SK nature of matter waves [3 of 3]

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THE CARRIER THEORY
Application of
new-physics.com

Application of the Carrier
Theory
In the light of the carrier
theory (see Eskade Postulate
3), the answer to de Broglie’s
wishes are quite direct and
affirmative – the electron is
being ushered into motion by
photons or phonons and
subsequently what is waving
are the photons, not the
particle itself.
This sounds simple, but in
detail it is a bit complicated.
Let us look at the story in
depth.

Eskade Postulates
Employed herein
Postulate 02 tells us that there
are two kinds of particles.
1. The first kind includes those
which are being ‘carried’ into
motion. They are passengers.
2. The others are the ‘carriers’
which send things into motion.
Postulate 03 states that in this
universe, the carriers found so far
are the photons and phonons,
and at times, the neutrinos. The
rest are carried.
At this moment, we only need to
deal with photons and phonons. Carrier
Carried or
passenger

Fairies for Photons
Photons are one of the most familiar
particles in physics. It has many properties:
Uncharged point-like quantum
Speed 𝑐𝑐
Energy ℎ𝑓𝑓 = ℏ𝜔𝜔
Momentum 𝑝𝑝 = ℎ/λ
Spin ℏ
There are also some other properties
such as polarization and helical
motions, but they will be dealt with
later. So instead of being looked at as a
point like quantum, we rather treat is
as a fairy or an angel on the quantum
scale.

A phonon also has many properties: it is a point-like quantum: speed 𝑣𝑣 similar to sound;
energy ℎ𝑓𝑓 = ℏ𝜔𝜔; momentum 𝑝𝑝 = ℎ/λ; spin not too certain, may be ℏ/2. Sounds like it
is a sibling of the photon. So we represent them by cherubs or elves.
Cherubs for Phonons

DE BROGLIE WAVE
The Eskade Concept of

The absorption of a photon
A free photon is approaching an
particle.
Before the rendezvous, the
photon has a free wavelength
𝜆𝜆γ.
The particle in question is
stationary and happens to be in
the path of the incoming photon.
It has no wave motion and no
linear motion as far as we are
concerned.
Free with long wavelength Immobile
𝜆𝜆𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
Photon Particl
e

A New Compound
It is in the Eskade theory that upon
collision, the photon is absorbed by the
particle, or rather, the two particles
coalesce together and become a
compound.
It is simply called the particle in motion,
not explicitly stating that it is a compound
made of two particles – a particle plus a
photon. It is set to motion because of the
photon content.
This is a fundamental theory never
published before.
Two particles become one
particle and move together

A Classical Particle
This is a perfect absorption.
No momentum or energy is
lost.
The momentum of the
photon becomes the
motivating agent. The photon
is the carrier and the particle
the carried.
This happens even in high
energy physics where
particles are accelerated to
high velocity in accelerators.
The compound moves as
one system and is
recognized as a single
moving particle in
current physics.

Resultant Frequency
unchanged
Though the photon is
absorbed by the particle, it is
not destroyed. It keeps on
pulsating at the same
frequency 𝑓𝑓𝛾𝛾. So its energy
remains unchanged.
The particle is now moving
and vibrating with the energy
and frequency of the
absorbed photon, that is 𝑓𝑓𝛾𝛾.
Absorbed photon
keeps on pulsating.
But since i

Resultant Wavelength
Changed – de Broglie wave
However, since the compound
particle is now slower, the
wavelength λ becomes shorter.
This new wavelength is
mistaken as the wavelength of
the particle.
It was postulated by de Broglie
in 1924 and was called the de
Broglie wave.
This was how the de Broglie
wave came into existence.
Absorbed photon keeps on pulsating
but with shorter wavelength
𝜆𝜆𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 → 𝜆𝜆𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
Photon wavelength become
particle wavelength

Diversions
My assumptions are that
in a de Broglie wave:
Firstly the wavelength is
not that of the electron,
but that of the compound.
Secondly, the momentum
is not the momentum of
the electron but that of
the photon.
And these are the true
ingredients of a de Broglie
wave.
𝜆𝜆 =
ℎ
𝑝𝑝
𝜆𝜆 =
ℎ
𝑝𝑝
Momentum of
Particle
Wavelength
of Particle
Momentum of
Carrier
Wavelength
of Carrier
Planck’s
Constant

Why couldn’t de Broglie find it?
de Broglie had tried hard to find the
nature of his waves for the most part
of his life thereafter. He could not
find it partly because he was working
most of the time along the line of
imaginary waves and mathematics.
Now that the nature is found, we can
use this new concept to explain ‘de
Broglie wave’. We can investigate
further into its properties and be able
to come to fruitful results.

