Physics - Molecular Theory of the Living Cell - page 33

Table 2.9 A tabular representation of the relation between the Heisenberg
Uncertainty Principle (HUP) and Bohr's Complementarity Principle
(BCP). The Planck constant, h, and the speed of light c are displayed in
the upper-left hand corner of the table to emphasize the fact that both HUP
and BCP are manifest only under the conditions where molecular
interactions play critical roles or objects under consideration move with
speeds close to that of light
h, c q p

t 1. Wave -

2. Kinematics
3. Spacetime
4. Continuity
5. Group property (superposition)
(A)

E - 1. Particle

2. Dynamics
3. Momenergy
4. Discontinuity
5.

Individuality

(B)

“momenergy” is the combination of momentum and energy that remains
invariant).
4. The continuity vs. discontinuity complementary pair may be viewed as the
philosophical basis for the wave vs. particle duality to the extent that wave is
continuous and particle is discontinuous in space.
5. The group vs. individuality complementary pair can also be viewed as a general
principle that accommodates wave vs. particle duality, if we associate wave with
superposition which presupposes more than one wave, i.e., a group of waves.

The phrase “A-B complementary pair” embodies the following notions:

1. A and B have well-defined meanings only in classical physics, i.e., in situations
where the quantum of action (i.e., the finite nonzero value of the product of
energy and time ) has no measurable effects and thus can be ignored.
2. In quantum mechanics where the quantum of action has significant effects
during the interactions between the object under observation and the measuring
apparatus, the object can no longer be described in terms of A and B but only in
terms of nonstandard, nonclassical models denoted by C in Fig. 2.5 that can be
characterized as “neither A nor B,” or as “both A and B.”
3. In relativity theory where objects under observation move at speeds close to that
of light, well beyond our ordinary experience, a similar complementarity princi-
ple may apply as pointed out by Bohr (1934, pp. 55, 98):
In both cases we are concerned with the recognition of physical laws which lie outside the
domain of our ordinary experience and which presents difficulties to our accustomed forms