15 Newtonian Mechanics

15 Newtonian Mechanics 【What is the Universe?】Dialogue with the Universe

 ・Three laws of Newtonian mechanics
1) Law of inertia・・・As for an object, unless power acts -- stillness -- linear uniform motion is carried out.
2) Equation of motion・・・At a mass point the acceleration(a) is proportional to the power(F) of acting then, and is in inverse proportion to the mass(m).
3) Action-reaction law
 ・Law of universal gravitation

○Newtonian mechanics can be used when treating movement of sufficiently later than the velocity of light in a macroscopic scale(0.1 mm or more). For example, in the space navigation in an artificial satellite or planetary exploration, it is calculable in sufficient accuracy using Newtonian mechanics in many cases.

【Change log】
20170501 Addition of a photo

15 ニュートン力学

15 ニュートン力学 【宇宙とは】宇宙との対話

1) 慣性の法則・・・物体は、力が作用しない限り、静止または等速直線運動する。
2) 運動方程式・・・加速度aは、そのとき質点に作用する力Fに比例し、質点の質量mに反比例する。
3) 作用・反作用の法則


20170501 写真の追加

14 Histry of the Universe

14 Histry of the Universe 【What is the Universe?】Dialogue with the Universe

0          The quantum fluctuation [2]
After 10^-36~10^-34 second  Inflation(10^-27→10^-3m、10^28→10^25K)[3]
~10^-32 second  Big Bang(10^-1m=10cm)[4]
After 10^-9 second The birth of mass(10^13K)[5]
After 1 second  The Universe had become the size of the solar system.
After 100 seconds   The birth of hydrogen and helium10^9K)
After 300,000 years  Transparent to radiation:The cosmic microwave background (CMB) is the oldest light in the universe.
(0^24m=82 million ly、3000K、Expansion rate of the universe: 60 times the speed of light)
After 0.5 billion years  The birth of stars
After 0.6 billion years  The birth of galaxies 
5 billion years ~     Second Inflation [6]
After 9 billion years   The birth of Solar system
After 13.8 billion years  Current    
(10^27m=90 billion ly、2.7K、Expansion rate of the universe: 3.5 times the speed of light)

※ Chronology of the universe [1]

【参 照】
1. Wikipedia: Chronology of the universe
2. No.23-1 The Birth of the universe:Quantum fluctuation
3. No.23-2 Inflation cosmology
4. No.23-4 The Big Bang model
5. No.25 Higgs field and Higgs Boson
6. No.23-2 Inflation cosmology

14 宇宙の歴史

14 宇宙の歴史 【宇宙とは】宇宙との対話 [1]

0          量子的揺らぎ [2]
10^-36~10^-34秒後  インフレーション(10^-27→10^-3m、10^28→10^25K)[3]
~10^-32秒後     ビッグバン(10^-1m=10cm)[4]
10^-9秒後       質量の誕生(10^13K)[5]
1秒後         宇宙が太陽系の大きさになる。(10^13m、10^10K)
100秒後        水素とヘリウムの誕生(10^9K)
30万年後       宇宙の晴れ上がり:マイクロ波背景放射で観察される
5億年後        恒星の誕生
6億年後        銀河の誕生
50億年後~      第2次インフレーション [6]
90億年後       太陽系の誕生
138億年後       現在

※ 宇宙の歴史 [7]

【参 照】
1. Wikipedia:宇宙の年表
2. No.24-1 宇宙の誕生:量子的ゆらぎ
3. No.24-2 インフレーション理論
4. No.24-4 ビッグバン理論
5. No.25 ヒッグス場とヒッグス粒子
6. No.24-2 インフレーション理論
7. 三菱電機”宇宙創生時の急膨脹「インフレーション」の証拠写真を撮る日”

13 The Birth and Life of Stars

13 The Birth and Life of Stars 【What is the Universe?】Dialogue with the Universe

13-1 The Birth of Stars
In the universe, 
Stars are born from chaos.
Stars and intelligence are being born while increasing the entropy.

