Top page (correct Bohr model including the two-electron atoms)
Strange "spin" is NOT a real thing
Pauli exclusion principle by Bohr model is more useful.
Rigorous proof that Schrodinger equation belongs to Bohr-Sommerfeld model
As you know, Schrodinger wavefunctions only show the probability density of the particles such as electrons, and can NOT express concrete particle's motion.
According to the standard interpretaion of the quantum mechanics, the moment we try to observe the particle, the probability density spreading in all space becomes a point particle (= collapse ).
Of course, this process must be faster-than-light (= nonlocal ), because it happens in less than a moment.
( See the case of hydrogen atom in Fig.1. )
(Fig.1) Wavefunction "collapse" is faster-than-light !
It is known that the particles such as electrons, protons, and C60 buckyballs show the wave property of interference.
For example, even when there is only one C60 buckyball molecule in the path, it shows the interference with itself in the two-slit experiment.
(Fig.2) A single C60 buckyball interferes with itself !
According to the standard quantum mechanics, this interference of a single C60 is caused by strange "superposition".
Strange to say, in this superposition state, a single C60 molecule can go through every path at the same time (= Fig.2 right ).
So it is impossible to express this weird state using real things.
You may think we should use the idea of a single particle and real de Broglie wave around it (= Fig.2 left ).
But if you admit the real de Broglie wave around the particle, the wavefunction collapse of Schrodinger equation (= Fig.1 ) becomes meaningless.
Because Schrodinger wavefunction can not express clear motion and image of the particle, it only shows the probability density.
And as you know, admitting real de Broglie wave means Bohr model (+ aether theory ).
So if you agree to the probability concept of the quantum mechanics, you must give up the very natural and "local" mechanism of Fig.2 left panel.
(Fig.3) Failure of various old Bohr's helium atoms.
As shown in this page ( failure of old Bohr's helium and chaotic classical atoms ), the three-body helium could not be explained by Bohr model, because they had no computers in 1920s.
On the other hand, the quantum mechanical variational method got approximate ground state energy of helium.
Though this quantum mechanical helium has no clear images, it replaced Bohr model due to the very difficult three-body problem.
From 1920s to 1980s-1990s when the computers become popular, people stopped doubting the quantum mechanics itself, though the quantum mechanical world is very strange and mysterious.
Now we have succeeded in expressing helium atom (+ Pauli exclusion principle ) more accurately than the latest quantum mechanicsl methods, as shown top page and this page using computers.
And the usual quantum mechanical textbooks should change the explanation about Bohr's electron radiating energy, as shown in this page.
In 1920s, they started to insist that Bohr magneton is caused by the strange spin not by the circular movement.
But this decision generated "mathematical" and unreal spinor, and forced us to give up asking what spin actually is.
(Fig.4) Electron spin is an illusion.
One electron is very light and small.
So by equating the angular momentum of the spinning sphere of the electron to 1/2 ħ, the sphere speed leads to more than one hundred times the speed of light.
And the fermion (such as spinning electron) doesn't go back to its original configuration by one rotation (= 360 degrees = 2π ).
As a result, we have to rely on mathematical spinor even in the final theory of superstring, NOT questioning what this spin really is.
( Many famous physics books avoid mentioning what this strange spin really is. )
Furthermore the fine structure of Bohr-Sommerfeld model was replaced by relativistic Dirac equation.
(Fig.5) Many-world interpretation and Bohmian mechanics.
To explain the nonlocal wavefunction collapse of Fig.1, the interpretations such as Copenhagen, many-world and Bohmian mechanics (= pilot-wave ) were thought up.
In Copenhagen interpretation, while we do not start the action of observation, the wavefunction keeps its superposition state.
And the moment we start to observe, the wavefunction collapses into the single point-particle !
So this interpretation treats our observers' existences too specially, and avoids explaining this mechanism clearly (= Shut up and calculate ! ).
In Bohmian mechanics (= pilot-wave theory, Fig.5B ), the moment we start to observe, the particle moves faster-than light to the observer's position.
Due to this tachyonic property (+ no spin and charge ), this theory is not generally accepted.
As a result, the many-world interpretation of Fig.5A is left.
In many-world, there are infinite different worlds of a single particle at the same time.
When we observe, we see one of these worlds, so the particle needs not move faster than light, though this quantum mechanical process is nonlocal.
Instead, we have to accept very strange infinite worlds ! ( Can you believe this weird theory ?? )
Infinite worlds continue to make infinite worlds (= infinite × infinite × infinite... ) ??
So if you give up "real" Bohr-Sommerfeld model, you MUST admit many-world interpretation as "reality".
And this many-world interpretation is related to the superstring theory which contains infinite kinds of six-dimensional space geometrical structures
These structures give different elementary particle models. ( So infinite "unreal" theories are included in the string theory. )
As a result, the idea of many worlds is very favorable to the string theory (= landscape).
