Youhei Tsubono

Setagaya-ku Tokyo 155-0033, Japan

♦ Japanese version ♦

New Bohr's chemistry

♦ Helium ( Fine structure, Bohr-Sommerfeld, Special relativity )

♦ Bell inequality violation. ( Delayed choice, Quantum computer )

♦ Quantum field theory ended. (Dirac hydrogen, QED, Higgs )

Nobel Prize, Physics. (14/10/13)

Bohr model, Nature. (14/9/17)
Criticize top journals. (15/3/31)

- Reason why Quantum Mechanics is wrong.
- Pauli exclusion and "realistic" Bohr's helium.
- Bohr model Neon, Argon. (15/3/25)

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

Quantum mechanics (= QM ) only shows the vague **probability** density **without** specifying the position and velocity of each particle.

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

To avoid **unnatural** observer-induced collapse (= Copenhagen ), only **fanciful** many worlds interpretation is left, because *realistic* view (= de Broglie-Bohm ) is impossible in QM.

So even first-rate universities ( see also this ) and journal believe and try to promote this **unreal** *parallel* worlds now. These tendencies clearly show the **crisis** of the current physics.

As a result, most physicists **avoid** investigating **true** mechanism of strange wavefunctions (= Shut up and calculate ! ).
But **escaping** from *unknown* things is **NOT** scientific attitude.

*(Fig.2) Proton's spin OK. Electron spin is illusion !*

An electron is very light and **small** (= almost point-like ).

As shown on 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. )

On the other hand, proton is much **heavier** and bigger (= 0.84 fm) 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 **unnaturally** 1000 times **stronger** than that of proton.

*(Fig.3) 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 spinor and 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 on 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, **believing** 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.4) Schrodinger's 2p radial wavefunction contains negative kinetic energy !*

Schrodinger's hydrogen contains **two** ( l > 0 ) classically forbidden (= **unreal** ) areas. See this (p.2-) and this.
In Fig.4 (= hydrogen 2p wavefunction ), *radial* kinetic energy must be **negative** (← *impossible* ! ) in two regions.

On the right of a2, the potential energy is greater than total energy, which means kinetic energy must be **negative**! To begin with, the idea that hydrogen **bound** electron can reach r = **infinity** is *unreasonable*.

On the left of a1, to *cancel* the increasing **tangential** kinetic energy.
radial kinetic energy must be negative. In this region, the potential energy is lower than total energy, so tunnel effect **doesn't** apply.

It is **impossible** that the signs of radial (= *negative* ) and tangential (= *positive* with angular momentum ) kinetic energies are **different** in this real world, which means Schrodinger's hydrogen is **unreal** and wrong.

*(Fig.5) 3s electron of sodium (= Na ) always "penetrates" inner electrons and nucleus !?*

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

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

From **commonsense** point of view, due to **repulsive** force between two helium electrons, they **cannot** keep *zero* angular momentum. Furthermore, frequent **collisions** surely make helium atom very **unstable**.

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 0 ( L is **NOT** zero ), so they **don't** crash into nucleus and inner electrons. Very **stable** and safe.

*(Fig.6) The only "theory of everything", 10-dimensional string theory is unreal.*

Reason why I argue that quantum mechanics and special relativity are wrong is the **only** theory of everything, **10-dimensional** string theory . See also this and this.

As Witten says, other theories such as twistor and
loop quantum are **NOT** complete unified thoery.

So *unless* you believe 10-dimensional string theory, you can **NEVER** be "*professors*", no matter how excellent you are. It's just a matter of **belief**, NOT talent.

Almost all important posts and 3 million $ prize are **monopolized** by **10**-dimensional string theory.

Furthermore, **11** dimensional M theory and **12** dimensional F-theory appear as new successors.

Of course, it's **impossible** that our *real* world adopts this **unrealistc** 10-dimensions.

In fact, **relativistic** quantum field theory violates special relativity, as shown in virtual particles (= tachyon, m^{2} < 0 ).

The present physics has to rely on this contradictory virtual particles, in QED, standard model ( Higgs ).

So the current quantum theory is filled with **inconsistent** concepts, which means **wrong**.

*(Fig.7) "Accidental" coincidence in fine structure Really happened ?*

The important point is that the fine structure of the hydrogen-like atoms was first obtaied by **Sommerfeld** using Bohr's orbit. It's surprising almost all textbooks intentionally **hide** this important facts

Later, Dirac equation got exactly the **same** solutions as Bohr-Sommerfeld model !

This accidental **coincidence** was called "*Sommerfeld Puzzle*" or "magic".
See this, this, this (p.12-), 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**."

About the derivation of Sommerfeld and Dirac fine structure, see this page and this page.

If you actually compare calculation with experimental value, you'll recognize the **accuracy** of Sommerfeld model.

*(Fig.8) Dirac equation is just equal to Sommerfeld model ( n = 2, case ).*

Fig.8 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* orbit.

Bohr-Sommerfeld model *doesn't* contain **unrealistic** electron spin, different from Dirac equation.

Then why did these completely **different** models give the **same** solution ?

Because for example, the energy level of 2s1/2 is just *equal* to 2p1/2 due to their common j = 1/2.

Considering these **unnatural** coincidences, you'll easily find, Dirac's hydrogen solution was gotten, **following** Sommerfeld's original solution.

*(Fig.9) Schrodinger's radial wavefunctions also satisfy n × de Broglie wavelength !*

It is famous that Bohr model uses de Broglie wavelength.

de Broglie wave is **real**, because Davisson-Germer experiment **confirmed** that existence.

So, Schrodinger's hydrogen must **also** rely on *de Broglie* relationship to obtain exact values.

Considering the **same** hydrogen solution of Bohr and Schrodinger's models, do both these models satisfy an **integer** multiple of de Broglie wavelength ?

In fact, this quantization rule is true **also** in Schrodinger's hydrogen, as shown on this page.