※ entropy: the degree of disorder
※ law of entropy increase: the laws of increasing of disorder in the universe
19 カオス.jpg

※The Carina Nebula (7,500 ly)  
(c)NASA,ESA,and M.Livio and the Hubble 20th Anniversary Team(STScI)

13-2 Life of Stars
○Big star burns out faster than small one.
 (Since stars have a limited supply of hydrogen in their cores, they have a limited lifetime as main sequence stars. This lifetime is proportional to f M / L, where f is the fraction of the total mass of the star, M, available for nuclear burning in the core and L is the average luminosity of the star during its main sequence lifetime. Because of the strong dependence of luminosity on mass, stellar lifetimes depend sensitively on mass.)[1]
○The lifetime of the sun is about 100 million years. The life of stars of 10 times weight of the sun is from 1 / 1000 to 1 / 100.
○The Sun formed about 4.6 billion years ago. It will exit the main sequence in approximately 5 billion years and start to turn into a red giant. [2]

1. The Life and Death of Stars NASA
2. Wikipedia:Sun

13 星の誕生と寿命

13 星の誕生と寿命 【宇宙とは】宇宙との対話

13-1 星の誕生

19 カオス.jpg

(c)NASA,ESA,and M.Livio and the Hubble 20th Anniversary Team(STScI)

13-2 星の寿命 【宇宙とは】宇宙との対話 [1]
(星の寿命は質量の 2 乗から 3 乗に反比例している。)
○太陽の寿命は約100 億年。太陽の10 倍の星の寿命はおよそ1/100 から 1/1000 の 1 億年から 1000 万年。

1. 星には寿命があるのでしょうか? 理科年表オフィシャルサイト


12 Expansion of the Universe

12 Expansion of the Universe 【What is the Universe?】Dialogue with the Universe

12-1 The expanding universe [1]
• Since the Big Bang, The universe has continued to expand.
・Everything is moving away from us, with a speed that is proportional to its distance. :The Hubble Law [2]
・ For expansion of the universe is the expansion of space-time itself, so it is also possible to exceed the speed of light.
・The universe is the same everywhere.:Uniformity
・Currently, the observable universe is expanding at 3.5 times the speed of light.
・Expansion of the universe is described in the general theory of relativity.
・ Outside of the observable universe is not known whether infinite or finite.

⇒ Therefore, in order to escape from our universe, rather than fly, it is necessary to exceed the time and space.


12-2 Standard candle -Observation of the size of the universe[3]
・Brighter Type Ia supernova is known to shine longer.・・・So, it is possible to know the specific brightness( absolute magnitude) of the star from the shining period.
・Thus, it is possible to determine the distance (D (kpc)) to the Type Ia supernova.


  Kpc: kiloparsecs =3.26 light year
  m :the apparent magnitude
 M :the absolute magnitude
・Supernova explosion is about once in a hundred years in one galaxy, but if you use a large enough telescope, you can see the 100,000 galaxies in the night sky of the size of the coin. And in every one of the galaxy, because it contains several billion of stars, in the order of magnitude of the coin, you can observe three explosions overnight. [4]
・By observation of the standard candle, it was possible to determine the Hubble constant with an error range less than 10%. As a result, the age of the universe could be estimated.

12-3 The Moon Moving Away

・Because of tidal forces between earth and moon, earth's rotation would gradually slow.
•As a result, the moment of the Earth's rotation (rotational force) is reduced, and the moment of the moon around the Earth increases, and the moon away from Earth (3.8 cm per year).

1.宇宙(The universe/Japanese) - Wikipedia
2.edX/Cosmology/Section1 Space and Time/Lesson1/Referende Notes 1
3.Cosmic distance ladder - Wikipedia:
4.A Universe from Nothing. Lawrence M. Krauss -2012

【Change log】
20170513 Addition of a photo of moon

12 宇宙の膨張

12 宇宙の膨張  【宇宙とは】宇宙との対話

12-1 膨張する宇宙[1]



12-2 標準光源-宇宙の大きさの観測[3]


  Kpc: キロパーセク=3.26 光年
  m :天体の見かけの等級
 M :天体の絶対等級

・超新星爆発は1つの銀河で百年に1回程度ですが、十分に大きな望遠鏡を使えば、コインの大きさの夜空の中に10万の銀河を見ることができる。そしてその銀河のひとつひとつには、数十億個もの恒星が含まれているので、コイン程度の大きさの中で、一晩に3個ほどの爆発を観測できる。[4] (p.56)