(Fig.6) Faster-than light (= "spooky" ) actions of photon pair.
If you try to explain the two slit experiment using a single particle and real de Broglie wave around it (= Fig.2, left ), the quantum mechanical physicists would attack you referring to Bell inequality violation.
But this Bell inequality violation is based on very supernatural and mysterious logic.
No matter how far two entangled photons are away from each other, the moment one photon (= A ) passes the filter A and change its polarizing axis, another photon (= B ) also makes its polarizing axis the same as filter A, which is very far away from B.
This process is faster-than light (= nonlocal ).
But as shown in this page, you can understand this mysterious phenomenon is caused by our misunderstanding about a photon "particle".
If we use usual dividable electromagnetic wave, we can explain this Bell inequality violation as a classical local theory.
Furthermore, if we stick to the photon particle, we have to admit very strange worlds of delayed choice experiment.
So it is natural that we consider a photon as electromagnetic wave instead of a rigid particle.
( It is a famous story that Willis Lamb opposed the photon "particle". )
But if we give up the concept of photon "particle", the quantum field theory such as QED, which tries to quantize photon, would be broken.
As galaxies are further away, the wavelengths of the photons emitted by them are stretched (= redshift ).
So they insist the universe is actually expanding rapidly on the assumption that Doppler shift and photon particles are real.
But as I said above, if we give up the existence of photon particle and admit some space medium, this interpretation of expanding universe may change.
Because if these are classical electromagnetic waves, while these waves are going through the space medium (= space ether ), they tend to lose their energies and cause redshift (= tired light ).
(Fig.7) Expanding universe or tired-light interpretation.
In fact, it seems that Hubble did not favor the expanding universe, and instead he liked the tired-light interpretation.
Expanding universe leads to very strange concepts of dark energy and Big Bang.
According to the general relativity, any space curvature of the universe must look the same (= isotropic ) irrespective of the observer.
Combining the expansion and Einstein equation, the early universe proved to include a singularity, which means the general relativity breaks down in the early universe, even if the universe is not uniform.
But they try NOT to give up the general relativity. Why?
And they try to link the rapid inflation of the universe to the increasing worlds of many-world theory.
( But I think many-world interpretation needs infinite worlds, which can NOT be replaced by any other things. )
Also in the black hole, which were derived from Schwarzschild radius, a singularity appears.
As you know, black hole absorbs everything, we can not observe it directly.
The existence of black hole is completely dependent on the general relativity.
( Einstein himself did NOT believe the black hole. )
(Fig.7-2) "Convenient" photon can pass through dark energy, matter, Higgs "uninjured"?
As I said above, strange expanding universe is based on the assumption that photon particle can get through the infinite things such as dark energy, matter, and Higgs particles which fill the whole universe, "uninjured". ( for extremely long time )
And as shown in this page (= single-photon interference ), the existence of photon particle is the origin of many-world like superposition.
And relativistic relation (= a square of energy and momentum ) causes the strange virtual particles, which violate relativity. ( See this page. )
So only from the present observed electromagnetic wave ( photon ? ), we can not know about the detailed early universe.
( The ratio of helium 4, hydrogen and lithium can NOT be the proof of imaginary Big Bang. )
Ignoring the space ether (= dark matter, gravity, gravitational lens ) leads to the misunderstanding about black hole.
Indirect measurement of "jet" and x-rays can NOT prove the invisible black hole, which violates relativistic causality.
The multiverse string theory likes these unobservable things and singularity, which are based on the general relativity.
Because, for now, the string theory is only one successful theory which may explain general relativity and quantum mechanics, which quantization method can be used to solve these problems.
But of course, if the general relativity is wrong, all these interpretations including string theory itself need to change.
And the general relativity is based on local inertial frame, so if the special relativity is wrong, the general relativity is wrong, too.
The rotation of the galaxy contradicts the general relativity.
Because even in the edge of the galaxy, the rotating speed does NOT become slower, which can not be explained from the viewpoint of centrifugal force and usual gravity (+ vacuum ).
(Fig.8) Dark matter is "rotation of space ether".
So the general relativity breaks down in the galaxy rotation.
( But they do not give up the general relativistic strong restrictions. This is strange. )
To cover this deficit, strange "dark matter" was introduced.
This dark matter (and energy) is said to account for most of the things existing in the universe.
But strange to say, we do NOT know what this dark matter really is, though the space has a large amount of it.
If we admit the ether in the vacuum, we can easily explain these phenomena, and all above interpretations drastically change.
The superstring theory relies on mathematical ghosts and Grassmann number, when it decides the very important critical dimensions of our "real" world.
Grassmann number is an anti-commuting value like fermions, and satisfies
(Eq.1)
So "integration" is equal to "differentiation" in Grassmann number !
If two Grassmann numbers ( cc=0 ) become zero, the integration should be zero, I think.
This is strange.
Anyway, this Grassmann number does NOT exist in this real world.
