愛因斯坦的宇宙與高空間 Parents of the Science / Hyperspace 數學與物理的交互作用 高文芳交大物理所2004/1/17 台中女中 / 台中一中

Galileo Galilei ( )

Issac Newton ( )

James Clerk Maxwell ( )

Albert Einstein (1879- )

Everything is physics 舉目所見 皆是物理 J. Schwinger Matter Physics 物質物理 Bio-Physics 生命物理 Social Physics 社會物理 [ 孔德 Auguste Comte, ]

數學與物理的交互作用 微積分 --- 牛頓重力場 微積分 --- 牛頓重力場 黎曼幾何 –- 愛因斯坦重力場 黎曼幾何 –- 愛因斯坦重力場 纖維束 Fiber Bundle --- 規範場 纖維束 Fiber Bundle --- 規範場 Calabi-Yau 流形 ---- Superstring Calabi-Yau 流形 ---- Superstring Hyperspace 高空間 / 表面宇宙 (Brane Universe) Hyperspace 高空間 / 表面宇宙 (Brane Universe)

Riemann, Georg Friedrich Bernhard Riemann, Georg Friedrich Bernhard 黎曼（ 1826 ～ 1866 ） 生於德國漢諾威 (Hanover) ，卒於義大利 Selasca 。黎曼在分析與幾何上有極廣泛與深入 的貢獻，其空間觀念與方法，影響及於現代理 論物理，尤其是廣義相對論。 25 歲得到哥廷根的博士學位，兩年後提出論文 〈 On the representation of a function by means of a trigonometrical series 〉申請哥廷 根的（無給）講師職位， 1854 年在偉大的 高斯面前發表就職演說〈 On the Hypothesis that forms the foundation of Geometry 〉 。在這篇演說中，黎曼為此 後一百五十年的微分幾何大業指出了方向，立 下了基礎，論文的本身不僅是個數學史上的一 篇傑作，並且在表達上也是一個典範。

統一場論 重力 重力 – 牛頓重力 F= GMm / r 2 電磁力 SU(1) 電磁力 SU(1) – 庫倫定律 F= kQq / r 弱交互作用力 SU(2) 弱交互作用力 SU(2) 強交互作用力 SU(3) 強交互作用力 SU(3)

Hermann Klaus Hugo Weyl [ ] 1918 He produced the first guage theory in which the Maxwell electromagnetic field and the gravitational field appear as geometrical properties of space-time He produced the first guage theory in which the Maxwell electromagnetic field and the gravitational field appear as geometrical properties of space-time.Maxwell

Gauge/Scale symmetry Fiber Bundle

Theodor Franz Eduard Kaluza [ ] Kaluza in 1919, sent a paper to Albert Einstein proposing a unification of gravity with Maxwell's theory of light Kaluza in 1919, sent a paper to Albert Einstein proposing a unification of gravity with Maxwell's theory of lightEinstein MaxwellEinstein Maxwell This paper was communicated by Einstein himself on 8 December 1921 for publishing This paper was communicated by Einstein himself on 8 December 1921 for publishingEinstein

Oskar Klein [ ] Klein assumed the fifth dimension to be periodic with a period l = c(2k) 1/2 /e where e was the charge of the electron and k was Einstein's constant of gravitation. The dimension was on the order of the Planck length. Klein assumed the fifth dimension to be periodic with a period l = c(2k) 1/2 /e where e was the charge of the electron and k was Einstein's constant of gravitation. The dimension was on the order of the Planck length. EinsteinPlanck EinsteinPlanck Klein's results were published in Nature in the autumn of Klein's results were published in Nature in the autumn of 1926.

Kaluza-Klein Theory of Hyperspace 重力場 電磁場 五維重力場 四維重力場 電磁場

Ed. Witten [1951- ] Ed. Witten [1951- ] Fields Medal, 1990 布蘭代斯大學 (Brandeis) B.A 歷史系 布蘭代斯大學 (Brandeis) B.A 歷史系 Princeton M.A / 羅文嘉 / Ph.D. in 1976 Princeton M.A / 羅文嘉 / Ph.D. in 1976 Harvard 博士後 ; Junior Fellow Harvard 博士後 ; Junior Fellow Princeton 物理教授 1980; Princeton 物理教授 1980; MacArthur Fellowship 1982 MacArthur Fellowship 1982 高等研究院 (Institute for Advanced Study) Professor in the School of Natural Sciences 1982 高等研究院 (Institute for Advanced Study) Professor in the School of Natural Sciences 1982 : 雖然他顯然是物理學家 Atiyah: 雖然他顯然是物理學家 ( 從他 的著作可知 ), 然而他主導數學的能力顯然 少有數學家可以出其右, 他以數學描述物理 觀念的能力也是近乎唯一. 其完美地運用物 理直觀, 開創新而深入的數學的能力, 一再 令數學界嘆為觀止 …. 數學是科學之母 物理是科學之父

Brandeis University 物理系

Randall-Sundrum 1999 高空間表面物理 Brane (hypersurface) Physics Brane 四維表 面 Bulk 我們住在這裡 Extra dimension 第五維

21 世紀的主流物理 -- 天文物理 Hyperspace and Space Travel 最熱門的行業 : 天文旅行社 1930 天外有天 1980 粒子天文物理 1990 宇宙學成為實驗科學 2000 顯學

Oh My GoD!

