© J.L. Gaasenbeek, B.Sc., P.Eng. 1990

__ABSTRACT__

It is proposed that: relativistic particles continue to gain kinetic energy in a particle accelerator, not because of an increase in their inertial mass, but because they travel along a helical path; all electromagnetic radiation consists of helical wave photons; electric currents consist of helical wave electrons.

__THE DUAL NATURE OF RELATIVISTIC PARTICLES__

As of today, physicists still have not been able to explain how light can behave like a stream of particles (photons) and at the same time can also behave like a wave, which has a frequency, wave length and amplitude.

Consequently, the best that can be done to describe the dual nature of
light is to use the particle model to explain some of the experimental
results and the wave/ether model to explain the rest.^{(1)}
Another mystery that confronted physicists early this century is nicely
summed up in the "Ultimate Speed Experiment".^{(2)} This experiment shows
how the kinetic energy of electrons that have been accelerated by a
Van de Graaf machine increases out of all proportion to their speed, as
they approach the speed of light C. In other words: V^{2}, as a function
of the kinetic energy of the electrons, appears to become infinitely
large as V approaches C. Of course, the reason V^{2} was plotted as a
function of the kinetic energy of the electrons is that Newtonian
mechanics state that the kinetic energy of a moving particle is equal to
1/2 mV^{2}, where m stands for the inertial mass of the particle.

However, since the experiment showed conclusively that the linear speed
of the electrons never exceeded C and since Einstein had shown that
energy (e) can be converted into mass (m) and vice versa, as expressed in
his famous formula e = mc^{2}, it was concluded that somehow the inertial
mass of the electrons increased as they approached the speed of light
C^{(3)}, as follows:

where:

m_{o} equals the rest mass; and

m_{v} the relativistic mass of the electron.

Exactly how a "relativistic particle" increases its mass when it is speeded up, only to lose it again, when it is slowed down, has never been satisfactorily explained.

Moreover, the relativistic electrons, similar to photons, behave both as particles and as waves. They also emit synchroton radiation, which is the "back e.m.f.", which prevents the accelerator from further accelerating the particles once they have attained a given maximum speed.

Again, "the difficulty, of course, is that the two concepts, waves and
particles, are so very different that they seem to exclude each
other". ^{(4)}
Eventually, Niels Bohr "resolved" the problem by means of his
"complementary principle", which states that: "The wave and particle
natures of either matter or radiation complement each other. It is not
possible to demonstrate an exclusive wave or particle nature of either
matter or radiation. Both models are required".^{(4)} Or, to paraphrase
Niels Bohr and others: the very nature of quantum mechanics is illogical
and consequently, one should not even try to find a rational
explanation. So much for science!
Interestingly, Einstein never agreed with Bohr's complementary principle,
a dispute which remains unresolved until this day.

__THE HELICAL PARTICLE WAVE__

Eventually, it occurred to me that in every instance when we talk about
waves, we assume that they require a medium to travel through. If we
throw a rock into the water, the waves it creates travel along the
surface of the water, momentarily moving the water molecules up and down
as they pass. Similarly, sound waves cannot travel through a vacuum,
i.e. there are no such things as sound particles.
Light, on the other hand, behaves quite differently. It travels best
through a vacuum and consists of a stream of particles called photons.
It finally occurred to me that the only way moving particles could form a
wave in a vacuum is if they followed a helical path, i.e. they form a
three-dimensional sine wave.^{(5)}

Figure l shows an isometric view of a helical particle wave.

__Figure 1__

* Isometric view of a helical particle wave*

For example, in case of a relativistic proton, it shows how its helical
velocity (V_{h}) can reach a multiple of C, as its linear velocity
component (V_{1}) approaches C. It also explains how particles can behave
like waves without the need for a medium to travel through. In fact, the
helical photon wave model explains all the characteristics of light, such
as:

(l) Light travels in straight lines.

(2) Interference and diffraction effects.

(3) Polarization of light.

(4) Light velocity independent of source velocity in a given electromagnetic frame of reference.

(5) Speed of light greater in air than in water.

(6) Fizeau's and Airy's experiments.

