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2.5.9 Contemporary Physics 3

2.5.9.1 Overview

Symmetric Theory was developed through Nanbu's Spontaneous Symmetry Breaking.

2.5.9.2 Details

2.5.9.2.1 Nambu's Spontaneous Break Symmetry in 1960 CE

2.5.9.2.1.1 Background

Some materials (metals) show zero electrical resistance and expulsion of magnetic fields (expulsion of magnetic affection) at a low temperature near absolute zero (superconductivity).
BCS Theory accounted for superconductivity as follows. As mentioned above, since spin quantum number of an electron is 1/2, electrons are fermions (substances). 2 fermions (substances) wouldn't exist together at the same point and resistance between 2 fermions occurs when they move. Generally electrons cause resistance to atoms of metal when they travel. However, at the low temperature, structure of the metal ("vibrating crystal lattice") is frozen, special interaction with the frozen protons forms a pair of 2 opposite spin electrons (with spin angular momentum of 1/2 and -1/2). Then the spin angular momentum of the pair generally becomes 1/2 + (-1/2) = 0 (spin=0: singlet: "spin up and spin down" or "spin down and spin up"). (Exceptionally spin=1: triplet: "spin up and spin up" or "spin down and spin down.") It means the pairs of electrons (Cooper Pairs) act like bosons (Bose-Einstein Condensate). Then the pairs of electrons move with no resistance to the metal, under superconductivity.
*Bose-Einstein Condensate is for example Superfluid Liquid Helium with no resistance (with no viscosity) near absolute zero. The property rapidly changes near absolute zero as vapor changes into dew condensation water on the surface of a cold glass (or as water changes into ice on the surface of a winter pond).
* "BCS Theory in Wikipedia" http://en.wikipedia.org/wiki/BCS_theory
* "Cooper Pair in Wikipedia" http://en.wikipedia.org/wiki/Cooper_pair
* "Bose-Einstein Condensate in Wikipedia" http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate
* "Superfluidity in Wikipedia" http://en.wikipedia.org/wiki/Superfluidity
On the other hand, mass of π meson is rather lighter compared with other particles related to nuclei (present-day Hadrons), according to traditional theories at that time, it was hard to be accounted for.
* "Pion in Wikipedia" http://en.wikipedia.org/wiki/Pion

Other than that in the first place, theory of "mass" (inertial mass) was unclear. "Mass" (inertial mass) would be a property of substances resisting force. Substances show gradual acceleration.
Light spontaneously travels, in contrast, substances reluctantly move resisting pressed by force. Those are empirical knowledge. However, there was no theory accounting for them (like 3-dimensional space, time, and so on).
Secondly, the Big Bang theory about the beginning of the universe was advocated.

2.5.9.2.1.2 Nambu's Claim

Nambu pointed out as follows.
The pair of electrons holds 2 electric charges. It means Law of electric charge conservation and U(1) Symmetry are (spontaneously) broken at low temperature near absolute zero. In addition, this scheme could generally be extended. Low temperature near absolute zero is a lower energy level state like vacuum space or other space (filled with Dirac's consecutive creation annihilation of particles in pairs everywhere based on the Vacuum Polarization, virtual particle-antiparticle pairs). In other words, unlike just after the Big Bang filled with an enormous amount of energy, energy level of present-day space is generally lower spontaneously breaking symmetry.
Anti-symmetry would be rather stable and common in space. The aspect of the anti-symmetric potential energy or the spontaneous symmetry breaking is sometimes compared to a Mexican hat or a wine bottle. In other words, it might be compared to changes of vapor, water, and ice depending on temperature as vapor at higher temperature shows little resistance, water at moderate temperature shows a considerable amount of resistance, and ice at lower temperature shows a large amount of resistance.
In addition, Nambu claimed that when symmetry is broken, waves change into easily transferrable (conductible) waves. For example, force is hard to be transferred through vapor and water, but easily transferred through a block of ice. Unlike vapor and water, force added to some blocks of ice quickly propagates through the ice. Since waves and particles are similar according to the Quantum Field Theory, these conductible waves were called Nambu-Goldstone Particles. Since the waves propagate quite fast, the particles are massless or quite light bosons. This is the true identity of superconductivity.
* "Spontaneous Symmetry Breaking in Wikipedia" http://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking
* "Goldstone Boson in Wikipedia" http://en.wikipedia.org/wiki/Goldstone_boson

2.5.9.2.2 Nambu-Jona-Lasinio Model and Chirality Symmetry Breaking in 1961 CE

2.5.9.2.2.1 Background

Nambu noted spontaneous symmetry breaking.

