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A Modern View of the Origin of the Universe

Cat: SCI
Pub: 1993
#: 9301b

Steven Weinberg





Sub Title

A Modern View of the Origin of the Universe


Steven Weinberg



  • The author is a winner of the 1979 Nobel Prize for Physics.
  • He prefaces: "What could be more interesting than the problem of Genesis? ... In just the last decade a detailed theory of the course of events in the early universe has become widely accepted as a standard model....it is exhilarating that we are now able to speak of such things with any confidence at all...."
  • 著者は1979年ノーベル物理学賞受賞者。
  • 巻頭言「宇宙創世の問題より興味深い問題があるだろうか。過去10年に初期宇宙の出来事についての詳細理論広く受け入れられるようになった。今や、この問題について確信をもって話ができることは幸いである。」


1. The Origin of the Universe:

In 1950s, the study of the early universe was not regarded as a respectable scientist would devote his time. There has not existed an adequate observational and theoretical foundation.

Now the standard model is widely accepted: 'big bang' theory.

<Summary of the history of the early universe>:

  • In the beginning there was an explosion.
    (Note: The Old Testament says ".......")
    This occurred simultaneously everywhere, filling all space from the beginning, with every particle of matter rushing apart from every other particle.
    (all space = a finite universe which curves back on itself like the surface of a sphere.)
  • 1/100 of a second:
    the temperature of the universe was about a hundred thousand million (10^11) Kelvin.
    the elementary particles (like electron, positron, neutrino, and photon) apart in this explosion.
  • Density of the cosmic soup:
    4 billion times that of water; a small contamination of protons and neutrons. The proportions were roughly one proton and one neutron for every billion electrons or positrons or neutrinos or photons.
  • The explosion continued the temperature dropped, reaching
    • 30 billion C. after 1/10 second
    • 10 billion C. after a second
    • 3 billion C. after 14 seconds
    • 1 billion C. after 3 minutes;
      cool enough for protons and neutrons to form into complex nuclei (deuterium, then helium)
  • At the the end of the first 3 minutes:
    the contents of the universe were mostly light, neutrinos, and antineutrinos, with small amount of nuclear material of about 73% hydrogen and 27% helium and small number of electrons left over from electron-positron annihilation.
  • After a few hundred thousand years:
    electrons to join with nuclei to form atoms of hydrogen and helium.
    The resulting gas begins to form clumps, ultimately condense to form galaxies and stars under the influence of gravitation.





  • 初めに爆発があった。
    この爆発は至る所で同時に発生し、すべての素粒子が互いに分離して全宇宙を満たした。(全宇宙とは、球の表面 の如くそれ自身が閉じた有限の宇宙)
  • 1/100秒後
    電子、陽電子、ニュートリノ、光子などの素粒子はこの爆発で分離。 宇宙スープの濃度:
    水の40億倍で、若干の陽子と中性子を含む。比率は陽子、中性子各1個に対し、電子、陽電子、ニュートリノ、光子は各約10億個。 爆発の経過と共に温度が低下
  • 1/10秒後:300億度
  • 1秒後:100億度
  • 14 秒後:30億度
  • 3分後:10億度
  • 最初の3分間の終わり:
    宇宙はほとんどは光、ニュートリノ、反ニュートリノからなり、若干の核種(水素73%、ヘリウム27%)および電子−陽電子の対消滅の残った少量 の電子から成る。
  • 数億年後:
Thfuture of the universe:
  • it may go on expanding forever, getting colder, emptier, and deader.
  • alternatively, it may recontract, breaking up the the galaxies and stars and atoms and atomic nuclei back into their constituents.
  • 永遠に膨張し、更に冷却し、空虚になり、そして死んでいく。
  • あるいは、再び収縮に転じ、銀河、恒星、原子、原子核は素粒子にまで崩壊していく。


2. The expansion of the universe:

<Proper motion>
The stars seem motionless. but they do move, at speeds of a few hundred km/sec. Distant stars change so slowly that their proper motion cannot be detected with even patient observation.

This impression of changelessness is illusory. The universe is in a state of violent explosion; galaxies are rushing apart almost at the speed of light.

Further we can extrapolate this explosion backward in time and conclude the all the galaxies must have been much closer in the past - so close that neither galaxies nor stars nor even atoms or atomic nuclei could have had a separate existence; the era called "the early universe."