Fig.9 shows radial amplitudes (= rR ) of Schrodinger's hydrogen.

Hydrogen radial wavefunctions are shown on these websites ( amplitude and probability ).

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

"rR_{10}", "rR_{20}" and R_{30} contains **1 ×**, **2 ×** and **3 ×** (= *integer* ! ) de Broglie wavelength in one orbit, respectively.
Angular momentums (= tangential part ) are also quantized in the same way.

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

In **both** models, the *principal* quantum number (= n ) is given by the **sum** of *radial* and *tangential* wave's quantum numbers.

*(Fig.10) Simple circular old Bohr's helium gived wrong energy (= -83.33 eV ).*

The most decisive reason for dismissing Bohr model is failure in explaining **helium** atom.

As shown in this section, simple helium model of Fig.10 right gives **wrong** ground state energy (= -83.33 eV ).

The helium **experimental** value is **-79.005147 eV** (= 1st + 2nd ionization energies, Nist, CRC ).

Of course, there were **NO** convenient computers in 1920s to simulate *three-body* motions (= **two** electrons + one nucleus ) like helium.

On the other hand, quantum mechanical variational methods can come close to experimental helium energy, as shown on this site.

Because when the chosen variational functions are simple, they could calculate **without** computers.

*(Fig.11) Calculated values depend on artificially "chosen" forms of trial functions.*

Helium atom contains two repulsive electrons, so Schrodinger equation **cannot** be solved.

**Insolubility** means we can **NEVER** know *true* calculated value of helium ground state energy.

In variational methods, first we **choose** some forms of helium wavefunctions.

**Within** this *chosen* form of wavefunction, we can know the **lowest** calculated value of total energy.

Of course, as the number of **terms** and variational ( **adjustable** ) *parameters* in wavefunction increases, we can obtain **lower** energy values.
But it's **impossibe** to calculate wavefunctions containing **infinite** terms and variational parameters.

So we can **NEVER** know what the **truly** lowest energy value becomes when we try wavefunctions including **infinite** kinds of variational parameters and terms.

In fact, as shown on this page, they artificially **fixed** ( ← NOT variational ! ) some variational parameters to obtain exact helium ground state energy. So, these are NOT first-principle at all.

*(Fig.12) When an electron is spherical conductor with classically collected charges, it radiates.*

Almost all textbooks explain that Bohr's accelerating electron loses energy and fall into nucleus like this and this. But Unfortunately these explanations are completely **wrong** as shown on this page.

It uses Poynting vector (= E × H ) as the energy flow. ( See this and this )

This Poynting vector is equal to the **change** of the electric and magnetic *energy densities* stored in the vacuum.

This electric energy density stored in the vacuum (= 1/2εE^{2} ) means the **potential energies** needed to **gather** infinitesimal minus (or plus) charges to the *spherical conductor*, overcoming **repulsive** force between those charges (= Fig.13 left, or see this, this, this ).

*(Fig.13) Bohr model electron is falling into nucleus ? ← Mind-control by textbooks ! *

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

There is **NO concept** such as "electric energy *density*" around a **single** electron.

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 by quantum mechanical textbooks.

Only when **more than** one charges are involved, they can radiate energy.

*(Fig.14) Complicated Schrodinger equation + determinants cannot handle large molecular system.*

For example, for two electrons to **avoid** each other even in *simple* helium atom, quantum mechanics needs more than **3000** terms ( ← **impractical** ! ), as shown on this site.

So, the current quantum mechanics cannot handle larger molecules.

Actually, in *applied* fields such as biology, **useless** quantum chemistry does **NOT** appear at all.

This interesting paper (p.5-) says the current ab-initio quantum chemistry is **NOT** ab-initio, because they rely on many **empirical** parameters. So "ab-initio" density functional theory (= DFT ) is **wrong** name.

In this **tough** situation surrounded by **useless** quantum wavefunctions, all they can do is create many kinds of **fictitious** quasi-particle (= NOT real elementary particle ).

To **conceal** uselessness of quantum mechanics, they made up a "**camouflage**" target called quantum computer.

The woking time of quantum computer is less than several **microseconds**.

Though they are **impractical**, the media often report it **only** as news item.

*(Fig.15) "Fake" quasi-particles will remain "fake" even 1000 years from now !*

According to Nature, a **fundamental** electron can **split** into three components such as "spinon" (= spin ! ), holon (= charge !) and orbiton (= orbital motion ! ). See also this site.

Of course, these are **fictitious** (= *unreal* ) quasi-particle.

So, these quasi-particle **cannot** exist independently outside the material. See this and this.

As you see, the current condensed matter physics just concentrates on creating **fictitious** quasi-particle instead of investigating true *underlying* mechanisms. See also list and quasi-electron.

Taking the trouble to create fictitious *quasi*-particles means physicists have **NO** intention of clarifying their true **underlying** mechanism using "**real**" particles, from now on. So science **stops** due to quantum mechanics.

*(Fig.16) What are size and shape of an photon ? ← "Shut up !" ← NOT science.*

In the internet forums ( see this and this ), questioners asked a **basic** questions " What **shape** does a single photon have ? ", "What is really a "**charge**" ?", because the present quantum mechanics **avoids** these **important** questions.

As you expected, the forum *mentor* (= moderator ) **avoided** describing what a photon and charge **really** are, and tried to *escape* into *complicated* QED (= quantum electrodynamics ).

But quantum field theories such as QED just show **abstract** creation (= a^{†} ) and annihilation (= a ) operators.

It **cannot** show concrete shape and size of a photon, which means they **lack** reality.

Also about charge, QED can say **nothing** more than the symbol "**e**".

When you see these questions and answers, you will easily find the current quantum mechanics tries to exclude "**inquisitive**" students from physical world, which tendency is very **harmful** for science progress.

*(Fig.17) Photon is Wave or particle ? → Shut up ! → this question remains "unsolved" forever ..*

Even in 21th century, we **cannot** progress and outgrow the **boring** concepts such as two-slit experiment and "photon is wave or particle ?", as shown in Scientific american.

