Youhei Tsubono

Setagaya-ku Tokyo 155-0033, Japan

♦ Japanese version ♦

New Bohr's worlds (atoms, molecules,bonds.) (13/ 10/16 new!)

♦ End of Quantum mechanics ! ( Fine structure, Sommerfeld, General relativity ) (12/ 12/30 new!)

♦ Bell inequality violation is an illusion. ( Delayed choice, Quantum computer is real ? ) (13/ 1/29 new!)

♦ End of Quantum field theory (QFT). (Dirac equation, Quantum electrodynamics, Higgs ) (13/ 1/20 new!)

Journal Nature's Bohr model. (14/ 4/13)

Criticize top journals. (14/ 4/24)

- Many worlds = Quantum mechanics is fantasy.
- Reason why Quantum Mechanics is wrong.
- All relativistic quantum field theories are false.
- de Broglie wave interference and Coulomb force.
- Calculation of New Bohr's helium. ( JAVA, C, Python. )

*(Fig.1) Quantum mechanics = Many worlds = Fantasy.*

Quantum mechanics only shows the vague **probability** density of a particle.

The instant we try to observe a particle, the probability wavefunction spreading all over the space **collapses** into **one** location.

There are **three** major interpretations (= Copenhagen, many-worlds, Bohm ) to explain this wavefunction collapse.

But all of these interpretaions have some fatal **defects**, and **lack** reality.

This indicates the quantum mechanics is **wrong**.

De Broglie Bohm interpretation regards each electron and ( **pilot** ) wave as **real** things.

But the electron of this Bohm theory has **NO** electric charge. It moves only by its pilot waves.

And this theory **cannot** explain **stable** helium atom at all. ( See Fig.1, right. )

*(Fig.2) Copenhagen vs. Many-worlds.*

In **Copenhagen** interpretation, while the ( sleeping ) observer **doesn't** see the particle, the particle is in **superposition** states.
The "superposition" means **one** cat can be both **dead** and **alive** at the **same** time !

But the instant the observer sees the cat (= particle ), the state of the cat is determined as dead **or** alive.

This Copenhagen interpretation is very **unnatural**.

Because, in the real world, **irrespective** of observer's existence, a cat (= thing ) is behaving **independently**.

As a result, many worlds theory was born, and accepted as the **most** correct interpretation.

In many worlds, the observer just sees one of **many worlds** (= cat's alive world or dead world ).

But this many-world theory needs **infinite** worlds for each cat.

So this interpretation is very **unrealistic** and just **fantasy**, though it's regarded as **standard** one.

*(Fig.3) Proton's spin OK. Electron spin is illusion !*

An electron is very light and small.

As shown in this page, even if we suppose one electron is as big as a proton, its spinning speed becomes more than **100** times the speed of light ( **> 100c** ) to reach 1/2 ħ angular momentum ( websites this p.5, this, this. )

( Actually, an electron is much smaller than a proton, so this speed must be much **faster** than this result. )

On the other hand, proton is much **heavier** and bigger than an electron.

So the spinning speed of this proton does **NOT** exceed the light speed ( **< c** ).

It is quite natural that we think the electron's spin is **false**, and spin magnetic moment (= Bohr magneton ) is caused by **orbital** motion like Bohr model.

Actually electron's magnetic moment is 1000 times **stronger** than that of proton.

*(Fig.4) After 360 degree rotation, the electron becomes a "different" thing.*

It is known that fermions such as electron and neutron **must** rotate twice (= **720 degree** = 4 π ) to be back. See Wiki.

At this moment, you find that these fermions have **NO** reality, because it is natural that **all** things in this **real** world return by **one** rotation.

Surprisingly, as shown in this page, this strange property was **confirmed** in actual experiments of neutron's **interference**, they insist. See also this site.

But of course, they **didn't** see neutron's rotation (= precession ) directly.

They just estimate their precession angle based on spin anglular momentum of 1/2 ħ.

If we adopt **ħ** ( instead of 1/2 ħ ) angular momentum like Bohr model, the **interpretation** of these experiments **change**.

For example, precession speed of gyroscope becomes half ( 2 → 1 rotation ), if the angular momentum becomes twice ( 1/2 ħ → ħ ). This is the **trick** of these mysterious neutron experiments.

These experiments only showed **one** rotation returns fermions with **ħ** angular momentum to their original state (= quite natural ! ).

*(Fig.5)*

In quantum mechanics, "**s**" state has **NO** angular momentum ( L = 0 ).

So, **1s** electrons of hydrogen and helium atoms always **crash** into nucleus ? ( ← **Impossible** ! )

This **helium** atom of quantum mechanics becomes extremely **unstable**, as shown in Fig.5 middle.

( De Broglie waves of these two electrons become **chaotic** by frequent **collisions** with nucleus. )

And the angular momentums of the outer electrons of **sodium** (= 3s ) and potassium (= 4s ) are also **zero**.

This means these outer electrons must continue **penetrating** inner n=1, 2 electrons' shells and nuclei !

So these quantum mechanical atoms are out of touch with reality.

On the other hand, angular momentums in Bohr model are always **greater** than 1 ( L is **NOT** zero ), so they **don't** crash into nucleus and inner electrons. Very **stable**.

*(Fig.6) A single C60 buckyball interferes with itself ! Bohr model vs. Many worlds (= fantasy ).*

Even a single C60 buckyball molecule can interfere with itself.

To explain this interference of a single particle in the double-slit experiment, the quantum mechanics needs "**many-world**" interpretation (= "superposition" ) to avoid faster-than-light collapse.

Wavefunction collapses in less than a momentu, so this speed is much **faster** than light.

( See also this page.)

Bohr model, which is based on real **de Broglie wave**, can explain this interference naturally, as shown in Fig.6 left.

De Broglie waves **accompany** particle's motion (= momentum ), which cause interference and **influence** particle's directions like Davisson-Germer experiment.

*(Fig.7) Bohr model electron is falling into nucleus ? ← Mind-control ! *

Unfortunately, Bohr model electron does **NOT** fall into nucleus, as shown in this page.

Most people are **deceived** by wrong explanations in standard textbooks and websites.

This Poynting vector is equal to the

This electric energy in the vacuum (= 1/2εE

But a single electron is **NOT** made from smaller charges. ( A single electron is the **smallest** charge. )

It means the vacuum electric energy (= 1/2εE^{2} ) in a single electron is **NOT** energy, as a result, Poynting vector itself is **meaningless** in this single electron's case.

So this wrong explanation is a kind of **brainwashing** about Bohr model, I think.

*(Fig.8) Dirac's hydrogen = Bohr-Sommerfeld model.*

The important point is that the **fine structure** of the hydrogen-like atoms was first obtaied by **Sommerfeld** using Bohr's orbit.

