SK nature of matter waves [3 of 3]

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THE CARRIER THEORYApplication of

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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 𝑐𝑐Energy ℎ𝑓𝑓 = ℏ𝜔𝜔Momentum 𝑝𝑝 = ℎ/λSpin ℏThere 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 WAVEThe 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 Particle


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 → 𝜆𝜆𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝Photon 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 =ℎ𝑝𝑝

𝜆𝜆 =ℎ𝑝𝑝

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 EQUATIONDeriving 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

λ𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = ℎ/𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

λ𝑝𝑝 = ℎ/𝑝𝑝𝑝𝑝


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

12𝑚𝑚𝑝𝑝𝑣𝑣𝑝𝑝2 =

12𝑚𝑚𝛾𝛾𝑐𝑐𝛾𝛾2

𝑚𝑚𝑝𝑝𝑣𝑣𝑝𝑝2 = 𝑚𝑚𝛾𝛾𝑐𝑐𝛾𝛾2

12𝑚𝑚𝑝𝑝𝑣𝑣𝑝𝑝2 =

12𝑚𝑚𝛾𝛾𝑐𝑐𝛾𝛾2

Kinetic energy of particle

Kinetic energy of photon


Eliminating ½ from both sides


Momentum of Wave

Now 𝑚𝑚𝑝𝑝𝑣𝑣𝑝𝑝 = 𝑝𝑝𝑝𝑝 is the momentum of the electron; and 𝑚𝑚𝛾𝛾𝑐𝑐𝛾𝛾2 = 𝑓𝑓ℎ is the energy of the photon. So:


Becomes:𝑝𝑝𝑝𝑝𝑣𝑣𝑝𝑝 = 𝑓𝑓𝛾𝛾ℎ

Swapping the relevant items, we have:

𝑣𝑣𝑝𝑝/𝑓𝑓𝛾𝛾 = ℎ/𝑝𝑝𝑝𝑝

This is in accordance with the principle of energy conservation. The photon is still vibrating at the same frequency.


2 x Kinetic energy of photon

Planck energy of photon


𝑝𝑝𝑝𝑝𝑣𝑣𝑝𝑝 = 𝑓𝑓𝛾𝛾ℎ𝑚𝑚𝑝𝑝𝑣𝑣𝑝𝑝 = 𝑝𝑝𝑝𝑝 is the momentum of the electron


The de Broglie Wave Equation

The equation 𝑣𝑣𝑝𝑝/𝑓𝑓𝛾𝛾 gives us the wavelength 𝜆𝜆𝑝𝑝:

𝑣𝑣𝑝𝑝𝑓𝑓𝛾𝛾

= 𝜆𝜆𝑝𝑝

Thus the de Broglie wavelength equation is:

𝜆𝜆𝑝𝑝 =ℎ𝑝𝑝𝑝𝑝

Which was proposed by de Broglie in 1924.


𝜆𝜆𝑝𝑝 = ℎ/𝑝𝑝𝑝𝑝


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 ENERGYAppendix


Relativistic Energy

The momentum 𝑝𝑝 in relativistic expression is:

𝑝𝑝 =𝑚𝑚𝑝𝑝𝑣𝑣

1 − 𝑣𝑣2𝑐𝑐2

𝑚𝑚𝑝𝑝 is the rest mass of the particle; 𝑣𝑣 the velocity of the particle; 𝑐𝑐the speed of light.

Squaring both sides:

(𝑝𝑝)2=𝑚𝑚𝑝𝑝𝑣𝑣


2

We arrive at:

𝑝𝑝2 =𝑚𝑚𝑝𝑝2𝑣𝑣2



Multiplying both sides by 𝑐𝑐2:

𝑝𝑝2𝑐𝑐2 =𝑚𝑚𝑝𝑝2𝑣𝑣2𝑐𝑐2


Or:

𝑝𝑝2𝑐𝑐2 =𝑚𝑚𝑝𝑝2 𝑣𝑣2𝑐𝑐2 𝑐𝑐

4


By adding and subtracting a term it can be put in the form:

𝑝𝑝2𝑐𝑐2 =𝑚𝑚𝑝𝑝2 𝑣𝑣2𝑐𝑐2 𝑐𝑐

4


=𝑚𝑚𝑝𝑝2𝑐𝑐4 𝑣𝑣2

𝑐𝑐2 − 1


+𝑚𝑚𝑝𝑝2𝑐𝑐4


= −𝑚𝑚𝑝𝑝2𝑐𝑐4 + 𝑚𝑚2𝑐𝑐4


The term 𝑚𝑚𝑜𝑜2𝑝𝑝4

1−𝑣𝑣2

𝑐𝑐2

is just the

relativistic mass m. So:

𝑝𝑝2𝑐𝑐2 + 𝑚𝑚𝑝𝑝2𝑐𝑐4 = 𝑚𝑚2𝑐𝑐4

Or

𝑚𝑚2𝑐𝑐4 = 𝑝𝑝2𝑐𝑐2 + 𝑚𝑚𝑝𝑝2𝑐𝑐4

which may be rearranged to give the expression for relativistic energy 𝑚𝑚𝑐𝑐 = 𝐸𝐸𝑝𝑝𝑝𝑝𝑝𝑝:

𝑚𝑚𝑐𝑐 = 𝐸𝐸𝑝𝑝𝑝𝑝𝑝𝑝 = 𝑝𝑝2𝑐𝑐2 + 𝑚𝑚𝑝𝑝2𝑐𝑐4

= 𝑝𝑝2𝑐𝑐2 + (𝑚𝑚𝑝𝑝𝑐𝑐2)2


At the same time, Einstein's theory of relativity pointed out that for a particle like a photon of zero rest mass 𝑚𝑚𝑝𝑝 = 0. So the relativistic energy becomes:

𝐸𝐸𝑝𝑝𝑝𝑝𝑝𝑝 = 𝑝𝑝2𝑐𝑐2 + (𝑚𝑚𝑝𝑝𝑐𝑐2)2

= 𝑝𝑝𝑐𝑐

𝐸𝐸𝑝𝑝𝑝𝑝𝑝𝑝 = 𝑝𝑝𝑐𝑐

SK nature of matter waves [3 of 3]

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