31 Mathematics

31 MathematicsWhat is the Universe?】Dialogue with the Universe

Mathematics is the alphabet with which God has written the Universe. -Galileo Galilei 1564 - 1642

Key wordSymmetry [1]

Forecast of mathematics:Those that do not can still prove.
It is well in the world of mathematics.

Mathematical history
About 7000 years ago  Number was born. (Mankind began to group living.)
16th century    Imaginary number is accepted.
・・・"Forgetting the mental anguish received with imaginary number, and merely introducing this." Gerolamo CardanoItaly 15011576
17th century  Minus is accepted in Europe.
・・・Descartes draws a number line.   René DescartesFrance 15961650
The first half of the 19th century  An imaginary number is denoted by an axis of coordinates.complex plane  Carolus Fridericus GaussGermany 17771855
1935  Gödel's Incompleteness Theorem
・・・Then, Turing(Aan Mathison Turing, UK 1912-1954) proved that there is no unific method of confirming beforehand whether a certain proposition is a proposition which cannot judge truth.
1964  Murray Gell-Mann (1929-)predicted the existence of quarks by the theory of pure mathematics(the group:SU (3)).

[1] Edward Vladimirovich Frenkel(1968-)

31 数学

31 数学【宇宙とは】宇宙との対話


○キーワード:対称性 [1]


7000年前 数字が誕生した。(人類が集団生活を始めた。)
16世紀  虚数を認める
・・・「虚数によって受ける精神的苦痛は忘れ、ただこれを導入せよ」カルダノ(イタリア 150176
17世紀  ヨーロッパでマイナスが認められる・・・デカルトが数直線を描く
                   デカルト(仏 15961650
19世紀前半  座標軸で虚数を現す:複素平面 ガウス(独17771855
1931年   不完全性定理 ゲーデル(オーストリア 190678
1964年  マレー・ゲルマン(1929-)は純粋数学の理論(群:SU(3))を使ってクォークの存在を予言した。

【参 考】
[1]  NHK 数学ミステリー白熱教室  エドワード・フレンケル(1968-)

30 What is the Universe?+The History of Cosmology

30 What is the Universe?+The History of CosmologyWhat is the Universe?】Dialogue with the Universe

Q:Why does the universe exist in spite of trouble
Q:Can a unified theory of the universe explain the universe accurately
Q:Or we need the Creator
Q:If so, the Creator gives the effect of something else in the universe
Q:And who created the Creator

Source: "Brief History of Time" Stephen William Hawking (issued April 15, 1995)

The history of cosmology
1895  William James(1842-1910) coined the term Multi-Universe(Multiverse).
1900   Max Karl Ernst Ludwig Planck(1858 -1947) advocated that the light, X-rays and other electromagnetic waves were released as a constant mass that he called quantum.
1905  Special relativity[1]・・・Theory of electromagnetism that Albert Einstein1879-1955 announced.
1913   Bohr's model(Niels Henrik David Bohr(1885-1962))・・・A pioneer of quantum mechanics (Old quantum theory).
Electron is a wave.
The length of the electrons orbit around the nucleus is an integer multiple of the electron wavelength (10 minus 10 square m).
(Bohr,  de Broglie)
1915-1916   General theory of relativityGeneral relativity(Einstein) [1] [Electromagnetic force + gravity]
Einstein explained that the gravity caused by the mass distort the space-time.
When written in Newtonian mechanics[2] the phenomenon of error increases (movement in the near to the speed of light or large gravitational field) can be correctly described.
· In general relativity, spacetime is expected never to stay inflated or deflated steady or the black hole[3] is expected to forme when a large mass to concentrate on limited space.
Einstein predicted the existence of gravitational waves[4] in 1916 in his general theory of relativity. 
1920s  Quantum mechanics
Atomic, electronic and electromagnetic waves have the characteristics of the particles and waves.
1922 Friedman found the expanding universe solutions in general relativity equations.
1925  Pauli exclusion principle
1926  Werner Heisenberg was put together the uncertainty principle[5].
Uncertainty principleIt is a characteristic of the system, such as the wave. In knowing pair of physical properties (eg position and momentum) at the same time, there is a fundamental limit of accuracy.
1928 Dirac theory
 ・Either both consistenttheory of quantum mechanics and special relativity
There is positron(antimatter) that is the partner of electron.
1929  Discovery of cosmic expansion(the redshift)Edwin Powell Hubble
1932   Discovery of positron(antimatter)
1934  Fritz Zwicky coined the term dark matter. [6]
1948 -Big Bang model [7]
   -Quantum electrodynamics, QED [Electromagnetic force ]
· Electromagnetic interaction acting between charged particles, including electrons is caused by the transfer of particles called photons.
1957 Bryce Seligman DeWitt (1923–2004)  coined the term many-worlds interpretation; MWI.
Peter Ware Higgs proposed the theory of generation of mass. [8]
Cosmic microwave background (radiation); CMBCMBR[7]discovered.
1968     Weinberg-Salam theory[9] [Electromagnetic force + Weak interaction]
1970  Penrose and Hawkins co-authored paper
On the basis of the general relativity theory, they were finally prove that should there was a big bang singularity in the very early universe.
In the singularity, the effect of small scale of quantum mechanics dealing can not be ignored.
· However, if you take into account the quantum effect, singularities disappear. ...?
Only one force was present in the beginning of the universe, then, the force was divided into electromagnetic force, weak interaction, strong interaction and gravity, so physicists  are trying to  expresse these four forces in one form.
 -Standard Model, SM [Electromagnetic force + Weak interaction+ Strong interaction] [9]
Grand unification theory or Grand unified theoryGUT[Electromagnetic force + Weak interaction+ Strong interaction] [10]
The late 1970s  Quantum chromodynamics [9]
1980s  Cosmology based on theory of elementary particles[10]
1981  Cosmic inflation Theory [11]
1984  Superstring Theory [12] [Electromagnetic force + Weak interactionStrong interaction Gravity]
1986~  Loop Quantum Gravity [13]
1995   M-theory[14] [Electromagnetic force + Weak interactionStrong interaction Gravity] 
1998  -Michael S. Turner coined the term dark energy. [6]
    Observed the accelerated expansion of the universeBrian P. Schmidt
2016   Studio Gooda coined structure of dark matter. [7]