Surprisingly, Dirac equation got exactly the **same** solutions as Bohr-Sommerfeld model ! ( See this page. )

( And the reason why **useless** quantum chemistry gives correct values is in this page. )

This accidental coincidence between Sommerfel's and Dirac's solutions was called "Sommerfeld Puzzle" or "magic".

See various websites ( this, this (p.12-14), this (p.9), this ).

Einstein **praised** Sommerfeld's model in his 1916 letter,

"Revelation. Your investigation of the spectra belongs among my most beautiful experiments in physics. Only through it do Bohr's ideas become completely **convincing**."

*(Fig.9) Dirac equation is just equal to Sommerfeld model ( n = 2, case ).*

Fig.9 upper shows Sommerfeld elliptic orbit ( n_{r} = 1, n_{φ} = 1 ) in the energy level of n = 2 ( ← n_{r} + n_{φ} = 2 ).

Surprisingly, Dirac's 2s1/2 and 2p1/2 states are completly **equal** to Sommerfeld's elliptic otbit, though their sources are completely **different** from each other, as shown in Fig.9 lower.

( Dirac hydrogen includes "spin" effects and Sommerfeld's does not. )

Furthermore, as shown in this page, Dirac's hydrogen contains many **wrong** states such as 1p1/2, 2d3/2 ....

In conclusion, fine structure means Bohr-Sommfeld model is **right** and much more reasonable.

*(Fig.10) Schrodinger's hydrogen, radial = an integer × de Broglie waves !*

Furthermore, Schrodinger's hydrogen also obeys an **integer** times de Broglie wavelength and Bohr-Sommerfeld **quantization** rule, as shown in this page.

Fig.10 shows radial amplitudes (= rR ) of Schrodinger's hydrogen.

See some websites ( amplitude and probability ).

Probability (= (rR)^{2} ) is given by a square of amplitude (= rR ).

"rR_{20}" and "rR_{31}" contains **2 ×** de Broglie wavelength in one orbit.
( rR_{30} contains **3 ×** waves. )

Angular momentums (= tangential part ) are also quantized, the sum of them gives principal quantum number (= n ).

These results are completely **equal** to those of Bohr-Sommerfeld model.

*(Fig.11) Schrodinger's 2P "radial" wave function ( angular momentum = 1 ).*

For example, in Schrodinger's 2P states, the radial kinetic energies ( T_{r} = 1/2mv^{2} ) become **negative** in both sides as shown in Fig.11.

In the region of a2 < r, potential energy V becomes **higher** than total energy E.

As a result, kinetic energy must be negative ( ← **Impossible** ! ).

In the region of r < a1, **tangential** kinetic energy ( =T_{t} ) becomes **unrealistically** larger.

To cancel this increase, **radial** kinetic energy (= T_{r} ) must be **negative**. ( ← NOT tunnel effect, because V < E. )

So, this Schrodinger's model is very unrealistic and **wrong**. ( See also this page. )

*(Fig.12) Angular momemtum L = 0 in S wavefunction → destructive interference of de Broglie wave ! *

Of course, Schrodinger equations completely **depend** on de Broglie theory ( p = h/λ ) in calculating various energies.

And as shown in this page, we can prove that Schrodinger's hydrogen **also** satisfies **an integer** multiple of de Broglie wavelength.

In Bohr-Sommerfeld model, the orbit becomes elliptic or circular, and **cannot** be linear.

So these angular momentums are **NOT** zero, and an electron **avoids** crashing into nucleus.

" An integer times " means the wave phases of these de Broglie waves **fit** each other at their ends, and **don't** cancel.

But in Schrodinger's hydrogen including "**s**" wavefunctions, the angular momentum L **can** be **zero** !

In these cases, the **opposite** phases of the electron's de Broglie waves **cancel** each other out (= destructive interference ), and **expells** the electron from this orbit, according to Davisson-Germer interference experiment.

This is one of reasons why they **NEVER** admit **real** de Broglie waves in quantum mechanics, and **strange** many-world **superposition** becomes dominant in top journals even now.

*(Fig.13) 2 × 1s electrons' angular momentum L = 0 ← unstable helium (= He ) !*

According to quantum mechanics, two electrons of helium ground state is in 1s state with **NO** angular momentum ( L = 0 ).

If so, two electrons of helium often **hit** the nucleus, and **rebound** from it.

Considering **chaotic** collisions with nucleus and another electron, two electrons tend to be **repelled** from their original orbits.

As I said in Fig.12, de Broglie waves of 1s orbit are cancelled out by their opposite phases.

So this helium atom with 2 × 1s electrons is extremely **unstable**, which is very **far** from actual stable helium.

As shown in this page, repulsive force of Pauli exclusion principle in lithium atom is as strong as **11 eV**.

This strong replusive force can **NEVER** be generated by **weak** spin-spin magnetic dipole interaction (= **1.0 × 10 ^{-5}** eV ).

So unrealistic "spin" is completely

*(Fig.14) History of Zeeman effect. *

As shown in this page, anomalous Zeeman effect of hydrogen atom can be explained by Sommerfeld's fine structure.

Each component of Balmer H_{α} doublet (= fine structure ) was separated in a **normal** Zeeman triplet ( Historical Development of Quantum theory, J. Mehra ).

If you search for Zeeman effect, you will find almost all lines of hydrogen and **lithium** atoms show **normal** triplet. ( They **renamed** them "Paschen-Back" effect, **conveniently**. )

Furthermore, this page shows spin-orbit interaction of sodium D line is completely **wrong** idea.

These are caused by **Coulomb** interactions with **inner** shell electrons, like singlet and triplet.

*(Fig.15) Mathematical trick = Change of variable.*

In fact, anomalous magnetic moment (= g-factor ) by quantum electrodynamics (= QED ) depends on completely **wrong** mathematical trick, as shown in this page.

In Fig.15, "change of variables" ( k = l - β ) **artificially** changed the result itself, though it's just calculation method.

( This is completely **mistake** in calculation. Of course, "intentional" mistake. )

Lamb shift also uses this g-factor value as its part, so QED Lamb shift is wrong, too.

And they try to add various effects to fit them with experimental results, which means this result is **NOT** natural.

Of course, if special relativity and Dirac's hydrogen are wrong, QED Lamb shift must be **replaced** by other interpretations.

In **higher** order perturbations (= more loops ), the number of variables we can **freely** manipulate **increases**.

So QED are like a **storehouse** of artificial and wrong **tricks**.

*(Fig.16) How big is a photon → Shut up and calculate !*

You may often hear famous **photoelectric** effect showed photon is a particle, because electrons are ejected by some photons (= **lights** ) with **frequencies** above some threshold.

But this explanation is **inconsistent**, and it's a famous story that Willis Lamb did **NEVER** believe a photon particle.

The light frequencies (= f ) is the inverse of light wavelength (= λ ) through c = fλ.