<Steps to know the expansion of the universe>

  1. <Doppler effect>
    by Johann Christian Doppler in 1842
    The light from moving away stars from the earth shifts toward longer (redder) wavelength. Moving toward us shifts toward shorter (bluer).
  2. <Frauenhofer lines>
    by Joseph Frauenhofer in 1814
    Dark lines are produced by the selective absorption of light of certain definite wavelengths.
  3. <Nebula>
    by Charles Messier in 1781; published catalog of Nebulae and Star clusters (Andromeda Nebula is M31, Crab Nebula is M1....)
  4. <Supernova>
    Explosions of one star approaches the luminosity of a whole galaxy.
  5. <Cepheid variables>
    by Edwin Hubble in 1923;
    a tight relation between the observed periods of variation of the Cepheids and their absolute luminosities. And he concluded that Andromeda Nebula is 900,000 light years (10 times farther) than the most distant known objects in our galaxy.
  6. <Extragalactic nebulae>
    by Vesto Melvin Slipher in 1910-20;
    Andromeda Nebula is moving toward the earth at 300 km/sec. But more and more of the larger spectral shifts toward the red end were discovered.
  7. <Exploding universe>
    by Hubble in 1929; observed a proportionality between the distances of galaxies and their speeds of recession.
  8. <Cosmological Principle>
    The Universe seems remarkable isotropic and homogeneous; it looks the same in all directions.
  9. <Hubble constant>
    Hubble by 1931; verified the proportionality between velocity and distance for galaxies and concluded that velocities increase by 170 km/sec for every million light years distance; thus, a velocity of 20,000 km/sec means a distance of 120 million light years.
  10. <Hubble constant - revised>
    by Allan Sandage of Palomar and Mt. Wilson; about 15 km/sec per million light years.
    The galaxies have not been moving at constant velocities,
    but have been slowing down by mutual gravitation. Therefore, we can refer the age of universe must be less than 20 billion years.
  11. <Age of our galaxy>:
    Our galaxy is about 10-15 billion years old; calculated by the rate of radioactivity (especially relative abundance of U-235 and U-238), stellar evolution and the red shift of distant galaxies.
  12. <Cosmological constant>
    in 1917 Albert Einstein mutilate his equations by introducing so-called cosmological constant to keep the elegance of the original theory (Universe should be homogeneous, isotropic and static. = Einstein's static universe)
    This constant could serve to balance the attractive force of gravitation at large distances.
  13. <Friedmann model>
    in 1922 Alexandre Friedmann provided; If the average density of the matter of the universe is less than a certain critical value, then the universe will expand forever. Or if it is greater than this critical value, then the gravitational fields are strong enough to stop the expansion of the universe, so that it will eventually implode back to indefinitely large density.
    The critical density is proportional to the square of the Hubble constant.
    The critical density equals 5 x 10^-30 grams per cubic cm, or three hydrogen atoms per 1000 litters of space.
  14. <Hubble diagram>
    Expansion or Contraction of the Universe:
    One way to tell whether or not the galactic velocities exceed escape velocity it to measure the rate of slowing down. If this deceleration is less (or greater) than a certain amount, then escape velocity is (or is not) exceeded.
    Luminosity-Distance (billion light years) is often called Hubble diagram.


  1. ドップラー効果:
    Johann C. Doppler (1842)による。地球から遠ざかる星からの光の波長は長くなり(赤方偏移)近づく場合は波長が短くなる(青方偏移)
  2. フラウンホーファー線:
    Joseph Frauenhofer (1814)による。一定の波長の光が選択的に吸収されて生じる暗線
  3. 星雲:
    Charles Messier (1781)によってカタログとして発表された星雲および星団(アンドロメダ星雲はM31、かに星雲はM1等)
  4. 超新星:
  5. セファイド変光星:
    Edwin Hubble (1923)により発見された脈動変光星(最初に発見されたケフェウス座δ星に由来)。変光周期と真の明るさの間に周期‐光度関係と呼ばれる強い相関関係がある。これによってアンドロメダ星雲までの距離は10万光年として、銀河系のどの物体より10倍以上も遠方にあると結論した。
  6. 銀河系外星雲:
    Vesto Melvin Slipher (1910-20)による。アンドロメダ星雲は地球に向かって秒速300/kmで近づいている。さらにずっと大きな赤方偏移を示す星雲が発見された。
  7. 膨張宇宙:
    Hubble (1929)は、銀河とその後退速度との間に比例関係を発見。
  8. 宇宙原理:
    宇宙は大局的には等方的で一様であり. 中心はなく, どの点も対等となる。
  9. ハッブル定数:
    Hubble (1931)は、銀河の距離と後退速度の間の比例関係を検証し、1百万光年毎に秒速170kmであると結論した。これは秒速2万kmは120百万光年に相当する。
  10. ハッブル定数(修正):
    Allan Sandage(Palomar and Mt. Wilson)は、1百万光年毎に秒速15kmと修正。銀河は必ずしも一定の速度で動いておらず、相互の重力によって速度が遅くなっている。その結果 宇宙の年齢は200億年以下と推定。
  11. 銀河の年齢:
  12. 宇宙定数:
    Albert Einstein (1917)は、一般相対性理論の重力方程式に挿入したいわゆる宇宙項で、これによって宇宙は等方で一様で静的であるという(アインシュタインの静的宇宙)元の理論が保たれる。この常数によって遠距離における重力による引力とバランスすることができた。
  13. フリードマン・モデル:
    Alexandre Friedmann (1922 )による。もし宇宙の物質が一定の臨界密度未満の場合は宇宙は永遠に膨張する。もしこの臨海密度超の場合は重力場は宇宙の膨張を止めて、限りなく収縮に向かう。
  14. ハッブル図:

3. Radiation background:

  • <Bell Telephone Laboratory>
    In 1964 Arno A. Penzias and Robert W. Wilson: intended to measure the radio noise coming from our own galaxy - in effect, from the sky itself. It is crucially important to identify any electrical noise that might be produced within the receiving system.
    They received a sizable amount of microwave noise at 7.35 cm that was independent of direction. This static did not vary with the time of day or with the season. It were not coming from the Milky Way, but from a much larger volume of the universe.
    • Incidentally, radio waves with wavelengths like 7.35 cm are known as "microwave radiation", and having an equivalent temperature of 3.5 degrees Kelvin.
  • Bernard Burke of MIT and P.J.E. Peebles argued that there ought to be a background of radio noise left over from the early universe.
  • Properties of Radiation: Wavelength / Black-body K

Kind of radiation


Photon energy
(electron volt)

Black body
temp. (K)
Radio (-VHF) > 100 mm < 0.00001 < 0.03
Microwave 0.1 - 100 mm 0.00001 -
0.03 - 30
Infrared 1 - 100μm 0.01 - 1 30 - 3,000
Visible 0.3 - 1μm 1 - 6 3,000 - 15,000
Ultraviolet 1 - 300 nm 6 - 1 K 15,000 - 3 M
X ray 0.01 - 1 nm 1 K - 100 K 3 - 300 M
γray < 0.01 nm > 100 K > 300 M
    • Remarks:
      Penzias and Wilson discovered the cosmic radiation background was 7.35 cm, which is microwave radiation.
    • The photon energy released by radioactive decay is about a million electron volts, so this is a γ ray.
    • The surface of the sun is at 5,800°K, so the sun emits visible light.
  • G.D. Birkhoff Theorem: (1923):
    In order to calculate the motion of any typical galaxy relative to our own, draw a sphere with us at the center and the galaxy of interest on the surface; the motion of this galaxy is precisely the same as if the mass of the universe consisted only of the matter within this sphere, with nothing outside.
  • Planck distribution: (by 1890s)
    It had become known that the properties of radiation in a state of thermal equilibrium with matter depend only on the temperature.
    Essentially the same formula also gives the amount of radiation emitted per second and per cm2 at any wavelength from any totally absorbing surface, so radiation of this sort is generally known as "black-body radiation."
  • Energy of a photon with a wavelength of 1 cm:
    0.000124 electron volts, and proportionally more at shorter wavelength.
    (Re: 1 eV = the energy gained by 1 electron in moving across a voltage drop of 1 volt.)
    • A typical photon in visible light with wavelength of 5 x 10^-5 cm: so its energy would be 0.000124 eV x 20,000 = 2.5 eV
    • The energy of a photon is very small in macroscopic terms, which is why photons seem to blend together into continuous stream of radiation.
    • Incidentally, chemical reaction energies are generally of the order of an eV per atom or per electron; to rip the electron out of a hydrogen atom takes 13.6 eV.
      Photons in sunlight also have energies of the order of an eV; it is what allows these photons to produce chemical reactions essential for life, such as photosynthesis.
    • Nuclear reaction energies are generally of the order of a million eV per atomic nucleus.
  • Einstein tells us that any photon's wavelength is inversely proportional to the photon energy:
    Hence, the typical wavelength of photons in black-body radiation is inversely proportional to the temperature.
    • an opaque body at an ordinary room of 300 degrees K will emit black-body radiation with a wavelength of 0.29 cm divided by 300. (= infrared radiation)
    • Surface of the sun is about 5,800 degrees K:
      will emit 5,000 Angstrom (visible wavelength)
  • Stefan-Boltsmann Law:
    The energy density is simply the number of photons per liter times the average energy per photon.
    • The number of photons per liter is proportional to the cube of the temperature.
    • While, the average photon energy is simply proportional to the temperature.
    • Hence the energy per liter in black-body radiation is proportional to the fourth power of the temperature.
    • Black-body radiation of 3 degrees K; then its energy density is 4.72 eV x 3 to the fourth power, or about 380 eV per liter.