WAVE-PARTICLE EQUATION
Deriving de Broglie’s

de Broglie Wave Equation
Let us have a fresh look at
de Broglie’s wavelength equation which
is:
λ = ℎ/𝑝𝑝
In the earlier days of de Broglie’s theory,
the electron (𝑒𝑒−) is the main particle in
concern. So we start our discussion with
the electron.
The Eskade Postulate 01 stated that all
particle motions are instigated by
phonons or photons, be it electrons or
any other matter.
λ = ℎ/𝑝𝑝
λ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 = ℎ/𝑝𝑝𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒
λ𝑒𝑒 = ℎ/𝑝𝑝𝑒𝑒

Eskade Carrier Postulate
By the carrier postulate (Eskade
postulate 01), and by the principle of
the conservation of energy, the
energy of the moving electron comes
entirely from the incorporated
photon. So the energy of the
composition resides with photons:
Electron kinetic energy
= Photon kinetic energy
1
2
𝑚𝑚𝑒𝑒 𝑣𝑣𝑒𝑒
2
=
1
2
𝑚𝑚𝛾𝛾 𝑐𝑐𝛾𝛾
2
2
= 𝑚𝑚𝛾𝛾 𝑐𝑐𝛾𝛾
2
1
2
2
=
1
2
𝑚𝑚𝛾𝛾 𝑐𝑐𝛾𝛾
2
Kinetic energy
of particle
Kinetic energy
of photon
2
2
Eliminating ½ from both sides

Momentum of Wave
Now 𝑚𝑚𝑒𝑒 𝑣𝑣𝑒𝑒 = 𝑝𝑝𝑒𝑒 is the momentum of the
electron; and 𝑚𝑚𝛾𝛾 𝑐𝑐𝛾𝛾
2 = 𝑓𝑓𝑓 is the energy of the
photon. So:
2
2
Becomes:
𝑝𝑝𝑒𝑒 𝑣𝑣𝑒𝑒 = 𝑓𝑓𝛾𝛾ℎ
Swapping the relevant items, we have:
𝑣𝑣𝑒𝑒/𝑓𝑓𝛾𝛾 = ℎ/𝑝𝑝𝑒𝑒
This is in accordance with the principle of
energy conservation. The photon is still
vibrating at the same frequency.
2
2
2 x Kinetic
energy of
photon
Planck energy
of photon
𝑝𝑝𝑒𝑒 𝑣𝑣𝑒𝑒 = 𝑓𝑓𝛾𝛾ℎ
𝑚𝑚𝑒𝑒 𝑣𝑣𝑒𝑒 = 𝑝𝑝𝑒𝑒 is the momentum of the
electron

The de Broglie Wave
Equation
The equation 𝑣𝑣𝑒𝑒/𝑓𝑓𝛾𝛾 gives us the
wavelength 𝜆𝜆𝑒𝑒:
𝑣𝑣𝑒𝑒
𝑓𝑓𝛾𝛾
= 𝜆𝜆𝑒𝑒
Thus the de Broglie wavelength
equation is:
𝜆𝜆𝑒𝑒 =
ℎ
𝑝𝑝𝑒𝑒
Which was proposed by de Broglie in
1924.
𝜆𝜆 𝑒𝑒 = ℎ/𝑝𝑝𝑒𝑒

Summary of de Broglie
particle-waves.
1) An electron can move because of
carrier particles such as photons or
phonons.
2) A moving electron is wave-like
because of the oscillating carrier.
3) The momentum of the electron is
the momentum of the carrier.
4) The kinetic energy of the electron is
the energy of the carrier.
5) The wavelength of a moving electron
is the shortened wavelength of the
carrier because of the heavier
electron.
Louis de Broglie (1892-1987)

Summary of Eskade
Postulates
1) Particles are moved by carrier
particles mainly photons or
phonons.
2) The vibrating nature of matter are
due to the photons or phonons as
in de Broglie waves.
3) Photons retain their vibration in
free or bound state, leading to the
principle of energy and momentum
conservations in low energy cases.