So these concepts of frequency and wavelength completely mean the properties of **classical** electromagnetic waves.

These **wrong** explanations are a kind of **mind-control** to protect strange quantum mechanics.

Actually, even if you ask some physicists "**how big** is a single photon ?", they **cannot** give clear answer at all.

QED says photon is a **point** particle. If so, "frequency" means point-like photon is **actually** oscillating ? This is strange.

And it is almost **impossible** that a point particle photon can **crash** into a point particle electron in photoelectric effect.

*(Fig.17) Polarization, Redshift --- Photon "particle" is impossible. *

If photon is a **particle**, how this particle can be **polarized** (ex. circularly or linearly polarized lights ). Impossible.

And accelerating universe theory insists that **redshift** is the result of some **extended** photon by expanded universe.

This means a single photon can be extended, and we can detect such a **big** photon ?

A single photon can be detected by some photodetector, in which an **electron** generated by the photon is amplified into a large electric **current**.

When this electric current crosses a certain **threshold** it reveals the presence of a photon.

So even if some continuous **classical** lights enter this photodetector, this detector **cannot** detect them or **mistake** them for a single photon.

( See Faking Bell inequalities by **classical** light, this or this. )

*(Fig.18) A single photon enters only one of two paths, NOT divided ? *

In the Mach-Zehnder interferometer, when one photon is split into the two different paths at the beam splitter (= BS1 ), we can detect one photon **only in one** of the two paths at the same time (= Fig.18 ).

This means that this single photon particle is **NOT** split into two, according to the *quantum mechanical interpretation*.

Of course, this **trick** exists in photodetector, as I said in Fig.17.

Suppose the light amount is between one and two photons. (= **slightly** less than two photon's light amount, so it's recognized as a single photon. )

Even if this single photon is **divided** at BS1, only one wave of them **crossing** detection threshold can be detected as a single photon.

*(Fig.19) Delayed choice experiment = Many-worlds = photon ?*

The instant you **insert** new beam splitter 2 (= BS2 ), this single photon suddenly show the **interference**, which means properties of **classical** electromagnetic waves.

If the single photon is **divided** into two paths at BS1, these divided lights **interfere** with each other at BS2.

The interference means this single photon is **actually** divided into two **different** paths at BS1.

As shown in this page, this experiment clearly demostrates the existence of the **electromagnetic waves** in both two paths.

So above some **threshold**, the photon is **recognized** at the single photon detector in Fig.18.

*(Fig.20) Bell inequality violation is impossible in this real world.*

You may often hear that Bell inequality violation denied hidden variable proposed by Einstein.

But unfortunately, there are not many books, which explain this Bell inequality simply.

This Bell inequality violation was found using a "photon" pair.

The moment a photon (= A ) passes through the filter A and turns its polarization in the direction of filter A, the polarization of photon B **also** becomes the same as **filter A**, no matter how far they are apart from each other. See also this page

This process includes three impossible and **convenient** assumptions.

First, the existence of filter is **too special**, though the filter is only one of infinite things in the universe.

Second, if the photon is a rigid and **point** particle, it can **NOT** polarize and satisfy Malus law (= cosθ ).

Third, this clearly contradicts relativistic theory.

As shown in this page, if we use the classical **electromagnetic waves**, we can explain this violation as **local** and **realistic** phenomenon.

( We should NOT get away from "**reality**" so easily. )

*(Fig.21) Many photons are necessary for detecting single Be+ ion. ← NOT each entanglement.*

It is said not only two photons but also beryllium ion (= Be+ ) pair can be **entangled**.

And detection efficiency of these Be+ ions are very high.
( See this page. )

The important point is that this experiment using Be+ ions **cannot** detect **each** entanglement of ion pair.

Because we need to detect as many as **60** photons to know each Be+ nuclear spin state.

So this is just average data of repeated experiments, does **NOT** see entangled states directly.

Furthermore, as shown in this site, several loopholes (= defects ) such as locality exist in these ion and atom entanglement.

There were **NO** entanglement experiments which closed all loopholes at the same time.

So even officially, entanglements have **NOT** yet been proved to be true.

*(Fig.22) Quantum computer is still "two ions" ?*

In fact, the researches about quantum computers already come to a dead end, and make **NO** progress.

Even under this strict situation, researchers and (top) journals **must** publish papers, which is the main reason why the world of "quantum computer" is often seen in various papers and news, though they **lacks** reality.

Even now in 2013, all they can deal with is **ONLY two** ions, or qubits for quantum computing.

( How can you make computers **only** from two ions ? Impossible. )

Furthermore, these coherent (= same motions ) times are only **84 milliseconds** (= ions ), and 500 **micro**seconds (= superconducting circuits ).
See this news or this.

And to make two ions' motions the same, almost absolute **zero** temperature is indispensable.

So these are completely **impractical** and useless as computers, as shown in this page.

*(Fig.23) 10 billion ions + "spin echo" signals do NOT mean entanglement.*

The recent news ( this and this ) say they had succeeded in keeping as much as **39** minutes coherence time at **room** temperature.

In Fig.23, "90 pulse" light brings down all ion nuclear spins toward the **same** direction. (= **start** of coherence ).

Gradually, each spin tends to turn toward **different** directions due to their different spin **precession** speed (= dephase, decoherence ).

But by applying "180 pulse", their phases (= precession directions ) can back to almost the same, again (= rephase ).

This system contains as many as **10 billion** ions.

So if only **a part** of these extremely many ions turn toward the same, spin echo can be detected, which is **considered** as coherence state.

They **don't** see the entanglement of each ion pair. Actually NMR quantum computers **don't** use entanglement.

This experiment is just **classical** mechanical phenomena. But they like to call it "quantum states".

*(Fig.24) Observer's "looking power" moves the charged particle ? = Paradox.*

In Fig.24, near the **neutral** current wire loop, one negative ( or positive ) charge is at rest in S frame.

But the instant the observer start to move (= S' ), this charge is **attracted** toward the current wires, which generate strange charges, as shown in Fig.24, right.

This is clearly fatal pardox, and has **NOT** been solved. See this page.

There are other fatal paradoxes such as Ehrenfest and belt conveyor ( see this page ) and right angle lever ( see this page. )

The important point is that these **true** paradoxes are **hidden** from almost all textbooks and educational places.

Almost all **teachers** and ( top ) journals dealing with standard model, string theory, SUSY and general relativity continue **deceiving** ordinary people and new students, **hiding** these paradoxes. This is most serious problem.

*(Fig.25) Twin paradox in the two identical satellites.*

From the viewpoint of one observer (= A ), the time of another moving observer (= **B** ) becomes always **delayed**.

But from B observer, A is moving, which means the time of **A** observer is always **delayed**.

This is called "twin paradox". See also this page.

