Top page ( Quantum mechanics is false )

Strange "spin" is NOT a real thing

*(Fig.1) Triplet, Singlet of Magnesium (= Mg ) mean large "Coulomb" energy ( NOT spin ).*

Singlet-triplet energy levels' splitting in alkaline-earth metals such as magnesium, calcium is said to be caused by spin-spin interaction.

But in fact, the electron's spin-spin (magnetic) interaction or spin-orbit (effective) magnetic interaction are too weak to explain the singlet triplet energy splitting.

As shown in Nist, the magnesium singlet (= 3s3p ^{1}p ) and triplet (= 3s3p ^{3}p ) energy levels are in the upper figure, using unit conversion ( cm-1 → eV ).

The energy difference between singlet and triplet is ver big = 1.63 eV.

And the energy difference between three triplet states is about 0.0025 ~ 0.0050 eV, which is also **too big** to explain by tiny electron spin-spin magnetic interaction..

It is natural to think these singlet-triplet energy splitting is caused by Coulomb electric interaction related to inner electrons instead of fictional electron spin.

*(Fig.2) Triplet state ? ← Only "Math", NOT physics.*

*(Fig.3) Singlet state ? ← What is the physical meaning of ± sign ?*

The singlet-triplet by electron spin is **non**physical.

As shown in the upper figure, both the singlet and triplet states include two electrons with up and down spins, and only the sign connecting ↑↓ ± ↓↑ is different, which states cannot be expressed by real things.

And it is unnatural that atomic energy levels of singlets have almost No link to triplet energy states.

*(Eq.1) Conversion of energy units. *

*(Fig.4) Spin-spin magnetic dipole energy is too small to explain triplet splitting. *

*(Fig.5) Spin-spin magnetic energy (= only 0.00002 eV ) is too small to explain actual magnesium's triplet energy splitting (= 0.0050 eV ).*

As shown on this and this-(33.9), electron spin-spin magnetic dipole energy is too **weak** (= **less than 0.0001 eV** ) to explain magnesium triplet energy splitting (= 0.005 eV ).

*(Fig.6) Spin-orbit interaction (< 0.00034 eV ) is too small to explain triplet splitting (= 0.005 eV ).*

Relativistic spin-orbit magnetic interaction is also **too weak** to explain the magnesium triplet energy splitting.

*(Fig.7) Both spin-spin and spin-orbit magnetic interactions are too small to explain triplet and singlet splitting that is caused by strong Coulomb interaction with inner electrons.*

As a result, we find that these triplet and singlet energy splitting are caused by strong **Coulomb** interactions between inner electrons and valence electrons, **neither** by spin-spin nor spin-orbit coupling.

*(Fig.8) Spin-spin magnetic dipole energy is too small ( < 0.0001 eV )*

Here we calculate spin-spin magnetic dipole energy or interaction and show the spin magnetic interaction is too **weak** (= spin magnetic energy is too small ) to explain triplet energy splitting, strong Pauli exclusion repulsion and ferromagnetism, so electron spin is **unreal**.

When the
distance between two electron spins (= spin magnet = Bohr
magneton ) is "z ( or distance r apart )", its magnetic energy (= E_{mg} ) becomes like Fig.8. See also this, this p.17, this, this-lower . Each spin magnetic moment is Bohr magneton (= μ_{B} )

Unrealistic electron spin is accidentally supposed to have the same magnetic moment = Bohr magneton as the Bohr's atomic orbit, as shown in this-lower.

Using these fundamental constants, you can calculate and estimate spin-spin magnetic dipole energy, which is far smaller (= about 0.0001 eV, when the distance between two spin magnetic moments is about 1 Å = 1 × 10^{-10} meter, this p.7-(12) ) than energies required to generate triplet splitting (= 0.005 eV ), strong Pauli exclusion repulsion (= about 30 eV ) or ferromagnetism (= 1 eV ), so electron spin is unreal.

*(Fig.9) Spin-spin magnetic dipole energy. Part II.*

When the direction of "z" is different from spin, the generalized form of magnetic field (= B ) caused by spin becomes like Fig.9.