  • <ベル電話研究所>:
    Arno A. PenziasとRobert W. Wilson (1964)は、我々の銀河、実際には空からやってくる無線雑音を測定した。これは受信システム内で発生するであろう電子ノイズを特定する上で重要であった。
    彼らは7.35 cmのマイクロ波ノイズを方向に関係なく受信した。このノイズは昼夜や季節に関わりなくやってきた。それは我々の銀河からではなく、ずっと大きな宇宙からやってきた。
    • 波長7.35 cmの電波はマイクロ波放射として知られ、これは絶対温度3.5度に相当。
  • Bernard Burke (MIT) と P.J.E. Peeblesとはこれは初期宇宙の残りとしての背景ノイズに違いないと議論した。
  • 放射の特性:波長/黒体温度K
  • 電磁波の種類

    電波(-VHF): <0.03
    マイクロ波: 0.03 - 30
    赤外線: 30 - 3K
    可視光線: 3K - 15K
    紫外線: 15K - 3M
    X線: 3M - 300M
    γ線: > 300M
    • 注:
    • γ線崩壊によって放射される光子エネルギーは百万eV。
    • 太陽表面温度は5,800度Kで、太陽は可視光を放射している。
  • Birkhoffの原理:(1923)
    ある銀河の我々に対する相対的な動きを計算する場合は、我々を中心とし、その銀河を表面 する球を描く。その銀河の動きはあたかも宇宙の質量がこの球の中だけと見なし、外側が考慮しないで計算すればよい。
  • プランクの放射法則:(1890迄)
    本質的には、全ての波長を吸収する表面からのいかなる波長の毎秒単位 面積当たりの放射量についても同じ式が成り立つ。この放射が「黒体放射」である。
  • 波長1cmの1光子のエネルギー
    0.000124 eVで、波長の短さに比例する。
    (注:1 eV = 1Vの電位差を横切ることによって1電子の得る運動エネルギー)
    • 可視光(0.5μm)のエネルギーは、約2.5eV
    • 光子のエネルギはマクロ的には非常にちいさいので、放射光の流れとしては光子は連続しているように見える。
    • たまたま化学反応のエネルギーは1原子あるいは1電子当たりの約1eVのレベル。
    • 核反応エネルギーは原子核当たり、約100万eVのオーダー。
  • アインシュタインによれば、どの光子の周波数も光子のエネルギーに反比例する。従って、黒体放射の光子周波数は温度に反比例する。
    • 室温300度K(27度C)における不透明の物体は0.29 cm / 300の黒体放射(赤外線に相当)をしている。
    • 太陽表面は5,800度Kなので、5,000オングストローム(可視光)を放射している。
  • ステファン・ボルツマンの放射法則:
    エネルギー密度=光子密度 x 光子当たりの平均エネルギー
    • 光子密度は温度の3乗に比例
    • 平均光子エネルギは温度に比例
    • 従って、黒体放射におけるエネルギー密度は絶対温度の4乗に比例する。
    • 3度Kの黒体放射のエネルギーは、4.72 eV x 3の4乗 
      =約380 eV




In 1989 COBE (COsmic Background Explorer) satellite map of temperature inhomogeneities in the cosmic microwave background over the entire sky. Higher than average regions are shown in red, cooler than average in blue. The total temperature range shown in +-200 millionths of K.

  • Density of nuclear particles:
    In the present universe is somewhere between 6 and 0.03 particles per thousand liters: Thus there are between 100M- 20,000M photons for every nuclear particles.
  • In the early universe, at temperature about 3,000 degrees K, the universe consists not of the galaxies and stars we see in the sky today, but only of an ionized and indifferentiated soup of matter and radiation
  • The energy in the mass of a nuclear particle is give by Einstein's formula E = mc^2 as about 939 M eV.
    • "Radiation-dominated era":
      At earlier times the temperature was above about 4,000 degrees K, in which most of the energy in the universe was in the form of radiation.
    • "Matter-dominated era":
      At about 3,000 degrees K, the contents of the universe were becoming transparent to radiation.
      The average energy of a photon in 3 degrees K is about 0.0007 eV, so that even with 1,000 M photons per neutron or proton, most of the energy of the present universe is in the form of matter, not radiation
    • The reaction will still occur if the energy of the individual photons is greater than mc^2; the energy will simply go into giving the material particles a high velocity. However, particles of mass m cannot be produced in collisions of two photons if the energy of the photon is below mc^2.
    • Boltzmann's constant:
      0.00008617 eV/degree K.
  • The lightest material particles are electron (e-) and positron (e+). The positron has opposite electrical charge but the same mass and spin. When a positron collides with an electron, the charges can cancel, with the energy in the two particles' masses appearing as pure radiation. The annihilation process can also run backward - two photons with sufficient energy can collide and produce an electron-positron pair, the photon energies being converted into the electron and positron masses.
  • Properties of some elementary particles:



Rest energy
(M eV)

Threshold temp
(B degK)