If you ask some physicists about this twin paradox, they will try to **avoid** this question, saying " ordinary people **don't** understand general relativity, so they have no rights to ask about this paradox. "

But in fact, famous GPS time correction includes this fatal twin paradox. See also this page.

They insist the time of moving satellite is delayed due to special relativity.

But from the moving satellite, the earth is moving, so the time on the earth is delayed.

This means GPS time correction **doesn't** prove the accuracy of the theory at all.

*(Fig.26) Ether was denied → virtual particles, dark matter, energy, Higgs.. = ether ??*

Though they rejected "ether", relativistic quantum field theories accept **infinite** virtual particles, dark matter, dark energy and Higgs **filling** all the vacuum.

This idea is completely **inconsistent** with special relativity, which denied "ether".

In fact, the kinds of "ether" have been **increased** much more in relativisitic quantum field theory !

Furthermore, a square of mass of Virtual particles **always** negative, which means they are "**tachyon**".

These virtual particles violating relativity are **indispensable** for all processes in QED and standard model.

So all these relativistic theories include **self-contradiction** from the beginning.

*(Fig.27) Ether rejected → redshift → expanding universe → black hole ! = relativistic TCA cycle ?*

In spite of fatal paradox, they rejected "ether", and insist red shift is caused by unrealistic accelerating universe, inflation, giving up "**tired**" light, though they introduced **infinite** dark matter, dark energy and Higgs **filling** all space.

Based on this **wrong** assumptions of red shift, they estimate the **distances** such as black hole and **quasar**.

Even though they are extremely far away from the earth, they emit strong electromagnetic waves. ( ← black hole ? )

Furthermore, **rejecting** ether means the space contains **nothing** except for galaxies.

So they insist there is **only** unrealistic black hole, which can explain these strong electromagnetic pulses.

Accepting black hole means accepting general relativity, which returns to expanding universe, like TCA cycle.

If we admit **one** ether-like matter in the space, we can explain the sources of these pulses (= ether and matter's **friction**. ) and **uniform** CMB (= cosmic microwave ) naturally.

( For example, ejected "jet" is very similar to a **tornado**. )

*(Fig.28) What does the "failure" of string theory mean ? *

The theory of everything, string theory needs as many as **10 dimensions**, and **cannot** predict anything due to its 10^{500} vacua.

Unfortunately, this unrealistic string theory is the **only** unified theory, which means the **failure** of the current quantum theory and relativity. See this page.

Because **enough** time have already passed to **exclude** all other gravity theories such as loop quantum gravity.

Besides the unrealistic string theory , the present quantum theory did NOT gain the approvals of great figures in the physics.

Einstein and Schrodinger resolutely **opposed** the unrealistic **quantum mechanics**.

And Dirac was very unsatisfied with the quantum electrodynamics (QED), which gives infinity.

And Feynman **disliked** the 10-dimensional string theory.

*(Fig.29-1) "21000" light-years away ! → Can you believe this result ??*

They insist gravitational waves were **indirectly** proved by observing the orbital period change of pulsar 1913+16.

General relativity predicts this orbital period decreases by **76.5 microseconds** per year. ( ← very small ! )

They try to determine **all** parameters such as two masses of binary star, its spinning speed, orbital radius, and their speeds, based **ONLY** on the electromagnetic **pulse** and its change. ( ← **impossible** ! )

The problem is that this neutron star is as long as **21000** light-years away from the earth ! See this site.

For example, it is **impossible** that we can know very slight **historical** change even on the earth **21000** years ago.

It is much more **impossible** that we can predict accurately **all** influences caused by **unknown** things such as dark matter, quantum fluctuations included in **21000** light-years path !

So this test of general relativity is very **doubtful**. See this page.

It is natural these very slight change is due to some space **matter**'s oscillation along the **extremely long** way.

*(Fig.29-2) Equivalence principle → Gravitational waves are cancelled out !?*

In fact, this gravitational waves are completely "**fake**" waves.

Tensors describing gravitaional waves are **NOT** true tensors (= pseudotensor ).

There are **two fatal defects** in this gravitational pseudotensors.

One is, that the form of this pseudotensors are **NOT** unique, as shown in this page.

So, we can artificially choose some **convenient** pseudotensor for experimental results.

Two is, that this energy-momentum pseudotensors completely **vanish** in some coordinate, which **contradicts** relativity.

*(Fig.30) Imaginary time ? arbitrary Lagrangian ← trick of QCD. *

Quantum chromodynamics ( QCD ) deals with strong force such as gluons and quarks.

The coupling constant of this QCD is extremely strong in low energy, which means this QCD cannot utilize usual perturbation methods.

So the current QCD depends on some numerical calculation to predict hadron masses.

The important point is that this QCD uses **imaginary** (= i ) time. So QCD lacks reality from the beginning.

And the Lagrangian for predicting hadron masses can be **changed** freely. ( ← free parameters ! )

It means this QCD has NO ability to predict anything, though it needs extremely long time (= about **a year** using many supercomputers ).

*(Fig.30') "Convenient" SUSY has more than 100 free paremeters ! *

It is said that supersymmetry is indispensable for hierarchy problem of Higgs mass, GUT, and dark matter.

But these reasons are only mathematical, **out of touch** with reality.

The important point is that this SUSY has extremely many **free** parameters we can adjust.

( Though MSSM, one of SUSY, has the smallest number of free parameters, it has more than **100** free paremeters. )

So, **convenient** SUSY can **NEVER** be denied like unrealistic string theory with 10^{500} vacua, which means various experiments for finding SUSY are just **meaningless**.

Furthermore, LSP (= lightest supersymmetric particle ) always accompany interactive processes in SUSY.

These LSP **cannot** be detected in any detectors like **neutrino**.

So these **missing** transverse energies can be **intentionally** interpreted as researchers like, I'm afraid.

*(Fig.31) Time gap without computers made condensed matter physics "unrealistic" math.*

In 1920s when quantum mechanics was born, there were **NO** computers.

So the researchers at that time were **NOT** able to compute three-body helium atom using computers.

Of course, if three body helium couldn't be treated, it is much more **impossible** to compute more **complicated** condensed matter, which contains almost **infinite** atoms

But even in these serious situations, researchers **had to** continue researching and publishing papers for better **posts**.

So many kinds of unrealistic quasiparticles were artificially created as mathematical tools, as shown in this page.

In high energy physics, unrealistic **10-dimensional** string theory is left as the **only** unified theory. This is disaster.

As you notice, these **fictitious** theories were needed to **fill** time gaps from 1920 to 1990s -.

In fact, general relativistic theories (= early universe, black hole ), QED, standard model, SUSY can be treated **by hand** (= pen and paper ), even when computers did **NOT** exist. This is the **main** reason why these fantasy theoires were **developed**.

*(Fig.32) Condensed matter physics = Ancient documents filled with math "hieroglyph".*

In about **1980**, the Apple II was produced as the first all-in-one computer.