(7) Stellar aberration (Bradley).

(8) Michelson-Morley experiment.

(9) The Compton effect.

(10) Light travels through a vacuum.

It follows from Figure l that the square of the helical speed of a
relativistic particle is equal to the square of its linear velocity
component, plus the square of its peripheral velocity component, or

You will notice that the direction in which the helical wave particle
travels changes continuously, i.e. the helical wave __velocity__ of the
particle changes continuously, whereas its __speed__ and angular velocity
remain constant.

Not only does the helical particle wave concept explain all the characteristics of light, etc., by means of a single model, but it allows one to calculate the exact position, velocity and spin of any relativistic particle without the need for such dubious concepts as:

- Einstein's time dilation and relativistic mass,

- Heisenberg's uncertainty principle, or

- Bohr's complimentary principle.

It next occurred to me that there must be a simple relationship that
exists between the helical speed (V_{h}) of a helical wave particle, its
peripheral speed (V_{p}) and its linear speed (V_{l}) in relation to the
speed of light (C).

Based on the experimental fact that the helical speed of a relativistic
particle tends to become infinitely large as its linear speed approaches
C, assuming that the mass of the particle remains constant, the following
formula suggests itself:

If we equate formula [2] with [3], we get a most surprising and encouraging
result as follows:

Since we are only dealing with the absolute values of V_{p}, V_{h} and V_{l},
we can dispense with the vector and numerical symbols.

In other words, it is not the mass of a relativistic particle that increases by a factor of but its helical speed!

That is to say, the momentum P of a (relativistic) helical wave particle is equal to:

[5] instead of:

This explains why physicists were able to calculate the correct answer, even though their understanding of the physical phenomenon was incorrect.

The kinetic energy K_{h} of a relativistic particle as a function of its
helical wave parameters is as follows:

where:

m = mass of h.w. particle

v = linear velocity component of the h.w. particle

A_{h} = helical wave amplitude of the particle

f_{h} = helical wave frequency of the particle

r = radius of the particle

f_{s} = spin frequency of the particle.

You will notice that in the above formula [6] the first term:

1/2 mV^{2} = the linear kinetic energy,

the second term:

= the peripheral kinetic energy,

and the third term:

= the spin kinetic energy
of the helical wave particle.

Finally, the wave length of the h.w. particle is equal to:

In summary, the wave length and frequency of a helical wave particle, of
given kinetic energy, depend on its temperature (which is a function of
f_{s}) and its helical wave amplitude.

__WHY RELATIVISTIC PARTICLES FOLLOW A HELICAL PATH__

At low velocities Newton's law F = ma [8] applies. However, once the speed of the particle that is being accelerated approaches the speed of light, equation [8] no longer applies for two reasons:

(l) The electromagnetic or electrostatic fields used to accelerate the particle can only travel at the speed of light C; i.e. you cannot carry a stone faster than you can run, but you can swing it around by a string as you run.

(2) The h.w. particle cannot travel faster than the electromagnetic radiation it emits in a given electromagnetic frame (or field) of reference (EFORS will be discussed in a future paper); i.e. you cannot cross the light barrier.

Consequently, when a particle is being accelerated, the only way in which it can increase its kinetic energy, once it reaches a relativistic speed, is to increase its helical velocity and/or its temperature or spin velocity. Accordingly, once it becomes a helical wave particle, it will

have:

- a linear momentum
- a peripheral or orbital momentum
- a spin momentum
- and a spinaxis angular momentum.

Consequently, the h.w. electron will continue to follow a helical trajectory, as it travels through a vacuum after it leaves the particle accelerator, because it cannot convert its peripheral, spin and spinaxis angular momentum into an increased linear momentum, because it is already traveling at a speed which approaches its maximum possible speed of C.

As a result, the gyroscopic (sideways) force, generated by the precessing
spin axis of the particle,^{(6)} will continue to act upon the particle
causing it to maintain its helical path. The same holds for any h.w.
particle, whether it carries an electrical charge or not.

