Re: Helical Particle Waves.


(See PS added below original reply.)

Subject: Helical Particle waves.
See: "http://www2.rideau.net/gaasbeek"; 'Selected Papers', Helical Particle
Waves, formula [3].


> Hello Sir,
>
> I really beleive that the mechanism governing EM waves is quite close to
the
> helical model you suggest. It surely makes more sense than what is
currently
> the accepted model.
>
> However I do have problems understanding how you arrived at the relation
shown
> here:
>
> "http://www2.rideau.net/gaasbeek/f1_3.gif";
>
> I would be very pleased if you can clarify this equation for me.
>
> Thanks in advance
> -------
>
............................................................
To -------,

In answer to your question above, I concluded that the kinetic energy of a
relativistic particle which is accelerated closer and closer to the speed of
light c continues to increase, not because its 'relativistic mass' increases
but because it continues to increase its speed by increasing its peripheral
speed.

That is to say, even though the helical wave particle can't travel or
progress through space at a speed greater than c, its helical speed can
increase to a speed greater than c as it is a combination of its linear AND
peripheral speed. Of course its helical wave VELOCITY continuously changes,
since it continues to change DIRECTION as it follows its helical trajectory.
However the kinetic energy of the relativistic particle is a function of its
speed, regardless of its direction, since k = 1/2 m v^2.

Now we know that the kinetic energy of the helical wave particle approaches
infinity as its linear velocity approaches c. Since its linear speed is
limited to c this means that its peripheral speed must become infinitely
large for its helical speed to become infinite. This means that for
practical purposes its helical speed approaches its peripheral speed when
its linear speed approaches c, since the peripheral speed contributes the
lion share to its kinetic energy.

Or as v(linear) approaches c, v(helical) approaches v(peripheral).
Or, v(linear) / c = v(peripheral) / v(helical) [3]

Now the above tends to hold for long helical waves of low frequency.
In reality the most energetic helical wave particles tend to be of high
frequency and short wave-length and amplitude. So how do these particles
continue to gain kinetic energy as they are accelerated, since their
peripheral speed tends to approach zero?

The explanation is that all helical wave particles spin around their own
axis as they travel along.
Long wave, low frequency helical wave particles spin relatively slowly
around their axis.
Short wave, high frequency helical wave particles spin rapidly around their
own axis.

Since the spin of a particle contributes to its kinetic energy, in the case
of a high frequency
helical wave particle, its spin contributes most to its kinetic energy
rather than its nearly none existent peripheral speed.

By the way, the sideways gyroscopic force the relativistic helical wave
particle exerts on itself is a function of the rate at which it spins around
its own axis and the rate at which its axis gyrates (the two are
inter-related since the latter is equal to its helical wave frequency) as it
travels along. Consequently, the higher the spin of a relativistic
particle, the smaller its amplitude and peripheral speed.

See formula [6].

Enjoy, Len.
.............................................................

PS: If we look at the electromagnetic spectrum it shows that for a given
frequency we get a given corresponding wavelength.
For example for a frequency of say 10^1.5 Hz. we get a corresponding
wavelength of around 10^7 meters or 10 km.

Next let us suppose that the amplitude of the wave (defined as the radius
of the helical photon wave trajectory) equals its wavelength.
Since the circumference of a circle is 2pie times its radius, it follows
that
the peripheral speed of each e.m. (helical wave) photon is 2pie or 6.28
times
the speed of light c.

The helical wave speed of the photon is equal to the square root of
(1c^2 + 2pie c^2) = 9.91 c. or about 9.91 times the speed of light.

Accordingly, when the amplitude of a long electromagnetic wave equals its
wavelength, the lion share of the kinetic energy of the photon is due to its
peripheral speed rather than its linear speed by a factor of 9.91 squared to
1 squared, or about 100 to one!

Enjoy, Len.
.............................................................................
....


.

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