So, even **1000** years from now, I bet we continue the same **boring** question such as "Photon is wave or particle ?" (+ **endless** interpretation ), as long as we stick to **unrealistic** quantum mechanics.

Basically, as shown on this page, all experiments dealing with photons rely on **wave** nature (= interference, phase, polarization ) of light.

As shown on this site (= abstract ), even Willis Lamb, Nobel winner, said "there is **NO** such thing as a photon."

*(Fig.18) Spin Hall, Berry phase, topological insulator are all quantum computer !? *

Though we often see the words of "quantum computers move a step" in various news and journals, researches on quantum computer have substantially made NO progress at all.

As of 2013, the quantum computer consists **only** of **two** unstable trapped ions ( independently controllable ) or superconducting qubits with **NO** computer's shape.

Their average working (= coherent ) time is only **micro**seconds. See also this site.

The present quantum mechanics **abuses** this *impractical* ( ← forever ! ) quantum computer as "**camouflage**" target.
So, **all** roads (= spin Hall, quasiparticle Majorana, topological insulator, Berry phase ) lead to **illusory** quantum computer !?

Very week spin Hall effect is **useless**. See this (p.10). They just saw light reflection, **NOT** spin itself.

They adopted **fictitious** monopole to explain spin Hall, **only** because their forms are *similar*. See this (p.3-).

Massless Dirac fermion is **NOT** light speed. So this concept **contradicts** special relativity.

Physicists don't say what Berry phase really is, which means it's just **artificial** mathematical (= unreal ) phase.

*(Fig.19) Charges move obeying classical electromagnetism in Flash memories.*

Though it is often said that **thanks to** quantum mechanics, we can utilize *leading-edge* computer technologies such as smartphone and semiconductor memories, these explanations are **NOT** true.

In fact, Steve Jobs, the founder of Apple, **dropped** out of college, but **achieved** great works by his **own** efforts. This means quantum mechanics which is taught in *universities* are completely **useless**.

For example, flash memories work obeying **classical** electromangetism ( **NOT** unrealistic quantum mechanics ). Most people are **brainwashed** into believing quantum mechanics is *useful* technology.

Depending on the **voltage** at the upper gate, electrons are attracted or not toward the middle layer, which state expresses "**bit**" ( 0 or 1 ). The amount of charges in the middle layer determines whether the following electrons can enter the target gate on the right. This is how computer works.

Though physicists argue that electron can tunnel through SiO2 **thanks to** quantum mechanics, this insulator must be **very thin** (= *~nm* ) to get electron through. So quantum tunnel is **NOT** supernatural phenomena but realistic ones caused by some heat or charge's **vibration**.

*(Fig.20) Uncertainty principle → position and velocity cannot be determined ! *

Accoring to uncertainty principle of quantum mechanics, we **cannot** know the position and momentum (= velocity ) of each particle, **simultaneously**. Thinking *commonsensically*, it is **impossible** to *predict* various dynamic behaviors of particles under this "uncertain" condition.

Even in usual **macro** world, we have to **specify** *both* position and velocity to move things and **predict** their behaviors. It's much more **impossible** to control things under *uncertainty* condition in quantum micro world.

Actually, in flash memories of Fig.19, each electron moves to designated positions ( which expresses "bit" ) depending on the **strength** of voltage, which **controls** the acceleration and velocity of electron.

Using **obscure** quantum mechanics, we **cannot** make definite "*plans*" inside tiny computers at all.

So the phrase such as "*thanks to* quantum mechanics" is **incorrect**, and a kind of **mind-control**.

*(Fig.21) The photon B polarization "imitates" A in the instant photon A passes the filter "a" ?*

According to quantum entanglement, the moment photon A *passes* the filter "a", the **polarization** of photon **B** becomes *parallel* to filter "**a**", no matter how far they (= B and "a" ) are separated from each other.

"Moment" means this signal from photon A to B are transmitted **superluminally**.

To begin from conclusion, this **unrealistic** interpretation is caused by the **delusion** that "**photon**" particle is real.

If we consider photon as classical **divisible** electromagnetic **waves**, this fantasy entanglement can be explained, as shown on this page. It is very **unnatural** that whether passing filter or not **determines** the fate of another **far-away** photon.

In fact, even formally, all three loopholes (= flaw of experiments ) have **NOT** been closed *simultaneously* according to this site (last), which means this superluminal entanglement has **NOT** been experimentally proved yet.

Only in photon case, superluminal link ( requiring 144 km separation ) was shown, though the detection efficiency is very low (= **artificial** choice of photon pairs = detection loophole ).

In atom-photon, ion-ion entanglements, *superluminal* link **cannot** be proved. See this (p.4).

*(Fig.22) Exchange, correlation functionals can be "freely" chosen.*

In this paper (p.2), though density functional theory (= DFT ) is first-principle, the exact exchange (= Pauli exclusion ) and *correlation* ( between electrons ) functional **forms** are **unknown**.

The best available functional for one application is often **NOT** the best for another.

So there is **NO** known *universal* exchange-correlation functionals in DFT ( see this, this (p.10), this (p.1) ).

"First-principle DFT" is clearly an **incorrect** ( exggerated ) name inviting *misunderstanding*.

Until now, **many** kinds of exchange-correlation functionals were proposed ( gradient, hybrid.. see this ).

As shown on this site (p.23), DFT is semi-**empirical** ( which **cannot** predict any values ).

After choosing convenient functionals, you can **artificially** fit *parameters* to get good answers.

*(Fig.23) Calculated values depend on artificially "chosen" forms of trial functions.*

As I said on this page, Schrodinger equations of multi-electrons **cannot** be solved, so all we can do is **artificially** choose some *convenient* trial functions for our purposes.

Ab-initio Hatree-Fock, CI methods also start from **choosing** basis sets (= wavefunctions ). See this.