When "r" is (anti)parallel to m_{l} (= magnetic moment ), this form is just equal to Fig.8.

So we use simple Fig.8 as spin-spin magnetic energy.

*(Fig.10) *

In Fig.10, the circular current I generates the magnetic field (= B ) at the point of "p".

Due to this circular elecric orbit, all magnetic fields other than z direction are **cancelled** out.

Only the **z** conponent (= dB cos α ) is left.

*(Eq.2) *

According to **Biot-Savart** law ( see this site ), magnetic field (= B ) is as shown in Eq.2.

"I" is electric current, "ds" is electric current **fragment**, and "r" is the distance between this fragment and the point "p".

*(Eq.3) *

In Eq.2, the unit vector in "r" direction is Eq.3.

Using Eq.3 in Eq.2, the z component of total magnetic field becomes

*(Eq.4) *

where

*(Eq.5) *

The result of Eq.4 is the same as this site.

Using Eq.5 and the definition of Iπa^{2} = magnetic moment (= Bohr magneton ), Eq.4 becomes Eq.6.

( About elliptical orbit, see this section. )

*(Eq.6) magnetic field B caused by one spin magnet with Bohr magnetoton*

The magnetic energy (= E

Considering this μ

*(Eq.7) Spin-Spin magnetic energy.*

If the circular current is spin, the orbital radius "a" is almost zero in Eq.7 right ( a → 0 ).

( Of course, when this "a" is not zero, this magnetic energy becomes **smaller**, as shown in Eq.7. )

Eq.7 result is the same as this site (33.9).

If we can know the distance (= z ) between two spins in outer orbitals of magnesium, the magnetic energy of Eq.7 is determined.

*(Fig.11) Estimated radius of 3s orbital in Mg.*

To know the average distance between two spins in outer orbitals of Mg, we use the simple model of Fig.11.

In Fig.11, two ( outer ) electrons are on the opposite sides of the core (= effective positive charge "**z**" ), and moving on the same orbit (= **3** × de Broglie wavelength ).

We use the sum of the 1st and 2nd **ionization** energies ( 7.646 + 15.035 =

Using this total energy, we obtain the radius of r = **1.7388 Å**, and the central effective charge z = 2.988.

This radius is almost same as this site.

About the detailed calculation, see this section.

*(Eq.8) Radius of hydrogen-like atom. *

The orbital radius is proportional to a square of principal number (= **n ^{2}** ), and in

*(Fig.12) Rough estimation of radius of Mg 3s orbital ( z = 3 ).*

The atomic radius of the ground state hydrogen ( z = 1, n = 1 ) is just Bohr radius (= 0.53 Å ).

So the orbital length of n = 3 is 9 × 0.53 = 4.77 Å.

Suppose the central charge of Mg2+ is about z = 3 ( this z becomes a little bigger than "2" due to "gap" of inner orbitals ).

This Mg radius becomes 0.53 × 9 / 3 = **1.59 Å**, which is similar to the result of **1.738 Å** of Fig.11.

( Considering the repulsive effect of another outer electron, the actual effective charge becomes less than "3". )

*(Fig.13) *

"r" of Fig.11 is radius of outer orbital of Mg.

So the distance (= r' ) between two valence electrons is **longer** than this radius, as shown in Fig.13 ( r' > r ).

Sspin-spin magnetic energy is given by this and the estimated magnesium radius (= 1.7388 Å )

*(Eq.8) Magnesium's estimated spin-spin magnetic energy is too small (= only 2.042 × 10 ^{-5} eV )*

So, the spin-spin magnetic dipole energy is less than **2.042 × 10 ^{-5}** eV.

This value is very small, which is about

*(Fig.14) Spin-Spin magnetic energy is too small (= 2.042 × 10 ^{-5} eV = 0.00002 eV ) to explain magnesium triplet energy splitting (= 0.005 eV ).*

You can easily understand it is **impossible** to explain triplet splitting using spin-spin magnetic interaction.

In spite of this fact, they **never** give up this strange "spin".