That is to say, in case of a helical wave electron, we may alter its helical wave frequency, wave length, amplitude and spin velocity by means of a magnetic lens, but it will remain a helical wave electron whose total energy stays substantially the same. Only if we slow the h.w. electron down to the point where it travels at a fraction of the speed of light, will it decay into a linear spinning electron, in which instance its dying peripheral momentum is converted into additional spin. Or, to put it in baseball terms: were a pitcher able to throw a baseball at a relativistic speed while standing on the moon, the ball would follow a helical trajectory, even though the moon has no atmosphere.

__PROPOSED NUCLEAR FUSION REACTOR__

Electromagnetic radiation such as a beam of light or a beam of deuteron
atoms that have been accelerated by means of a particle accelerator, are
both complex helical particle waves. They consist of multiple
counter-rotating concentric helical particle waves of different
frequencies that together form a particle beam, such that the helical
wave frequency (f_{h}) of each concentric h.p.w. is inversely proportional
to its helical wave amplitude (A_{h}).

An ordinary light beam, which is a complex helical photon wave, usually will not interfere with another similar light beam. However, if a monochromatic light source such as a laser is used, its light beam will readily interact with another laser beam, providing both beams are of the same frequency and are properly phased.

Consequently, it is proposed that two helical deuteron beams of the same frequency can also be made to interact, causing the deuterons to fuse.

Such an "inertially confined, helical deuteron wave, nuclear fusion reactor" would consist or four deuteron beams, each of which intersects the other three beams at the same l09.47 degree angle. Each helical wave deuteron beam would be fine tuned by means of a direct current electromagnetic lens. Since each beam would induce a ripple in the direct current that powered its magnetic lens which is indicative of its frequency, this feedback signal could be used to adjust the current through each lens such that each beam had the same frequency.

The helical wave deuteron beams would be aligned and properly phased by electrostatic x and y plates.

Ideally, the frequency of the deuteron beams (or the ^{3}He beams) should
match their optimum (resonance) frequency at which nuclear fusion will
most readily occur.

How do we know that this is going to work?

The fact is that these kind of collisions have already been observed, although their significance was not realized at the time.

In their article, "High Energy Collisions Between Atomic Nuclei"^{(7)},
W.M.C. McHarris and John O. Rasmussen, list a series of unexplained
phenomena related to anomalons (heavy relativistic atoms), all of which
are readily explained when we think of anomalons as helical wave atomic
nuclei.

One of their findings was that anomalons will readily collide with other particles. This, of course, is not surprising as a helical wave particle has a much larger "collision cross-section" than a linear wave particle.

McHarris and Rasmussen go on to make the following statement:

"At lower energies the colliding nuclei can be in contact for a period of time, many orders of magnitude longer than the time it takes a nucleus to vibrate or the time it takes a relativistic particle to travel the diameter of a nucleus. Hence, in even a grazing encounter, two low-energy nuclei have opportunity to fuse or partially fuse."

Consequently, tuned h.p.w. collisions satisfy Lawson's criteria^{(8)} for
nuclear fusion of: high density, high temperature (high kinetic energy)
and long confinement time. Moreover, the proposed reaction is a highly
efficient one since each h.w. deuteron is tuned to meet its counterpart.

The result will be an artificial star whose luminosity will depend on the density of the deuteron beams. Containment and removal of heat should not prove a problem as the spherical vacuum chamber, that houses the fusion star, can be made any convenient size.

In summary, start-up or shutdown of the fusion reactor should be instantaneous. The power developed can be readily controlled by varying the density of the deuteron beams and radioactive by-products should be minimal.

__HELICAL WAVE ELECTRONS AS RELATED TO SUPERCONDUCTIVITY__

If we compare an electrical circuit to a hydraulic one, we realize that the pump does not create the water, it merely pumps the water around which is already in the pipe.

Similarly, an electrical generator does not create the electrons, it merely pumps the electrons around which are already in the electrical conductor.

In other words, we can compare an electrical conductor to a pipe filled with ping pong balls from one end to the other, even when no current flows through the conductor.

However, the moment we push one extra ping pong ball in at one end, all the balls move over one ball diameter, which causes one ping pong ball to drop out the other end. Consequently, the ball we pushed into one end of the pipe is a different ping pong ball from the one that fell out the other end.

