Paul Dirac
"A physical law must possess mathematical beauty."
“as a sort of faith with us that any equations which describe fundamental laws of nature must have great beauty in them. It was like a religious faith with us.”
Dirac 的信念應該是當時很多物理學家的信仰，就我所知， parity conservation 也是當時的信仰，李楊絕對不是普通小孩子，其他人也不是明知不說破，恐怕是字典裡根本擺不下 parity violation 這個詞。現在看似乎很自然，當時看「恐怕」是很不自然的胡思亂想。場是field 的翻譯，數學也有field 翻譯成 體，兩者也是不同的東西。
我們常說 particle and field，粒子與場是一體兩面，像量子力學發展早期粒子與波的關係一樣。最早的場是電磁場，最早的具象應該是Faraday 提出的磁力線，慢慢演化成場的觀念。
每一個粒子都是一種場，光子就是電磁場的化身，或者說光子就是電磁場，光子是具象化的看法，可以用場描述，描述場的理論就是場論。
粒子就是場，有點像人性，粒子的存在是靠和別人的交互作用，反應自己的存在，粒子的影響力就是場，「看不見的」場在凡人眼中看起來就是粒子。我在朋友眼中的圖像，是靠我們的交互作用累積而成。
電子會受電磁場影響，可以想像成電子和光子的碰撞，光子和帶電粒子之間這種具像化的圖像，主要歸功費曼發明費曼圖來描述粒子間的碰撞。
終戰前後高能物理最成功的發展與成果，就是弄清楚電磁場粒子與場的關係，同齡的費曼、Schwinger 和小他們五歲的數學天才 Dyson 三人共同寫下歷史的故事，非常精彩、有趣，包括歐本海默曾在研討會公開讚賞Schwinger、無情羞辱費曼（他聽不懂費曼在說什麼、說費曼滿嘴胡說八道、不讓他繼續講，還嘲笑、戲弄 Dyson，我就是因為這樣不太喜歡 歐本海默）。
有千里馬還要有伯樂，曼哈頓計劃理論物理組大哥大Hans Bethe （我的數學祖系中的師祖）就是邀請Feynman and Dyson他們來Cornell 的伯樂，Bethe （和beta 同音）好幾次擋下歐本海默、刻意護佑他們兩人，才能造就當年的物理革命。
我每次都講得口沫橫飛🐶
也許是，會翻譯成場的緣由，可能是翻譯的人讀過各種經書吧。
你可能是看Dyson 的自傳 disturbing the universe 吧？ 他的交響樂曲引述費曼、Schwinger，還犯了戰略錯誤引述日本也在做，少人知曉的 Tomonaga ，幫助三個人拿諾貝爾獎，自己卻因為得獎人數限制錯過。
當時一片驚訝，有人問他沒獲獎有遺憾嗎？他輕描淡寫的說沒有遺憾，可他寫的「自傳」詳述整個事件始末，書名還取disturbing the universe ，擺明就是說自己撼動宇宙，居功厥偉。
後來他觸角四處伸展，什麼都做、什麼都想做，還戲稱自己和主流物理垂直，感嘆自己獨走江湖的孤寂。
我忘了牛頓了，場的起源應該是牛頓的重力場。
費曼的數學也很厲害，他的路徑積分是一套完整的數學架構，他也從小展現驚人的數學計算能力，擅長走偏鋒，用神奇方法化簡無法計算的難題。
只是他在發展費曼圖時，不曉得著了什麼道，他就是認為他亂搞一通可以算出正確答案，好像不在意用場論解析他的費曼圖。
傳說他常在研討會問人家在算什麼，人家算半年或一年的計算，而且只有固定角度的結果，他半小時就算完所有角度的結果，問人家什麼角度，代進去以後和他的結果吻合，就告訴人家：你沒有算錯！
人家慫恿他寫下推導過程，結果他寫了一篇完全沒有圖的聖經級論文，讓大家大失所望。投稿時還被嫌「別人也算得出來，你的計算有什麼用？」，最後Bethe 幫他修潤一下，傳說還直接跟editor 下軍令，要期刊不得拒絕，才順利發表。
另一個角度看，正經八百的數學天才Dyson，數學功力應該是另一種意象的高費曼好幾級，也無法接受費曼近似瘋狂、語無倫次的鬼畫符，才會出手幫他料理。
1921 年，量子論奠基者普朗克（Max Planck，1918 年得主）力薦愛因斯坦應憑廣義相對論得獎；瑞典物理學家奧森（Carl Oseen）則提名光電效應。
諾貝爾委員會指派古爾斯特蘭（Allvar Gullstrand，1911 年醫學獎得主）與阿瑞尼士分別撰寫報告。前者批評相對論難以驗證；後者則認為不宜太快頒出第二個量子理論相關獎項。
最終，委員會竟宣布——1921 年「物理獎從缺」。[3]
直到翌年，普朗克再度提議將「1921 年度」獎項補頒給愛因斯坦、1922 年的獎則給玻爾。理由很簡單：
「若五十年後，愛因斯坦的名字不在諾貝爾名單上，世人會怎麼看？」
1922 年 11 月 10 日，瑞典皇家科學院正式通知：
愛因斯坦獲頒 1921 年度諾貝爾物理學獎，表彰他「對理論物理的貢獻，特別是對光電效應定律的發現」。
愛因斯坦接獲消息時，正在前往日本的輪船上。他婉拒出席典禮。瑞典皇家科學院只好允許他日後補行演講。
隔年 1923 年 7 月 11 日，愛因斯坦於哥特堡向瑞典國王與兩千名聽眾發表演說——主題是「相對論」而非「光電效應」。[4]
這篇講稿，最終被視為他的正式諾貝爾演講，也象徵了那場關於「誰該得獎」的歷史圓滿落幕。
