot be determined within an uncertainty which is less than the angle
2
y
subtended by the diameter of the lens: it is thus impossible to tell at what angle within the
angular aperture of the lens the photon is scattered;
Bohr's point is that it is the
wave-particle duality of radiation that makes it impossible to measure the momentum of
the electron: while gamma radiation may appropriately be described in terms of the particle
model, it is the indispensability of the wave model for the interpretation of the experiment
that precludes the precise measurement of the momentum of the electron.
...
(2.43)