So, in the case of an electrical conductor, what do the ping pong balls consist of? In a copper wire, each copper atom has a pair of outer thermal electrons which are loosely coupled to it as compared to its other electrons, which is why a copper atom has a 2+ valence. Like the ping pong balls, when an electrical current is made to flow through the wire, as two electrons are pushed in one end two come out the other end, as each pair of orbital electrons has moved over from one copper atom to the one next to it. The temperature of the copper atoms is a function of how fast they vibrate in their fixed position. This in turn depends on how fast the two thermal electrons orbit their respective copper atoms. Infrared electromagnetic radiation consists of helical wave photons of a given frequency. When they interact with the thermal electrons they cause them to speed up which, in turn, causes the copper atoms to vibrate faster with the result that their temperature increases. Conversely, should the thermal electrons radiate more infrared helical wave photons than they receive, the copper atoms will slow or cool down, since all fast moving electrons radiate electromagnetic radiation.

Now, since the thermal electrons make up the electric current which flows through the copper wire, it follows that the electrons will continue to orbit the copper atoms as they pass them by. In other words, they travel along a helical path!

After all, just because two orbital electrons jump from one copper atom to the next one, does not mean that they give up their angular velocity or, for that matter, their spin. (The only time this would happen is if the conductor is cooled down close to absolute zero degrees, in which case, the orbital velocity and spin of the thermal electrons is minimal to start with.)

In summary, the above leads us to the inescapable conclusion that all electrical currents consist of helical wave electrons, because if we add a linear velocity component to an electron which is already traveling in a circle, the resulting trajectory will be helical, i.e. the two thermal copper electrons will describe a double helix.

Normally, when an electrical current flows through a copper conductor, the copper atoms are so closely spaced and the orbital velocity of the thermal electrons is so great at room temperature, that the resulting high frequency helical wave electrons give off energy to the vibrating copper atoms, as they are forced to zig zag through them. Or, to put it in familiar terms, the electrical resistance of the conductor to the flow of electrons causes the conductor to heat up. However, if the copper atoms were arranged to be in line with each other, as well as regularly spaced, the helical wave electrons would not have to zig zag through the conductor and could be tuned to the copper matrix, by lowering the temperature of the conductor, so there is no exchange of energy between the helical wave electrons and the copper atoms.

That is to say, if the helical wave frequency of the electrons matches the thermal frequency of the copper atoms and the wave length of the helical wave electrons matches the distance between the copper atoms, there will be no exchange of energy between the electrons and the copper atoms.

In a sense, the copper atoms would not be able to tell the difference between their own orbital thermal electrons, when there was no electrical current flowing and the passing helical wave electrons when an electrical current did flow through the copper conductor. Finally, the same electrostatic attraction between the positively charged copper atoms and the negatively charged electrons (as well as other forces) which cause them to orbit the copper atoms when no current is flowing, prevents the helical electron waves from disintegrating.

The net result is a total lack of electrical resistance (superconductivity).

__CONCLUSIONS__

The helical particle wave theorem explains many physical phenomena for which no logical explanations currently exist. It also raises several new questions, some of which I hope to address in future papers.

__REFERENCES__

(l) A.P. French, Special Relativity, Table 2-1, Page 58, Evidence Bearing On The Nature Of Light.

(2) A.P. French, Special Relativity, Pages 6 to 11, Ultimate Speed Experiment.

(3) A.P. French, Special Relativity, Figures 1-5, Page 23, Variation Of Enertial Mass With Speed For Electrons.

(4) Halliday and Resnick, Second Edition, Fundamentals Of Physics, Page 811.

(5) J.L. Gaasenbeek, Abstract: Foundation For Proposed Theorems Of relativity (2), Speculations In Science And Technology, Volume 9, Number 4, 1986.

(6) Higdon and Stiles, Engineering Mechanics, Page 530.

(7) McHarris and Rasmussen, Scientific American, January 1984.

(8) Halliday and Resnick, Second Edition, Fundamentals of Physics, Page 927.

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