1. No. 16 Theory of Relativity
2. No. 15 Newtonian Mechanics
3. No. 81 Black Hole
4. No.29 Gravitational Wave
5. No.18 Uncertainty principle
6. No.11 Dark Matter and Dark Energy
7. No.20 The Big Bang model
8. No. 24 Higgs Boson
9. No.21 Standard theory(Standard model)
10. No.23 Cosmology based on theory of elementary particles
11. No.23-2 Inflation cosmology
12. No.25 Superstring Theory
13. No.26 Loop Quantum Gravity
14. No.27 M-theory

15. No.88-4-2 A Structure of Dark Matter

30 宇宙とは?+宇宙論の歴史

30 宇宙とは?+宇宙論の歴史【宇宙とは】宇宙との対話



1895年 ウィリアム・ジェームズ 多元宇宙という言葉を作る。
1900年 マックス・プランク(1858 -1947) は、光、X線その他の電磁波は、量子と彼
1905年 特殊相対性理論 [1]アルベルト・アインシュタイン1879-1955が発表した電磁気の理論。[電磁気力]
1913年 ボーアの原子模型(ニールス・ボーア(1885-1962)):電子は波で、原子核を回る軌道の長さは波長(10のマイナス10乗m)の整数倍(ボーア、ド・ブロイ)
1915-1916年 一般相対性理論 [1] [電磁気力+重力]
1920年代 量子力学
1922 年 フリードマンが一般相対論方程式の中に膨張宇宙解を見つけた。
1925年 パウリの排他原理
1926年 ヴェルナー・ハイゼンベルグが、不確定性原理[5]をまとめあげた。
1928年 ディラック理論・・・量子力学と特殊相対性理論のどちらとも整合性のある理論
1929年 宇宙膨張(銀河の赤方遷移)の発見(エドウィン・パウエル・ハッブル
1932年 陽電子(反物質)の発見
1934年 フリッツ・ツビッキーが暗黒物質を提唱 [6]
-量子電磁力学(Quantum electrodynamics, QED[電磁気力]
1957年  ブライス・デウィットが多世界解釈を提唱。
1968年 インバーグ=サラム理論[9] [電磁気力+弱い力]
1970年 ペンローズとホーキングの共著論文
標準理論( Standard Model, SM) [電磁気力+弱い力(+強い力)] [9]
大統一理論(Grand unification theory or Grand unified theoryGUT[電磁気力+弱い力+強い力]  [10]
1970年代後半 量子色力学 [9]
1980年代 素粒子論的宇宙論 [10]
1981年 インフレーション理論 [11]
1984年 超弦理論(Superstring theory 1984) [12] [電磁気力+弱い力+強い力+重力]
1986年~  ループ量子重力理論 [13]
1995年 M理論[電磁気力+弱い力+強い力+重力] [14]
1998年 -マイケル・ターナー 暗黒エネルギーという言葉を作る。[6]
2016年 スタジオ・グーダ! 暗黒物質の構造を提案 [15]

【参 照】
1. No.16 相対性理論
2. No.15 ニュートン力学
4. No.29 重力波
5. No.18 不確定性原理
6. No.11 暗黒物質と暗黒エネルギー
7. No.20 ビッグバン・モデル
8. No.24 ヒッグス粒子
9. No.21 標準理論(標準モデル)
10. No.23 素粒子論的宇宙論
11. No.23-2 インフレーション理論
12. No.25 超弦理論
13. No.26 ループ量子重力理論
14. No.27 M理論