12-3 遠ざかる月 


【参 考】
1. Wikipedia:宇宙
2. オンライン講座:edX/Cosmology/Section1 Space and Time/Lesson1/Referende Notes 1
3. Wikipedia:標準光源
4. 「宇宙が始まる前には何があったのか?」ローレンス・クラウス(2013年11月刊)

20170513 月の写真を追加

11 Dark Matter and Dark Energy

11 Dark Matter and Dark Energy 【Exploring the universe】Dialogue with the Universe

11-1 Dark Matter
・Dark matter is matter and energy, which is supposed to describe the structure of the universe and the operation of the galaxy. (Fritz Zwicky in 1934) [1]
・It is named darkness from the fact that is not only not emitting light but also not reflecting.
・Dark matter is distributed spherically around the galaxy.
・From it is to us that can not be only three spatial dimensions recognition, dark matter can not be seen in motion in the other seven spatial dimension to us. [2]
・Mass of dark matter is a kinetic energy of the particles(Elementary particle? In superstring theory, it is string that vibrates at a high frequency) in motion in the other seven spatial dimensions. [2]
・It can be detected by the gravitational lens effect.
※True nature of galaxies [3]

・Neutralino that is the lightest and stable particle in supersymmetric particles is one of the leading candidates for dark matter.
・Neutralino, that is the partner of photon and Z boson or the the Higgs particle, and that is electrically neutral. It's spin is 1/2. So neutralino particles is such as relatives of neutrino.
※Candidate for dark matter [4]

11-2 Dark Energy
・In observation of galaxies and galaxy clusters(Cosmic structure) that have been made in the 1990s, if the space has to be flat, only dark matter was suggested that not be explained only about 25% of the universe mass. If the dark energy compensate about 70% of the remaining, can be explained that the universe is flat.
・The universe(space-time) is expanding at an accelerated pace. The dark matter and substances act as a brake against the expansion of the universe in order to attract each other by gravity. On the other hand, dark energy acts as a repulsive force. ・・・?
・And the universe (space-time) even though continued accelerated expansion, the density of dark energy does not become thin.
・The identity of the dark energy is not known. [5] (Related to the quantum theory of gravity ...?)

11-2-1 The identity of dark energy (hypothesis 1) [7]
• The same kind of energy with vacuum energy which caused inflation in early universe.

・In that case, dark energy does not change it’s density of energy even the universe continues to expand.
Then, regardless of whether the curvature of the universe is either positive or zero or negative, the universe will dilute and spread without limit.

• On the other hand, it is thought that the dark energy causes phase transition and the energy density will be substantially zero.
(In the inflation of early universe, the vacuum energy density became almost zero by the phase transition of vacuum, as a result, accelerated expansion had stopped.)
• In this case, when the curvature of the universe is positive, the universe is likely to turn to contraction from expansion.

11-2-2 The identity of dark energy (hypothesis 2) [7] [8]
・Phantom energy is a hypothetical form of dark energy that is even more potent than the cosmological constant at increasing the expansion of the universe
・If it exists, it could cause the expansion of the universe to accelerate so quickly that a scenario known as the Big Rip would occur.

11-2-3 The identity of dark energy (hypothesis 3) [7]
・In this case, vacuum energy which caused inflation in early universe is left in the current of the universe.

・However, compared to the energy value of the vacuum that should remain theoretically, the value of dark energy observed even smaller 120 digits.
・This problem happens in order to the energy of the vacuum has a feature that "the energy density is constant" . If the density is constant, the amount of energy of the vacuum is rapidly increases with the cosmic expansion.
・So, a theory appeared. In this theory, the identity of dark energy is the unknown energy which is similar to the vacuum-energy, energy density is decreased with the lapse of time.・・・?
  • This unknown-energy was named "Quinntessen (fifth element)".
11-2-4 The identity of dark energy (hypothesis 4) [7]
・In this case, dark energy does not exist. (p.208)
・In order to general relativity coming a little change in large scale, such as several hundreds of million light-years or several billion light-years, the universe accelerates expansion.