*(Fig.15) Spin-orbt magnetic coupling is too small to explain the magnesium's triplet energy splitting (= 0.005 eV ).*

*(Fig.16) Doublet of hydrogen (= H ) and triplet of magnesium (= Mg ).*

As shown on this site ( or Nist ), **hydrogen** fine structure (= doublet ) between *2p3/2* and *2p1/2* is about **0.000045 eV**.

On the other hand, triplet energy splitting of magnesium is as large as **0.0050 eV**. See Nist and use this.

According to the current quantum mechanics, triplet splitting **must** be caused by change of spin directions in 3s-3p orbitals.

But actually, **neither** spin-spin nor spin-orbit magnetic energy can explain this triplet energy splitting.

*(Fig.17) Core charge of magnesium is much bigger then Z = 2 !?*

The magnesium has two valence electrons ( in this case, one is **3s**, and another is excited to **3p** ).

So the Ma2+ ion has about **Z = +2** central core charge.

From the viewpoint of 3p electron, core charge Z is moving around 3p electron, and generates magnetic field (= B ), which is the origin of spin-orbit magnetic energy according to the paradoxical Einstein relativistic theory.

But if you try to get triplet energy splitting (= 0.0050 eV ) using relativistic spin-orbit magnetic energy, this central core charge becomes **unrealistically** as big as **Z = 4.40**.

This result clearly shows spin-orbit coupling has **nothing** to do with Mg triplet ( of course, singlet ).

*(Fig.18) Energy splitting (= ΔE ) by spin-orbit interaction. *

It is known that energy splitting by spin-orbit coupling is proportional to **Z ^{4}** ( Z is central charge ), and in inverse proportion to

↑ Angular momentum quantum number L or l (= ell ) is equal to ( L = 1 ) in all atomic p states, so we need to focus only on Z and n to compare relativistic spin-orbit magnetic energies between different atoms.

Hydrogen doublet is **n = 2** energy level. Magnesium in this case is **n = 3** energy level.

Angular momentums of "**p**" orbital are the **same** in both atoms ( l = 1 in H and Mg ).

*(Fig.19) How big is central core charge Z in Mg ?*

As a result, the central core charge Z of Mg must be much **bigger** than H to explain large **discrepancy** between this energy splitting of Mg and H.

( Of course, central charge of H is Z = 1 ).

*(Fig.20) Effective core charge of Mg becomes as large as Z = 4.40 !?*

Using Fig.18 and Fig.19 ( comparing the values of H and Mg ), we can know the central core charge Z of Mg.

As shown in Fig.20, this charge of Mg becomes as large as **Z = 4.40** !

Of course, this central core charge Z = 4.40 is **too big** and unrealistic.

This calculation result clearly proves spin-orbit coupling has **nothing** to do with Mg triplet enegy splitting, because it's too **weak**.

*(Fig.21) What is effective core charge Z in Mg ?*

We can know true effective core charge Z based on ionization energy of Mg.

The first ionization energy of Mg is **7.646 eV**.

( This electron is "3s". Of course, "3p" electron is farther away from nucleus, so Z becomes **smaller**. )

*(Fig.22) *

As you know, hydrogen ionization energy of 1s electron is **13.606** eV.

In 1s hydrogen, Z = 1 and n = 1.

*(Fig.23) What is effective core charge Z in Mg ?*

From Fig.21 and Fig.22 we get the relation of Fig.23.

Z of Fig.23 means effective core charge from the viewpoint of Mg 3s electron.

( Caution: this Z contains Mg nucleus and **all** electrons including **another** 3s electron except one outmost 3p electron. )

*(Fig.24) Effective core charge Z in Mg.*

Solving Fig.23, we get the true effective core charge **Z = 2.249** based on the experimental magnesium's ionization energy.

*(Fig.25) Wide discrepancy between true and "fake" core charges.*

Comparing Fig.24 ( true Z = **2.24** ) and Fig.20 ( Z = **4.40** by spin-orbit ), you can easily find that spin-orbit coupling is **too weak** to explain Mg triplet (= so the too weak relativistic spin-orbit magnetic interaction needs unrealistically-large fictional core charge Z = 4.40 ).