EINSTEIN’S RELATIVISTIC ENERGY
Appendix

Relativistic Energy
The momentum 𝑝𝑝 in relativistic
expression is:
𝑝𝑝 =
𝑚𝑚𝑜𝑜 𝑣𝑣
1 −
𝑣𝑣2
𝑐𝑐2
𝑚𝑚𝑜𝑜 is the rest mass of the particle;
𝑣𝑣 the velocity of the particle; 𝑐𝑐
the speed of light.
Squaring both sides:
(𝑝𝑝)2
=
𝑚𝑚𝑜𝑜 𝑣𝑣
1 −
𝑣𝑣2
𝑐𝑐2
2
We arrive at:
𝑝𝑝2
=
𝑚𝑚𝑜𝑜
2
𝑣𝑣2
1 −
𝑣𝑣2
𝑐𝑐2

Multiplying both sides by 𝑐𝑐2:
𝑝𝑝2
𝑐𝑐2
=
𝑚𝑚𝑜𝑜
2
𝑣𝑣2 𝑐𝑐2
1 −
𝑣𝑣2
𝑐𝑐2
Or:
𝑝𝑝2
𝑐𝑐2
=
𝑚𝑚𝑜𝑜
2 𝑣𝑣2
𝑐𝑐2 𝑐𝑐4
1 −
𝑣𝑣2
𝑐𝑐2
By adding and subtracting a term it
can be put in the form:
𝑝𝑝2 𝑐𝑐2 =
𝑚𝑚𝑜𝑜
2 𝑣𝑣2
𝑐𝑐2 𝑐𝑐4
1 −
𝑣𝑣2
𝑐𝑐2
=
𝑚𝑚𝑜𝑜
2 𝑐𝑐4 𝑣𝑣2
𝑐𝑐2 − 1
1 −
𝑣𝑣2
𝑐𝑐2
+
𝑚𝑚𝑜𝑜
2 𝑐𝑐4
1 −
𝑣𝑣2
𝑐𝑐2
= −𝑚𝑚𝑜𝑜
2 𝑐𝑐4 + 𝑚𝑚2 𝑐𝑐4

The term
𝑚𝑚𝑜𝑜
2 𝑐𝑐4
1−
𝑣𝑣2
𝑐𝑐2
is just the
relativistic mass m. So:
𝑝𝑝2
𝑐𝑐2
+ 𝑚𝑚𝑜𝑜
2
𝑐𝑐4
= 𝑚𝑚2
𝑐𝑐4
Or
𝑚𝑚2
𝑐𝑐4
= 𝑝𝑝2
𝑐𝑐2
+ 𝑚𝑚𝑜𝑜
2
𝑐𝑐4
which may be rearranged to give
the expression for relativistic
energy 𝑚𝑚𝑚𝑚 = 𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟:
𝑚𝑚𝑚𝑚 = 𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑝𝑝2 𝑐𝑐2 + 𝑚𝑚𝑜𝑜
2
𝑐𝑐4
= 𝑝𝑝2 𝑐𝑐2 + (𝑚𝑚𝑜𝑜 𝑐𝑐2)2

At the same time, Einstein's
theory of relativity pointed
out that for a particle like a
photon of zero rest mass
𝑚𝑚𝑜𝑜 = 0. So the relativistic
energy becomes:
𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑝𝑝2 𝑐𝑐2 + (𝑚𝑚𝑜𝑜 𝑐𝑐2)2
= 𝑝𝑝𝑝𝑝
𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑝𝑝𝑝𝑝

SK nature of matter waves [3 of 3]

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