諾貝爾獎，頒的是「那件事」，不是「那個人」。
每年頒獎季，媒體總聚焦「誰得獎」，卻少有人問「為什麼那件事重要」。學術界有時也陷入名利遊戲，甚至有人借力打力、有意無意否定後輩創意。這正是愛因斯坦、費曼等人所厭惡的風氣。
費曼曾說他父親教他：「不要為榮譽而活。」
「I can’t stand it. It hurts me.」
他還嘲諷高中母校的精英社團：他們入選後的任務，就是決定誰有資格加入精英行列。
1931 年，愛因斯坦寫信給諾貝爾委員會，說海森堡與薛丁格的貢獻應各自獨立獲獎。若他決定，他會先頒給薛丁格——因為影響更深遠。
結果，海森堡獲得1931年獎，薛丁格與狄拉克於1932年並列得獎。
只能說歷史的節奏，總有它自己的韻律。
在科學史上，有的人 honor the prize，有的人則 are honored by the prize。
波爾、海森堡、薛丁格、狄拉克屬於前者。
而愛因斯坦——是自成一流的存在。
獎項的榮耀，早已追不上他的思想光芒。
📚 參考資料
[1] Einstein Papers Project, Vol. 2, p. 100
[2] NobelPrize.org, Ceremony Speech, 1921
[3] Palash B. Pal, The Incredibly Strange Story of Einstein’s Nobel Prize, Resonance, 27 (2022) 1857
“Insbesondere erscheinen mir die Schwarzkörperstrahlung, die Photolumineszenz, die Erzeugung von Kathodenstrahlen durch ultraviolettes Licht und andere den Entstehungs- oder Umwandlungsprozessen des Lichtes angehörige Erscheinungen besser verstanden, wenn man voraussetzt, daß die Energie des Lichtes nicht kontinuierlich im Raume verteilt ist.”
— A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt” (Annalen der Physik 17, 132–148, 1905)
“In particular, black-body radiation, photoluminescence, the generation of cathode rays by ultraviolet light, and other phenomena associated with the creation and transformation of light seem to me to be more readily understood if one assumes that the energy of light is not continuously distributed in space.” [1]
This concise yet revolutionary statement on the nature of light quanta appeared in the introduction of Einstein’s 1905 paper On a Heuristic Point of View about the Creation and Conversion of Light. It opened an entirely new path for understanding black-body radiation and the photoelectric effect. After years of experimental confirmation, it became one of the foundations of quantum theory and eventually earned Einstein the 1921 Nobel Prize in Physics (awarded in 1922).
By then, Einstein had already completed his most transformative work—not only the photoelectric effect, but also the theory that reshaped humanity’s perception of space and time: relativity.
Remarkably, four epoch-making ideas—the light-quantum hypothesis, Brownian motion, special relativity, and mass–energy equivalence—were all published in the same year, 1905, now remembered as Einstein’s Annus Mirabilis, or “miracle year.”
