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All atoms through de Broglie waves

Realistic atomic Neon structure

*(Fig.1) "Photon" is just abstract math symbol (= a ^{†} ), without physical shape.*

Quantum mechanics claims that the classical Coulomb force is caused by photon exchange.

But **clear** mechanisms of "*attractive*" and "**repulsive**" Coulomb forces remain **unknown**.

In fact, this **photon** causing *Coulomb* force is **virtual** photon, so **NOT** real ( see this, this, this ).

Surprisingly, this **virtual** photon is superluminal tachyon, **violating** Einstein's relativity ( see this, this ).

By the way, what is the physical **shape** and *size* of a single **photon** ?

Unfortunately, quantum mechanics cannot answer this **basic** question.

In QED, these *photons* must be described using **abstract** Feynman diagram.

This Feynman QED has **NO** ability to show photon's **clear** picture at all.

All quantum mechanics can show is **meaningless** math *symbols* ( see this, this p.3 ).

It contains only **rough** actions, "a photon is **created** (= a^{†} )", or "*annihilated* (= a )". That's all, **NOT** physics.

*(Fig.2) Light frequency (= f ) equal to c/λ (= light wavelength ) proves "Wave" !*

Though almost all textbooks say photoelectric effect proposed by Einstein proved **particle** nature of "**photon**", this *far-fetched* interpretation is clearly "**brainwashing**" by textbooks.

Electrons are "**emitted**" from metals, when illuminated by *light* of higher **frequency** than some threshold, irrelevant to its intensity. So they ( this, this, this ) affirmed that light is "**particle**".

But as you know, light **frequency** (= f ) is equal to c/λ (= **wavelength** ). See this site.

"Frequency" and "**wave**length" clearly mean "**wave**" ( NOT particle ! ) nature of light.

So, the idea "photoelectric effect = light *frequency* = photon " is one of **mind-controls** by textbooks and media, like Bohr's accelerating electron ( though it does **NOT** lose energy ).

In fact, Lamb (= Nobel winner ) argued that the photoelectric effect happens without photon.

**Imaginary** "photon" is necessary for quantum field theory such as Higgs and string theory.

But these photon's **operators** (= a^{†}, this, this p.5 ) are just **abstract** math *symbols* with **NO** realistic shapes.

*(Fig.3) The wavelength of radio wave (= one of lights = photon ? ) is 1000 meter !*

About the unphysical photon, see this page.

*(Fig.4) Davisson-Germer experiment showed an electron is de Broglie wave.*

In Davisson-Germer experiment, they accelerated electrons by electric fields and made them reflected by nickel crystal.

de Broglie wavelength of an electron is gotten from the electric field strength and **interference** pattern of a *single* electron.

Experimental results **agreed** with de Broglie relation.

So **de Broglie** waves themselves are **realistic** concepts, though quantum mechanics **avoids** commenting it.

This experiment showed an single electron has *wave*-like property, in which the **opposite** wave phases **cancel** each other, and **expel** the electron.

*(Fig.5) One de Broglie wavelength of electron.*

When an electron moves, **electric** fields (= E ) around the electron also moves with it.

So this *spreading* electric field causes *de Broglie* waves, which can be confirmed by Davisson-Germer experiment.

We can naturally think this de Broglie wave is a kind of longitudinal waves through some *medium*.

If so, double slit interference can be explained by this "**real**" de Broglie waves, **NOT** by "fantasy" many-worlds.

**Longitudinal** wave consists of "*low*" (= **sparse** ) and "*high*" (= **dense** ) pressure areas.

It is thought that an electron **pushes** the field around it toward "dense" area, and is moving with "low" pressure area.

About the electron interacting with light, see this page.

*(Fig.35) de Broglie relation.*

According to de **Broglie** relation, the momentum ( p = mv ) is expressed as ( p = h/λ ).

Here, p = momentum, m = mass, v = velocity, h = Planck constant, λ = wavelength.

As shown on this site, total energy (= E ) of electromagnetic wave is linearly **proportional** to *frequency* (= f ) through the relation of **E = hf**, which is confirmed in photoelectric effects.

Surprisingly, in any **other** particles such as electrons and protons, their *frequency* is **proportional** to their total **energy**, if de Broglie relation is satisfied ! Here we explain it.

*(Fig.36) Electron is slower ( v → 1/2 v ), its wavelength becomes longer ( λ → 2λ ).*

When an electron's velocty (= v ) becomes half (= 1/2 ), its total ( kinetic ) energy (= E ) becomes **1/4** of the original value, because E is proportional to a **square** of velocity ( E = 1/2 mv^{2} ).

According to de Broglie relation ( mv = h/λ ), the electron's wavelength becomes **twice** ( λ → 2λ ), when the velocity becomes **half**.

Considering wave relation ( v = fλ ), the electron's **frequency** (= f ) becomes **1/4** of the original value in this case.

As you see, also in **electron**'s de Broglie wave, the energy is **proportional** to frequency ( E/f = constant ) !