*(Fig.26) Triplet, Singlet of Mg have Nothing to do with "Spin" .*

Using true effective core charge (= Z = 2.24 instead of the too large Z = 4.40 ), the relativistic spin-orbit magnetic coupling energy becomes as small as 0.00034 eV (= far smaller than the magnesium's triplet energy splitting of 0.005 eV ).

As you see Fig.26, the energy difference between singlet and triplet is much bigger (= **1.63 eV** ).

So it is much more **impossible** to insist this wide energy gap is caused by very weak spin.

They insist this large enery gap (= 1.63 eV ) is due to the difference of (nonphysical) symmetric and antisymmetric wavefunction, as shown in Fig.31.

*(Fig.27) "Symmetric" and "antisymmetric" wavefunctions can cause large energy gap ?*

*(Fig.28) Triplet, Singlet splitting in Ca is too large for spin-spin (-orbit) coupling.*

Triplet and singlet energy levels are on this site.

Converting energy unit ( cm-1 → eV ) by

*(Eq.9) *

We obtain Fig.28.

If you compare Fig.28 (= Ca ) with Fig.26 (= Mg ), you will understand energy splitting (in triplet ) in Ca is **larger** than Mg.

So it is much more **impossible** that spin-spin ( or -orbit ) coupling is involved in this triplet.

*(Fig.29) Estimated radius of Ca from ionization energy.*

The sum of 1st and 2nd ionization energy of Ca is **17.984** eV, as shown on this site.

Like Fig.11, we suppose helium-like model in Ca, and its total energy is -17.984 eV.

In this model, the radius (= r ) becomes **2.6036 Å**, which is **longer** than Mg.

The calculation method is the same as this section.

*(Fig.30) Spin-spin magnetic energy is 1/1000 times triplet splitting in Ca.*

Using the approximate radius of Fig.29, we find the spin-spin magnetic dipole energy in Ca outer orbital becomes very small.

(= **0.6082 × 10 ^{-5}** eV, about the method, see this )

This result shows it is **impossible** to explain triplet splitting (= 0.0131 eV in Ca ) by the tyny spin-spin magnetic interactions (= 0.000006082 eV ) also in calcium.

*(Fig.31) Doublet of H 2p and triplet of Ca 4p.*

The triplet energy intervals of Ca is much **larger** than hydrogen 2p doublet.

As I said above, spin-spin interaction has NO relation with this triplet.

So there is **ONLY** spin-orbit coupling left, if "spin" is involved in this triplet.

*(Fig.32) Effective core charge Z becomes unrealistically too large. ( Z = 2 → 6.946. ) *

Like in this section, we suppose triplet of Ca is due to spin-orbit coupling (= relativistic spin-orbit magnetic energy ), and calculate effective core charge Z (= total charge containing Ca nuclear and all innter electrons except one outer 4p electron ).

If so, this charge Z becomes unrealistically too big ( Z = **6.946** ) to explain large energy interval of **0.0131** eV.

As a result, spin-orbit coupling proves to be **NOT** involved in this triplet, either.

*(Fig.33) True effective charge Z = 2.68.*

Using the first ionization energy of 6.113 eV, we can know the true effective core charge Z, like in this section.

This true effective charge (= 2.68 ) based on ionization energy is **much smaller** than Z = 6.94.

Again, spin-orbit coupling proves to have **NO** relation with triplet splitting.

*(Fig.34) Triplet, Singlet splitting in Sr is too large for spin-spin (-orbit) coupling.*

Triplet and singlet energy levels of Sr are shown on this site.

Converting energy unit ( cm-1 → eV ) by

We obtain Fig.34.

If you compare Fig.34 (= Sr ) with Fig.26 (= Mg ), you will understand energy splitting (in triplet ) in Sr is much **larger** than Mg.

So it is much more **impossible** that spin-spin ( or -orbit ) coupling is involved in this triplet.

*(Fig.35) Radius of helium-like model in Sr.*

The sum of 1st and 2nd ionization energy is **16.725** eV in Sr, as shown on this site.