Among them, relativity became the theoretical cornerstone of modern cosmology. Subsequent research built upon it to win numerous Nobel Prizes, and its practical consequences—most notably the operation of the GPS system—pervade modern life.
Many have wondered why Einstein did not receive the Nobel Prize for relativity itself. Despite multiple nominations, he went unawarded for years, prompting debate within both the scientific community and the Nobel Committee.
This ambivalence was captured by Svante Arrhenius, Chair of the Nobel Committee for Physics, in his official presentation speech on 10 December 1922:
“There is probably no physicist living today whose name has become so widely known as that of Albert Einstein. Most discussion centres on his theory of relativity. This pertains essentially to epistemology and has therefore been the subject of lively debate in philosophical circles. It will be no secret that the famous philosopher Bergson in Paris has challenged this theory, while other philosophers have acclaimed it wholeheartedly. The theory in question also has astrophysical implications which are being rigorously examined at the present time.” [2]
This shows that, even in 1922, the scientific world was still grappling with the conceptual shock that relativity had dealt to our understanding of time and space—while philosophers debated its epistemological implications.
In 1921, Max Planck—himself the 1918 laureate for quantum theory—again nominated Einstein, citing his contributions to general relativity. Another eminent physicist, Carl Oseen, nominated him for the photoelectric effect instead.
The Nobel Committee appointed two evaluators: Allvar Gullstrand (1911 laureate in Physiology or Medicine) reviewed relativity, while Arrhenius reviewed the photoelectric effect. Gullstrand argued that relativistic effects were too small to measure; Arrhenius thought it premature to grant another quantum-theory prize.
As a result, the 1921 Nobel Prize in Physics was left unawarded—a decision that caused widespread controversy. [3]
The following year, Planck proposed that the 1921 prize be retrospectively given to Einstein and the 1922 prize to Niels Bohr. By then, consensus had formed:
“Imagine, fifty years from now, if Einstein’s name were absent from the list of Nobel laureates—what would people think?”
On 10 November 1922, the Royal Swedish Academy of Sciences officially informed Einstein that he had been awarded the 1921 Nobel Prize in Physics,
“for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect.”
Arrhenius summarized the achievement in the closing section of his speech:
“Einstein’s law of the photo-electrical effect has been extremely rigorously tested by the American Millikan and his pupils and passed the test brilliantly. Owing to these studies by Einstein the quantum theory has been perfected to a high degree and an extensive literature grew up in this field whereby the extraordinary value of this theory was proved. Einstein’s law has become the basis of quantitative photo-chemistry in the same way as Faraday’s law is the basis of electro-chemistry.” [2]
At the time of the announcement, Einstein was already aboard a ship to Japan and thus unable to attend the Stockholm ceremony. The Academy made a rare exception, allowing him to deliver his Nobel Lecture later.
In July 1923, Einstein visited Sweden and addressed King Gustaf V and an audience of 2,000 in Gothenburg—not on the photoelectric effect, but on relativity. [4]
Since no other official text was available, this lecture became his formal Nobel address, closing one of the most curious episodes in Nobel history.
The Nobel Prize is awarded for a discovery, not to a person.
Each year, as speculation swirls about the winners, attention naturally turns to personalities rather than to the discoveries themselves. Yet the essence of the Nobel Prize lies in the work, often meaningful only to specialists, while the public merely sees the spectacle. Still, perhaps a little spectacle serves its purpose.
Some critics claim that the Nobel tradition has made science too theatrical; others are consumed by its allure. The academic world has, in turn, spawned countless imitative prizes, sometimes distracting scholars from true curiosity.
Worse still, certain self-proclaimed authorities, confident in their prestige, have stifled younger generations—unwittingly extinguishing many futures.
A wise professor once told me:
“Some people honor the prize; others are merely honored by the prize.”
Bohr, Heisenberg, Schrödinger, Dirac—these were scientists who honored the prize through their work.
Einstein, however, stood apart—he transcended the prize itself.
Richard Feynman might be placed in that same category. He once said his father taught him to despise honor:
“I can’t stand it. It hurts me.”
He even mocked elite societies that existed solely to decide who deserves to be called an elite.
In a letter dated 20 September 1931, Einstein wrote to the Nobel Committee that both Heisenberg and Schrödinger had made independent and equally significant contributions, and each should be recognized individually. If forced to choose who should receive the prize first, he said, he would choose Schrödinger—for his deeper influence.