15. No.88-4-2 暗黒物質の構造

29 Gravitational Wave

29 Gravitational Wave【What is the Universe?】Dialogue with the Universe

29-1 What are Gravitational Waves?[1] [2]
○ Gravitational waves are ripples of spacetime that propagate at the speed of light.
○Albert Einstein predicted the existence of gravitational waves in 1916 in his general theory of relativity. 
○On February 11, 2016, the LIGO Scientific Collaboration and Virgo Collaboration teams announced that they had made the first observation of gravitational waves, originating from a pair of merging black holes using the Advanced LIGO detectors. On June 15, 2016, a second detection of gravitational waves from coalescing black holes was announced. [3] [4]
○"Gravitational waves go through everything. They are hardly affected by what they pass through, and that means that they are perfect messengers," said Prof Bernard Schutz, from Cardiff University, UK. [3]
○In the framework of quantum field theory, the graviton is the name given to a hypothetical elementary particle speculated to be the force carrier that mediates gravity. However the graviton is not yet proven to exist and no reconciliation yet exists between general relativity which describes gravity, and the Standard Model which describes all other fundamental forces.

29-2 What can we know and what is possible by the gravitational wave?
1)Direct observation of black holes
2)Construction of quantum gravity theory, the integration of general relativity and quantum theory (construction of theory to integrate the four forces of the universe)
3)Direct observation of the big ban and the earlier of the universe
4)Communication in the universe or between the parallel universe 

29-2-1 Direct observation of black holes 
○Nothing can escape from a black hole, so it is impossible to see one directly. (Quantum field theory does predict that black holes give off an extremely tiny amount of thermal radiation, but it's so little that it we can't detect it from Earth.)
○Measurement of the waveform and amplitude of the gravitational waves from a black hole merger event makes possible accurate determination of its distance. [5]
○The accumulation of black hole merger data from cosmologically distant events may help to create more precise models of the history of the expansion of the universe and the nature of the dark energy that influences it. [5]

29-2-2 Construction of quantum gravity theory, the integration of general relativity and quantum theory
○One of the difficulties of quantum gravity is that quantum gravitational effects are only expected to become apparent near the Planck scale, a scale far smaller in distance (equivalently, far larger in energy) than what is currently accessible at high energy particle accelerators. [6]
○A quantum gravity theory is required in order to understand problems involving the combination of very high energy and very small dimensions of space, such as the behavior of black holes, and the origin of the universe. [6]

29-2-3 Direct observation of the big ban and the earlier of the universe
○What is currently observable is only the surface of the big bang.
○If we observe primordial gravitational waves, the inside of the big bang can be seen. Their detection exclude different models of inflation. Their detection exclude different models of inflation.

※The universe expanded approximately 10 ^ 30 times in the inflation era. In addition, since the transition to Friedman space-time, The universe inflated about 10 ^ 60 times together. Therefore, information of the initial Planck scale has not been disturbed by the Big Bang which come after inflation.

29-2-4 Communication in the universe or between the parallel universe
○Because graviton travels through the extra dimensions, communication of between parallel universes of using the gravitational waves can be expected. [7] [8]

29-3 Observation of gravitational waves
29-3-1 LIGO(Laser Interferometer Gravitational-Wave Observatory)
○LIGO is one side of the 4km michelson laser interferometer.
○LIGO succeeded in direct observation of gravitational waves in 2015. [3] [4] Gravitational waves are a prediction of the Theory of General Relativity.
※LIGO [9]

○LIGO’s passive damping system holds the all-important mirrors perfectly still through a 4-stage pendulum called a "quad". [10]


29-3-2 eLISA(Evolved Laser Interferometer Space Antenna)[11]
○The eLISA concept has a constellation of three spacecraft, arranged in an equilateral triangle with 1 million-kilometre arms as a ESA(European Space Agency) mission.
○LISA is good at gravitational wave detection at low frequencies than LIGO and VIRGO.
○A tentative launch date is 2034.

1. Wikipedia:Gravitational wave
2. LIGO”What are Gravitational Waves?”
3. Pallab Ghosh Science correspondent, BBC News “Einstein's gravitational waves 'seen' from black holes”
4. Maddie Stone”Scientists Have Detected Gravitational Waves Again” 2016
5. Wikipedia:First observation of gravitational waves
6. Wikipedia:Quantum gravity (QG)
7. No.28 The Parallel Universe
8. No.96 Communication with the alien
9. Robert Naeye”Gravitational Wave Detection Heralds New Era”at SKY & TELESCOPE 2016
10. LIGO”LIGO Technology”
11. Wikipedia:Evolved Laser Interferometer Space Antenna