Mean life
Photon γ



<Leptons> weak interaction
Neutrino νe, ν-e



νμ ,ν-μ



Electron e-, e+



Muon μ-, μ+



2.197 x 10^-6
<Hadrons> strong interaction
Pi meson π



0.8 x 10^-16
π+, π-



2.60 x 10^-8
Proton p, p-



Neutron n, n-




  1. "Rest energy" is the energy that would be released if all the mass of the particle were converted into energy. (million eV)
  2. "Threshold temperature" is the rest energy divided by Boltzmann's constant; it is the temperature above which a particle can be freely created out of thermal radiation (billion degree-K)
  3. "Mean life" is the average length of time the particle survives before it suffers a radioactive decay into other particles (seconds)
  4. This table can tell which particles could have been present in large numbers at various times in the history of the universe; they are just the particles whose threshold temperature were below the temperature of the universe at that time.
  5. Early universe at above the threshold of 6 billion degrees can be considered to be composed predominantly of photons, electrons, and positrons, not just photons alone.


1989年、COBE (宇宙背景探査衛星)による全天における宇宙背景放射(マイクロ波)の不均一な温度地図。100万分の200度K±の温度変化(赤が高く、青が低い)

  • 原子核の密度:
  • 初期宇宙では、温度が約3,000度Kで、宇宙は今日我々が見るように銀河や恒星から出来ていないで、イオン状態の物質と放射の未分離スープの状態であった。
  • 原子核の質量にあるエネルギーはアインシュタインの公式E = mc^2によって、約939M eVとなる。
    • 放射優勢の時期:
    • 物質優勢の時期:
      3度Kにおける光子の平均エネルギーは0.0007 eVであり、中性子や陽子に対し、10億個もの光子があったとしても、現在の宇宙のほとんどのエネルギーは放射ではなく物質の形態である。
    • もし光子それぞれのエネルギーがmc^2より大きければ反応が起こり、エネルギーが粒子に高速度を与えることになる。しかしもし光子のエネルギーがmc^2より小さければ2つの光子衝突によって質量 mは生成されない。
    • ボルツマン定数:
      0.00008617 eV/度K
  • 最軽量の素粒子は電子(e-)と陽電子(e+)である。陽電子は電荷が反対で、質量 ・スピンは同じである。陽電子が電子と衝突すると電荷が消滅し、2つの粒子の質量 に相当するエネルギーが放射される。対消滅のプロセスは逆に起こり得る。十分なエネルギーを得ると2つの光子は衝突し、電子−陽電子の対を生成する。光子のエネルギーは電子と陽電子の質量 に変換される。



光子 γ
<レプトン> 弱い相互作用
ニュートリノ νe, ν-e
νμ ,ν-μ
電子 e-, e+
ミュー粒子 μ-, μ+
<ハドロン> 強い相互作用
パイ中間子 π
π+, π-
陽子 p, p-
中性子 n, n-

  1. "Rest energy"(静止エネルギー)は、粒子の全質量がエネルギーに転換した場合に放出されるエネルギー(百万eV)
  2. "Threshold temperature"(臨海温度)は、Rest energyをボルツマン定数で割った温度(K)。この温度以上ならば粒子は熱放射から自由に生成され得る(十億度K)
  3. "Mean life"(平均寿命)は、粒子が放射性崩壊によって他の粒子に変化するまでの平均寿命(秒)
  4. この図は、どの粒子が宇宙の歴史の各段階で多く存在していたかを示す。宇宙のそれぞれの時点での臨海温度以下の粒子のみが存在できる。
  5. 60億度K以上の初期宇宙では、光子だけでなく、他に電子、陽電子が存在していたと考えられる。


4. Reactions in the early universe:

  • Electric Charge:
    We can create or destroy pairs of particles with equal and opposite electric charge, but the net electric charge never changes.
  • Baryon Number:
    Baryon includes proton, neutron and heavier unstable particles known as hyperon. Baryons and antibaryons can be created or destroyed in pairs; however the total number of baryons minus the numbers of antibaryons never changes. We attribute a baryon number of +1 to the proton, neutron and hyperon, and -1 to the corresponding antiparticles; the rule is then that the total baryon number never changes.
  • Lepton Number:
    Lepton includes light negatively charged electron and muon, plus an electrically neutral particle of zero mass called neutrino and their antiparticles (positron, antimuon and antineutrino). Despite their zero mass and charge, neutrinos and antineutrinos are no more fictitious than photons; they carry energy and momentum like any other particle. The total number of leptons minus the total number of antileptons never changes.
  • A good example; radioactive decay of a neutron n into a proton p, an electron e-, and an antineutrino νe-.