2.5.9.2.2.2 Nambu-Jona-Lasinio Model

Nambu applied the Symmetry Breaking to Chiral Symmetry. Then it turned out that if Chiral Symmetry is broken, space (vacuum) is everywhere filled with (massless) pairs of "particle and antiparticle" (massless pairs of "Quark and Antiquark" with the total spin=0 acting like bosons) and the original Quarks (existing Quarks) interact with the pairs. The travel of the original Quarks is resisted by the interactions with the particles, and the resistance is mass. Quark's mass is mostly accounted for by Chiral Symmetry Breaking and the resistance of "Quarks (deficient in Chiral Symmetry)" to "Quark-Antiquark pairs condensate (with the total spin=0 acting like bosons)." ("Quark's deficiency in Chiral Symmetry" comes from Chiral Symmetry Breaking. "Quark-Antiquark pairs condensate" comes from Chiral Symmetry Breaking. "Quark-Antiquark pairs condensate" is spread everywhere in the universe.)

*Chiral Symmetry is the concept that particles of a helicity are independent and wouldn't be affected by the other helicity particles. It means left-handed particles wouldn't be affected by right-handed particles, and right-handed particles wouldn't be affected by left-handed particles. In contrast, if Chiral Symmetry is broken, left-handed particles and right-handed particles affect each other.
Nambu presumed that the Universe just after the Big Bang had Chiral Symmetry where particles travel at the speed of light. The original Chiral Symmetry came from no resistance to particles' propagation and particles' travel at the speed of light.
For example, Reference Frames at various speed in the Special Theory of Relativity should be remembered. From a standpoint of the Ground, Ground's coordinates or Ground's Reference Frame seems stationary. However, the earth and the solar system are traveling in the universe. Absolute rest (stationary) reference frame wouldn't be determined. In contrast, crew of spaceships might assume their coordinates (reference frames) are moving fast. However, since Absolute rest (stationary) reference frame wouln't be specified, spaceship's reference frame might possibly be rather near absolute rest (stationary).
Thus absolute speed of reference frames wouldn't be determined. Any reference frame wouldn't have special meaningful speed. Any reference frame's speed wouldn't be special or distinctive.

*Chiral Symmetry and the speed of particles would be explained as follows.
The following is an example of a particle with left-handed spin in a reference frame with seemingly low speed (yet possibly traveling backward at a high speed).

Next, if the speed of the particle is rather low, from a standpoint of seemingly rather high speed reference frame (yet possibly rather low speed), the same particle is recognized as traveling backward then, as right-handed spin. Thus if the speed of the particle is lower than the speed of light, "whether left-handed or right-handed" is rather unclear and the helicity is unclear. "Left-handed" and "right-handed" get similar to a certain extent.

In contrast, the following is a particle with the speed of light.
First, from a standpoint of seemingly low speed reference frame (yet possibly traveling backward at a high speed), the particle is left-handed.

Next, even from a standpoint of seemingly high speed reference frame (yet possibly low speed), the same particle is still recognized as left-handed. If particles travel at the speed of light, the helicity is constant and Chiral Symmetry is realized regardless of reference frames' various possibilities required from the Special Theory of Relativity.

*
"Chiral Symmetry in Wikipedia" http://en.wikipedia.org/wiki/Chiral_symmetry
* "Chiral Symmetry Breaking in Wikipedia" http://en.wikipedia.org/wiki/Chiral_symmetry_breaking
* "Nambu-Jona-Lasinio Model in Wikipedia" http://en.wikipedia.org/wiki/Nambu%E2%80%93Jona-Lasinio_model
The original creation of Dirac's virtual particle-antiparticle pairs could be theorized by Heisenberg's Uncertainty Principle. Since encounter of a particle and an antiparticle instantly results in the annihilation of the particles, presence of the pair is temporary like virtual.
Then the original virtual particles would be simply created and the temporary pairs would be "particle (L)-antiparticle (L)" or "particle (R)-antiparticle (R)."
However, when the temperature of the universe decreased, Chiral Symmetry is broken and L and R became similar to a certain extent. Then "particle (L)-antiparticle (R) pairs" and "particle (R)-antiparticle (L) pairs" with rather long life with the total spin=0 acting like bosons are created like below everywhere in the universe. Since the pairs act like bosons, they wouldn't be like substances. (Specifically, "particles" here are "quarks") They have rather long life as referred to as "condensate" after "Bose-Einstein Condensate."

