Biology Reference
In-Depth Information
Statement 2.52 is often synonymously expressed as follows:
Quons are complementary union of waves and particles.
(2.53)
Waves and particles are the complementary aspects of quons.
(2.54)
Statements 2.53 and 2.54 clearly satisfy the three criteria of the
complementarian
logic
presented in Sect.
2.3.3
, if quons are identified with the C
term, and waves and particles with A and B terms. According to complementarism
(Sect.
2.3.4
), C transcends the level where A and B have meanings. Perhaps this
provides one possible reason for the endless debates among quantum physicists
over the real nature of C, i.e., light, electrons, and other quons.
There are two kinds of waves discussed in physics - (1) what may be called
“physical waves” whose amplitude squared is proportional to the energy carried by
waves, and (2) “nonphysical” or “information waves” (also called “proxy waves,”
“quantum waves,” or “probability waves” in quantum mechanics) whose ampli-
tude squared is proportional to the probability of observing certain events occur-
ring. According to the Fourier theorem, any wave can be expressed as a sum of
sine
waves
, each characterized by three numbers - (a)
amplitude
,(b)
frequency
,and(c)
phase
. A generalization of the Fourier theorem known as the “synthesizer theo-
rem” (Herbert 1987) states that any wave, say X, can be decomposed into (or
analyzed in terms of) a sum of waveforms belonging to any waveform family,
say W, the sine waveform family being just one such example. The waveform
familyWwhose members resemble X the closest is referred to as the
kin waveform
family
, and the waveform family M whose members resemble X the least is called
the “conjugate” waveform family of W. That is, the waveform family W is the
conjugate of the waveform family M. When X is expressed as a sum of W
waveforms, the number of W waveforms required to synthesize (or describe)
wave X is smaller than the number of M waveforms needed to reconstruct X
wave. The numbers of waveforms essential for reconstructing wave X in terms
of W and M waveforms are called, respectively, the “spectral width” (also called
“bandwidth”) of W and M waveform families, denoted as
D
Wand
D
M. The
synthesizer theorem
states that the product of these two bandwidths cannot be
less than 1.
D
W
D
M
>
1
(2.55)
Inequality
2.55
is called the
spectral area code
(Herbert 1987) and can be used to
derive the Heisenberg Uncertainty Relation, since the momentum attribute of quons
is associated with the sine waveform family (with spatial frequency, k, which is the
inverse of the more familiar temporal frequency, f) and the position attribute is
associated with the impulse waveform family; these two waveform families are
conjugates of each other.
Most biologists, including myself until recently, assume that the wave-particle
duality is confined to physics where microscopic objects (e.g., electrons, protons,
neutrons) are studied but has little to do with biology since biological objects are
much too large to exhibit any wave-particle-dual properties. I present below three
pieces of evidence to refute this assumption.