Like Fig.11, we suppose helium-like model in Sr, and its total energy is -16.725 eV.

In this model, the radius (= r ) becomes **3.3747 Å**, which is **longer** than Mg.

*(Fig.36) Spin-spin magnetic energy is 1/10000 times triplet splitting in Sr.*

Using the approximate radius of Fig.35, we find the spin-spin magnetic dipole energy in Sr outer orbital becomes very small.

(= **0.2793 × 10 ^{-5}** eV, about the method, see this section. )

This result shows it is

*(Fig.37) Doublet of H 2p and triplet of Sr 5p.*

The triplet energy intervals of Sr is much **larger** than hydrogen 2p doublet.

As I said above, spin-spin interaction has NO relation with this triplet.

So there is ONLY spin-orbit coupling left, if "spin" is involved in this triplet.

*(Fig.38) Effective core charge Z becomes unrealistically too large. ( Z = 2 → 11.409 ) *

Like in this section, we suppose triplet of Sr is due to spin-orbit coupling, and calculate effective core charge Z.

If so, this charge Z becomes **unrealistically too** big ( Z = **11.409** ) to explain large energy interval of **0.0488** eV.

As a result, spin-orbit coupling proves to be **NOT** involved in this triplet, either.

*(Fig.39) True effective charge Z = 3.23.*

Using the first ionization energy of 5.695 eV, we can know the true effective core charge Z, like in this section.

This true effective charge (= 3.23 ) based on ionization energy is **much smaller** than Z = 11.409.

Again, spin-orbit coupling proves to have **NO** relation with triplet splitting.

*(Fig.40) Triplet, Singlet splitting in Ba is too large for spin-spin (-orbit) coupling.*

Triplet and singlet energy levels are shown on this site.

Converting energy unit ( cm-1 → eV ) by

We obtain Fig.40.

If you compare Fig.40 (= Ba ) with Fig.26 (= Mg ), you will understand energy splitting (in triplet ) in Ba is much **larger** than Mg.

So it is much more **impossible** that spin-spin ( or -orbit ) coupling is involved in this triplet.

*(Fig.41) Estimated radius of Ba.*

The sum of 1st and 2nd ionization energy is **15.211** eV in Ba, as shown on this site.

Like Fig.11, we suppose helium-like model in Ba, and its total energy is -15.211 eV.

In this model, the radius (= r ) becomes **4.246 Å**, which is **longer** than Mg.

The calculation method is the same as this section.

*(Fig.42) Spin-spin magnetic energy is 1/10000 times triplet splitting in Ba.*

Using the approximate radius of Fig.41, we find the spin-spin magnetic dipole energy in Ba outer orbital becomes very small.

(= **0.140 × 10 ^{-5}** eV )

This result shows it is

*(Fig.43) Doublet of H 2p and triplet of Ba 6p.*

The triplet energy intervals of Ba is much **larger** than hydrogen 2p doublet.

As I said above, spin-spin interaction has NO relation with this triplet.

So there is ONLY spin-orbit coupling left, if "spin" is involved in this triplet.

*(Fig.44) Effective core charge Z becomes unrealistically too large. ( Z = 2 → 15.984 ) *

Like in this section, we suppose triplet of Ba is due to spin-orbit coupling, and calculate effective core charge Z.

If so, this charge Z becomes unrealistically too big ( Z = **15.984** ) to explain large energy interval of **0.1088** eV.

As a result, spin-orbit coupling proves to be **NOT** involved in this triplet, either.

*(Fig.45) True effective charge Z = 3.71.*

Using the first ionization energy of 5.211 eV, we can know the true effective core charge Z, like in this section.

This true effective charge (= 3.71 ) based on ionization energy is **much smaller** than Z = 15.984.

Again, spin-orbit coupling proves to have **NO** relation with triplet spilitting in Ba.

*(Fig.50) Energy levels of Calcium (= Ca ).*

If you see the energy levels of Ca (= Nist ) carefully, you will find quantum numbers and their orders are very **unreasonable**.

In usual periodic table, "3d" orbitals are **lower** than 4p orbitals in the energy levels.