p +






Baryon #




Lepton #






  • 電荷:
    粒子を等しい正負の電荷をもつ粒子に作ったり壊したり出来るが、電気量 の和は不変である。(電荷保存則)
  • バリオン数(重粒子数):
    バリオンとは陽子、中性子や重たく不安定なハイペロンと呼ばれる素粒子をいう。バリオンと反バリオンとは対になって作られあるいは壊される。陽子、中性子、ハイペロンをバリオン数+1とし、対応する反粒子を-1とすると、バリオン数は不変で ある。
  • レプトン数(軽粒子数):
    レプトンとは、負電荷をもつ電子やミューオン、および電荷をもたないゼロ質量 のニュートリノおよびこれらの反素粒子(陽電子、反ミューオン、反ニュートリノをいう。質量 もゼロ、電荷もゼロというニュートリノや反ニュートリノは光子より架空という訳ではない、それは他の素粒子同様にエネルギーと運動量 をもつ。レプトンの合計数量と反レプトンの合計数量との差は不変である。
  • わかりやすい事例として、中性子nが放射性崩壊をして、陽子pと電子e-と反ニュートリノνe-になる。


5. The first Three Minutes:

I will adjust the speed of our film to the falling temperature of the universe. Unfortunately, I cannot start the film at zero time and infinite temperature.

  • <I cannot start the film at zero time>
    1.5 x 10^12 degrees K; 0.01 seconds; the universe contains large number of pi mesons, which weigh about 1/7 as much as a nuclear particle.
    Pi mesons interact very strongly with each other and with nuclear particles.
    Quark theory suggests that around several million million degrees K, the hadrons would simply break up into their constituent quarks, just as atoms break up into electrons and nuclei at a few thousand degree, and nuclei break up into protons and neutrons at a few thousand million degrees. The universe could be considered to consist of photons, leptons, antileptons, quarks, and antiquarks, all moving essentially as free particles.
    (But the puzzle of the nonexistence of isolated free quarks is one of the most important problems facing theoretical physics the the present moment.)
  • <First Frame>
    10^11 degrees K; above threshold temperature for electrons and positrons:
    Despite its rapid expansion, the universe is nearly perfect thermal equilibrium. The universe is so dense that even the neutrinos (here means neutrinos and antinueutrinos) are kept in thermal equilibrium with the electrons, positrons, and photons by rapid collisions with them and with each other.
    The total energy density of the universe at this temperature is 21 x 10^44 eV per liter, which is equivalent to a mass density of 3.8 billion kg/liter.
    The most important reactions are:
    • Antineutrino (νe-) plus proton (p) yields positron (e+) plus neutron (n) (and vice versa)
    • Neutrino (νe) plus neutron (n) yields electron (e) plus proton (p) (and vice versa)
    • How large the universe was at very early times?
      Since the temperature of the universe falls in inverse proportion to its size; this gives a circumference of about four light years.
  • <Second Frame>
    3 x 10^10 degrees K; 0.11 seconds have elapsed.
    Nothing has changed qualitatively - the contents are still dominated by electrons, positrons, neutrinos, antineutrinos, and photons, all in thermal equilibrium.
    The small number of nuclear particles is still not bound into nuclei, but with falling temperature the heavier neutrons to turn into the lighter protons than vice versa. 38% neutrons and 62% protons.
  • <Third Frame>
    10^10 degrees K; 1.09 seconds have elapsed. Decreasing density and temperature have increased free particle of neutrinos and antineutrinos, no longer in thermal equilibrium with electrons, positrons or photons. ("decoupling")
    The total energy density decreases, now equivalent to mass density 380 K times that of water. Now proton-neutron balance; 24% neutrons and 76% protons.
  • <Fourth Frame>
    3 x 10^9 degrees K; 13.82 seconds have elapsed. Now below the threshold temperature for electrons and positrons, so rapidly to disappear as major constituents of the universe. From now on, the temperature of the universe means that of photons.
    A proton and a neutron can form a deuterium with extra energy and momentum being carried away by a photon. The deuterium nucleus can then collide with a proton or a neutron, forming helium three (He3, two protons and a neutron), or tritium (H3, a proton and two neutrons). Finally H3 collide with a neutron and H3 collide with a proton, forming ordinary helium (He4, two protons and two neutrons). The balance now is 17% neutrons and 83% protons.
  • <Fifth Frame>
    10^9 degrees K, 3 minutes and 2 seconds have elapsed. The electrons and positrons have mostly disappeared, and the chief constituents are now photons, neutrinos and antineutrinos. The universe is now cool enough for H3 and He3 as well as ordinary He nuclei to hold together. The decay of free neutron is beginning to be important; the balance is now 14% neutrons, 86% protons.