11-3 Observation
・There is attempt to observe dark matter or dark energy.

11-3-1 XMASS
・The XMASS collaboration, led by Yoichiro Suzuki at the Kavli IPMU, has reported its latest results on the search for warm dark matter. Their results rule out the possibility that super-weakly interacting massive bosonic particles (bosonic super-WIMPs) constitute all dark matter in the universe. [9]

11-3-2  International Linear Collider(ILC)[6]
・The design and associated R&D activities associated with the International Linear Collider (ILC) are performed by a global collaboration consisting of working group and national laboratories in Europe, the Americas and Asia.
・It is possible to explore the identity of the Higgs boson and dark matter and dark energy by the ILC.
• Linear accelerator of approximately 31 kilometres to hit electron and positron
・A site-specific one located in the Kitakami highland in the Iwate prefecture in northern Japan.(2013)

11-3-3 Subaru Measurement of Images and Redshifts
・SuMIRe (Subaru Measurement of Images and Redshifts) is a project to reveal the origin and fate of the Universe by elucidating the nature of dark matter and dark energy via imaging and spectroscopy. [10]

1. Why dark matter is assumed?
1) By the third law of Kepler, from the orbital period and the semi-major axis of the two stars we can obtain the sum of the mass of the stars.
     M:Sum of the mass of stars(solar mass)
p:Orbital period(year)
a:Semi-major axis of two stars(astronomical unit: au)
2)When estimating the total mass of galaxies, based on the movement of the galaxy its periphery, the result is a few hundred times the mass which is estimated based on the total luminance of galaxies and the number of galaxies observed optically.
3)Therefore, it is assumed that there are substances that are not visible.
2. 「宇宙は何でできているのか」村山 斉(Japanese)
3. Hitoshi Murayama “From the Big Bang to Dark Energy” Coursera of The University of Tokyo
4. Dennis SILVERMAN”More About Supersymmetry”
5.Dark Energy, Dark Matter - NASA Science - Science@NASA
6. International Linear Collider
7.No.87 Future of the Universe
8. Wikipedia:Phantom energy
9. The Kavli Fundation/Recent News
10. SuMIRe Project

11 暗黒物質と暗黒エネルギー

11 暗黒物質と暗黒エネルギー 【宇宙とは】宇宙との対話

11-1 暗黒物質
(1934年にフリッツ・ツビッキーによって銀河団中の銀河の軌道速度における"欠損質量" (missing mass) を説明するために仮定された。)[1]
・暗黒物質の質量は、他の7個の空間次元で運動している粒子(素粒子? 超弦理論では、高い周波数で振動する弦)の運動エネルギー。[2]
※True nature of galaxies [3]

図:8 [4]

11-2 暗黒エネルギー

11-2-1 暗黒エネルギーの正体(仮説1)[8]



11-2-2 暗黒エネルギーの正体(仮説2)[8]

11-2―3 暗黒エネルギーの正体(仮説3)[8]




11-3 観測

11-3-1 XMASS
東京大学国際高等研究所カブリ数物連携宇宙研究機構の鈴木洋一郎(すずき・よういちろう)特任教授らのXMASS(エックスマス)実験グループは、岐阜県飛騨市の地下1000mに設置したXMASS検出器を用いて暗黒物質の候補のひとつであるボゾン粒子(スピンが0や1の素粒子)のSuper-WIMP(スーパー ウィンプ)について世界最高感度で探索を行い、この粒子が宇宙の暗黒物質であるというシナリオを否定した。(2014年9月)[9]

11-3-2 国際リニアコライダー計画( International Linear Collider、略称ILC)[6]
・電子と陽電子をぶつける全長31kmの直線状の加速器 [7]

11-3-3 すみれ計画 [8] 
・すみれ:Subaru Measurement of Images and Redshifts (SuMIRe)
・2400個の銀河のスペクトル解析を同時に行うことのできる超広視野分光器(PFS プライムフォーカススペクトログラフ)は2017年稼働予定。

