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The Derivation of Planck’s Law
This monograph presents a method to derive Planck's law by a technique linking particle and wave action, thus resolving the dichotomy between particle and wave characteristics of electromagnetic energy propagation. In addition, the resulting template provides a "quantum lever" enabling an advanced tool for the manipulation of the nuclear electromagnetic domain.
The technique hinges on a proposed model for
photons based on a dynamic motion template of a point mass traveling in a
helical spiral pattern [1]. A cylindrical pattern results, enabling the
visualization of imaginary "contrails" left in the wake of the point
mass.
The cylinder produces a
radius, r. Due to coupled forward action, the point mass synchronizes the
superimposed circular motion such that the forward velocity, VF, is
equal to the speed of light, c. In
addition, the tangential velocity, VT, is also equal to the speed of light, c.
Therefore, when viewed from the side, the pattern of the point mass scribes into
a perfect sine wave.
The circumference of the
cylinder is 2pr
and equals the wavelength, l,
of the forward sine wave because one wavelength travels in the same time as
one circumference. The circumference view projects on the imaginary cylinder or
the so-called “barrel” view. Pictorially, the model follows: 
An oblique view enables a
descriptive view of the helical spiral in Figure 1. When viewed from the side at
a right angle, a sine wave results as follows:
Animated
view of particle to wave motion
The dimension, C, denotes the circumference
of the cylinder scribed by the helical spiral in Figure 1, whereas, c represents
the speed of light. One period of revolution in Figure 1 equals one period
of the sine wave in Figure 2. The frequency, f, equals the reciprocal of the
period, 1/T. In the axial view of the spiral, the circumference, C, equals the
wavelength, l,
because the point mass scribes one revolution in the same time one wavelength is
traveled. We know this
certainly because equal perpendicular velocities generate a perfect spiral
pattern.
Hence:
C = l
(where C is the circumference)
The conservation of angular
momentum applies to the circular motion about the axis of travel. Therefore, a
mass, m, "initializes," light particle. Specifically, we combine radius, r, of the circle tangent to the
forward motion, and the velocity of light, c, to obtain:
mvr = constant
or:
mcr = constant
Since 2pr
is the circumference, C, which is also the wavelength, l.
of the forward
Motion, we have:
mcr = mcl/2p
= constant
mcl
= 2pr
· constant
We denote the constant
as h,
or Planck's constant in angular form
2pr
· constant = 2ph
Since 2ph
also a constant, we set this equal to Planck' s constant:
h = 2ph
Then:
mcl
= h
(Heisenberg's Uncertainty Principle)
Recalling that c = lf,
we have:
mcl
= mcc/f = h
mcc/f= h
mc2 = hf
We recognize that mc2
is the total energy so:
E =mc2 =hf
The total relativistic
energy sums from the tangential component and the forward component:
˝ mc2 +
˝ mc2
= mc2
In the helical spiral
pattern, connected streams of particles produce sinusoidal light waves such as
radio waves. Polarization occurs when the top dead center of the spiral orients
in a synchronized pattern. Interference, diffraction and refraction produces
wave pattern modes scribed out by the underlying particles. The model provides a
connection between the wave and the particle. No longer are the two modes of
nature considered "dichotomous"
phenomena [2].
1.
Gryzinski, M., "Spin-Dynamical Theory of the Wave-Corpuscular
Duality", International Journal of Theoretical Physics, Vol. 26,
No.10, 1987, pp. 967-980.
2.
Englert, B.G., Scully, M. 0., Walker, H., "The Duality in Matter and
Light", Scientific American, December 1994, pp. 86-90.
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