History played out accordingly: Heisenberg won the 1932 prize (awarded in 1933), and Schrödinger shared the following year’s prize with Dirac. As always, history keeps its own rhythm.
[1] Einstein Papers Project, Vol. 2, p. 100
[2] NobelPrize.org, Ceremony Speech (1921)
[3] Palash B. Pal, “The Incredibly Strange Story of Einstein’s Nobel Prize,” Resonance 27 (2022) 1857
[4] Einstein’s Nobel Lecture, 1923
導讀摘要
1905 年，愛因斯坦連發四篇震撼物理界的論文，從光量子假說到相對論，重塑了人類對自然的理解。然而，當他終於獲得諾貝爾獎時，獎項卻並非因「相對論」，而是「光電效應」。這背後，是一段關於懷疑、信念與科學制度的故事。
「對我而言，假設光的能量在空間中的分布不是連續的，更容易理解黑體輻射、光致發光（photoluminescence）、紫外線產生的陰極射線，以及其他與光的產生或轉換相關的現象。」[1]
這段話出自愛因斯坦 1905 年論文〈關於光產生與轉換的啟發性觀點〉（On a Heuristic Point of View about the Creation and Conversion of Light）。這一年，愛因斯坦發表了四篇改變世界的論文，主題涵蓋光量子假說、布朗運動、特殊相對論與質能互換。
短短一年，四次震撼——因此被稱為愛因斯坦的「奇蹟年」（Annus Mirabilis）。
愛因斯坦
相對論徹底顛覆了時空觀，是現代宇宙學的基石，並已多次獲後來的諾貝爾獎肯定。從 GPS 系統到重力波觀測，今日的科技幾乎都離不開它。
然而，當1922年愛因斯坦終於被頒發1921年度的物理獎時，理由卻是「光電效應」。
為何不是相對論？
原因並非否定理論的價值，而是——那個年代，世界還沒有準備好接受它。
阿瑞尼士（Svante Arrhenius），諾貝爾物理學委員會主席，在 1922 年的頒獎典禮上這樣說：
「今天，可能沒有哪位物理學家像阿爾伯特·愛因斯坦那樣廣為人知，而大多數討論都集中於他的相對論上。不可否認，相對論本質上屬於認識論，因此成為哲學界激烈辯論的主題……同時，相對論具有重要的天文物理學意義，正接受嚴格的檢驗。」[2]
當時的學界仍在震盪，哲學家柏格森（Henri Bergson）甚至公開挑戰愛因斯坦。對許多人而言，相對論不只是物理學，更觸動了人類對「時間」與「真實」的想像。
1921 年，量子論奠基者普朗克（Max Planck，1918 年得主）力薦愛因斯坦應憑廣義相對論得獎；瑞典物理學家奧森（Carl Oseen）則提名光電效應。
諾貝爾委員會指派古爾斯特蘭（Allvar Gullstrand，1911 年醫學獎得主）與阿瑞尼士分別撰寫報告。前者批評相對論難以驗證；後者則認為不宜太快頒出第二個量子理論相關獎項。
最終，委員會竟宣布——1921 年「物理獎從缺」。[3]
直到翌年，普朗克再度提議將「1921 年度」獎項補頒給愛因斯坦、1922 年的獎則給玻爾。理由很簡單：
「若五十年後，愛因斯坦的名字不在諾貝爾名單上，世人會怎麼看？」
1922 年 11 月 10 日，瑞典皇家科學院正式通知：
愛因斯坦獲頒 1921 年度諾貝爾物理學獎，表彰他「對理論物理的貢獻，特別是對光電效應定律的發現」。
阿瑞尼士在頒獎詞中說：
「愛因斯坦的光電效應定律已被美國的密利根及其學生極為嚴格地驗證。這項研究使量子理論更完備、更精確，也成為定量光化學的基礎，就如法拉第定律之於電化學一般。」[2]
這段致詞讓光電效應成為量子物理的起點，也為日後的半導體與光子學鋪下了道路。
愛因斯坦接獲消息時，正在前往日本的輪船上。他婉拒出席典禮。瑞典皇家科學院只好允許他日後補行演講。
隔年 1923 年 7 月 11 日，愛因斯坦於哥特堡向瑞典國王與兩千名聽眾發表演說——主題是「相對論」而非「光電效應」。[4]
這篇講稿，最終被視為他的正式諾貝爾演講，也象徵了那場關於「誰該得獎」的歷史圓滿落幕。
諾貝爾獎，頒的是「那件事」，不是「那個人」。
每年頒獎季，媒體總聚焦「誰得獎」，卻少有人問「為什麼那件事重要」。學術界有時也陷入名利遊戲，甚至有人借力打力、有意無意否定後輩創意。這正是愛因斯坦、費曼等人所厭惡的風氣。
費曼曾說他父親教他：「不要為榮譽而活。」
「I can’t stand it. It hurts me.」
他還嘲諷高中母校的精英社團：他們入選後的任務，就是決定誰有資格加入精英行列。
1931 年，愛因斯坦寫信給諾貝爾委員會，說海森堡與薛丁格的貢獻應各自獨立獲獎。若他決定，他會先頒給薛丁格——因為影響更深遠。
結果，海森堡獲得1931年獎，薛丁格與狄拉克於1932年並列得獎。
只能說歷史的節奏，總有它自己的韻律。
在科學史上，有的人 honor the prize，有的人則 are honored by the prize。
