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Unrealistic "Spin".
Spin's tricks.

Spin hall effect doesn't mean "Spin".

Rare-earth metals don't have "Spin".

Truth of Triplet with NO spin (14/2/21).

- "Spin" is an illusion, again.
- Ferromagnetism and diamagnetism are NOT "spin".
- Anomalous Zeeman effect of hydrogen does NOT mean "spin".
- Spin waves, magnons, XY models are unreal.
- Sodium D lines = Spin-orbit interaction !?

*(Fig.1) Electron spin ? How ? Illusion ?*

"Spin" is one of the most important and fundamental concepts in the current quantum theory.

"Spin" is **indispensable** for Pauli exclusion principle, entanglement, fermi statistics, particle physics and string theory.

But strange to say, if you try to ask some specialists in these fields about what "spin" really is, they **cannot** give clear picture about spin at all.

It's very strange, though as many as **100** years have passed since quantum mechanics and "spin" were born.

Because as shown on this page, "spin" **cannot** be described using real objects.

Even if you rotate spin 1/2 particle by 360 degree, it **cannot** return to its original configuration.

And a single electron is a point-like particle with small mass, its spinning speed must **exceed** the light speed by far.

*(Fig.2) Point particle → spinning speed is much faster than light !*

In the **ground** state hydrogen atom, the magnetic moment of an electron is known as **Bohr magneton** (= μ_{B} ).

In Bohr model, this magnetic moment is generated by usual **circular** movement of an electron.

But as quantum mechanics **lacks** angular momentum ( L = 0 ) and circular movement, this magnetic moment μ_{B} is caused by "spin", they insist. ( See also this page. )

As you see in Fig.2, it is **impossible** that **point**-like particle electron generates angular momentum 1/2 ħ.

Angular momentum is given by mv×r, where radius "r" is almost **zero** in point particle.

As a result, rotating speed "v" must be much **faster** than light to reach 1/2 ħ.

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

On the other hand, heavy proton with some size can produce "real" spin, **NOT** exceeding light speed.

So nuclear spin is **real**, and electron spin is an **illusion**, it's only **circular** orbit like Bohr model.

In fact, the magnetic moment of electron spin is about **1000** times bigger than that of proton !

This wide discrepancy indicates electron spin is rotating in circular orbit with some radius, **NOT** on its own axis.

See also this page.

*(Fig.3) Spin really causes ferromagnetism and Pauli exclusion ?*

In textbooks, they say each spin of atom tries to be **parallel** to each other in ferromagnetism.

And in Pauli exclusion principle, the third spin **cannot** enter the same orbital, where "up" and "down" spin particles already exist.

This means spin magnetic moment (= up or down ) has the **power** enough to cause these phenomena ?

In fact, spin magnetic moment is **too weak** to cause these ferromagnetism and Pauli exclusion principle, because the magnitude of spin-spin interaction is extremely **small**, only fine structure level (= **1.0 × 10 ^{-5}** eV ).

*(Fig.4) Repulsive force of Pauli exclusion principle is very strong (= about 11 eV in Li ).*

According to this book ( Quantum chemistry 6th edition, by Ira N. Levine, p 292 ), the ground state energy of lithium becomes lower than **-214.3 eV**, if all three electrons enter **1s** orbitals.

On the other hand, the experimental value of actual lithium is **-203.5 eV** in which one of three electrons enters **2s** ( NOT 1s ) orbital.

This means the third electron is **expelled** from 1s orbital by some force, though Coulomb attraction of nucleus is **strong** enough.

This mysterious **repulsive** force of about **11 eV** is due to Pauli exclusion principle, as shown in Fig.4.

*(Fig.5) Spin-Spin interaction is too weak.*

In Pauli exclusion principle, "spin" direction is crucial factor for deciding whether each electron enters the same orbital or not.

But magnetic dipole interaction of spin is basically **too weak** (= about fine structure level, **1 × 10 ^{-5}** eV. ), which can

This means we need **other** concepts to describe this strong repulsive force of Pauli exclusion.

If "spin" ( magnetic moment ) is too weak, there is only one thing left.

As shown on this page, **de Broglie** wave ( destructive ) interference is the main generator of this Pauli repulsive force.

*(Fig.6) Origin of ferromagnetism = Spin ??*

In ferromagnetism, they insist "spin" of each atom such as Fe tends to be **parallel** to each other.