*(Fig.37) Momentum ( p = h/λ ) is constant.*

Here we think about the case when the momentum (= p ) is **common** in both of "light" electron and "heavy" proton.

So through de Broglie relation ( λ = h/p ), their wavelengths (= λ ) are the **same**, too.

Due to **heavier** mass ( M_{p} ) of proton, the velocity (= V ) of proton becomes much **lower** than that (= v ) of electron.

So the total kinetic energy ( E = 1/2 M_{p}V^{2} ) of proton is much **smaller** than electron (= 1/2 mv^{2} ).

*(Fig.38) Energy (= E ) is proportional to frequency (= f ) in electron and proton.*

Again, through the wave relation of v = fλ, we can find the proton's frequency.

As shown in Fig.38, between proton and electron, the relation of energy (= E ) **proportional** to frequency (= f ) **holds** true.

So not only in electromagnetic wave but also in electrons and protons, the **frequency** has an **important** meaning to determine their total **energy**.

*(Fig.39) Total energy in electron and proton.*

Using Fig.37, we find the proton's kinetic energy is much smaller than electron due to its large mass, even when their momentums are the same.

*(Fig.40) Ratio of electron's to proton's masses.*

Proton (= M_{p} ) is much **heavier** ( 1836 × ) than electron's mass (= m_{e} ).

*(Fig.41) Frequency = velocity / wavelength.*

Through wave relation, we find the proton's frequency becomes much **smaller** than electron.

( Here the wavelengths ( momentums ) of electron and proton are the **same**. )

*(Fig.42) Light's energy is proportional to its frequency, too.*

It is known that light's energy is also proportional to its frequency through the relation of **E = hf**.

The important point is that the speed of the light is always **constant** "c", different from other particles.

This means there is **NO** concept such as "acceleration" in light ( and neutrino ).

When electron's ( or proton's ) wavelength changes, **both** of its velocity and momentum changes.

So the electron's frequency is inversely proportional to a **square** of wavelength, as shown in Fig.36.

On the other hand, due to **neglecting** light speed change, the light frequency is just inversely proportional to its wavelength.

As you see, de Broglie wavelength ( λ = h/p ) expresses "**contraction**" ( or expansion ) of the field by the *momentum* (= impulse ), compared to its equilibrium state, **irrelevant** to the *velocities* of various particles.

*(Fig.43) *

Here we investigate the relation between electron's frequency (= f_{e} ) and emitted light's frequency (= f ).

In Fig.43, total kinetic energy of electron (= 1/2mv^{2} ) is equal to light's energy (= hf ) **emitted** from the electron.

*(Fig.44)*

Using wave relation ( v = fλ ) and de Broglie relation ( λ=h/p ), we find that the **electron**'s ( de Broglie ) frequency (= f_{e} ) is **two times** bigger than the emitted **light** frequency (= f ).

*(Fig.45) Oscillating electron emits light and gradually loses its energy. *

In Fig.45, we think about the case in which oscillating electron **gradually** *emits* light and loses its kinetic energy.

The initial electron's frequency is equivalent to **2** × f (= emitted light frequency ), as shown in Fig.44.

The more light the electron emits, it loses more energy, and its oscillation becomes **slower** ( to be zero ).

It means the **average** electron's frequency becomes **half** of the original value (= 1/2 × f_{e} = **f** ) .

As a result, we can prove there is an **important** relation between electron's and emitted light frequencies. Planck constant (= h ) connects light and electron.

*(Fig.46) Transition from excited ( n = 2, f=4 ) state to ground state ( n =1, f = 2 ).*

In Fig.46, the excited state of 2 × de Broglie wavelength **returns** to ground state (= 1 × de Broglie wavelength ).

Accelerated by Coulomb force, the final **frequency** of *de Broglie* wave of excited **electron** becomes f = **4**.

We can think the **afterimage** of stable ground state de Broglie wave **remains** during excitation, and it is supposed to be f = **2**.

These two de Broglie frequencies before and after transition are **different**, so they **don't** fit each other.

The **crash** between these two de Broglie waves causes **swell** with the frequency ( 4-2 = **2** ), which is the **difference** between two states.

The excited de Broglie wave is **attenuated**, while it emits light.

So the **average** frequency of emitted light becomes half of 2 (= **1** ), as is explained in Fig.45.

*(Fig.47) Transition from excited ( n = 2, f=2 ) state to ground state ( n =1, f = 4 ). *

In fact, according to Virial theorem, kinetic energy T is the **absolute** value of total energy E ( T = |E| ).

As I said in Fig.36, electron's frequency (= f ) is **proportional** to its *kinetic* energy.

So the electron frequency in the upper energy level is lower than the lower level, like their kinetic energies. Also in this case, the frequency difference becomes 4 - 2 = 2, like Fig.46.

So the difference in **total** energies is just **equal** to the *difference* in **kinetic** energies (= frequency ) in these bound state orbits, which can explain photoelectric effect correctly in the **realistic** way. See this.

2015/5/17 updated. Feel free to link to this site.