  • <ゼロ時間から始まっていない>
    1.5 x 10の12乗度K, 0.01秒後。宇宙には核子の1/7の質量をもつパイ中間子が大量 に存在している。パイ中間子は相互にまた核子と強く相互作用している。
  • <1コマ目>
    この温度における宇宙のエネルギー密度は21 x 10の44乗 eV/リットルで、これは38億kg/リットルに相当する。
    • 反ニュートリノ(νe-)と 陽子(p) によって、陽電子(e+)と中性子(n) を生成。
    • ニュートリノ(νe)と中性子 (n)によって、電子(e)と陽子(p)を生成。
    • 初期宇宙の大きさは?
  • <2コマ目>
    3 x 10の10乗度K; 0.11秒経過
    質的には変化なし。中身は電子、陽電子、ニュートリノ、反ニュートリノ、光子からなり、熱平衡状態にある。少量 の各紙はまだ核にしばりつけられていないが、温度降下に伴いより重い中性子は軽い陽子に変化したり、またその逆もある。その比率は中性子38%に対し陽子は62%。
  • <3コマ目>
    10の10乗度K; 1.09秒経過。
  • <4コマ目>
    3 x 10の9乗度K; 13.82秒経過。
  • <5コマ目>
    10の9乗度K, 3分2秒経過。
  • >Top
  • <A Little Later>
    0.9 x 10^9 degrees K, 3 minutes and 46 seconds passed. A dramatic event occurs; the temperature drops to the point at which deuterium nuclei can hold together; almost all of the remaining neutrons are immediately cooked into helium nuclei.
    The balance is 13% neutrons, 87% protons.
  • <Sixth Frame>
    3 x 10^8 degrees K, 34 minutes and 40 seconds passed. The electrons and positrons are now completely annihilated except for the small excess of electrons needed to balance the charge of the protons.
    Nuclear processes have stopped - now mostly bound into helium nuclei or free protons, with about 22 - 28% helium by weight.
  • <After 700,000 years>
    The universe will go on expanding and cooling, where electrons and nuclei can form stable atoms; the lack of free electrons will make the contents of the universe transparent to radiation; and the decoupling of matter and radiation will allow matter to begin to form into galaxies and stars.
  • <After another 10 billion years>
    Living beings will begin to reconstruct this story.
    In addition to the large amount of helium produced at the end of the first 3 minutes, there was also a trace of deuterium and light helium isotope He3. The deuterium abundance is very sensitive to the density of nuclear particles at the time of nucleosysthesis: if 20 ppm of deuterium was really created in the early universe, then there must have been (and is now) just about 1.1 billion photons per nuclear particle.
  • I do not believe that scientific progress is always best advanced by keeping an altogether open mind. The great thing is not to be free of theoretical prejudices, but to have the right theoretical prejudices. The standard model of the early universe has some success, and it provides a coherent theoretical framework for future experimental programs.
  • <その少し後>
    0.9 x 10の9乗度K, 3分46秒経過
  • <6コマ目>
    3 x 10の8乗度K, 34分40秒経過 電子と陽電子は、陽子の電荷に相当する僅かの過剰な電子を残し、完全に消滅。核反応は停止し、ほとんどがヘリウムの原子核または自由陽子に取り込まれる。ヘリウムは重量 比で22-28%を占める。
  • <70万年後>
  • <100億年後>
    最初の3分間で大量のヘリウムが生成され、また僅かな重水素やヘリウム3同位 体も残存した。重水素の量は核合成の時期における核子の濃度に大きく関係する。もし初期宇宙で20 ppmの重水素が生成されたとすれば、核子当たり11億の光子が生成されたことになる。
  • 科学の進歩は常にオープンマインドであればいいというものではないと思う。重要なことは、理論的な偏見から自由でないということで、むしろ正しい理論的偏見を持つべきである。初期宇宙における標準モデルがある程度成功し、将来の実験計画について一貫した理論的枠組みを与えている。


6. Epilogue:

The UNIVERSE will certainly go on expanding for a while; the standard model gives an equivocal prophecy: It all depends on whether the cosmic density is less or greater than a certain critical value.