Subsequently, if a realistic original Quark (L) encounters a "Quark (R)-Antiquark (L) pair condensate," a Virtual "Quark (L) - Antiquark (L) pair" is created (then instantly be annihilated) and Quark (R) is remaimed. Then if the remained Quark (R) encounters a "Quark (L) - Antiquark (R) pair condensate," a Virtual "Quark (R) - Antiquark (R) pair" is created (then instantly be annihilated) and Quark (L) is remained.
The resistance during the process is mass.
* "Vacuum Polarization in Wikipedia" http://en.wikipedia.org/wiki/Vacuum_polarization
* "Virtual Particle in Wikipedia" http://en.wikipedia.org/wiki/Virtual_particle

In addition, Nambu presented the interpretaion that π Mesons (Pions) responsible for Strong Force are a kind of Nambu-Goldstone Bosons consisting of Quark-Antiquark pair, created through Chiral Symmetry Breaking, regardless of π Mesons' mass.
* "Pion in Wikipedia" http://en.wikipedia.org/wiki/Pions

2.5.9.2.3 Jonsson's Double-Slit Experiment in 1961 CE

Background
Double-Slit Experiments on coherent light such as laser beam were performed by Young in 1805 CE. According to the experiment, a laser beam was emitted to a screen beyond (through) a barrier with 2 slits. The screen showed some stripes of light.

Since light was mostly recognized as waves, it was naturally interpreted as the result of interference. (Light is electromagnetic waves consisting of electricity (electrons) and magnetism (photons) fluctuating in intensity.) The illustration below shows interference of waves at a certain moment advancing to the screen. (The yellow arcs represent the tops of waves.) The amplified intersection points advance to the screen. Then the dots on the screen represent the location of stripes.

Jonsson's Double-Slit Experiment
A similar but different experiment on electrons (a kind of substances) was performed by Jonsson in 1961 CE. According to the experiment, electrons were emitted one by one to the screen beyond (through) a barrier with 2 slits.
Electrons were commonly recognized as particles of substances at that time. If electrons are particles of substances, 2 stripes of electrons' trace would be created on the screen depending on the 2 slits like below.

However, the experiment showed a pattern with some stripes more than 3. The result was similar to that of light. It couldn't be accounted for according to the traditional interpretaion of electrons as particles.
In this case, when an electron is emitted, widely spread waves advance toward the barrier, pass through the both slits, then waves spread from the both slits causing interference like light. (Reaching the screen, a part (or an aspect) of widely spread waves would be recognized as a particle.)

The essence of an electron is widely spread waves, thought it could be commonly recognized as a particle according to the traditional consideration.
Similarly, as mentioned before, the essence of a particle of substances is widely spread waves as de Broglie predicted. A particle is merely a partial aspect of widely spread waves. The concept of "particle" is a mere fable.
*However, as mentioned before, the convenient term "particle" is still employed below representing partial aspects of widely spread waves.
* "Double-Slit Experiment in Wikipedia" http://en.wikipedia.org/wiki/Double-slit_experiment
*It should be noted that waves of light (in Young's Double-Slit Experiments on Light) are fluctuation of particles' (photons') intensity (fluctuation of particles' (photons') number). In contrast, waves of electrons in Jonsson's Double-Slit Experiments on electrons are fluctuation of something composing a particle (an electron). The meanings of the waves are totally different.

2.5.9.2.4 Glashow's Fundamental Theory of Electroweak Interaction in 1961 CE

Background
Unified Theory on the Electromagnetic Force and the Weak Force (Electroweak Interaction) was sought.
Gauge Symmetric Theory was presented.
Schwinger examined SU(2) symmetry model yet unsuccessfully.

Glashow's Fundamental Theory of the Electroweak Interaction
Glashow, a disciple of Schwinger, presented SU(2)xU(1) symmetric theory relating to the Electroweak Interaction and 3 kinds of particles (Weak Bosons) relating to the Weak Force.
* "Sheldon Lee Glashow in Wikipedia" http://en.wikipedia.org/wiki/Sheldon_Lee_Glashow

2.5.9.2.5 Gell-Mann and Ne'eman's Eightfold Way in 1961 CE

Background
Classification theory for Baryons and Mesons were sought.

