Physics - Molecular Theory of the Living Cell - page 32

Table 2.8 Two kinds of complementarity in physics. The quoted phrases are from Murdoch
(1987, p. 67)
Complementarity Classical mechanics Quantum mechanics

Wave vs. particle “Fall apart” “Come together”

( Logical incompatibility)
Position vs. momentum

“Go together” “Fall apart”

Spacetime vs. momenergy
Kinematics vs. dynamics
( Empirical or epistemic incompatibility )

Kinematic and dynamic attributes in quantum mechanics are mutually exclusive in the
sense that they cannot be simultaneously measured; they are, in this sense, espistemically
incompatible.
As pointed out by Bohr (1934, p. 60), it is only in classical physics that
momentum and energy can be measured precisely on the basis of spatio-temporal
measurements (i.e., space and time “go together” with momentum and energy). In
quantum physics, where effect of the quantum of action is large enough to be
negligible, these properties are no longer deterministically related and hence “fall
apart” (Murdoch 1987, p. 67).
The Heisenberg uncertainty relations/principle can be expressed in two equiva-
lent forms (Murdoch 1987):

ðÞD p D q ðÞ h = 2 p (2.38)

ðÞD E D t ðÞ h = 2 p (2.39)

where D q, D p, D t, and D E are the uncertainties about the position, momentum, time,
and energy associated with moving objects, respectively, and h is the Planck
constant. As evident in these equations, the two horizontal pairs, namely, q and
p and t and E, are related by Heisenberg uncertainty principle, while the two vertical
pairs, namely, q and t and p and E, are related kinematically and dynamically ,
respectively (Table 2.5 ) (Murdoch 1987, pp. 80-85).
We can represent these relations diagrammatically as shown in Table 2.9 , where
the Heisenberg uncertainty principle appears in the margins - the horizontal margin
for the q and p conjugate pair, and the vertical margin for the t and E conjugate pair.
Thus, we may refer to Eqs. 2.38 and 2.39 as the horizontal uncertainty principle and
the vertical uncertainty principle , respectively. In contrast, Bohr's Complementar-
ity Principle appears as a diagonal in the interior of the table. There are six
complementary pairs listed in the diagonal boxes in Table 2.9 that are related to
Bohr's complementarity concept:

1. The wave-particle complementary pair (Murdoch 1987, pp. 58-61).
2. The kinematic-dynamic complementary pair (Murdoch 1987, pp. 80-88).
3. The spacetime-momenergy complementary pair (just as “spacetime” is the
combination of space and time that remains invariant in general relativity, so