But we needed to wait for more powerful computers until **1990s** to deal with **complicated** molecular interactions.

As I said, this extremely **long** ( 1920 - 1990 ) time **gap** caused many **unrealistic** theories.

Even after highly efficient computers appeared in 1990s, the conventional math ( NOT physical ) quasiparticles and **old** methods were left like **ancient** spells.

At first glance, you will find these old approaches become ancient **documents**, and **NOT** effective at all now in 21th century. ( See BCS theory, Spin Hall effect and Topological insulator ).

Because quasi- and virtual particles themselves are **unreal**.

*(Fig.33) How "fantasy" theories were made ?*

Quantum mechanics has **NO** reality.

It admits faster-than-light entanglement and many-worlds (= superpositions ).

But there were no other theories left under the conditions of NO computers in 1920s.

So even various ( top ) journals deal with these **fictitious** phenomena now in 21th century.

These theories are completely **unrealistic**, so they made **NO** progress at all ( ex. quantum computer ).

The serious problem is various mass **media** such as TV news, webnews, and newspapers are **promoting** these **fantasy** theories.

They are **deceiving** ordinary people, and giving **bad** influences to them.

They **must** make efforts to report experimental results as they are, **NOT** hiding their **defects**. ( This is the **true** role of mass media, I think. )

For example, Higgs news got quickly around the world last year.

But in spite of these vast news, ordinary people **don't** understand clear mechanism how Higgs gives mass to elementary particles.

Mass media try to report **ONLY** attractive parts, and **unrealistic** ones as much as possible.

Unfortunately, Higgs is just virtual **math** operator. This is the truth.

*(Eq.1) More than 80 years have passed. → QM cannot do anything.*

Solving Schrodinger equations of multi-atomc system is **impossible**.

So the present quantum chemistry **cannot** treat complicated condensed matter physics and molecular biology.

( Density functional theory is **NOT** ab-initio, because it relies on **rough** approximations such as LDA. )

As shown in this page, this page and
this page, the concept of **de Broglie wave** is indispensable for all molecular and atomic processes. ( We cannot **treat** them, based **only** on Coulomb interaction. de Broglie wave is **always** necessary. )

Investigating detailed properties of this de Broglie waves is most **urgent** task, I think.

As shown in this page ( Bohr model hydrogen ), the orbital length of Bohr model is just an **integer** times de Broglie wavelength.

This concept agrees with the Davission and Germer experiment [4].

*(Fig.34) Davisson-Germer experiment showed an electron is de Broglie wave.*

In Davisson and Germer experiment, an electron is accelerated by the electric field and reflected by nickel crystal.

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

They agreed with each other (= de Broglie relation ).

This experiment showed an single electron has wave-like property [5], in which the **opposite** wave phases **cancel** each other, and **expel** the electron (Fig.34).

*(Fig.35) de Broglie wave ends fit.*

Not to cancel de Broglie wave, both ends of an electron wave in hydrogen atom need to **agree** with each other with respect to wave phases.

*(Fig.36) Old Bohr's helium.*

In old Bohr's helium (Fig.36), two electrons are moving at the opposite sides of the nucleus in the same circular orbit (= **one** de Broglie wavelength ).

Considering Fig.34 and Fig.35, two electrons of old Bohr's helium are clearly **unstable** due to de Broglie wave **destructive** interference.

Actually, old Bohr's helium of Fig.36 gives **wrong** ground state energy of helium.

In circular orbit of helium, equating the centrifugal force to the Coulomb force, we have

*(Eq.2)*

where r is the circular orbital radius (meter), e is the electron charge

The circular orbital length is supposed to be an integer (n) times de Broglie's wavelength of the electron, we have

*(Eq.3)*

where h/mv means the **de Broglie's wavelength**.

The total energy E of the helium is the sum of the kinetic and the Coulomb potential energy of the two electrons, so

*(Eq.4)*

Solving the above three equations (Eq.2-4), the ground state energy (n=1) becomes **- 83.33 eV**.

This value is *lower* than the *experimental value -79.005 eV*.

Furthermore when some atoms such as oxygen come close to old Bohr's helium, its wave phases easily become **chaotic** due to the external force of other atoms, which is inconsistent with strong **stability** and **closed shell** property of helium atoms.

*(Fig.37) Various old Bohr's helium atom.*

In 1910s - 1920s, Lande (= outer and inner orbits, Fig.37A), Langumuir (= two parallel orbits, Fig.37B, two linear oscillating orbits, Fig.37C), Kramers (= 120 degree angle crossed orbits, Fig.37D ), and Heisenberg (= coplanar and inclined orbits, Fig.37E,F ) were trying to get better Bohr's helium atom.

But No old helium models could explain the correct ground state energy, **stability**, and **closed shell** property of helium atom.

Because about that time, they did not have **computers** to calculate three-body helium atom.

*(Fig.38) Autoionization in the classical helium atoms*

As shown in this page, helium has two electrons and one nucleus, so almost all cases show **unstable** autoionization (= one of the two electrons goes to infinity ) in the classical helium atoms.

( This classical helium does **not** consider de Broglie waves.)

If the helium structure has not been defined, the development of all the physics and chemistry would have **stopped** at that point.

In 1928-1930, Hylleraas succeeded in getting the approximate value of the helium ground state energy using the Schroedinger equation.

The quantum mechanical method has an advantage to be able to calculate approximate values **without computers**.

But the quantum mechanics can NOT show concrete probability and particle's state of two electrons of helium.

*(Eq.5) Quantum mechanical helium*

When Z=2, Eq.5 means the Hamiltonian of the helium atom. ( Δ = ∇^{2} )

When we try to get the correct value of the ground state energy of the helium atom, we have to use **more than a thousand- terms** variational functions of

*(Eq.6) Quantum mechanical helium.*

Of course, we can NOT imagine the helium's actual configuration from these many mathematical terms of Eq.6.

And this latest calculation value is -79.015 eV [9], which is a little **different** from the experimental value of -79.0051 eV.

On the other hand, our new Bohr's helium atom as shown in the latter section can get **more correct** answer of -79.0035 eV.

( This little difference between 79.0035 eV and 79.0051 eV is what we call "relativistic" effect, which value is good. See also this page. )

Also in other atoms and molecules ( see this page ), quantum mechanical methods can not give clear state of electrons, which **obstructs** the development of nanotechnology, and is the main reason why **many-world** concept becomes dominant.

*(Fig.40) Stable and independent two de Broglie waves. (= perpendicular to each other.)*

To avoid the problems of vanishing de Broglie's wave in the upper section, we suppose another model as shown in Fig.40.

As shown in Fig.40, this new Bohr's helium consists of two electron orbits which are **perpendicular** to each other.

If the two orbits are **perpendicular** to each other, their wave phases are **independent** from each other and **stable**.