Eightfold Way
Gell-Mann and Ne'eman independently claimed Eightfold Way Theory in relation to the classification of Baryons and Mesons. Classification employing "Isospin 3-Component" and "Hypercharge" showed clear SU(3) Symmetry.
* "Eightfold Way in Wikipedia" http://en.wikipedia.org/wiki/Eightfold_Way_(physics)
*Details are explained below, in Gell-Mann's Quark Model, as Baryon Octet and Meson Nonet.

2.5.9.2.6 Gell-Mann's Quark Model in 1963 CE

Background
A considerable number of particles were discovered. Since such many particles couldn't be fundamental particles, particles had to be classified to find further fundamental principles.
On the other hand, light fermions such as electrons were named "Leptons" ("small" in Greek) and particles associated with the "Strong Interaction (Strong Force)" (such as protons, neutrons, Lambda particles, Baryons, π mesons, K mesons, and Mesons) were named "Hadrons" ("stout" in Greek).
Other than that, Gell-Mann found classification of Eightfold Way.

Gell-Mann's Quark Model

Basic Principle

Gell-Mann claimed as follows.
Presuming the horizontal axis " Isospin 3-Component (I3) " and the vertical axis " Hypercharge (Y) ," hadrons showed clear symmetry such as SU(3) Symmetry as follows.
(Hypercharge is merely defined as " Y = B + S ." Hypercharge is not associated with electric charge and so forth. "B", the Baryon Number, is merely the number indicating whether the particle is a Baryon or not. B of Baryons is 1. B of other particles is 0. "S" is strangeness.)
(Both Λ0 and Σ0 are located at the center, at the same location.)

8 Baryons of 1/2 spin formed a hexagon (Baryon Octet). (Both the Σ0 particle and the Λ0 particle are at the center.)
It implies these Baryons consist of 3 elements, named "Quarks." Specifically, the context is explained as follows.

One quark (named "Up Quark") was presumed holding properties illustrated through the arrow-(u) in the direction of the upper-right on the coordinates. (I3 of +1/2 and Y of +1/3)
Another quark (named "Down Quark") was presumed holding properties illustrated through the arrow-(d) in the direction of the upper-left on the coordinates. (I3 of -1/2 and Y of +1/3)
The 3rd quark (named "Strange Quark") was presumed holding properties illustrated through the downward arrow-(s). (I3 of 0 and Y of -2/3)
Then for example, the proton (p) is explained to be a composite of u, u, and d. 2 u arrows and 1 d arrow correspond to the properties of the proton (p).
For example, the neutron (n) is explained to be a composite of u, d, and d. 1 u arrow and 2 d arrows correspond to the properties of the neutron (n).
For example, the Xi-0 particle (Ξ0) is explained to be a composite of u, s, and s. 1 u arrow and 2 s arrows correspond to the properties of the Xi-0 particle.
For example, the Lambda-0 particle (Λ0) is explained to be a composite of u, d, and s.
Since protons and neutrons are common and relatively light, up quark and down quark would be common, relatively light, and similar. Then "up quark" and "down quark" are presumed similar and later categorized as "1st generation of quarks" unlike "strange quark" (2nd generation).
Thus properties of Baryons could be explained to be composites of 3 quarks.
* "Generation (Particle Physics) in Wikipedia" http://en.wikipedia.org/wiki/Generation_(particle_physics)

Baryons with 3/2 spin were predicted. The predicted Baryons with 3/2 spin forms a triangle as follows, called "Baryon Decuplet."

On the other hand, mesons show another hexagonal symmetries. For example, mesons of 0 spin is illustrated as follows, called "Meson Nonet."

Since spins of mesons are 0 or 1 and mesons are generally lighter than baryons, it implies mesons consist of 1 quark and 1 antiquark.
In this case, 3 kinds of quarks (up quark, down quark, and strange quark) and 3 kinds of antiquarks (anti-up quark, anti-down quark, and anti-strange quark) should be presumed.
Antiquarks have opposite properties of quarks respectively, as shown by opposite arrows.
For example, a π+ meson consists of 1 up quark and 1 anti-down quark. (Antiparticles including anti-down quark have opposite electric charge of the original particle. Then the electric charge of an anti-down quark is +1/3.)
Other than that, mesons of 1 spin forms Meson Nonet as well.
On the other hand, anti-baryons consisting of 3 antiquarks, forming Anti-Baryon Octet and Anti-Baryon Decuplet could be presumed.
* "Quark Model in Wikipedia" http://en.wikipedia.org/wiki/Quark_model
* "Quark in Wikipedia" http://en.wikipedia.org/wiki/Quark
* "Antiparticle in Wikipedia" http://en.wikipedia.org/wiki/Antiparticle

2.5.9.2.7 Nambu and Greenberg's Color Charge Quantum Number in 1964 CE

Background
Baryons with 3/2 spin were predicted by Gell-mann.
The Ω- particle was discovered in 1964 CE. The Ω- particle was then presumed consisting of 3 strangeness quarks, 3 x 1/2 spins contrary to the Pauli Exclusion Principle.