So these methods are **NOT** first-principle at all, as shown on this (p.6) and this.

All these parameters are **fixed** in calculation, which means
the current ab-initio quantum chemistry such as DFT and Hartree-Fock **cannot** guess exact experimental values.

Instead,
they just **choose** ( NOT solve ! ) proper trial wavefunctions and free parameters, which give actual values.

Again, the name of "*first-principle*" gives rise to **misunderstanding** among ordinary people.

*(Fig.24) Quantum mechanical hydrogen atom is too unstable to exist.*

You easily find that **realistic** de Broglie waves such as pilot wave are **impossible** in Schrodinger's hydrogen, in which *orbital* angular momentum of ground state (= 1s ) is **zero**.

This means an electron of hydrogen often **penetrates** or crashes into nucleus !

If so, the **opposite** phases of this electron's de Broglie wave **cancel** each other in **linear** motion.

( A wave of 1 × de Broglie wavelength consists of **a pair** of ± *opposite* phases. )

As a result, the de Broglie wave **vanishes** and the electron is expelled, according to Davission-Germer experiment. Furthermore, real wave model cannot explain nagative radial kinetic energy on **both** ends.

Of course, if you try to explain two-slit and atomic structure using **real** de Broglie waves, you have to admit some **ether**-like matter spreading over the vacuum space, **against** special reltivity.

*(Fig.25) Various media, universities, journals "deceive" students by hiding fatal paradoxes.*

Though various media and textbooks argue that special ( general ) relativity has *passed* many tests, and is believed to be one of most *successful* theories, these comments are big **lies**

In fact, there are fatal paradoxes ( see this and this ) such as Lorentz force and right-angle lever, which can prove special relativity is wrong.

Though various sites argue these paradoxes have been solved, they have to depend on **fictitious** concepts.

Depending on **illusory** concepts such as center of rotation, force flow means these paradoxes have **NOT** been solved. So they **proved** special reltivity includes fatal flaws, which are exposed in movements in **two**-directions.

Special relativity is the foundation of various important theories such as QFT, QED and Higgs.

So various media try to **hide** these fatal paradoxes from people. Actually you **cannot** find these paradoxes in various books.

If you compare **harsh** criticism ( this, this ) against *superluminal* neutrino and **indulgence** in BICEP2 mistaken inflation, you'll notice **too much** power of relativists **distorts** the current physical facts.

*(Fig.26) All reaction paths in accelerators must include "unreal" virtual particles !*

The current particle physics always **needs** unrealistic **virtual** particles in the process of reaction.

These virtual particles **disobey** special relativity (← a square of mass, **m ^{2}** must be

Though almost all textbooks say these tachyon-like virtual particles can be explained by *uncertainty* principle, this logic is completely **inconsistent**.

Even if quantum mechanics can explain this *unrealistic* virtual particle, it does **NOT** change the fact that special relativity is **violated**. Anti-particle annihilation also generates **heavy** virtual photons !

So the current relativistic quantum field theories such as standard model and QED are **self-contradictory**, which means they are **wrong**.

*(Fig.27) Higgs, fractional-charge quarks, W, Z bosons are all "unreal".*

The recent interesting news say "Shocking ! Higgs was NOT discovered. ", though Higgs boson got Nobel prize.
Because there is **NO** conclusive evidence for Higgs boson, as shown in this and this, BICEP2 again.

As shown in this sites, they are just convinced that the detection of two ( a little excess ) ** lights** shows Higgs, though there is **NO** certain evidence for this **far-fetched** interpretation. Higgs discovery is just **delusion**.

Actually, if some government officials ( who adjust budgets ) ask *CERN* physicists when they can **take out** Higgs from accelerator, the physicists would just say, "It's **impossible** to take out Higgs from accelerator **forever**."

Because there are **NO** realities in elementary particles with extremely short lifetime, which appear (← ? ) **only** inside accelerators. So LHC has **NOT** proved "**infinite**" Higgs ( sea ) spreading all over our **real** universe.

Calorimeters in accelerators cannot measure each *kientic* energy and light *frequencies*. See this, this, this (p.5). So fractional-charge quarks and **missing** energies indicating SUSY are **doubtful**.

*(Fig.28) Why we cannot detect Higgs and W boson in the common laboratory ? ← NOT real.*

Just after Nobel prize, books such as "Higgs fake" had been published.

Because Higgs **lacks** reality, **different** from electrons ( protons ). No smoke without fire.

In the ordinary beta decay, W- boson is said to be generated in the process of neutron's changing into proton.

At this moment, Higgs **must** exist there to give mass to W boson.

If so, we can detect **both** Higgs and W boson (= 80 × protons ! ) decay in the process of **ordinary** beta decay even in *laboratory*, **NOT** relying on giant accelerators.

But **neither** of them can be detected in the process of *ordinary* beta decay.

This means Higgs and W boson produced ( ? ) inside accelerators are completely **different** from *infinite* Higgs and W bosons ( in beta decay ) defined by standard model. So, they are inconsistent, and **NOT** real.

Also inside accelerators, these W bosons are just **virtual** ( NOT real ) particles, because they do **NOT** satisfy the basic rule of energy conservation.

Higgs (= **125** GeV ) → 2 × W bosons (= 80+80 = **160** GeV ! ). Impossible.

*(Fig.29) Mathematical trick = Change of variable affects the calculated results !?*

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

In Fig.29, "change of variables" ( k = l - β ) **artificially** changes 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 **artificial** 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.

It's **unnatural** that *penetrating* nuclei is involved in very small hyperfine.

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.30) "Density" of dark energy and the "distance" between Sun and earth remain the same !? *

This year, the breakthrough physics prize 3 million $ was given to **unrealistic** accelerating universe.

The current physics just escapes into **unprovable** early universe, **avoiding** atomic mechanisms *before* us ( ex. spin ).