On the other hand, in antiferromagnetism ( or diamagnetism ) such as MnO, each spin tends to be **antiparallel** to each other.

So the **origin** of (anti) ferromagnetism is "spin", as most textbooks say ??

In fact, spin magnetic ( dipole ) moment interaction is **too weak** to cause (anti) ferromagnetism.

*(Fig.7) Origin of ferromagnetism = Exchange interaction "J" ??*

In the current quantum theory, they describe the force of (anti) ferromagnetism as coupling constant (= J ) in Heisenberg model.

The magnitude of coupling constant (= exchange interaction ) is as big as **1 eV**, which is much **stronger** than spin magnetic dipole interaction (= **10 ^{-5} eV** ).

Spin magnetic moment interaction is much **too weak** to account for most magnetic materials such as ferromagnet, as is referred to in various sites ( See
this (p.7 or 8),
this (p.5),
this (p.20),
this (p.7) ).

Spin dipole interaction is as small as **0.3 K** as temperature expression, which is easily **broken** at room temperature.

( For example, iron can become ferromagnetism at **1043 K**, which is much bigger than 0.3 K. )

*(Fig.8) De Broglie wave interaction is the origin of ferromagnetism.*

Spin - spin magnetic interaction is unrealistically **too weak** to describe magnetic materials.

Again, there is only one thing left.

Electron movement causing magnetic field is accompanied by **de Broglie** wave. ( See also this page. )

Like strong repulsive Pauli exclusion, it is quite natural that we think these synchronous de Broglie waves makes ferromagnetism **stable** at room temperature.

As shown in Davisson-Germer experiment, de Broglie wave interference has the power to change the direction of Coulomb force.

*(Fig.9) Singlet and Triplet are just "math" symbols.*

It is said "spin" is the origin of singlet and triplet terms of atoms.

But in fact, the energy difference of these singlet and triplet levels is as much as **Coulomb** interaction, which **cannot** be explained by spin magnetic interaction. ( See Fig.10. )

Furthermore, these singlet and triplet states are completely **different** from real ones.

Both in T2 of triplet and singlet (=S ), one of two electrons is "up" spin, another is "down spin".

So these T2 and S are the **same** energy states ?

But they insist these states are different, using math symbol (= ± ).

These strange math symbols (= ± ) denoting up and down spins **cannot** be expressed using real physical objects.

As a result, singlet and triplet states are **other** things such as Coulomb interaction in multi-electron atoms, **Not** "spin".

*(Fig.10) Singlet and Triplet are as strong as Coulomb interaction. *

In the book, Story of Spin ( S. Tomonaga ), they say singlet and triplet **cannot** be caused by spin-spin interaction.

----------------------------------

[ p.84 ] Now what is the order of magnitude of the spin-spin interaction E_{s,s} ?

We can answer this from the experimental data given in figure 5.2 by compareing the levels of the **singlet** and **triplets** terms. ---- Then we find that the interaction between spins is quite **large**.

[ p.85 ] However such energy of "**magnetic**" origin causes a difference between (n, l, 0) and (n, l, 1) of only the order of magnitude of splittings seen in alkali **doublet** (= fine structure ) levels.

On the contrary, from figure 5.2 we see that the difference is as **big** as that of "**electric**" origin.

This was an **enigma** for many years.

-------------------------------------

See also Truth of Triplet in detailed version.

*(Fig.11) Anomalous Zeeman effect of H atom ? ↓ = Bohr-Sommerfeld model. *

It is known that the spectrum lines in hydrogen atom is much **fewer** than other alkali atoms such as sodium and potassium.

If we suppose electron "spin", energy levels of H atom **must** be much more spilt.

So they came to insist various levels of H atom **accidentally** agree with each other ( 2s1/2 = 1p1/2 ... ), as shown on this page.

In the definition of **normal** Zeeman effect, each "n" energy level should have **singlet** ( NOT doublet ) term, and is split into **triplet** under magnetic field.

Most websites ( and books ) say H atom also exhibits anomalous Zeeman effect.

But this anomalous Zeeman of hydrogen can be explained by Sommerfeld's fine structure.

In H atom, each fine structure doublet is split into ( **normal** ) triplet ( 2 × 3 = 6 ).

*(Fig.12) J Mehra's book. *

On page 659 of the Historical Development of Quantum Theory v.1 part2 ( J. Mehra ).