Nambu and Greenberg's Color Charge Quantum Number
Nambu claimed a new quantum number should be introduced to account for the Ω- particle. It means 3 quarks can coexist, if the values of the new quantum number of the 3 quarks differ. If the values of the new quantum number of the 3 quarks differ, the coexistence doesn't contradict the Pauli Exclusion Principle. The new quantum number consisting of 3 kinds was later compared to "color" and named "color charge" rather than "numbers."
The Strong Force between quarks was explained employing 3 colors and gluons as follows. Gluons are the particles mediating the Strong Force between quarks.
A quark has a property compared to "color" ("red," "green," or "blue"). A baryon consists of a "red" quark, a "green" quark, and a "blue" quark. (Since a baryon (such as a proton and a neutron) has 3 colored quarks, the overall color of a baryon is compared to "white.")
For example, a proton is illustrated as follows.

A proton consists of 2 up quarks and 1 down quark along with 3 kinds of colors, "red," "green," and "blue." An influence of a gluon is expressed by a purple wave.
Other than that, for example a π+ Meson is illustrated as follows.
(As Meson Theory claims, for example a π+ meson mediates the (Strong) force between a proton and a neutron.)

Subsequently, a red quark of the proton changes into blue creating a "red and anti-blue gluon." (In other words, firstly a "blue and anti-blue gluon" is created (like Dirac's consecutive creation and annihilation of (virtual) particles in pairs based on the Vacuum Polarization), secondly the red of the quark and the blue of the gluon are exchanged.)
* "Vacuum Polarization in Wikipedia" http://en.wikipedia.org/wiki/Vacuum_polarization
* "Virtual Particle in Wikipedia" http://en.wikipedia.org/wiki/Virtual_particle
* "Gluon in Wikipedia" http://en.wikipedia.org/wiki/Gluon

Then as a simplified explanation, the "red and anti-blue gluon" approaches the other (original) blue quark.

The red of the gluon and the blue of the quark are exchanged, the quark changes into red, and the "blue and anti-blue gluon" is annihilated. Such continuously transformational exchangeability would be associated with (continuous) SU(3) Symmetry.

(A "red and anti-blue gluon" was employed in this example, while 8 kinds of color combinations are presumed relating to gluons (like baryon octet), such as "red and anti-green," "green and anti-red," "green and anti-blue," and "blue and anti-red.")
The Strong Force shows SU(3) Symmetry in relation to the 3 colors.
This explanation on the Strong Force employing "color charge" was named Quantum Chromodynamics (QCD).
Yet this would be the simplified explanation of the Strong Force between quarks mediated by gluons' color exchange (unaware of involvement of mesons or Sea Quarks at that time). This model could be called "Naive QCD Model" in contrast to later "Realistic QCD Model."

2.5.9.2.8 Discovery of CP-Symmetry Violation in 1964 CE

Background
CP-Symmetry was claimed instead of C-Symmetry Violation and P-Symmetry Violation on the Weak Force (Neutrinos).

CP-Symmetry Violation
Cronin and Fitch discovered CP-Symmetry Violation on the Weak Force in 1964 CE.
* "CP Violation in Wikipedia" http://en.wikipedia.org/wiki/CP_violation

2.5.9.2.9 Higgs Mechanism in 1964 CE

2.5.9.2.9.1 Background

Mass of Quarks was mostly accounted for by Nambu-Jona-Lasinio Model. Nambu claimed Quark's mass is the resistance of "Quark deficient in Chiral Symmetry" to "Quark-Antiquark pairs with the total spin=0 acting like bosons" spread everywhere in the universe.
However, mass of electrons and Weak Bosons was not yet accounted for.