【参 考】
1) ケプラーの第三法則により、二つの星の公転周期と軌道長半径から二つの星の質量の和を求めることができる。
       M:二つの 星の質量の和(太陽質量)
2) 銀河団の全質量をその周縁の銀河の運動に基づいて推定すると、その結果は光学的に観測される銀河の数および銀河団の全輝度に基づいて推定された質量の数百倍となる。
3) 従って、目に見えない物質(暗黒物質)が存在するものと推測される。
2.「宇宙は何でできているのか」村山 斉(2010年刊)
3. 村山斉 “From the Big Bang to Dark Energy” Coursera of The University of Tokyo
4. 山下雅樹”暗黒物質“
5. Wikipedia:ダークエネルギー
6. Wikipedia:国際リニアコライダー計画
7. International Linear Collider
8.「気が遠くなる未来の宇宙のはなし」佐藤 勝彦(2013年刊)(p.209)
9. 東京大学国際高等研究所カブリ数物連携宇宙研究機構

10 Constitutes of the Universe 

10 Constitutes of the Universe 【What is the Universe?】Dialogue with the Universe

10-1 Constitutes of the Universe [1]
(1) Substance・・・・・4.83% by weight of the universe
・Heavy elements •  :0.03%
・Neutrino      :0.3%
・Stars        :0.5%
・Hydrogen・Helium :4%
(2) Energy・・・・・・・ 0.17% 
(3) Dark matter ・・・ 26.8% 
• Dark matter does not interact with the electromagnetic force. This means it does not absorb, reflect or emit light. In fact, researchers have been able to infer the existence of dark matter only from the gravitational effect. 
(4) Dark energy ・・・ 68.3%
・Dark energy is hypothetical energy to explain the accelerated expansion of the universe and result of observation that the the majority of the mass of the universe is unknown identity.
(Hawking suspects that it is vacuum energy.)
Figure1 Constitutes of the Universe [2]

10-2 Observation of the total amount of substance [3]
○The total amount of the substance in the universe is estimated from the measurement of the gravitational lens effect and X-ray radiation of galaxy clusters.
• The total mass of the galaxy clusters are associated with the temperature of the gas in clusters of galaxies that emit X-rays.

10-3 Virtual particle [3]
:Particles which is assumed in the calculation without being observed.
・In calculating the reaction between the particles in accordance with the quantum field theory, by considering virtual particles, correct answer is obtained.
・For example, the fine structure of the spectrum of the hydrogen atom can be calculated with high accuracy.
・Electromagnetic force is mediated by photons and virtual photons.
・According to the quantum theory of electromagnetic, the electrostatic field occurs by the charged particles releasing virtual particles of zero energy.
・・・According to the quantum theory of electromagnetic, the electrostatic field occurs by releasing of virtual particles of zero energy from charged particles .
・・・Zero-energy particles may proceed even to the ends of the universe without disappearing.
※If zero-energy particles are released, law of the conservation of energy is not violated.

• In addition, inside the proton and the neutron, gluons and virtual gluons, that convey the strong force acting between quarks, constantly born and disappear.

○Features of virtual particles
・They are virtually and apparently "short-lived".
・Phenomena such as breaking the law of conservation of energy occurs.
・Positive and negative charge particles occur in pairs.

○ Energy of virtual particles 
・Energy of virtual particles can be calculated by following equation.
Energy of virtual particles = Total energy - Energy of real particles
※real particles:Consider actual particles to be divided into real particles and virtual particles
※Method of calculation
• Virtual particles disappear in infinitesimal time.
・The measured value of energy of a system is inversely proportional to the length of the measurement time.
• So, the particles that disappear in infinitesimal time have the energy of infinity.
・In order to obtain energy of virtual particles as finite value, we subtract energy of total energy and energy of real particles.

○Vacuume energy ⇔ Cosmological constant ⇔ Dark energy ⇔ Energy of virtual particles・・・Unresolved problem
・Vacuum energy behaves equivalent to the cosmological constant.(1967 Yakov Borisovich Zel'dovich)
・However, unfortunately, against empty space, the estimated value of the energy on the virtual particles are 120 orders of magnitude greater than all of the other energy in the universe!


1. Wikipedia:宇宙
2. Chris Blake”Dark energy and dark matter”
3.A Universe from Nothing. Lawrence M. Krauss -2012