If the electron tries to obey repulsive Coulomb force completely and lay down its orbit, the **destructive** interference of their de Broglie waves expel the electron. ( See Fig.36. Of course, these wave phases are **chaotic**, and unstable in this case. See also this page. )

Two de Broglie waves are just perpendicular to each other, **avoiding** destructive interference.

So there is **NO** more space for the **third** electron to enter this helium (= **Pauli exclusion** principle can be explained ! )

*(Fig.41) New Bohr's helium (= A.) is not electrically polarized.*

As you know, helium atom does **NOT** form compounds with other atoms, and has the **lowest** boiling point in all atoms.

Unfortunately, the quantum mechanical electron spin has **NO** power to stop forming compounds, because the magnetic moment of spin is very **weak** in comparison with Coulomb force.

( Spin interaction = very tiny fine structure level. )

So **ONLY** de Broglie waves is left to explain this important property of helium.

As shown in Fig.41 left, when the two electron orbits are **perpendicular** to each other, the space around 2e+ nucleus becomes just **neutral**.

( In this case, two negative electrons are **equally** distributed around the 2e+ nucleus both in vertical and horizontal directions. )

And due to the destructive interference of de Broglie wave, these states **continue** even when other atoms come close to helium.

In other helium models, the space is electrically polarized, and their wave phases easily become **chaotic** when other atoms are close to them.

Of course, there is no space for the third electron to enter in Fig.40 model (= Pauli exclusion principle ).

*(Fig.42) Two same-shaped orbital planes are perpendicular to each other. *

Next we calculate the new helium using simple computer program.

Fig.42 shows *one quarter* of the orbits.

Electron 1 starts at (r1, 0, 0), while electron 2 starts at (-r1, 0, 0).

*(Fig.43) The two electrons have moved one quarter of their orbitals.*

In Fig.43, the electron 1 is crossing y axis *perpendicularly*, while electron 2 is crossing z axis.

When the two orbits are crossing perpendicularly, the motion pattern as shown in Fig.42 and Fig.43 is the most *stable* one.

( If the electrons are moving like Fig.42 and 43, the potential energy becomes the **lowest**. )

Here we investigate how the electrons of the helium are moving by calculating the Coulomb force among the two electrons and the nucleus **at short time intervals**.

The computer programs of JAVA ( version 1.5.0 ), simple C languages and Python ( 2.7 ) to compute the electron orbit of the helium are shown in the link below.

Sample JAVA program

C language program

Python program.

As shown in Fig.42 and Fig.43, the helium nucleus is at the origin.

The electron 1 initially at ( r1, 0, 0 ) moves one quarter of its orbital to ( 0, r2, 0 ), while the electron 2 initially at ( -r1, 0, 0 ) moves to ( 0, 0, r2 ).

As meter and second are rather large units for measurement of atomic behavior, here we use new convenient units

*(Eq.7) New units of time and length.*

From Eq.7, the accelaration is

*(Eq.8)*

If you copy and paste the above program source code into a text editor, you can easily compile and run this.

First we input the initial x-coordinate r1 (in MM) of electron 1 (see Fig.42 ), and the absolute value of the total energy |E| (in eV) of helium.

From the inputted values, we calculate the **initial velocity** of the electron 1.

And at intervals of 1 SS, we *compute the Coulomb force among the two electrons and the nucleus*.

When the electron 1 is at ( xx, yy, 0 ), the electron 2 is at ( -xx, 0, yy ) (in MM). (See Fig.42 and Fig.43.)

Change MM to meter as follows; x (m) = xx × 10^{-14}. y (m) = yy × 10^{-14}.

So the x component of the acceleration ( m/sec^{2} ) of the electron 1 is,

*(Eq.9) x component of the acceleration.*

where the first term is by the Coulomb force between the *nucleus and the electron 1*, and the second term is by the force between the *two electrons*.

Considering the helium nuclear mass (= *alpha particle*), we use here the **reduced mass** (= rm ) except when the center of mass is at the origin.

*(Eq.10)*

See also reduced mass of three-body helium.

In the same way, the y component of the acceleration (m/sec^{2}) is,

*(Eq.11) y component of the acceleration.*

Based on that calculation value, we *change the velocity vector and the position of the electrons*.

We suppose electron 1 moves only on the XY-plane, so the z component of the acceleration of the electron 1 is not considered.

If we consider all components of the Coulomb force against the electrons, the electron's motion becomes as shown in Fig.36 (= old Bohr's helium ).

But in Fig.36, the two electrons are **packed in one orbit** of one de Broglie's wavelength.

So their de Broglie wave phases are cancelled (= destructive interference ).

We also calculate de Broglie's wavelength of the electron from the velocity ( λ = h/mv ) at intervals of 1 SS.

The number of that wave ( λ in length ) contained in that short movement section ( the sum of them is WN ) is,

*(Eq. 12)*

where (VX, VY) are the velocity of the electron 1 (in MM/SS), the numerator is the movement distance (in meter) for 1 SS. the denominator is de Broglie's wavelength (in meter).

Here, the estimated electron's orbit is divided into more than **one million** short segments for the calculation.

When the electron 1 has moved one quarter of its orbit and its x-coordinate is zero (Fig.43), this program *checked the y-component of the electron 1 velocity* ( **last VY** ).

When the last VY is zero, two electrons are *periodically* moving around the nucleus in the *same* orbitals as shown in Fig.42 and Fig.43.

After a quarter of the orbit, the program displays the following values on the screen,

r1, VY, preVY ( VY 1 SS ago ), and (mid)WN ( the total number of de Broglie's waves contained in **one quarter** of the orbit ).

Table 1 shows the results in which the last VY is the closest to zero.

E (eV) | r1 (MM) | WN | WN x 4 |
---|---|---|---|

-78.80 | 3082.0 | 0.250323 | 1.001292 |

-79.00 | 3074.0 | 0.250006 | 1.000024 |

-79.003 | 3074.0 | 0.250001 | 1.000004 |

-79.0037 | 3074.0 | 0.250000 | 1.000000 |

-79.005 | 3074.0 | 0.249998 | 0.999992 |

-79.01 | 3074.0 | 0.249990 | 0.999960 |

-79.20 | 3067.0 | 0.249690 | 0.998760 |

WN × 4 is the total number of de Broglie's waves contained in one round of the orbital.

The experimental value of helium ground state energy is **-79.005147 eV** ( Nist, CRC 2012 ).

This result shows the relativistic correction to the energy = -79.005147 - (-79.0037) = **-0.001447 eV**.

The theoretical ground state energy value of the *helium ion (He+)* can be gotten from usual Bohr model or Schrodinger equation using the reduced mass.

This value is **-54.41531 eV**.

And the experimental value of He+ ground state energy is **-54.41776 eV** (Nist).

So the relativistic correction to the energy in He+ ion is -54.41776-(-54.41531) = **-0.00245 eV**.