2.5.9.2.9.2 Higgs Mechanism

Nambu accounted for Quark's mass employing existing particles. In contrast, Higgs claimed a new convenient particle with spin=0 spread everywhere over the universe, later Higgs particles (Higgs Bosons) to account for mass of electrons and Weak Bosons (and Neutrinos). (Consequently, this convenient new particle was the correct solution.)
Higgs presumed that just after the Big Bang Higgs particles (Higgs Bosons) had no influence on other particles because the high temperature just after the Big Bang resulted in randomness (symmetry) of particles including Higgs particles (Higgs Bosons). However, when the energy level (temperature) of the universe (space) got lower, symmetry breaking occurred and Higgs particles (Higgs Bosons) changed the property (condensed) without forming pairs (since the spin is 0) to resist other particles' motion.

*On the other hand, for example photons don't have this property of resistance (mass). It is accounted for that Symmetries prevent or reduce the property of resistance (mass). As mentioned before, photons show perfect Gauge Symmetry. (Since photons are bosons, not fermions, they are associated with Gauge Symmetry.) The property of resistance (mass) in relation to photons seems prevented by this perfect Gauge Symmetry. Bosons seem generally prevented by Gauge Symmetry from occurring the property of resistance. (On the other hand, since Gauge Symmetry of the Weak Force is broken in part, Weak Bosons consequently have a considerable amount of mass at present-day temperature.)
In contrast to Gauge Symmetry of Bosons, the property of resistance (mass) in Fermions seems reduced by Symmetry on Fermions (Chiral Symmetry), while all fermions have mass at present-day temperature losing Chiral Symmetry.
Symmetry seems cancel or reject the effect of Higgs Bosons and Quark-Antuquark pairs relating to the property of resistance (mass).

*Higgs mechanism accounts for some 2% of mass of quarks. Consequently, quarks deficient in symmetry firstly face slight (some 2%) resistance of Higgs particles (Current Mass), then secondly the quarks deficient in symmetry face formidable (some 98%) resistance of particle pairs and so forth (Constituent Mass).
* "Higgs Mechanism in Wikipedia" http://en.wikipedia.org/wiki/Higgs_mechanism
* "Higgs Boson in Wikipedia" http://en.wikipedia.org/wiki/Higgs_boson
* "Current Quark Mass in Wikipedia" http://en.wikipedia.org/wiki/Current_quark_mass
* "Current Quark in Wikipedia" http://en.wikipedia.org/wiki/Current_quark
* "Constituent Quark Mass in Wikipedia" http://en.wikipedia.org/wiki/Constituent_quark_mass

2.5.9.2.10 Bell's Inequality in 1964 CE

2.5.9.2.10.1 Background

As mentioned before, in relation to Quantum Entanglement, based on the assumption of Realism and the Principle of Locality, Einstein in 1935 CE advocated that observation result of a wave (particle) had been fixed in advance pior to observation and unknown "hidden variables" containing observation result of a wave (particle) should be sought.

2.5.9.2.10.2 Bell's Inequality

In relation to Einstein's "hidden variables," Bell presented a practical way to examine the presence or the absence of "hidden variables" and Einstein's assumption including the Principle of Locality.
Bell presumed 3 devices measuring spins along different directions (angles). Presuming a basic direction (axis) "X", device "Alice" measures spin along X. Device "Bob" measures along a different direction from X by an angle θb. Device "Carol" measures along a different direction from X by an angle θc.
Then spins of a wave measured by 3 devices (spin by Alice, spin by Bob, spin by Carol) would be for example tentatively described here as
(up, down, down).
(In this case spin by Alice is "up" as on the left, by Bob is "down" as at the center, and by Carol is "down" as on the right.) (It should be noted that spin of a wave (particle) can be measured once. Yet, for example, if spin of the 1st wave (particle) is measured by Alice and spin of the other entangled wave (particle) is measured by Bob, then spin of the 1st wave (particle) measured "by Bob" can be presumed. For example, if the overall spin is 0 as examplified before and the entangled wave's (particle's) spin measured by Bob is "up," the 1st wave's (particle's) spin measured by Bob would be "down.")

Then there would be 8 patterns of spins of a wave (particle) by 3 devices as
(by Alice, by Bob, by Carol).
(up, up, up)
(up, up, down)
(up, down, up)
(up, down, down)
(down, up, up)
(down, up, down)
(down, down, up)
(down, down, down)

Then incidence ratios of the 8 patterns vary depending on the angles of devices, θb and θc.
The 8 incidence ratios would be respectively expressed as follows.
R(up, up, up)
R(up, up, down)
R(up, down, up)
R(up, down, down)
R(down, up, up)
R(down, up, down)
R(down, down, up)
R(down, down, down)
Since R are incidence ratios, the sum of 8 R is "1".