--------------------------------

In 1922, Otto Oldenberg obtained the following results :

For weak fields, each component of Balmer H_{α} **doublet** was separated in a **normal** Zeeman triplet, but for strong fields, the Zeeman patterns of the **doublet** changed into the Zeeman pattern of a singlet line.

---------------------------------

They just call these **doublets** "anomalous Zeeman effect" in hydrogen atom.

But as you know, these doublets (= fine structure ) can be completely explained by Bohr-Sommerfeld model, **Not** depending on strange "spin".

*(Fig.13) History of Zeeman effect. *

According to the above book, anomalous Zeeman effects are often seen in multi-electron atoms such as Na, Cd, Mg..

In mercury (= Hg ), as much as 11 split lines were observed under magnetic fields in 1898.

The important point is that they **didn't** mention hydrogen atom, when they say about **anomalous** Zeeman effect ( Fig.11 is the **only** exception ).

And this book also say most multi-electron atoms ( **excluding** light atoms H, He, Li ) exhibit much more **complex** lines than simple doublet and triplets.

As a result, Heisenberg and Lande thought anomalous Zeeman effect is caused by **core** electrons, Not spin, at first.

And various atoms and metals do **NOT** obey Lande g-factor.

This fact made Russell and Saunders create **new** concepts such as jj coupling and jk coupling.

*(Fig.14) Normal Zeeman.*

Light atoms such as lithium and helium are usually **NOT** mentioned as an example of anomalous Zeeman effect.

On page 450 of the above book, they say " the red lithium line had **NOT** been separated so far. They found a **triplet**, which surprised them very much.

Because lithium is clearly **different** from sodium and potassium cases.

After that, they came to insist lithium atom exhibits Paschen-Back (= almost normal Zeeman ) effect.

As electrons of atoms **increase** in number, more separated lines are observed.

This tendency clearly shows anomalous Zeeman effect is caused by interactions with **other** electrons, **Not** "spin".

*(Fig.15) Spin magnitude is NOT "1/2" according to quantum mechanics ?*

Under the magneic field, we can observe Bohr magneton as spin magnetic moment.

This means spin anglar momentum S = ± 1/2 in the direction of magnetic field (= B ).

Strange to say, according to quantum mechanics, **true** spin anglular momentum is **bigger** than 1/2, as shown in Fig.15

**True** magnitude of angular momentum must be expressed using "square root" due to spin **precession**, they insist.

*(Fig.16) Spin + Spin ?*

The problem happen when we think about the sum of spins in multi-electron atoms.

They just simply sum up spins of all outer electrons as total spin effect.

So when two electrons exist, total spin in the direction of magnetic field becomes 1/2 + 1/2 = **1**, they insist.

As a result, the **true** magnitude ( in the direction of precession ) of their total spin becomes a **square root of 3**, as shown in Fig.16 ?

*(Fig.17) Spin + Spin ← self-contradiction !*

But when you subsitute S = 1 into the equaiotn of a square root of S(S+1), this result becomes a square root of 2, ( **NOT** 3 ! ).

This is completely **inconsistent** with the result of Fig.16 and Fig.15, and self-**contradiction**.

So when two electrons exist in two ( different ) outer orbitals, they are **fine-tuning** precession states of each other so that the total spin becomes **just** a square root of 2 ? **Impossible** !

As you feel, these quantum interpretation about spin is very **unnatural** and unrealistic.

*(Fig.18) Lande g factor is real ?*

As shown on this page, Lande g factor is based on very **unnatural** precessions.

In multi-electron atom, we need to sum up each spin like Fig.18, they insist.

As a result, the **self-contradiction** of Fig.16 and Fig.17 occurs.

*(Fig.19) Observed magneton in the direction of magnetic field H.*

Using Lande g factor of Fig.18, Hamiltonian of observed atomic magneton in the direction of magnetic field H becomes like Fig.19.

The important point is that quantum number (= M_{j} ) in z direction is an **integer**, Not a "square root" of J(J+1).

*(Fig.20) Observed magneton in the direction of magnetic field H.*

Data of metallic ion magnetic moments such as Gd2+, Fe3+ and Cr3+ are seen in this paper ( W.E. Henry, Phys. Rev. 88 559, 1952 ).

As shown in Fig.20, each saturation magnetization becomes an **integer** times **Bohr magneton** (= μ_{B} ).

Gadolinium ion is **7.0** × μ_{B}.

