# 永恆的對稱：艾瑪．諾特（Emmy Noether）

“I do not see that the sex of the candidate is an argument against her admission as a Privatdozent. After all, the Senate is not a bath-house.” – David Hilbert

1933 年，納粹在德國橫行無道，擁有猶太血統的諾特被哥廷根大學開除。她移民到美國，在賓夕法尼亞州博懋學院（Bryn Mawr College）繼續做研究。可惜的是於 1935 年，她被診斷出有個卵巢囊腫，要入院做手術切除。手術之後三天，諾特情況慢慢好轉，然而在第四天她突然發高燒並陷入昏迷，未幾離世，享年 53 歲。

# 重力波GW170104再證愛因斯坦理論正確

GW170104 還告訴了我們很多訊息。例如，這次結合的兩個黑洞，至少有一個的自轉並非與它們互繞的平面方向相同。換句話說，至少其中一個黑洞的自轉軸是傾斜了的，就好像地球的自轉與公轉平面之間有個夾角一樣。這個發現，顯示兩個黑洞可能並非於同一雙星系統中誕生，而是在誕生後才互相捕捉，形成雙黑洞系統。

# 重力是什麼？愛因斯坦的廣義相對論

$x' = x - u_x t$
$y' = y - u_y t$
$z' = z - u_z t$
$t' = t$

$x' = \frac{x - u t}{\sqrt{1-{(u/c)}^2}}$
$t' = \frac{t - xu/c}{\sqrt{1-{(u/c)}^2}}$

1907 年，愛因斯坦突然靈機一觸，想到了等效原理（equivalence principle）。試想像我們身處一艘太空船裡，太空船沒有窗戶。我們發現自己感覺就如日常一樣。那麼，我們能否分辨太空船究竟正停泊在地球上，還是以與地球的地心加速度大小一樣的加速度往上加速？愛因斯坦說，我們不可能分辨得到。另外一個假想實驗是我們身處一部電梯之中，然而我們感受不到任何重力。那麼我們又能否分辨電梯究竟正在往下跌，還是漂浮在太空之中？愛因斯坦說，我們同樣不可能分辨得到。等效原理指出，重力和加速度並不單止效應相同，兩者實際上是同樣的東西！

1915 年暑假，愛因斯坦受數學家希爾伯特邀請到哥廷根科學院（Akademie der Wissenschaften zu Göttingen）講了六場講座。他們互相交流了意見，而希爾伯特也開始尋找正確的廣義相對論公式。希爾伯特的進展非常快，漸漸令愛因斯坦感受到很大壓力，他害怕希爾伯特會比自己先找到正確公式。愛因斯坦在同年 11 月於柏林普魯士科學院（Preußische Akademie der Wissenschaften）講了四場講座，並在最後一場發表了他發現的廣義相對論方程式：

$G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8 \pi G}{c^4} T_{\mu\nu}$

「時空告訴物質如何運動，物質告訴時空如何彎曲。」

1907年諾貝爾物理獎：阿爾伯特・邁克生

# 卡西尼號：在土星環看見宇宙

To boldly go where no man has gone before. – Star Trek

1997年10月15號升空的卡西尼號曾兩度探訪金星，借助金星重力使出天體力學絕技「重力助推」，金星重力就好像彈弓把卡西尼號彈射飛向外太陽系。然後它又掠過月球和地球、小行星2685以及木星，然後於2004年7月1號進入環繞土星軌道。

1671年，法國天文學家喬凡尼・卡西尼（Giovanni Domenico Cassini, 1625-1712）發現了土衛三、土衛四、土衛五和土衛八。卡西尼也發現了土星環的一條主要縫隙，現在我們稱之為卡西尼環縫。因為卡西尼和惠更斯對土星的觀察和研究貢獻，他們成為了土星天文研究的代名詞。

——《土星環》

NASA卡西尼號最後任務網頁

# 比賽是對學問的侮辱

「世事洞明皆學問，人情練達即文章。」——曹雪芹《紅樓夢》

Dear Koichi,

I was very happy to hear from you, and that you have such a position in the Research Laboratories.