But as you see Fig.50, 4p orbital (= triplet ) is **lower** than 3d orbitals.

( In Fig.50, the top (= 4s^{2} ) is ground state, and the lower configuration means higher energy levels. )

And in 4s4d configuration, the order of triplet and singlet is **reversed**.

( Usually, triplet → singlet. But in 4s4d, singlet → triplet. )

*(Fig.51) Energy levels of Mg and Sr. "4f" appears ONLY in Mg ?*

In magnesium, the energy **intervals** of triplets are **chaotic**.

( 3s3p-- **20** cm-1, 3s3d-- **0.02** cm-1, 3s5p-- **2.0** cm-1 ).

And "**4f**" energy levels exist **only** in magnesium, but **don't** exist in strontium and barium .

This is strange.

Though "3d" orbital is lower than "4p" in energy levels, but in Mg, "**3s4p**" becomes **lower** than "**3s3d**".

This is strange, too.

In Sr, "**triplet**" (= 3 ) appears first in 5s4d, but "**singlet**" (= 1 ) appears first in 5s5d.

Again, this is one of **artificial** manipulations.

So the concepts of these triplet and singlet were produced by considering **ONLY** unrealistic quantum numbers.

They completely **ignored** the **magnitude** of energy ( ← though very important ! ) and their orders.

*(Sp.1) *

In the upper section, we deal with simple circular orbit.

In this section, we show the magnetic moment of elliptical orbit becomes the **same** as circular orbit like Sp.1

*(Sp.2) *

In the system of central force, the areal velocity (= A ) is **constant** like Sp.2.

*(Sp.3) *

The total area of ellipse is equal to "πab".

Time period (= T ) of one-orbit is given by the total area (= πab ) / A.

Using Sp.2 and Sp.3, the current I becomes

*(Sp.4) *

The magnetic moment (= M ) is given by the current I × area.

( When you divide some area into infinitesimal loops, you will find this law holds in any forms of current. )

As a result,

*(Sp.5) *

"3p" orbital has the angular momentum of 1 × ħ.

Substituting ħ into Sp.5, we obtain the **Bohr magneton** as the orbital magnetic moment of "**3p**".

*(Sp.6) 3p = Bohr magneton.*

*(Sp.7) 3s outer orbitals of Magnesium.*

In Sp.7 magnesium model, two 3s outer electrons are moving on the common orbit at the velocity "**v**", on the opposite sides of the nucleus.

The effective positive charge of the core (= Mg nucleus + all inner electrons ) is "**z**".

And the orbital radius is "**r**".

Equating the centrifugal force to the Coulomb force, we have

*(Sp.8)*

where "m" is the electron mass.

The left side is centrifugal force, and the first term of the right side is Coulomb attractive force between the core and each electron.

The second term is the repulsive force between two electrons.

The circular orbital length is supposed to be an **integer** (n) times de Broglie wavelength ( λ = h/mv ) of the electron.

*(Sp.9)*

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

*(Sp.10)*

Suppose the total energy E of Sp.10 is equal to the sum of 1st and 2nd ionization energies ( E = -22.681 eV ).

Solving the the simultaneous equations of Sp.8-Sp.10, we can obtain the radius "r" and effective charge "z".

From Sp.9,

*(Sp.11)*

Substituting Sp.11 into Sp.8, we have

*(Sp.12)*

From Sp.12

*(Sp.13)*

Substituting Sp.11 and Sp.13 into Sp.10,

*(Sp.14)*

Here we treat Mg with two valence electrons as **helium**-like atom.

The total energy of these two outer electrons is supposed to be the sum of 1st and 2nd ionization energies ( see this site ) like Sp.15.

*(Sp.15)*

Substituting Sp.15 ( "eV" → "J" ) and n = 3 into Sp.14,

*(Sp.16)*

Using the following values,

*(Sp.17)*

The central effective charge z becomes

*(Sp.18)*

Substituting z = 2.988 and n = 3 into Sp.13, the radius "r" becomes

*(Sp.19)*

2014/2/21 updated. Feel free to link to this site.