Engineering - Molecular Theory of the Living Cell - page 139

Equation 5.44 indicates that the Airy experimental result is 100% uncertain as
to whether light is wave or a particle. In other words, the crisp answers [2], [3],
and [4] are all 100% uncertain with respect to the question whether they are true
relative to the Airy experimental data.
14. In Sect. 2.3.4 , the logical relation between the HUP and Bohr's Complemen-
tarity Principle (BCP) was substantially clarified based on a geometric argu-
ment which may be viewed as a species of the so-called table method (Ji 1991,
pp. 8-13). The result is that

The HUP presupposes Bohr's complementarity principle (BCP) and BCP can give rise to
uncertainty principles including HUP. (5.45)
Statement 5.45 may be referred to as the non-identity of the uncertainty and
complementarity principles (NUCP).

5.2.8 The Universal Uncertainty Principle

Although the quantitative form of the uncertainty principle was discovered by
Heisenberg in physics in 1926 (Lindley 2008), the essential notion behind the
uncertainty principle appears to be more general. Theoretical support for such a
possibility can be found in the so-called “spectral area code” (Herbert 1987,
pp. 87-89),

D W D M > 1 (5.46)

where D W and D M are the spectral widths (or bandwidths) of conjugate waves W
and M, respectively. A spectral width is defined as the number of waveforms into
which a wave can be decomposed. The size of a bandwidth is inversely related to
the closeness with which a wave resembles its component waveforms. Inequality
5.46 is called the “spectral area code,” since the product of two numbers (i.e.,
bandwidths D M and D W) can be viewed as an area ( vis-a`-vis lines or volumes).
When wave X is analyzed with the W prism (or software), a particular bandwidth
D W of the output W waveforms is obtained, which is an inverse measure of how
closely the input wave X resembles the members of the W waveform family.
Similarly, when X is analyzed with the M prism, another bandwidth D Mis
obtained, which is an inverse measure of how closely the input wave X resembles
the members of the Mwaveform family. Since W and M are mutual conjugates (i.e.,
polar opposites), it is impossible for wave X to resemble W and M both. Hence,
there exists some restriction on how small these two spectral widths can get for the
same input wave. Such a restriction is given by Eq. 5.46 .
To relate the spectral area code to the Universal Uncertainty Principle, it is
necessary to make two additional assumptions: (1) All human knowledge can be
quantitatively expressed in terms of waves (each wave having three characteristic
parameters, amplitude, frequency, and phase) and (2) The Fourier theorem and its