And in the string theory, we have to use the "mathematical" trick of zeta function of
(Eq.2)
Of course, the calculation of Eq.2 is wrong.
But string theory uses this wrong math to keep symmetry as shown in this page.
As long as we do not deny this strange string theory, the concepts of above black hole and expanding universe can survive, I think.
Of course, as we can not go to the edge of the universe, early universe, and inside the black hole, we can not know their real states.
Frankly speaking, the present cosmology relies too much on the imaginary concepts, along with the imaginary string theory.
(Fig.9) String theory = Many world interpretation.
The conclusion is that the string theory, which contains infinite kinds of different theories, is just equal to the many world interpretation.
And personally I think if the quantum mechanics is correct, we MUST admit this very strange many worlds.
So if you try to avoid many worlds, all you can do is to accept Bohr model, because many-world and string theories are completely dependent on the quantum mechanics.
Or you have to be a philosopher, when you try to talk about the quantum mechanics.
(Fig.10) Relativity has survived due to the influential Dirac equation.
As shown in this page, the main reason why the relativity has survived until now exists in Dirac equation, which equation is used in quantum electrodynamics, standard model, and superstring theory.
It is often said that the g-factor calculation in the quantum electrodynamics (QED) shows the validity of the quantum theory and string theory, which can deal with divergence.
But as shown in this page, if we use usual Dirac algebra, we can manipulate the g-factor by transferring excessive values to γ term (= vertex ), which is removed artificially.
The important point is that ordinary people can hardly approach these very complicated theory.
So all they can do is to believe these "mathematical" ( not physical ) worlds, as popular science books say to them.
I myself had believed the quantum mechanics, until I studied these very complicated QED for more than two years.
( This very complicated quantum field theory is the largest obstacle to the development of "real" science, I think. )
And this mathematical quantum field theory and unuseful quantum chemistry were main two reasons why I started to doubt the quantum mechanics.
( Knowing these theories set me free from the "brainwashing". )
(Fig.11) What is Higgs ? Sea ? Resistance ? or only Math ?
You may think if the space is filled with Higgs particles, its meaning is just equal to the "aether".
But they try NOT to admit this fact.
Because Higgs particle is relativistic Klein-Gordon equation, which depends on the special relativity. ( See this page. )
The standard model based on these infinite Higgs particles (field) is clearly inconsistent with the relativity, which denied aether, I think.
And if infinite Higgs (about 125 times proton ) exist around us, why we can NOT feel this heavy particle at all ?
Some people try to say Higgs "field" is different from Higgs particle, and heavy Higgs particles are "hidden" in the field. But this sounds like a "excuse" to me.
If we admit aether (dragging), we do not need to rely on very abstract relativistic quantum field theory, and strange virtual particles, which contradicts relativity.
(Fig.12) Photon's "mass term" is NOT invariant under gauge transformation.
As shown in this page, the reason why they needed Higgs particle exists in the relativity.
The very strong restriction of the relativity made them create gauge theory (= gauge symmetry ).
Probably many ordinary people do not understand this very abstract reason well, because the present standard model is only a "mathematical" thing.
(Fig.13) New Bohr's helium (= A.) is not electrically polarized.
As shown in this page, if the two electrons are just symmetric and perpendicular to each other, there are no imbalance of the minus charged electrons around the nucleus (= neutral, Fig.13A ).
If the two orbits are asymmetric, the space around the nucleus is polarized (= plus or minus charges in Fig.13B).
The polarized atoms tend to interact with each other and form weak binding (see also Fig.13C).
So in this case, the helium easily becomes "liquid", which contradicts the fact.
We have to rely on de Broglie wave interference, when we try to excplain this force which makes the two orbits perpendicular to each other and neutral distribution.
The quantum mechanical helium does not mention this force, so it can NOT explain electrically nonpolarized helium atom.
( As you know, the spin-spin (magnetic) interaction is much weaker than Coulomb force. )
Of course, this concrete version of de Broglie wave means "real" aether, which is moving with the earth.
As long as we can not calculate the three-body helium using computers, we had to rely on Dirac equation and relativity, though it includes fatal paradoxes.
The high precision tests of quantum electrodynamics (QED) supports the present quantum theory, though the quantum mechanical world is very strange.
As you know, the anomalous magnetic moment (g-2) is the most accurate QED test.
Lamb shift is "vague" and difficult to measure to high-order.
( And Lamb shift calculation in QED uses various "ad hoc" methods to match the experimental results.)
But in this page ( g-factor of QED can be changed freely ! ), we explain about the fact that g-factor of QED can be manipulated artificially in plain words.
( If you do not have enough time to study QED, see this page ).
You may have often seen the comments like " high-order accurate calculation means QED is the most successful theory in the world ! " in popular science books.
But I think these people saying such a thing have not done the QED g-factor calculation by themselves.
2012/9/4 updated. Feel free to link to this site.