Iron ion is **5.0** × μ_{B}.
Chromium ion is **3.0** × μ_{B}.

And oxygen molecule shows **2.0** × μ_{B} ( P.Curie, 1895 ).

So Bohr-Sommerfeld **quantization** holds in these atoms.

See also this page.

*(Fig.21)*

Magnetic moment of these ions cannot be measured individually.

They measure the states of **compounds** like Fig.21.

So when the influences by other atoms are strong, magnetic moment becomes more complex.

Actually, many **neutral** metals such as Fe, Cr and Gd **cannot** be described using Lande g factor.

Effects by other atoms are big, they insist.

*(Fig.22)*

Cr3+ has three outer electrons in **3d** orbitals.

According to Hunt law, total angular momentum L and spin S become "3" and "3/2" in Cr3+.

As I said above, very **weak** spin magnetic moment has **NO** power to make them all parallel.

Do you think the rule of Fig.22 is **too simple** and too good to be true ?

*(Fig.23) Cr3+ ion disobeys Lande g factor.*

In fact, transition metals such as Ti3+, V3+, Cr3+, Fe2+, Co2+, Ni2+, and Cu2+ do **NOT** obey Lande g factor.

Strange to say, the total angular momentum (= L ) of these ions becomes completely **zero**, they insist.

Though the angular momentum of Cr3+ in Hunt law is L = "3", this L becomes "**0**" by the influence of surrounding atoms, they insist. Do you think these interpretations are inconsiderate and **too good** to be true ?

( See also this page. )

In most textbooks, they tend to use effective Bohr magnetic number, which is expressed as a square root of J(J+1).

But as I said in Fig.20, these J(J+1) and S(S+1) are **NOT** observed values.

From intergers gotten from experiment, they only calculate a squre root in each effetive number.

So all of these transition metallic ions show an **integer** times Bohr magneton like Bohr model.

*(Fig.24) Gd3+ ion also shows an integer times Bohr magneton.*

According to Hunt law, total angular momentum and spin of Gd3+ become like Fig.24.

Each spin belongs to **different** orbital.

So it is very **unnatural** that total spin angular momentum of "7" spins becomes **just** S = 7/2, though each electron is **separated** from each other.

*(Fig.25) Gd3+ ion also shows an integer times Bohr magneton.*

In most textbooks, effective Bohr magnetic number "7.94" is shown as Gd3+ ion.

But as I said in Fig.20. observed magnetic number becomes an **integer** times Bohr magneton also in Gd3+.

They just calculate 7.94 based on 7.0.

Square root of J(J+1) itself means **unrealistic** "precession", which **cannot** be observed directly.

*(Fig.26) "Spin" is just math symbols ?*

Fig.26 is **Heisenberg** spin model, which is often used even in the current condensed matter physics.

But this model is too **abstract** to describe various **complicated** and dynamic phenomena.

Depending on whether J is negative or positive, this atom becomes ferromagnet or antiferromagnet, they insist.

As you feel, it is **impossible** to express actual electron's complicated **motion** in various atoms, using **only** three **simple** math symbols (= J, S, S ).

They have **given up** asking what "spin" and Pauli exclusion principle really are, **forever**.

So all they can do is to rely on very **abstract** math symbols.

Parameter "J" must be determined from experiment ( **NOT** from theory ). They just try to fit model to actual data.

*(Fig.27) XY model ?*

**Conveniently**, they introduced "**XY**" model, in which each spin turns toward **x** or **y** directions.

If "x" and "y" spin directions are also allowed, the concept of "spin" becomes very **doubtful**.

Beucause this XY model is completely **inconsistent** with parallel and antiparallel rule of spins.

And when spin is in the x direction, there are **three different** spin states such as "up", "down" and "**horizontal**".

As a result, as many as three electrons can enter the **same** orbital.

It means Pauli exclusion principle **breaks** down. This is strange.

*(Fig.28) XXZ model ?*

Furthermore, in XXZ model, each spin can turn toward **various** directions (= x, y, z ! ).

Each parameters such as J and Δ need to be determined from experiment.

Because each metal contains almost **infinte** atoms, they **cannot** compute all effects by quantum chemistry.

They often use density functional theory (DFT) in condensed matter and band calculation.

Because DFT doesn't take so much time.

Instead, this DFT must use **artificial** approximations such LDA and various potentials to fit experimental results.