If the **acceleration** of expansion of our universe is true, the motive power (= dark energy ? ) to expand universe would **NOT** be *diluted* by expansion ! So they invented "*convenient*" concepts such as "negative pressure" (= unreal ).

Furthermore, as shown on this site and this site, they argue the **distance** between the earth and Sun remains the **same**, no matter how fast our universe expands. So this idea of "accelerating" universe is **too good** to be true, and **lacks** reality.

It is natural that the light gradually **loses** its energy by Compton effect during extremely **long** time ( ~**billion** light years ).

When the light collides with some object ( dusts ) with **finite** mass, it always **loses** energy, and causes redshift ( **NOT** by *fantasy* expansion ).

*(Fig.31) It's impossible that all microwaves can keep their uniformity for extremely long years.*

They argue the most conclusive evidence for this expanding universe is **uniform** cosmic microwave background (= CMB ). But thinking *commonsensically*, this idea is just **impossible** as shown on this page.

They argue that the original uniformity in *small* area was **expanded** to be *uniform* for **13.7** billion years.

But each microwave has been **influenced** by various different **dusts** and debris for such an extremely **long** time.

This means during this process, the *uniformity* originally possessed by ancient lights would have been completely **gone**.

So the idea that CMB is a **snapshot** of the early universe ( this, this ) just after Big Bang is
very **unreasonable**. (← *13.7* billion years = *snapshot* !? )

Furthermore they have to depend on **superluminal** inflation to explain
the original *uniformity* 13.7 billion years ago.

They insist this doubtful inflation just after Big Bang can be confirmed by observing very **faint** B-mode pattern in polarized light.

But the curling pattern of this B-mode is Only **0.4 μK** (= 0.4 × 10^{-6} K ) in temperature, as shown on this site.

So it's much more **impossible** that this very weak B-mode polarization is **left** as it is for **13.7 billion** years. Gravity wave is **artificial** concept, too.

*(Fig.32) It's impossible for black hole to be generated within "finite" time.*

Though variou journals and media refer to black hole, as if it were *real*, black hole absorbing everything including lights cannot be directly observed.

They just **estimate** its existence based on X-rays emitted (← ? ) from materials *around* black hole.

So the black hole itself is just an **imaginary** concept which has **NOT** been experimentally confirmed.

Actually, the universe is filled with other gamma rays and X-rays from **unknown** sources.

In fact, it is **impossible** for black hole to be generated "within" **finite** time (= age of universe ).

As mass becomes **denser** in the process of forming black hole, the time becomes **slower** due to its stronger gravity.

To form black hole, dead star must be **condensed** by its own gravity enough to make the time of event horizon stop (= gravitational collapse ).

As shown on this site, if you watch black hole formation from a safe distance ( ex. *earth* ), you can **NEVER** see material moving near event horizen due to severe dime dilation (= time **stops** ! ).

So *within* age of universe, the formation ( in which materials **must** move ) of black hole is **impossible**.

*(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 *realistic* theories under the conditions of **NO** computers in *1920s*.

So even 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, which **weird** situations prove that the current basic physics includes fatal **defects**.

They are **inciting** ordinary people to believe these **unrealistic** concepts using fascinating "*fake*" images.

For example, the original Higgs is just *abstract* math operators with **NO** clear picture.

But various media ( see this and this ) try to plant *stimulating* "fake" images of **God** particle in people.

The same can be said for **impractical** (← forever ) quantum computers ( see this and this ).

*(Fig.34) Theory of Everything = 10 dimensional string theory is abstract "Math" with NO clear pictures.*

This **harmful** tendency is seen also in *Hollywood* world.

According to NYTimes, the movie "
Theory of Everything " was released.

So various media including Hollywood try to spread "**unrealistic**" theories such as 10-dimensional string theory using **showy** and fascinating images.

The technology and performances by actors and actress in Hollywood were very **realistic** and superb.

In other words, this very fascinating Hollywood's world can be *misused* to **seduce** ordinary people into believing **fictitious** theories (= extradimensions ).

This tendency is very **dangerous** especially for **newcomers** in physics.

In fact, quantum field theory including string theory (= the **only** theory of everything ) is a collection of abstract ( wrong ) math symbols with **NO** physical images. See this, this and virtual particles.

The media and string theorists must stop **misleading** people and students into "**impossible**" theories ( Big Bang, inflation ) **utilizing** captivating Hollywood's world and celebrated actors, as shown on this site.

*(Fig.35) 2 × 1s electrons' angular momentum L = 0 ← unstable helium (= He ) !*

According to quantum mechanics, two electrons of helium ground state are in 1s state with **zero** angular momentum.
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** and **unstable**.

As I said in Fig.24, de Broglie waves of 1s orbit are *cancelled* out by their opposite phases.

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

As shown on 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 this helium model by quantum mechanical " spin" **cannot** explain the important property of actual helium atom.

*(Fig.36) Spin-spin interaction energy is only 10 ^{-6} eV, which is easily broken at 0.05 K !*

As shown on this page and this site (p.7), spin-spin *dipole* (= Bohr magneton ) interaction enegy is **too weak** ( < **0.3 K** in temperature expression ) to explain actual ferromagnetism ( **1043 K** in Fe temperature ! ).

For example, the bond length between Fe-Fe is about 2.8 Å (= 2.8 × 10^{-10} meter ). See this site (p.2).

Using this page, this site, this site (p.6), we find spin-spin dipole interaction becomes only **4.55 × 10 ^{-6} eV** (=

Pauli exclusion principle **cannot** be explained by *too weak* spin-spin interaction, either.

As shown on this site, lithium with **3 × 1s** configuration gives **lower** (= 8.46 = **-230 eV** ) than experimental value (= **-203 eV** ) using Hartree → eV.

This wide discrepancy ( **27 eV** = 230 - 203 eV ) shows this Pauli repulsive force is caused by other **strong** effects such as de Broglie wave interference.

Furthermore, sodium D line splitting is **too wide** to be explained by spin-orbit coupling.