波爾、海森堡、薛丁格、狄拉克屬於前者。
而愛因斯坦——是自成一流的存在。
獎項的榮耀，早已追不上他的思想光芒。
📚 參考資料
[1] Einstein Papers Project, Vol. 2, p. 100
[2] NobelPrize.org, Ceremony Speech, 1921
[3] Palash B. Pal, The Incredibly Strange Story of Einstein’s Nobel Prize, Resonance, 27 (2022) 1857
[4] Einstein’s Nobel Lecture, 1923
Feynman：
I don't know anything about the Nobel Prize. I don't understand what it's all about or what it's worth. If the people in the Swedish Academy decide that X, Y or Z wins the Nobel Prize, then so be it. I won't have anything to do with the Nobel Prize. It's a pain in the ass. I don't like honors. I appreciate it for the work I did and for the people who appreciate it. I know there are lots of physicists who use my work. I don't need anything else. I don't think there is any sense to anything else. I don't see that it makes any point that someone in Sweden decides that his or her work is noble enough to receive a prize. I've already got the prize! The prize is the pleasure of finding the thing out; the kick is the discovery. The observation that other people are using it. Those are real things; the honors are unreal to me. My Papa brought me up this way. I can't stand it. It hurts me . . .
諾貝爾獎是給「那件事」，不是給「那個人」。
一件事通常是無數人的努力，也很難認定哪些人才是開路先鋒、哪些人貢獻最大。糟糕的是，聚焦那些人，常常讓事情失焦。更糟糕的是，有些人為了追逐，迷失方向，流風所及，讓各種榮譽成為追逐對象。
最糟糕的是，衍生的制度讓學術界迷失方向、亂貼貼標籤。讓少數自以為先知的人，任意評量別人的努力與成就。
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https://gemini.google.com/share/8b2c416b0691
https://g.co/gemini/share/53b37a61e711
文中數字指的是（數量級約）略數值。太陽地球距離目前約為1.5億公里，和1.28億公里數量級很接近。鬩神星繞日橢圓軌道相當扁，與地球最遠距離約為146億公里。太陽直徑約為1.39百萬公里。 Gemini會自編對白，很難導正⋯好在誤差可以接受。
https://g.co/gemini/share/f0a804d1dc7d
https://g.co/gemini/share/5094c4d99c53
生命只是能量的轉換、流動
https://g.co/gemini/share/758746342fdc
英文版本
https://g.co/gemini/share/b0f3e1809bca
https://g.co/gemini/share/4b62237b0990
Story created by Gemini Storybook
未來的量子教室
https://g.co/gemini/share/48c4d3085984
The quantum coin classroom
pi~/= 3.14285714286 =2 x 3 x 17 x 3081232493/10^11
~/=22/7
圓周率可以公投嗎？ 草包可以
科學人
1894年，愛好數學的醫生古德溫（Edward J. Goodwin）自認找到一種運用尺規作圖解開圓周率的方法。
他對自己的發現十分滿意，滿意到甚至為此草擬法案，將他的證明列入家鄉印第安納州的法條。法條的其中一項是聲稱圓周率 π 等於3.2，而不是公認的3.14159......。做為回報，他允許州政府免費使用他的證明，不需支付權利金。
想當然，這種荒謬的法案肯定不會過的吧？不，當初還真的過了。
為什麼這麼扯的法案過得了？這就要說說其中被丟來丟去的審查過程⋯⋯