So these DFT is **NOT** ab-initio at all, though they **like** to call it "ab-initio DFT". This name is NOT ture.

*(Fig.29) ↓ Spin-orbit interaction ?*

Each metal contains various atoms, so it is **impossible** to estimate spin-orbit interaction without relying on some approximation and experimental results.

λ of Fig.29 is spin-orbit coupling constant, which **cannot** be determined only by theory itself.

Because this λ **varies** complexly depending on binding states and environment.

First, it is impossible to see unreal spin itself, so we cannot confirm spin-orbit interactions **really** exist

As I said above, tha magnitude of spin-orbit interaction is almost same as fine structure of Bohr Sommerfeld model.

*(Fig.30) Magnon, spin wave = "math" symbol, NOT physics.*

Spin waves are said to be propagating in magnetic materials.

They are also called "magnon", which is a collective excitation of electrons' spin structure.

Of course, this magnon is **unreal** quasiparticle.

Magnon is "boson", which is just creation (= a^{†} ) and annihilation (= a ) "math" operators.

It is said that these spin waves can be detected by neutron scattering.

But there are many **other** factors influencing neutron's scattering and energy change.

So it is **impossible** to prove the existence of spin wave itself directly.

They only estimate their existence.

( Though "quasiparticle" itself does **NOT** really exist.... )

*(Fig.31) Quasiparticle "magnon" causes spin wave ??*

**Artificial** transformation like Fig.31 is one of the main reasons why I often say "spin" is just math, **NOT** physics.

Using creation (= a^{†} ) and annihilation (= a ) operators of magnon (= Fig.30 ), they try to express "Spin" compoment (= S ), which is called Holstein-Primakoff transformation.

But as you see Fig.31, the forms of these transformations were artificially introduced by our human beings, and do **NOT** mean the truth of nature.

*(Fig.32) Spin relations ?*

If we use the transformation of Fig.31, we can derive spin relations like Fig.32.

So they insist, quasiparticle magnon causes "spin wave".

Can you think these **abstract** "math" operators really exist ?

*(Fig.33) Spin Hamiltonian ?*

Using this transformation in Heisenberg spin model of Fig.26 and do some approximations, we can get Hamiltonian of Fig.33.

Performing Fourier transformation of Fig.34 in Fig.33,

*(Fig.34) *

we have

*(Fig.35) Creation of magnon = Spin wave energy ??*

In Fig.35, when quasiparticle magnon (= a^{†}a ) is created, spin wave is generated, they insist.

Of course, we **cannot** see these **unreal** quasiparticles and waves directly.

They just estimate these existences from some change of scattered neutrons. or lights.

Neutrons are said to be scattered by some magnetic moment, but there are various **other** factors influencing these scattering results.

So "spin wave" itself is only an **imaginary** thing.

In fact, even the **latest** experiments and theories dealing with "spin" are based on very **artificial** tricks.

There are good ( bad ) examples proving spin theories have **NO** reality in the page of Tricks in "Spin".

*(Fig.36) Sodium fine structure is too big to be explained by a single electron's spin.*

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

On the other hand, the fine structure between *3p3/2* and *3p1/2* of **sodium** is as big as **0.0021 eV**, as shown on this site.

Approximately, we can consider the outer 3p ( or 3s ) electron of sodium is moving around **Z = +1** central **core** charge.

( "Core" is the total charge of Na nucleus and **all** electrons contained in n = 1 and 2 orbits. )

From the viewpoint of this outer electron, the core charge is moving around in the opposite direction, which causes magnetic field at the point of the electron having "spin".

As a result, spin-orbit interaction is produced, they insist.

*(Fig.37) Core charge of sodium is much bigger than Z = 1 !?*

In this section, we explain the reason why this big fine structue in sodium is very **unreasonable** with respect to spin-orbit interaction.

Both in hydrogen and sodium's outer (= 3p ) electron, the effective central (= core ) charges they feel are about Z = **+1e**.

But the discrepancy between these H and Na spin-orbital interactions are **too wide**.

This means the effective central charge in sodium is much **bigger** than Z = 1 (= about Z = **3.54** in Na ), which is very **unreasonable** and unrealistic. See also this page.

*(Fig.38)*

As shown on this site (p.9), the energy by spin-orbit interaction becomes like Fig.38.