So, as long as we stick to these **contradictory** spins, pursuing the *true* mechanism are **hampered**.

*(Fig.37) 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, each of with predicts a **different** universe.

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

**Enough** time has already passed to **exclude** all other gravity theories such as loop quantum gravity.

Besides the unrealistic string theory , the present quantum theory itself 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, which gives infinity.

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

So there had been one **trouble** after another in the quantum theory and relativity since they were born, indicating the existence of fundamental **defects** in them.

*(Fig.38) Quantum mechanics obstructs the elucidation of "true" (= real ) microworlds.*

Quantum mechanics introduced in 1920s has been exposed to **criticism** due to its **unreality** such as superluminal spin and many-worlds (= Schrodinger's cat ).

Basically, quantum mechanics **avoids** clarifying clear mechanism of microphenomena and sticks to **vague** scientific attitude.

Due to its **inability** to compute multi-particle *dynamics*, quantum mechanics created **fictitious** quasi-particles and "*imaginary*" target of quantum computer, which state easily **breaks** within **nano**seconds, completely **impractical**.

As you see, living things including our human bodies are highly **sophisticated** nano-*machines*, which is far **beyond** our current knowledge.

So, as long as we keep **avoiding** a clear picture of micro-phenomena, it is obviously **impossible** to *cure* various serious **diseases** such as cancer, HIV, ALS, severe allergy, dementia ..., **forever**.

*(Fig.39) 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, which picture **contradicts** angular momentum zero of "s" state.

*(Fig.40) de Broglie wave ends fit.*

To avoid cancelling de Broglie wave, both ends of electron's wave in hydrogen atom need to **agree** with each other with respect to wave phases.

*(Fig.41) Old Bohr's helium. Two de Broglie waves cancel each other.*

In old Bohr's helium (Fig.41), **two** electrons are moving on the **opposite** sides of the nucleus in the *same* circular orbit (= **one** de Broglie wavelength ).

Considering Fig.39 and Fig.40, two electrons of old Bohr's helium are clearly **unstable** due to de Broglie wave **destructive** interference. ( **Opposite** wave phases, ±ψ exist on the other sides in 1 × wavelength orbit.)

Actually, old Bohr's helium of Fig.41 gives **wrong** ground state energy of helium.

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

*(Fig.42) Old Bohr helium.*

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

*(Fig.43) Circular orbit = 1 × de Broglie wavelength.*

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

*(Fig.44) Energy of old Bohr's helium.*

Solving the above three equations ( Fig.42-44 ), the ground state energy ( n=1 ) becomes **- 83.33 eV**.

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

*(Fig.45) Old Bohr's helium does NOT agree with experiments.*

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.46) Old Bohr's helium can NOT keep 1 × de Broglie wavelength*

In Fig.46 left, only one electron is moving around helium nucleus.

This orbital length is just **1 ×** de Broglie wavelength, which means "**stable**".

Of course, the **field** in this orbit is affected by the electron's momentum (= mv = **pressure** ) and contracts depending on its strength.

In **old** Bohr's helium model, two electrons are moving in the **same** one orbit on *opposite* sides of nucleus.

When another **moving** electron enters the same orbit, the force (= pressure ) **acting** on their surrounding field becomes **twice** ( mv → 2mv ).

As a result, the original 1 × de Broglie wavelength **cannot** be kept as it is in Fig.46 right.

See "real" de Broglie waves and electromagnetic fields.

*(Fig.47) Various old Bohr's helium atom.*

In **1910s - 1920s**, Lande (= outer and inner orbits, Fig.47A), Langumuir (= two parallel orbits, Fig.47B, two linear oscillating orbits, Fig.47C), Kramers (= 120 degree angle crossed orbits, Fig.47D ), and Heisenberg (= coplanar and inclined orbits, Fig.47E,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. See this.
Because about that time, they did not have **computers** to calculate *three*-body helium atom.

*(Fig.48) Quantum mechanical helium*

When Z=2, Fig.48 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 ( see this page ).

*(Fig.49) Quantum mechanical helium > 1000 terms !?*

Of course, we can NOT imagine the helium's actual configuration from these many mathematical terms of Fig.49.

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. )

*(Fig.50) "Unreal" Quantum mechanical helium cannot give probability density.*

Different from simple hydrogen atom, two electrons of helium are **avoiding** (= moving ) each other due to repulsive Coulomb force.

So it is **impossible** to define *stationary* **probability** density of two electrons in helium.

As a result, the wavefunction (= more than **1000** terms ! ) of quantum mechanical helium, which **cannot** give any particle's informations, is completely **useless**.

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.51) 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.51.

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 can be **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.41. Of course, these wave phases are **chaotic**, and unstable in this case. )

*(Fig.52) Old Bohr's helium = electrons are expelled. New Bohr helium = stable.*

In **1 ×** de Broglie wavelength orbit, the *opposite* sides of nucleus contain the **opposite** wave phases, which **cancels** another phase.

When two de Broglie waves are just **perpendicular** to each other, they can **avoid** *destructive* interference between these *opposite* phases.

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

*(Fig.53) New Bohr's helium (= A.) is not electrically polarized.*

As you know, helium atom does **NOT** form any *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 **stability** and independence of helium.

As shown in Fig.53 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.
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.

*(Fig.54) New Bohr's helium can explain Pauli exclusion principle. Too weak Spin cannot.*

Of course, there is **NO** space for the third electron to enter in Fig.51 model (= Pauli **exclusion** principle ).

Because, if the third electron enters the orbit of 1 × de Broglie wavelength in this new Bohr's helium, it **cannot** be **perpendicular** to *both* of two other waves.

On the other hand, in *old* Bohr helium, the third electron of Li *can* enter this orbit, because it does **NOT** depend on **cancellation** between de Broglie waves.

**Spin-Spin** magnetic dipole moment interactions are **too week** to explain strong Pauli exclusion principle.

For example, fine structure of hydrogen is **ONLY** 0.000045 eV. Spin-spin coupling is **weaker** than it.