Next, incidence ratio (probability) of
"Alice=up and entangled wave by Bob=up" is expressed as P(A, B),
"Bob=up and entangled wave by Carol=up" is expressed as P(B, C), and
"Alice=up and entangled wave by Carol=up" is expressed as P(A, C).
For example, if spin of the other entangled wave (particle) by Bob is "up," it means the spin of the 1st wave by Bob is "down."
Then
P(A, B)=R(up, down, up) + R(up, down, down)
P(B, C)=R(up, up, down) + R(down, up, down)
P(A, C)=R(up, up, down) + R(up, down, down)
Then
P(A, B) + P(B, C) = P(A, C) + R(up, down, up) + R(down, up, down)
Since incidence ratios are not naturally less than zero, "R(up, down, up) + R(down, up, down)" is not less than zero.
Then if Quantum Entanglement is real and the Principle of Locality is correct (it means spins of waves (particles) have been secretly fixed in advance as Einstein advocated "hidden variables"),
" P(A, B) + P(B, C) ≧ P(A, C) ."
Roughly, this is Bell's Inequality.
* "Bell's Theorem in Wikipedia" http://en.wikipedia.org/wiki/Bell%27s_theorem

2.5.9.2.11 Penzias and Wilson's Discovery of Cosmic Microwave Background Radiation in 1965 CE

Background
Gamow, Alpher, and Herman predicted cosmic microwave background radiation based on the Big Bang Theory.

Penzias and Wilson discovered the cosmic microwave background radiation. The discovery proved the Big Bang Theory.

2.5.9.2.12 Miyazawa's Supersymmetric Theory in 1966 CE

Background
Yang-Mills Symmetric Theory improved contemporary physics, while various unsolved problems were remained.

Miyazawa's Supersymmetric Theory
Miyazawa claimed Supersymmetric Theory, but ignored at that time.

2.5.9.2.13 Weinberg-Salam Theory in 1967 CE

Background
Glashow presented SU(2)xU(1) symmetric theory in relation to Electroweak interaction and 3 kinds of particles (Weak Bosons) responsible for the Weak Force. However, common particles aside from quarks wouldn't provide continuously transformational exchangeability (changeability) in contrast to continuously transformational exchangeable (changeable) Gauge Symmetric Theory.
On the other hand, Big Bang Theory was recognized, Symmetry Breaking Theory was presented.
Based on Symmetry Breaking, Higgs mechanism explained the mechanism of mass.
The range of the Weak Force was rather short like Strong Force associated with mesons. Mesons have mass and it implied the particles relating to the Weak Force have mass. On the other hand, photons have no mass.

Weinberg-Salam Theory
Weinberg and Salam completed mechanism of the Electromagnetic Force and the Weak Force introducing Symmetry Breaking Theory to Glashow's SU(2)xU(1) symmetric theory.
They claimed just after the Big Bang (10-10sec after the Big Bang) the 2 forces and the employed bosons were indistinguishable because of the high temperature complying with continuously transformational exchangeable (changeable) SU(2)xU(1) symmetry. If there were SU(2) symmetry, particles would be able to continuously (gradually) change into other particles like quarks.
However, as the energy level of the universe decreases, symmetry breaking occurred, 3 kinds of particles (bosons) were separated losing continuously (gradual) transformational exchangeability (changeability) into other particles, the 3 kinds of particles (Weak Bosons) faced the Higgs mechanism and the 3 kinds of particles got mass.
* "Electroweak Theory in Wikipedia" http://en.wikipedia.org/wiki/Weak_force#Electroweak_theory
*Thus, continuous (gradual) transformations in (conceptual) internal space like Gauge Transformations mean the gradual change of the property of particles, gradually changing into other particles.
*Thus, the 3 forces (the Electromagnetic Force, the Weak Force, the Strong Force) or their bosons (Photons, Weak Bosons, Gluons) mostly comply with Gauge Symmetries. On the other hand, some symmetries are curiously particularly violated around the Weak Force.
*Beta Decay is specifically as follows. There are 2 kinds of Beta Decays, to be precise. The representative one would be Beta minus decay. As far as Beta minus decay, for example in cobalt-60, a "down quark" in a neutron (consisting of "up" "down" "down") changes into an "up quark" and a short-lived Weak (minus) Boson (with mass). Then the neutron changes into a proton (consisting of "up" "down" "up"). On the other hand, the Weak (minus) Boson changes into an electron and an antineutrino.
* "Beta Decay in Wikipedia" http://en.wikipedia.org/wiki/Beta_decay
Beta minus Decay would be depicted as follows in a Feynman Diagram.