α and Ry are constants, so the principal quanum number (= n ), angular momentum (= l ), and central ( core ) charge (= Z ) are **crucial** factors for deciding this interactive energy.

*(Fig.39)*

Both in 2p (= H ) and 3p (= Na ) fine structures, the angular momentum (= l ) is equal to **1**, so total angular momentum j = 1 ± 1/2, which are completely the **same** in H and Na.

So the **difference** between H and Na are **only** principal quantum number ( n = 2 or 3 ) and core charge ( Z = 1 or ? ).
See also this site .

*(Fig.40) Energy difference between p3/2 and p1/2*

Eq.40 shows the energy difference between p3/2 and p1/2.

Here α is fine structure constant, and Ry is Rydberg constant.

The principal quantum numbers (= n ) of Na and H are " **3** " and " **2** ", respectively

So the energy difference is **smaller** in Na, if core charge Z is the common ( Z = 1 ).

*(Fig.41)*

But the energy difference of Na is much **larger** than H.

( 0.0021 / 0.000045 = **46.6** times bigger ).

So the effective core charge (= Z ) of Na must be much **bigger** than "1", which is **strange**.

*(Fig.42) Effective "Z" becomes too big (= 3.5 ), if spin-orbit coupling is true.*

From Eq.40 and Eq.41, the effective core charge of Na becomes as large as Z = **3.54**, which is **unrealistic**.

This core charge is the total charge summing up Na nucleus and **all** 1n, 2n electrons.

The charge of Na+ ion ( excluding only 3s electron ) is about **+1e**.

So, this core charge "Z" **must** be close to "**1**" also in Na.

On page 144 of "Modern Atomic and Nuclear Physics" ( Fujita Yang, Joseph H.Hamilton ).

↓

-----------------------------------------------------------------------

However, calculation of the spilitting of the **3P** level in sodium is a little difficult ...

Substituting the effective charge Z_{eff} into Eq.4.42 (= Fig.40 ) to replace Z, and using experimentally measured value ΔU = 2.1 × 10^{-3} eV, we may calculate from Eq.4.42 ( n = 3, l = 1 ), **Z _{eff} = 3.5**.

----------------------------------------------------------------------

In conclusion, it is very **unnatural** that we consider the fine structure of Na D lines is caused by spin-orbit interaction.

As far as I see various websites and textbooks, there are **NO** reasonable reason why the Na fine structure is much bigger than H.

*(Fig.43) Coulomb and large (core) orbit - orbit interactions generate Na D lines.*

In the present Lange g factor, they insist there are **No** magnetic moments in the **inner** (= core ) electrons in Na.

But from the realistic viewpoint, the inner shells contain various large **orbital** motions.

So we can naturally think the various **Coulomb** interaction and large magnetic moment of **inner** electrons cause this large fine structure in sodium D lines.

Spin- orbit interaction is **too weak** to explain sodium D lines.

*(Fig.44)*

As shown on this page or the book "Story of Spin" ( S. Tomonaga ), the fine structure by Bohr-Sommerfeld model is just **equal** to spin -orbit interaction using Thomas factor.

In Fig.44, " k = 2 " corresponds to "l = 1".

Substituting "n = 2" and " k = 2 " into Fig.44, the energy difference between 2p3/2 and 2p1/2 is just equal to 0.000045 eV (= experimental value ).

So the Bohr-Sommerfeld model can explain this fine structure correctly **without** relying on unrealistic "spin".

According to Fig.44, the energy difference between 3p and 3d is about 0.0000044 eV, which is close to Lamb shift

So very small Lamb shift can be explaied by various **other** factors, **NOT** by strange **virtual** particles and divergence.

*(Fig.45) What is effective core charge Z from ionization energy ?*

In Fig.42, if spin-orbit interaction is real, effective core charge Z of sodium becomes much bigger (= **3.54** ) than "1".

We can know this effective core charge from **ionization** energy of sodium ( 3s ) outer electron.

This ionization energy of sodium is **5.14** eV.

*(Fig.46) *

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

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

*(Fig.47) *

From Fig.45 and Fig.46, we get the relation of Fig.47.

Z of Fig.47 means effective core charge from the viewpoint of Na 3s electron.

*(Fig.48) *

From Fig.47, we get Z = **1.84** as the effective core charge of sodium.

This value (= 1.84 ) is completely **different** from **3.54** of Fig.42.

See also this site (p.5, n.48).