As a result, **Only** de Broglie wave's **interference** is left for describing **strong** Pauli exclusion principle.

*(Fig.55) Two same-shaped orbital planes are perpendicular to each other. *

Next we calculate the new helium using simple computer program.

Fig.55 shows *one quarter* of the orbits.

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

*(Fig.56) The two electrons have moved one quarter of their orbitals.*

In Fig.56, 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.55 and Fig.56 is the most *stable* one.

( If the electrons are moving like Fig.55 and 56, the potential energy becomes the **lowest**. )

I thank Tao greatly for giving youtube of this helium !

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.55 and Fig.56, the helium nucleus is at the origin.

The electron 1 initially at ( r1, 0, 0 ) moves **one quarter** of its orbit 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

*(Fig.57) New units of time and length.*

From Fig.57, the accelaration is

*(Fig.58)*

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

When you run this program ( for example, JAVA ) in command prompt, the following sentences are displayed on the screen.

*(Fig.59)*

First we input the *initial* x-coordinate r1 = **r** (in MM) of electron 1 (see Fig.60 ), and press "enter" key.

In Fig.59, we input "**3060**", which means the **initial x** coordinate of **electron 1** is 3060 MM = 3060 × 10^{-14} meter. The initial x coordinate of electron 2 becomes -3060 MM, automatically.

Next we input the **absolute** value of the total energy |E| (in eV) of helium.

In Fig.59, when we input "**79.0**", and press enter key, it means total energy of this helium is **-79.0 eV**.

*(Fig.60) Initial states. "r" is initial x coordinate of electron 1.*

From the inputted values, we calculate the **initial velocity** of the electron 1 ( = 2 ) in y ( z ) direction.

Total potential energy (= V ) of the initial state of Fig.60 becomes

*(Fig.61) Initial total potential energy V.*

The first term of right side in Fig.61 is the potential energy between two electrons and 2e+ helium nucleus.

The second term is the repulsive potential energy between two electrons.

*(Fig.62) Initial velocity "v".*

Total kinetic energy of two electrons is given by total energy (ex. -79.0 eV ) minus potential energy (= V ).

So from inputed values of Fig.59, we can get the initial velocity of each electron.

The initial velocity of electron 1 ( 2 ) is in y ( z ) direction.

*(Fig.63) Change unit of velocity.*

Using the new unit of Fig.57, this program changes "m/s" into "MM/SS" in the initial velocity.

Because it is **convenient** when calculating each acceleration and de Broglie wave at intervals of **1 SS** (= 10^{-23} seconds ).

*(Fig.64) Positions of two electrons.*

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

When the electron 1 is at ( x, y, 0 ), the electron 2 is at ( -x, 0, y ). (See Fig.55 and Fig.56.)

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

*(Fig.65) x component of the acceleration.*

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

*(Fig.66) Distances among two electrons and nucleus.*

Due to **symmetric** positions of two electrons, when electron 1 is at ( x, y, 0 ), the electrons 2 is at ( -x, 0, z ), in which **z = y**.

As a result, the **distance** between electron 1 and nucleus is given by the first relation of Fig.66.

The second relation is the distance between 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.

*(Fig.67)*

See also reduced mass of three-body helium.

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

*(Fig.68) 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.41 ( see why old Bohr's helium is impossible ).

But in Fig.41, the two electrons are **packed in one orbit** of one de Broglie's wavelength.

So their de Broglie wave **oppsite** phases (= ±ψ) are cancelled (= destructive interference ).

*(Fig.69) De Broglie waves in each segment.*

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,

*(Fig.70)*

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.71), 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.55 and Fig.56.

*(Fig.71) Computing results ( input: 79.00 eV, r1 = 3060 MM ).*

After moving **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 ).

*(Fig.72) When total energy is just -79.00 eV, 1/4 de Broglie wave is 0.250006.*

This program gives results when r1 is from inputted value (ex. 3060 ) to r1+100 (= 3160 ).

As shown in Fig.71, when r1 is **3074** MM, last **VY** velocity of electron 1 becomes the **smallest** ( VY = 0.000000 ).

This means when r1 ( initial x coordinate ) = *3074* × 10^{-14} meter, these electron's orbits become just **symmetric** and stable.

In this case, the number of de Broglie wave contained in **a quarter** of its orbit becomes **0.250006**.

So, **one orbit** is 0.250006 × 4 = **1.000024** de Broglie wavenlength. ( ← **NOT** 1.000000 )

As shown in Table 1, when inputted energy is **-79.0037 eV**, de Broglie wave becomes just **1.000000**.

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

The result of total energy of new Bohr's helium becomes **-79.0037 eV**.

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** (= 1st + 2nd ionization energies, Nist, CRC ).

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 includes **self-contradiction**.

*(Fig.73) Hydrogen and Helium atoms.*

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

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

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.74) n × de Broglie wavelength → stable even after many orbital motions.*

As you know, the energy levels of hydrogen is **quantized**, because its orbital length is an **integer** (= n ) times de Broglie wavelength.

Even in Schrodinger equation, this de Broglie relation holds.

As shown in Fig.74, when the orbital length is just **n ×** de Broglie wavelength, their wave phases **fit** each other at any points.

So, even after **arbitrary** orbital motions, these de Broglie waves **can** keep its original waveform **stably**.

The waveform (= wavelength ) of de Broglie waves show electron's **momentum** (= p ) through p = h/λ.

So keeping its waveform means electron's **motion** is stable.

*(Fig.75) NOT integral de Broglie wavelength → destructive interference. → cancelled !*

When the orbital length is **NOT** an integer times de Broglie wavelength, their wave phases do **NOT** agree with each other at the starting point.

In this case, after the electron rotates around the nucleus *many times*, it causes many different waves with **different** phases inside the **same** orbit.

As a result, they **cancel** each other due to **destructive** interference, and become **unstable** electron's motion.

