Setagaya-ku Tokyo 155-0033, Japan
♦ Japanese version ♦
New Bohr's worlds (atoms, molecules,bonds.) (13/ 10/16 )
♦ End of Quantum mechanics ! ( Fine structure, Bohr-Sommerfeld, Special relativity ) (14/ 6/11 new! )
♦ Bell inequality violation is an illusion. ( Delayed choice, Quantum computer is real ? ) (13/ 1/29 )
♦ End of Quantum field theory (QFT). (Dirac equation, Quantum electrodynamics, Higgs ) (13/ 1/20 )
Journal Nature's Bohr model. (14/ 6/23)
Criticize top journals. (14/ 7/29)
(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 interpretation 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 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. )
( 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 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 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 ! ).
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 on this page.
Most people are deceived by wrong explanations in standard textbooks and websites.
But a single electron is NOT made from smaller charges. ( A single electron is the smallest charge. )
It means the vacuum electric energy (= 1/2εE2 ) 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 on 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 ( nr = 1, nφ = 1 ) in the energy level of n = 2 ( ← nr + nφ = 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 has "spin", but Sommerfeld's doesn't. )
Furthermore, as shown on 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 on 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 ).
"rR20" and "rR31" contains 2 × de Broglie wavelength in one orbit.
( rR30 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 ( Tr = 1/2mv2 ) 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 ( =Tt ) becomes unrealistically larger.
To cancel this increase, radial kinetic energy (= Tr ) 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 on 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 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 unrealistic "spin" is completely useless in actual helium stability.
(Fig.14) History of Zeeman effect.
As shown on this page, anomalous Zeeman effect of hydrogen atom can be explained by Sommerfeld's fine structure.
Each component of Balmer Hα 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 on 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 on 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 on this page, if we use the classical electromagnetic waves, we can explain this violation as local and realistic phenomenon.
(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 on 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 microseconds (= 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 on 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.
(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 10500 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 on 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 ( see this page ).
The important point is that this SUSY has more than 100 free parameters we can adjust.
So, convenient SUSY can NEVER be denied like unrealistic string theory with 10500 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 on 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
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 on 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 on 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 .
(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.
Experimental results agreed with de Broglie relation.
This experiment showed an single electron has wave-like property , 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. Two de Broglie waves cancel each other.
In old Bohr's helium (Fig.36), two electrons are moving on 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. ( Opposite wave phases exist on the other sides.)
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) 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
(Eq.3) 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
(Eq.4) Energy of old Bohr's helium.
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.
(Eq.5) 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.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 on 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.6) Quantum mechanical helium
When Z=2, Eq.6 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.7) Quantum mechanical helium > 1000 terms !?
Of course, we can NOT imagine the helium's actual configuration from these many mathematical terms of Eq.7.
And this latest calculation value is -79.015 eV , 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.39) "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.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. )
(Fig.41) Old Bohr's helium = electrons are expelled. New Bohr helium = stable.
In 1 × de Broglie wavelength, the opposite sides of nucleus contains the opposite wave phases, which cancels another phase.
When two de Broglie waves are just perpendicular to each other, they can avoid destructive interference.
So there is NO more space for the third electron to enter this helium (= Pauli exclusion principle can be explained ! )
(Fig.42) 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 stability and independence of helium.
As shown in Fig.42 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.43) 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.40 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 Pauli exclusion principle.
(Fig.44) Two same-shaped orbital planes are perpendicular to each other.
Next we calculate the new helium using simple computer program.
Fig.44 shows one quarter of the orbits.
Electron 1 starts at (r1, 0, 0), while electron 2 starts at (-r1, 0, 0).
(Fig.45) The two electrons have moved one quarter of their orbitals.
In Fig.45, 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.44 and Fig.45 is the most stable one.
( If the electrons are moving like Fig.44 and 45, 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
As shown in Fig.44 and Fig.45, 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.8) New units of time and length.
From Eq.8, the accelaration is
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.
First we input the initial x-coordinate r1 = r (in MM) of electron 1 (see Fig.47 ), and press "enter" key.
In Fig.46, 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.46, when we input "79.0", and press enter key, it means total energy of this helium is -79.0 eV.
(Fig.47) 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.47 becomes
(Eq.10) Initial total potential energy V.
The first term of right side in Eq.10 is the potential energy between two electrons and 2e+ helium nucleus.
The second term is the repulsive potential energy between two electrons.
(Eq.11) 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.46, we can get the initial velocity of each electron.
The initial velocity of electron 1 ( 2 ) is in y ( z ) direction.
(Eq.12) Change unit of velocity.
Using the new unit of Eq.8, 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.48) 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.44 and Fig.45.)
So the x component of the acceleration ( m/sec2 ) of the electron 1 is,
(Eq.13) 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.
(Eq.14) 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 Eq.14.
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.
See also reduced mass of three-body helium.
In the same way, the y component of the acceleration (m/sec2) is,
(Eq.16) 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 ).
(Fig.49) 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,
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.45), 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.44 and Fig.45.
(Eq.18) Computing results.
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 ).
(Eq.19) 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 Eq.18, 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|
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 has self-contradiction.
(Fig.50) 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.51) 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.51, 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.52) 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.53) When two orbits of helium are NOT perpendicular ..
In Fig.53 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.54) 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.52, 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)|
Table 4 shows three electron atoms such as lithium.
|Atoms||r1 (MM)||WN x 4||Result (eV)||Experiment||Error (eV)|
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.55) 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.55 model, the outer electrons of upper and lower crash into each other, while they are orbiting around the nucleus.
(Fig.56) 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.57) Neutral Neon's eight orbits of valence electrons.
In Fig.57, for example, the orbits of the electron 3 and 5 ( e3 and e5 ) have two common vertices, and perpendicular to each other, like
(Fig.58) Orbits perpendicular to each other.
In Fig.57 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.59) Comparison of forces acting on C electron.
Fig.59 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.60) 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.61) 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.62) 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.63) "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.
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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.