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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)
(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, m2 < 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 ( 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 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 ).
"rR10", "rR20" and R30 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 (= 1/2εE2 ) 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 (= 1/2εE2 ) 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 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 microseconds. 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.
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, m2 must be nagative ) ! See this, this, this, this.
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 (= 0.05 K ! ).
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 10500 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 nanoseconds, 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 , 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
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
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.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/sec2 ) 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.
See also reduced mass of three-body helium.
In the same way, the y component of the acceleration (m/sec2) 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,
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|
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)|
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, 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.
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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.)
2014/12/10 updated. Feel free to link to this site.