  • If the cosmic density is less than the critical density:
    Our descendants will see thermonuclear reactions slowly come to an end in all the stars, leaving behind various sorts of cinder; black dwarf stars, neutron stars, perhaps black holes. The cosmic backgrounds of radiation and neutrinos will continue to fall in temperature.
  • If the cosmic density is greater than the critical density; then the universe is finite and its expansion will eventually cease, giving way to an accelerating contraction.
    • If the cosmic density is twice its critical value, then the universe is now 10 billion years old; it will go on expanding for another 50 billion years, and then begin to contract. After 50 billion years the universe would have regained its present size, and after another 10 billion years it would approach a singular state of infinite density. During the early part of the contracting phase, astronomers will be able to observe both red shifts (from distant galaxies) and blue shifts (from nearby objects) .
    • As the universe begins to contract, the temperature will start to rise. When the universe has recontracted to 1/100 its present size, the radiation background will begin to dominate the sky: the night sky will be as warm (300 degrees K) as our present sky at day.
    • 70 million years later the universe will have contracted another tenfold, and our heirs will find the sky intolerable bright. Molecules in planetary and stellar atmospheres and in interstellar space will begin to dissociate into their constituent atoms, and the atoms will break up into free electrons and atomic nuclei.
    • After another 700,000 years, the cosmic temperature will be at ten million degrees; then stars and planets will dissolve into a cosmic soup of radiation, electrons, and nuclei.
    • In another 22 days, the nuclei will then begin to break up into their constituent protons and neutrons. soon after that, electrons and positrons will be created in great numbers in photon-photon collisions, and the cosmic background of neutrinos and antineutrinos will regain thermal communion with the rest of the universe.
  • <Oscillating model>
    If this is our future, it presumably also is our past. The present expanding universe would be only the phase following the last contraction and bounce. It is assumed that there was a previous complete phase of cosmic expansion and contraction. Such oscillating model, like the steady-stage model, nicely avoids the problem of Genesis.
    • However, in each cycle the ratio of photons to nuclear particle is slightly increased by a kind of friction as the universe expands and contracts. As far as we know, the universe would then start each new cycle with a new, slightly larger ratio of photons to nuclear particles. So it is hard to see how the universe could have previously experienced an infinite number of cycles.
  • It is almost irresistible for humans to believe that we have some special relation to the universe, that human life is not just a more-or-less farcical outcome of a chain of accidents reaching back to the first three minutes, but that we were somehow build in from the beginning.

6. 結語:

この宇宙は、しばらくは確実に膨張し続ける。その後の予言については、標準モデルではあいまいである。すべては宇宙密度が一定の臨界量 以下かそれ以上かにかかっている。

  • もし、宇宙密度が臨海密度以下の場合は、我々の子孫はすべての恒星における熱核反応が徐々に終わり、暗い矮星、中性子星、あるいはブラックホールを残す。宇宙の背景放射とニュートリノは引き続き温度低下を示す。
  • もし宇宙密度が臨海密度より大きい場合は、宇宙は有限でその膨張はいずれ終了し、収縮を開始することになる。
    • もし宇宙密度が臨海密度の2倍とすると、宇宙は今100億年なのであと500億年は膨張し続け、それから収縮し始める。500億年後に宇宙は再び現在の大きさに戻り、その後は100億年かけて無限大の密度の特異点に近づく。収縮の初期段階では、天文学者は赤方偏移(遠方の銀河)と青方偏移(近くの物体)の両方が観測できる。
    • 宇宙が収縮を始めると、温度は上昇に転じる。宇宙が現在の1/100に収縮すると、背景放射は空を覆い、夜空でも300度Kになり昼間のように輝く。
    • 7千万年後は宇宙はさらに10倍に収縮し、我々の子孫は空が耐えられないように明るく輝くのを見るだろう。惑星や恒星の大気や恒星間の分子はそれらを構成する原子に分解し、さらに原子は自由電子と原子核に分解。
    • さらに70万年後には、宇宙温度は1000万度となり、恒星や惑星は放射、電子、原子核からなる宇宙のスープ状に分解。
    • さらに22日後、原子核は、陽子や中性子に分解し、間もなく電子や陽電子が膨大な量 の光子同士の衝突によって生成される。宇宙の背景はニュートリノと反ニュートリノによって再び宇宙全体が満たされる。
  • <振動モデル>
    上記は我々の未来であるならば、それを我々の過去とみなすこともできる。現在の膨張宇宙は過去の収縮およびその反転の結果 かもしれない。過去においては宇宙の膨張と収縮を完全に繰り返すと想定するという説がある。この振動モデルは、静止モデルと同様に、宇宙創生問題をうまく避けることができる。
    • しかしながら、各サイクル毎に光子の核子に対する比率は摩擦のように宇宙の膨張と収縮に伴い若干増加する。我々の知る限り、光子の核子に対する比率はほとんど増えないので、宇宙はまった新しい状態からサイクルを開始するように見える。従って宇宙が過去に無限回のサイクルを経験したとは見なせない。
  • 人類が宇宙に特別な関係をもっている、即ち、人類の生命は、宇宙創生の最初の3分間に起こった偶然以来の連鎖の滑稽な結末ではなく、最初からそうなるべくしてなったのだと信じたいという考えにほとんどは抗しがたいものがある。
  • Since my childhood, there is the basic question: "Where are we from, and where are we going?" There has been no satisfactory answers to this for a long time. But this book seems to describe closer answers to this.
  • In 21st. century, we must continue to pursue the answer to such basic questions - about universe, about life, about our future and about our raisons d'etre.
  • 子供の頃からの基本的な質問がある。「我々はどこから来て、どこへ行こうとしているのか?」長い間これに対する満足する答えがなかった。しかしこの本はそれに近い答えが書いてあるような気がする。
  • 21世紀には、これらの基本的な質問に対する答えを引き続き探し続けなければならない。我々の宇宙・生命・未来そして存在意義について...

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