The theoretical ground state energy value of the *hydrogen atom (H)* can be gotten from usual Bohr model or Schrodinger equation using the reduced mass, too.

This value is **-13.5983 eV**.

And the experimental value of H ground state energy is **-13.59844 eV** (Nist).

So the relativistic correction to the energy in hydrogen atom is -13.59844-(-13.5983) = **-0.00014 eV**.

The electron's velocity of the neutral helium atom is slower than helium ion, but faster than hydrogen atom.

So the relativistic correction in neutral helium atom should be *between -0.00245 eV and -0.00014 eV*.

The above calculation value of **-0.001447 eV** is just between them !

As a **control** program, we show the program of hydrogen-like atoms ( H and He+ ) using the **same** computing method as above. Try these, too.

JAVA program ( H or He+ )

C language ( H or He+ )

Here we use the new unit ( 1 SS = 1 × 10^{-23} second ) and compute each value at the intervals of 1 SS.

If we change this definition of 1 SS, the calculation results of the total energy (E) in which the orbital length is just one de Broglie's wavelength change as follows,

1 SS = ? sec | Result of E(eV) |
---|---|

1 × 10^{-22} | -79.00540 |

1 × 10^{-23} | -79.00370 |

1 × 10^{-24} | -79.00355 |

1 × 10^{-25} | -79.00350 |

This means that as the orbit becomes more smooth, the calculation values *converge* to **-79.00350 eV**.

The programs based on other 1 SS definition is as follows,

Sample JAVA program 1 SS = 1 × 10^{-25} sec, calculation takes much time.

Old sample JAVA program 1 SS = 1 × 10^{-22} sec--fast but the result and Eq.no are a little different

The standard helium model of the quantum mechanics has the spin-up and spin-down electrons.

So it seems to generate no magnetic field.

But to be precise, in **all areas** except in the part at just the same distance from the two electrons, magnetic fields are theoretically produced by the electrons even in the standard helium model.

( Because they do not stick to each other. )

So as the electrons move to cancel the magnetic field out, they lose energy by emitting electromagnetic waves.

Actually, one-electron atom hydrogen has the magnetic moment, two-electron atom helium has no magnetic moment.

So the *standard quantum-mechanical helium model has self-contradiction.*

In this new helium, the two symmetrical orbits crossing perpendicularly are *wrapping the whole helium atom* completely.

See also Why "solitary" helium doesn't form compounds ?.

( The Bohr model hydrogen which has only one orbit, *can not* wrap the direction of the magnetic moment completely. )

It is just **consistent** with the fact of the strong **stability** and the **closed** shell property of helium.

*(Fig.44) Hydrogen and Helium atoms.*

These orbits are all just *one de Broglie's wavelength*.

Surprisingly, this new atomic structure of Bohr's helium is applicable to **all other** two and three electron atoms ( ions ).

Atoms | r1 (MM) | WN x 4 | Circular orbit | Result (eV) | Experiment | Error (eV) |
---|---|---|---|---|---|---|

He | 3074.0 | 1.000000 | -83.335 | -79.0037 | -79.0051 | 0.001 |

Li+ | 1944.5 | 1.000000 | -205.78 | -198.984 | -198.093 | -0.89 |

Be2+ | 1422.0 | 1.000000 | -382.66 | -373.470 | -371.615 | -1.85 |

B3+ | 1121.0 | 1.000000 | -613.96 | -602.32 | -599.60 | -2.72 |

C4+ | 925.0 | 1.000000 | -899.67 | -885.6 | -882.1 | -3.50 |

N5+ | 788.0 | 1.000000 | -1239.8 | -1223.3 | -1219.1 | -4.20 |

O6+ | 685.3 | 1.000000 | -1634.38 | -1615.44 | -1610.70 | -4.74 |

F7+ | 607.3 | 1.000000 | -2083.3 | -2062.0 | -2057.0 | -5.00 |

Ne8+ | 544.5 | 1.000000 | -2586.7 | -2563.0 | -2558.0 | -5.00 |

Table 4 shows three electron atoms such as lithium.

Atoms | r1 (MM) | WN x 4 | Result (eV) | Experiment | Error (eV) |
---|---|---|---|---|---|

Li | 1949.0 | 1.000000 | -203.033 | -203.480 | 0.47 |

Be+ | 1427.0 | 1.000000 | -388.785 | -389.826 | 1.04 |

B2+ | 1125.0 | 1.000000 | -635.965 | -637.531 | 1.56 |

C3+ | 928.0 | 1.000000 | -944.46 | -946.57 | 2.11 |

N4+ | 790.5 | 1.000000 | -1314.25 | -1317.01 | 2.76 |

O5+ | 688.0 | 1.000000 | -1745.70 | -1748.82 | 3.12 |

F6+ | 609.4 | 1.000000 | -2237.60 | -2242.21 | 4.61 |

Ne7+ | 546.0 | 1.000000 | -2791.15 | -2797.12 | 5.97 |

About the calculation method, see this page.

In the standard model of the quantum mechanics (QM), it is said that the electrons are stable as electron clouds, which are **not** actually moving.

They say this is the reason why the electrons don't fall into the nucleus radiating energy in QM.

But if so, how do we explain about the relativistic corrections to the energy (caused by the high electron's velocity) and the use of the **reduced mass** ?

If we use the reduced mass of an electron, the calculation results of the hydrogen energy levels becomes more accurate.

Does this mean that the electron and the nucleus are **actually** moving around the center of mass ?
So the quantum-mechanical model contains self-contradiction also in this subject.

And if Dirac's hydrogen is wrong the intepretation of Lamb shift needs to change.

This very little Lamb shift relies on the assupmtion of metastable 2S1/2 by the photon, which Willis Lamb himself did not believe.

See also de Broglie wave, Virial theorem, and Zeeman effect.

In the neutral neon (Ne), how are *eight* outer shell (valence) electrons moving ?

Again the quantum mechanics **cannot** show any clear images at all.

The neutral neon has **ten** electrons, in which two 1S electrons are *very close* to the nucleus.

So "approximately" these **eight** outer electrons are moving around one +8e central nucleus (+10e-2e = +8e).

*(Fig.45) Neutral Neon model*

Considering repulsive Coulomb forces among **eight** valence electrons ( e0 - e7 ), these outer electrons are distributed like regular **hexahedron**.

In this hexahedron configuration, the outer 8 electrons are most **stable**.

But different from other atoms such as carbon, in Fig.45 model, the outer electrons of upper and lower **crash** into each other, while they are orbiting around the nucleus.

*(Fig.46) Upper and lower electrons' crash.*

As explained above, mysterious Pauli exclusion principle is caused by two 1s orbits, which are **perpendicular** to each other.

So also in **noble gases** such as Neon, this **de Broglie wave**'s nature is naturally related.