Due to gaps in 1s and 2s electron's shells, effective core charge which 3s electron feels becomes a little bigger than "1".

But "Z = 3.54" is **too big** and unrealistic.

*(Fig.49) *

This is clearly self-**contradiction**, and shows spin-orbit interaction of sodium D lines is **wrong**.

( Of course, 3p electron is more apart from Na nucleus, so effective core charge must become **smaller** than 1.84. )

Also in other alkali metals such as K, Rb, Cs, the concept of spin orbit coupling is **violated**.

See also this page.

*(Fig.50) Spin angular momentum can be macroscopically seen ?*

It is said that Einstein-de Haas effects showed "Spin" means "**actual** rotation".

But if spin is rotation, its spinning speed **must** be much **faster** than light speed, as I said in this section.

This is strange.

In Fig.50 left, the magnetic field B in the iron cylinder is zero, and the magnetic dipole moment vectors (= μ ) of its atoms are **randomly** oriented.

In Fig.50 right, when a magnetic field is set up along the cylinder's axis, the μ line up parallel to and the cylinder begins to **rotate**. See this site p.4 or
this.

Some physicists at that time wrongly thought when atomic spins inside cylinder change its direction of spin (= angular momentum ) by **external** magnetic field of coils, other atoms inside the cylinder may rotate in the opposite direction of atomic spins to conserve total angular momentum inside cylinder.

↑ This idea of total angular momentum conservation inside cylinder is **wrong** due to the existence of external magnetic force (= For the total angular momentum inside cylinder to be conserved, Only atoms inside the cylinder have to influence each other without external magnetic force ).

Because atomic spins inside the cylinder were changed by **external** (= Not internally ) magnetic force from the electric current of the coils, hence, the total angular momentum inside the cylinder is Not conserved (= because external force changes their spin angular momentum direction )

The wrong interpretation of this experiment came from physicists having No way to figure out the realistic mechanism or image of how unrealistic electron spins interact with external electromagnetic fields when changing its directions.

Some people say this experiments proved spin g factor = "**2**".

But this experiment is extremely **difficult**, and needs **forcible** interpretation.

( Even if **each** spin direction changes, the **whole** cylinder does **NOT** need to rotate ! ← Point. )

And the original Einstein experiment showed g factor is just "**1**" like classical orbit.

*(Fig.51) Spin = "actual" rotation ?? → speed > 100 c*

On page 78-79 in the book, "Einstein's unification", by Jeroen van Dongen,

----------------------------------------

Einstein and de Haas's **first** measurements gave results that were equivalent to g = **1.4**.
It was soon clear that a systematic error had crept in: the magnetic field used had been too weak. A second, improved measurement gave a more **satisfactory** result: **g = 1.02** +- 0.10. ( ← **classical** orbit ! )

Einstein and de Haas concluded that Ampere's hypothesis had been fairly confirmed by our observations.

The discovery of electron-spin, in 1925, could also give a theoretical explanation of that value ( g = "**2**" ).

Why Einstein and de Haas measure a value g (= 1 ) ?

Their experimental arrangement in all likelihood still allowed for too many systematic errors.
The **earth's magnetic** field, for instance, was a disturbing factor.

------------------------------------------

As you see, the original Einstein de Haas's experiment showed g factor is "**1**" like classical orbit.

And this experiment is extremely difficult, **susceptible** to earth magnetic field. See also this site.

*(Fig.52) Spin angular momentum can really rotate the "whole" cylinder ?*

The problem is that the change of each spin angular momentum can **really** rotate the **whole** iron cylinder ?

Of course, each electron ( or proton ) is **separated** from each other.

This means the **magnetic** field acts as some **force** to change each angular momentum.

This magnetic field can transmit through vacuum, so they can influence many atoms inside **coil**.

It is natural that we think their angular momentums (= magnetic moments ) are **mainly** transmitted to atoms inside **coils** rather than **fiber**.

Because **depending** on electrons' motions (= current I ) inside **coil**, the directions of spin in the cylinder change. Or imagine **Faraday** law. So electrons inside coil and cylinder are **influencing** each other.

And even if each electron spin becomes parallel to each other, the whole sylinder does NOT need to rotate, unless protons are influenced.

( For example, ferromagnets such as iron are **NOT** rotating. )

So the interpretation of these experiments are very **artificial**, and **cannot** be accepted as it is.

2013/12/26 updated. Feel free to link to this site.