Unfortunately your letter made me unhappy for you seem to be truly sad. It seems that the influence of your teacher has been to give you a false idea of what are worthwhile problems. The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to. A problem is grand in science if it lies before us unsolved and we see some way for us to make some headway into it. I would advise you to take even simpler, or as you say, humbler, problems until you find some you can really solve easily, no matter how trivial. You will get the pleasure of success, and of helping your fellow man, even if it is only to answer a question in the mind of a colleague less able than you. You must not take away from yourself these pleasures because you have some erroneous idea of what is worthwhile.

You met me at the peak of my career when I seemed to you to be concerned with problems close to the gods. But at the same time I had another Ph.D. Student (Albert Hibbs) whose thesis was on how it is that the winds build up waves blowing over water in the sea. I accepted him as a student because he came to me with the problem he wanted to solve. With you I made a mistake, I gave you the problem instead of letting you find your own; and left you with a wrong idea of what is interesting or pleasant or important to work on (namely those problems you see you may do something about). I am sorry, excuse me. I hope by this letter to correct it a little.

I have worked on innumerable problems that you would call humble, but which I enjoyed and felt very good about because I sometimes could partially succeed. For example, experiments on the coefficient of friction on highly polished surfaces, to try to learn something about how friction worked (failure). Or, how elastic properties of crystals depends on the forces between the atoms in them, or how to make electroplated metal stick to plastic objects (like radio knobs). Or, how neutrons diffuse out of Uranium. Or, the reflection of electromagnetic waves from films coating glass. The development of shock waves in explosions. The design of a neutron counter. Why some elements capture electrons from the L-orbits, but not the K-orbits. General theory of how to fold paper to make a certain type of child’s toy (called flexagons). The energy levels in the light nuclei. The theory of turbulence (I have spent several years on it without success). Plus all the “grander” problems of quantum theory.

No problem is too small or too trivial if we can really do something about it.

You say you are a nameless man. You are not to your wife and to your child. You will not long remain so to your immediate colleagues if you can answer their simple questions when they come into your office. You are not nameless to me. Do not remain nameless to yourself – it is too sad a way to be. Know your place in the world and evaluate yourself fairly, not in terms of your naïve ideals of your own youth, nor in terms of what you erroneously imagine your teacher’s ideals are.

Best of luck and happiness.

Sincerely,
Richard P. Feynman

# 天才與悲劇：馬克斯・普朗克 (Max Planck)

“Ich hege nicht den Wunsch, Neuland zu entdecken, sondern lediglich, die bereits bestehenden Fundamente der physikalischen Wissenschaft zu verstehen, vielleicht auch noch zu vertiefen.” – Max Planck

“…using no notes, never making mistakes, never faltering; the best lecturer I ever heard.” – Lise Meitner

$E = h \nu$

“I was ready to sacrifice any of my previous convictions about physics.” – Max Planck

“He [Max Planck] was, by nature, a conservative mind; he had nothing of the revolutionary and was thoroughly skeptical about speculations. Yet his belief in the compelling force of logical reasoning from facts was so strong that he did not flinch from announcing the most revolutionary idea which ever has shaken physics.” – Max Born

1905年，愛因斯坦利用普朗克的光量子概念解釋了光電效應。普朗克和其他物理學家漸漸接受量子論的真實性，量子力學在20世紀初以極速發展。今天，我們從前沿物理到生物導航，都可以找到量子現象與普朗克常數的身影。2018年，國際計量委員會（International Committee for Weights and Measures）將在巴黎的會議中舉行投票，決定是否以普朗克常數重新定義質量的單位：公斤。普朗克於1900年提出的量子，在118年後仍然深深影響著人類的科學發展。

“My Führer!

I am most deeply shaken by the message that my son Erwin has been sentenced to death by the People’s Court.

The acknowledgement for my achievements in service of our fatherland, which you, my Führer, have expressed towards me in repeated and most honouring way, makes me confident that you will lend your ear to an imploring 87-year old.

As the gratitude of the German people for my life’s work, which has become an everlasting intellectual wealth of Germany, I am pleading for my son’s life.

Max Planck”

1944年，普朗克於柏林的家被空襲摧毀，他的所有科學紀錄和書信全部化為灰燼。為逃避戰火，他與瑪加和兒子逃到哥廷根。最後，艾連的死令普朗克失去生存希望。量子物理之父普朗克於1947年10月4號與世長辭。