2.5.9.2.14 Nambu's String Theory in 1969 CE

Background
A considerable number of elementary particles were discovered. They couldn't be the minimum elements. Elementary particles should be summarized under a new theory.

String Theory
Nambu claimed String Theory. But it was unsuccessful at that time.

2.5.9.2.15 Kobayashi and Masukawa's CKM Matrix in 1973 CE

Background
As mentioned before, Beta Decay (conversions between neutrons and protons) was theorized through the Weak Force (and Weak Bosons) radiating electrons and antineutrinos (or positrons and neutrinos). On the other hand, as mentioned above, a neutron consists of 1 "up quark" and 2 "down quarks," a proton consists of 2 "up quarks" and 1 "down quark." Then Beta Decay would be interpreted as conversions between "down quark" and "up quark."
On the other hand, Beta Decay was not exclusively between neutrons and protons, a Lambda particle (consisting of u d s ("up" "down" "strange")) a little showed Beta Decay changing into a proton (u u d). It would be interpreted as "strange quark" a little changed into "up quark." It means "the 2nd generation of quarks (strange quark)" changed into "the 1st generation of quarks." The quark conversions a little occur across the generations. Cabibbo presented the ratios of cross conversions through 2x2 Cabibbo matrix in relation to the Weak Force in 1963 CE.
On the other hand, CP-Symmetry Violation (CP Violation) was discovered in relation to some 0.1% of long-lived neutral Kaon (K0L) (consisting of "down quark," "anti-strange quark," "anti-down quark," and "strange quark") in 1964 CE.
* "Kaon in Wikipedia" http://en.wikipedia.org/wiki/Kaon

CKM Matrix
Kobayashi and Masukawa accounted for CP-Symmetry Violation (CP Violation) presuming 3 generations of quarks and quark mixing over the 3 generations. They claimed 3 generations of quarks, 2 x 3= 6 kinds of quarks in total, and the quark mixing ratios between the generations through CKM Matrix to account for the CP Violation.
* "CKM Matrix in Wikipedia" http://en.wikipedia.org/wiki/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa_matrix"
* "CP Violation in Wikipedia" http://en.wikipedia.org/wiki/CP_violation

2.5.9.2.16 Rubin's Discovery of Dark Matter in 1975 CE

Background
Zwicky presumed unknown mass in the universe to account for velocities of stars in the Milky Way.

Dark Matter
Calculating galaxy rotation curves, Rubin claimed the presence of an enormous amount of unknown mass in the universe. The unknown mass amounted to some 10 times than the observable mass.
* "Dark Matter in Wikipedia" http://en.wikipedia.org/wiki/Dark_matter

2.5.9.2.17 Barnes' Realistic QCD Model in 1977 CE

Background
QCD explained the Strong Force to a certain extent. However, some problems remained. For example, as meson theory claims, short range forces such as the Strong Force and the Weak Force require mediating particles with mass. On the other hand, virtual (temporary) creating and annihilating particles and antiparticles were presumed.

Realistic QCD Model
Barners claimed colors of gluons virtual (temporary) quark-antiquark pairs would be created associated with gluons and the colors of gluons would be transfered to other quarks. The virtual (temporary) quark-antiquark pairs mediate the Strong Force and they would be called "Sea Quarks."
* "Sea Quarks in Wikipedia" http://en.wikipedia.org/wiki/Quark#Sea_quarks
* "American Scientists the Search for QCD Exotics" http://www.americanscientist.org/issues/issue.aspx?id=778&y=0&no=&content=true&page=3&css=print
* "QCD Vacuum in Wikipedia" http://en.wikipedia.org/wiki/QCD_vacuum
For example, the following figure would be laid between the figures, "Color Exchange 1" and "Color Exchange 2" above.

Then an example of the general depiction of Realistic QCD Model would be as follows.

*Nuclear Force such as bonding between a proton and a neutron is similar to the above. As the Meson Theory implied, Nuclear Force is similarly mediated by quark-antiquark pairs.
* "Nuclear Force in Wikipedia" http://en.wikipedia.org/wiki/Nuclear_force