President BTWN the Bushes

景美 木柵

Expanding Universe

Edwin Hubble ( ) 一九二三年，他在威爾遜 山天文台用當時最大的 二點五米口徑的反射望遠鏡 拍攝了仙女座大星雲的照片

The Hooker Telescope on Mt. Wilson Picture Credit: Mount Wilson Observatory

Astronomers think most of the universe is made of dark energy, followed by dark matter. The remainder of the cosmos consists of ordinary matter, most of it locked up in stars and clouds of gas Astronomers think most of the universe is made of dark energy, followed by dark matter. The remainder of the cosmos consists of ordinary matter, most of it locked up in stars and clouds of gas

Scientists speculate that the universe began an accelerated rate of expansion halfway into its 15 billion-year life when objects began flying apart from one another at a much faster rate Scientists speculate that the universe began an accelerated rate of expansion halfway into its 15 billion-year life when objects began flying apart from one another at a much faster rate

The red rings denote galaxies expanding at a slow rate while the green one show an accelerated rate. The farthest know supernova exploded as the universe's expansion was slowing down The red rings denote galaxies expanding at a slow rate while the green one show an accelerated rate. The farthest know supernova exploded as the universe's expansion was slowing down

CMB

Robert Wilson/Arno Penzias 1965

Array for Microwave Background Anisotropy (AMIBA)

數學是科學之母 物理是科學之父 宇宙是科學之子 結論 :

凡所有相 皆是虛妄 若見諸相非相 即見如來

The central area of the Orion Nebula is called the "Cavern." Astronomers have identified more than 700 young stars at different stages of formation buried inside this region. In the center of the image are four very hot and massive stars, which radiate a torrent of ultraviolet radiation. This radiation "illuminates" the cloud, enabling us to see it, although not in a way that a light bulb lights a room. Rather, the intense ultraviolet radiation causes the cloud to glow. The central area of the Orion Nebula is called the "Cavern." Astronomers have identified more than 700 young stars at different stages of formation buried inside this region. In the center of the image are four very hot and massive stars, which radiate a torrent of ultraviolet radiation. This radiation "illuminates" the cloud, enabling us to see it, although not in a way that a light bulb lights a room. Rather, the intense ultraviolet radiation causes the cloud to glow.

Eagle Nebula Where are the "baby" or embryonic stars? If you look very closely at the column, you may see protrusions that look almost like fingers. These "fingers" probably contain embryonic stars which astronomers call "protostars." However, it is unlikely that many will "grow up" and shine like our sun. Where are the "baby" or embryonic stars? If you look very closely at the column, you may see protrusions that look almost like fingers. These "fingers" probably contain embryonic stars which astronomers call "protostars." However, it is unlikely that many will "grow up" and shine like our sun.

These photos - the first to reveal the pancake shape of orbiting gases and dust - is evidence that planet formation is common in our Milky Way Galaxy. Presently, 47 planets have been identified outside our solar system. If planets are common, then extraterrestrial life may be common as well ! These photos - the first to reveal the pancake shape of orbiting gases and dust - is evidence that planet formation is common in our Milky Way Galaxy. Presently, 47 planets have been identified outside our solar system. If planets are common, then extraterrestrial life may be common as well !

Star Cluster NGC 1850 The glorious yellow stars shown in this picture are probably similar to our Sun. These stars are in the Large Magellanic Cloud, a galaxy 166,000 light- years away from our own Milky Way Galaxy. The glorious yellow stars shown in this picture are probably similar to our Sun. These stars are in the Large Magellanic Cloud, a galaxy 166,000 light- years away from our own Milky Way Galaxy.

This is a picture of the star Eta Carinae. At 150 times the mass of our Sun, it is one of the most massive stars currently known. Eta Carinae is actually on the brink of destruction. Despite these explosions, the core remains intact. Eta Carinae probably will blow off its outer layers many times. This is a picture of the star Eta Carinae. At 150 times the mass of our Sun, it is one of the most massive stars currently known. Eta Carinae is actually on the brink of destruction. Despite these explosions, the core remains intact. Eta Carinae probably will blow off its outer layers many times.

This beautiful image is called the Cat's Eye Nebula. It shows a white dwarf star surrounded by colorful shells of gas. The white dwarf star was formed when the core of an old red giant star collapsed inward and blew off its outer layers. (The shells of gas you see here used to be the outer layers of the old red giant.) White dwarf stars are no larger than Earth, but are very dense; one cubic centimeter of a white dwarf can have a mass of more than 2 million kilograms ! This beautiful image is called the Cat's Eye Nebula. It shows a white dwarf star surrounded by colorful shells of gas. The white dwarf star was formed when the core of an old red giant star collapsed inward and blew off its outer layers. (The shells of gas you see here used to be the outer layers of the old red giant.) White dwarf stars are no larger than Earth, but are very dense; one cubic centimeter of a white dwarf can have a mass of more than 2 million kilograms !

Supernova 1987A Supernova 1987A

A schematic HR Diagram

西元 1054 年 宋史 客星 至和元年五 月已丑，出天關 東南，可數寸， 歲餘稍沒

西元 1054 年 宋至和元 年五月已丑 宋史 客星出天關東南， 可數寸，歲餘稍沒

如果宇宙一年相當於於地球一百 五十億年，那麼。。。 150 億年 =1.5×1010 年 150 億年 =1.5×1010 年 宇宙年曆 宇宙年曆 年 月 天 小時 小時 分 秒 地球年 地球年 150 億年 150 億年 12 億年 12 億年 4.1 千萬年 4.1 千萬年 1.7 百萬年 1.7 百萬年 2.9 萬年 2.9 萬年 476 年 476 年