*(Fig.76) When two orbits of helium are NOT perpendicular .. *

In Fig.76 helium, two orbits are **NOT** completely perpendicular to each other.

In this case, at the point of intersection (= point 1 ), two de Broglie waves in the **same** direction **overlap**.

As I said, these wave **phases** are **opposite** to each other, because helium's orbit is **1** × de Broglie wavelength.

So a part of their waves is **cancelled** out.

*(Fig.77) Waves are cencelled → NOT an integer × de Broglie wavelength.*

If a part of their de Broglie waves is cancelled due to the opposite phases, it does **NOT** satisfy n × de Broglie wavelength.

So, as I said in Fig.75, after arbitrary orbital motions, many **different**-phase waves overlap, and **cancel** each other.

This is the reason, why two orbits of **stable** helium must be just **perpendicular** to each other.

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, summary .

*(Fig.78) Spin-spin dipole energy (= 0.0001 eV ! ) vs. Pauli exclusion energy= 27 eV.*

According to Pauli exclusion principle, two electrons **cannot** be in the **same** state in "spin".

So they argue that the third electron of Li must enter *higher* **2s** state instead of lower 1s. See this.

Of course, if this third electron of Li can enter the ground **1s** state, its total energy becomes much **lower** (= stable ), because the **shorter** distance between an electron and nucleus **lowers** *Coulomb* energy.

As shown on this site, *3 × 1s* electrons in Li gives **-230 eV** (= 8.46 Hartree ), which is much **lower** than the true Li ground state energy (= **-203 eV**, 7.48 Hartree ). This energy difference is "**27 eV**" !

But electron **spin-spin** *magnetic* dipole interaction is **too weak** to explain this **strong** Pauli *repulsive* force. Electron **spin**'s magnetic moment is Bohr magneton. Classical dipole-dipole energy is this.

In this and this, when the interelectronic distane is **1 Å** (= hydrogen diameter ), the spin-spin magnetic energy is very *weak* (= **0.0001 eV** = 1.7 × 10^{-23} J, use this ), which **cannot** explain *Pauli* exclusion.

*(Fig.79) "up" ↔ "down" spins = attract ? Lithium can contain 3 × 1s electrons !*

For example, we suppose "up" and "down" **opposite** spins **attract**, and the *same* (= "up" and "up" ) spins *repel* each other.

In this case, the combination of three "up", "down" and "up" spins is **allowable**.

Because, as shown in Fig.79, this combintion contains **2** × **attractions** and *1* × *repulsion*, so the total is **attraction** !

This is the reason why spin direction cannot explain Pauli exclusion principle in Lithium 2s third electron.

*(Fig.80) Eight valence electrons = regular hexahedron.*

Neon is stable noble gas, and has **eight** valence electrons in **n = 2** orbitals.

Considering **symmetric** distribution due to repulsive Coulomb forces, regular hexahedron is natural.

In Bohr-Sommerfeld model, principal quantum number, n = 2 means **2 ×** *de Broglie* wavelength orbits.

See new Bohr model Ne, Ar in detail.

*(Fig.81) 2 × de Broglie wavelength orbits. Each is a pair of opposite phases.*

As shown in Davisson-Germer experiment, each de Broglie wavelength consists of a **pair** of ± phases, which are **opposite** and cancel each other.

2 × de Broglie wavelength orbits can contain **2** electrons, as shown in Fig.2.

There are 4 *midpoints* (= **2** midlines ) with **zero** phases between ±phases.

*(Fig.82) 2 × de Broglie wavelength orbits. Each is a pair of opposite phases.*

As shown in Bohr model Neon, we can consider 4 elliptical orbits crossing each other pependicularlly.

"Perpendicular crossing" means avoiding destructive interference. See Helium case.

*(Fig.83) Each electrons can move independently from other "annoying" phases.*

Fig.83 shows the periodic movements of **all** eight electrons in Bohr model Neon.

( Here only "e1" and "e2" orbits are shown, because this is easy to see. )

8 electrons of neon can move *smoothly*, **NOT** crashing into other electrons.

*(Fig.84) Electrons always cross other "opposite" wave phases, "neutralizing" total phases.*

As seen in Fig.83 and Fig.84, each electron can cross other electrons' orbits **perpendicularly**, when they are **opposite** wave phases to each other.

"*Perpendicular* crossing" means each de Broglie wave can **avoid** *destructive* interference.

And crossing of "**opposite**" wave phases can **neutralize** total wave phases at all points.

"**Neutralization**" of wave phases means any *other* electrons can be **free** from other wave ( bad ) influences, and move stably and **independently**. See this page

*(Fig.85) Maximum orbits = midpoint lines + 2 (= two perpendicular orbits )*

When each orbit **crosses** another orbit **perpendicularly**, they can avoid destructive interference.

When atoms contain more than two orbits, other orbits must be on the **midpoint** lines (= *zero* phase ) **NOT** to be disturbed.

So, the **maxium** number of orbits in Ne becomes "**4**" (= 2 × *perpendicular* + 2 × **midlines** ).

4 × de Broglie wavelength contains **4** midlines, so the total orbital number of Kr becomes "**6**".

The **odd** numbers of "3", "5", "7" orbits are asymmetrical and **unstable**.

So the orbital numbers of "**Ar**" (= 3 × waveslength ), "*Xe*" (= 5 × waveslength ) remain the **same** as "**Ne**" and "*Kr*".

So we can get the generalized **common** rules, "*perpendicular* orbits" and "**avoiding** destructive interference" in all atoms based on **de Broglie** wavelength. See also this page.

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.86) Comparison of forces acting on C electron.*

Force unit **1000** = force between -e and +e, which are *Bohr radius* apart.

Fig.86 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.87) 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.88) 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.89) 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.90) "Long" (= middle ) or "short" bond length determines their property.*

As shown on 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.55 ) 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.)

2014/12/10 updated. Feel free to link to this site.