To avoid this crash, using helium **perpendicular** de Broglie waves, the eight outer electrons' orbits are thought to be

*(Fig.47) Neutral Neon's eight orbits of valence electrons.*

In Fig.47, for example, the orbits of the electron 3 and 5 ( e3 and e5 ) have two **common** vertices, and **perpendicular** to each other, like

*(Fig.48) Orbits perpendicular to each other.*

In Fig.47 model, the eight valence electrons don't crash into each other.

And the eight valence electrons **don't** need to enter into a single common plane, when they are passing each other.

And each two electrons having two common vertices are **perperndicular** to each other like helium model above.

( Pairs are e1-e7, e3-e5, e2-e4, e0-e6. )

So the eight outer electrons have their own **different** orbits.

Considering the symmetric structure of polyhedron, and de Broglie wave's **destructive** interference, this eight outer electrons is the **limit** of n = 2 (= two de Broglie wavelength ) energy levels. (= **Pauli exclusion principle.** )

( Different from n = 1, the orbit can be elliptical due to radial de Broglie wave. )

Of course, about the Neon, this model is still an estimation.

So I'm glad if someone could find better and **realistic** Neon model.

Using this program of this page, we find the **protruded** valence electron (= "e0" ) is the **key** factor to determine various covalent bond **length**.

As I said, these forms are determined by **both** of Coulomb and de Broglie theories.

*(Fig.49) Comparison of forces acting on C electron.*

Fig.49 shows forces acting on carbon electron "e0" in C-C, C-H, C-N and C-O single bonds.

Considering carbon can **keep** tetrahedral structure in various bonds, it is natural forces acting on C electron are almost **equal** to each other.

Actually, these forces (= CF ) are **1643, 1343, 1558, 1614**, very similar to each other ! even in different C-C, C-H, C-N, C-O bonds.

( These bond lengths are average experimental values. C-O single bond is from acetic acid. )

molecular bond | bond length | Force on e0 |
---|---|---|

C - H | 1.0900 Å | CF = 1343 |

C - C | 1.5351 Å | CF = 1643 |

C - N | 1.4700 Å | CF = 1558 |

C - O | 1.3640 Å | CF = 1614 |

C - F | 1.3500 Å | CF = 1605 |

C - Si | 1.8500 Å | CF = 1602 |

C - P | 1.8400 Å | CF = 1584 |

C - S | 1.8200 Å | CF = 1708 |

C - Cl | 1.7700 Å | CF = 1626 |

Table 5 shows forces (= CF ) acting on carbon electron "ele 0" in various bonds.

Surprisingly, in different bonds, these forces (= CF ) become almost **same** !

This means **common** mechanism is working, and carbon's tetrahedral structure is **kept** in various bonds.

The concept of "discrete" electrons is a key point, because the **difference** among these **bond lengths** are clearly caused by this property.

For example, in chlorine, its nucleus is more **exposed** due to 3 de Broglie wavelength, so bond length needs to be **longer** to make force CF the same value as other bonds.

*(Fig.50) When they choose steric hindrance or covalent bonds. *

You often see the explanations such as " six hydrogen atoms of ethane tend to **avoid** each other." or "protein structures are very limited due to their **steric hindrance**".

So this means each atom "always" avoids other atoms ?

On the other hand, various atoms except for noble gases can form stable **covalent** bonds.

Though each atom "**avoids**" each other, why they can form **stable** and tight covalent bonds ??

*(Fig.51) Lennard-Jones potential cannot explain the transition to covalent bonds*

Lennard-Jones potential is often used to express forces among molecules such as van der Waals forces.

In this potential, when the distance between two particles is very **long**, they **attract** each other weakly.

On the other hand, when two particles come closer to each other than some **threshold** length, they start to **repel** each other.

This repulsive force is caused by collisions of electron cloud and Pauli exclusion principle, they insist.

But this Lennard-Jones potential **cannot** explain why very **stable** and tight **covalent** bonds are formed in **much shorter** bond length.

*(Fig.52) C-C = 1.5400 Å is an equilibrium length.*

In this page, we show C-C bond length (= **1.5351 Å** ) is indispensable for the **stability** of both C nuclei, using computer program.

If C-C bond length is **shorter** than 1.5351 Å, **attractive** force between e0 and C1 becomes too stronger, and it's **unstable** (= periodic electron motion is **broken** ).

And if C-C bond length is **longer** than this, **repulsive** force between two C nuclei becomes dominant, and it's **unstable**, because the influence of protruded electron "e0" is weaker.

This is the **true** mechanism of C-C bond length.

*(Fig.53) "Long" (= middle ) or "short" bond length determines their property.*

As shown in this page, to form stable covalent bonds, two atoms need to come **close** to each other than some **threshold** length.

When it is **longer** than the threshold length, **repulsive** forces among electrons or nuclei become **dominant** and causes **steric hindrance**.

As two atoms come closer to each other than some threshold length, the **attractive** power of protruded valence electron (= "e0" of Fig.49 ) becomes **strong** enough to **cancel** repulsive force between nuclei

And in these short covalent bond length, electrons of two atoms tend to **periodically avoid** each other, which is the origin of bond energy.

( These kinds of periodic avoiding motions are difficult to form in very long bond length. )

In usual proteins, almost all distances between two atoms are **longer** than covalent bond length, so they tend to cause **steric hindrance**.

[1] N. Bohr, Philos. Mag. 26, 1 (1913).

[2] A. Sommerfeld, Ann. d. Physik 51, 125 (1916).

[3] P.A.M. Dirac, The Principles of Quantum Mechanics (Fourth Edition).

[4] C. Davisson, and L. H. Germer, Nature 119, 558 (1927).

[5] A. Tonomura, J. Endo, T. Matsuda, et al., Am. J. Phys., 57, 117 (1989).

[6] A. A. Svidzinsky, M. O. Scully and D. R. Herschbach, Proc. Natl. Acad. Sci. U.S.A. 102, 11985 (2005).

[7] A. A. Svidzinsky, M. O. Scully and D. R. Herschbach, Phys. Rev. Lett. 95, 080401 (2005).

[8] G. Chen, Z. Ding, S-B Hsu, M. Kim and J. Zhou, J. Math. Phys. 47, 022107 (2006).

[9] G.W.F. Drake, M. M. Cassar, and R. A. Nistor, Phys. Rev. A 65, 054051 (2002).

[10] G. E. Uhlenbeck and S. A. Goudsmit, Nature 117, 264 (1926).

[11] H. Rauch et al., Phys. Lett. 54A, 425 (1975).

PDF version(2010/4)

PDF old version(2009/2) (The reduced mass isn't used in this old paper. And here, 1SS = 1 × 10^{-21} sec. So the calculation values are a little rough and different from the above correct values.)

2014/1/15 updated. Feel free to link to this site.