2024年10月4日（金）
ロスト・イン・数学
今週の書物/
『Lost in Math』
Sabine Hossenfelder 著
Basic Books (2018)
『数学に魅せられて、科学を見失う』
ザビーネ・ホッセンフェルダー 著、吉田三知世 訳
みすず書房、2021年刊
物理学はもう何十年ものあいだ、顕微鏡でもとらえられない小さい量子と、望遠鏡でもとらえられない遠くの宇宙とを追いかけてきた。理論物理学者たちは数学を使って自然現象を説明しようとし、実験物理学者が観測によって理論物理学者たちの説明の妥当性を検討する。ほとんどの場合、実験物理学者の検討は、理論物理学者の言うことの否定で終わる。
小さいものの観測は、CERN (Conseil européen pour la recherche nucléaire、欧州原子核研究機構) の LHC (Large Hadron Collider、大型ハドロン衝突型加速器) に代表される さまざまな加速器で行われている。
陽子や中性子といった粒子は、「電子顕微鏡でぎりぎり見ることのできることのできる原子」の 10万分の1 というとてつもなく小さいものなので、直接観察することができない。そこで加速器で粒子と粒子を衝突させ、衝突後の粒子の崩壊の軌跡を観測することで 粒子のことをわかろうとしているわけだ。
量子力学の世界は、superposition（重ね合わせ）や quantum entanglement（量子もつれ）のことを持ち出すまでもなく、私たちのいる力学の世界とは、なにからなにまで違う。力学の世界にいる私たちが、力学の世界の実験装置を使い、量子力学の世界のことをわかろうというのだから、加速器を使っての実験はとても難しいものになる。
遠いものの観測は、ALMA (Atacama Large Millimeter/submillimeter Array、アタカマ大型ミリ波サブミリ波干渉計（アルマ望遠鏡）) に代表される電波干渉計や、JWST (James Webb Space Telescope、ジェイムズ・ウェッブ宇宙望遠鏡) に代表される宇宙望遠鏡で行われている。
ALMA を用いた大規模探査の観測データの中から、131億年前の宇宙で塵に深く埋もれた銀河が発見されたという。131億光年離れた天体が放った電磁波（光や電波）は、131億年の時間をかけて地球に届くので、観測されたものは、その銀河の131億年前の姿だ。
宇宙で遠くを見ることは、昔を見ることと同じ。131億年前のその場所に塵に埋もれた銀河があったからといって、今その場所に同じものがあるわけではない。46億年前に太陽ができ、45億4000万年前に地球ができたということだから、（ビッグバンからたった7億年しか経っていない）131億年前の宇宙がこうでしたといわれても 素直に「はい、そうですか」とは言えない。
小さい量子を追いかけてきた物理学者たちも、遠くの宇宙とを追いかけてきた物理学者たちも、どちらも行き詰った感じに見える。Standard Model (標準モデル) とか Grand Unified Theory (大統一理論) とか、夢のようなことが話されるようになって久しいが、今のところ何のブレークスルーも示されてはいない。
で、今週は、物理学の現在を考える本を読む。『Lost in Math』（Sabine Hossenfelder 著、Basic Books、2018年刊）だ。日本語訳も『数学に魅せられて、科学を見失う』（ザビーネ・ホッセンフェルダー 著、吉田 三知世 訳、みすず書房、2021年刊）として出版されている。
本を開いて はじめに出てくる「Preface」が強烈だ。数十億ドル（数千億円）を使いながら、物理学者たちは もう何十年も「もうすぐ素晴らしい発見がある」と言い続けてきた。加速器を建設し、人工衛星を打ち上げ、地下や山頂に観測機器を据えてきたが、新しい事実が明らかになることはなかったということを、まず書いている。
その上で、物理学者たちを裏切ったのは数学ではなく、数学の選び方だったという。自然はエレガントでシンプルだと信じていた物理学者たちは、結局 エレガントでシンプルな数式にたどり着くことはなかった。どんな法則が宇宙を支配していようが、それは物理学者たちが期待していたものとは違っていた。そういう結論を「Preface」で書いてしまっているのだ。
自然法則は美しいものなのだと信じてしまったホッセンフェルダーが、何かを信じるということは、科学者がやってはならないことではないのかという思いにたどり着く。探求し続けるという科学が、信じるという宗教になってしまってはいけない。そのメッセージは重い。
ホッセンフェルダーは、第1章から第5章まで、もはや物理学が理解できていない自分に気づき（第1章）、カッコいいアイデアが時にはひどく失敗すると知り（第2章）、教育を通して学んだことをまとめ（第3章）、物理学者として生きていくことの難しさに直面し（第4章）、理論物理学者たちの想像力に驚く（第5章）。
第6章から第9章までの「量子力学という魔術のようなもの・理解できないはずのものが、いったいなぜ理解できてしまうのか（第6章）」「もし自然法則が美しくなかったら（第7章）」「ひとりの弦理論研究者を理解しようと試み、ほぼ成功しそうになる（第8章）」「あるとされる さまざまな粒子を誰も見ていないのはなぜか（第9章）」というような話も、それぞれに興味深い。
そしてたどり着いた第10章で、ホッセンフェルダーは第1章から第9章までの説明をする。「私は九つの章を使い、理論物理学者たちは過去の美の理想に固執して袋小路にいるということを証拠を挙げながら主張してきた」というのだ。「えっ」と思って読み返してみると、確かにそうだ。それを読み取れなかった私は、何を読んでいたのだろう。がっかりは大きい。
そんなことはともかく、ホッセンフェルダーは「ヒッグス粒子の質量の問題」「強いＣＰ問題」「宇宙定数が小さいという問題」などが、矛盾ではなく、数の一致に関するもの・美に関する懸念なのだという。
ホッセンフェルダーは思索の後、三つの教訓を得る。「問題を数学で解決したいなら、それが本当に問題であるか確かめる」「仮定を明言する」「観測による導きが必要だ」という教訓は、言い換えれば「物理学は数学ではない」ということになる。「物理学は自然を記述する数式を選択する学問だ」というあたりまえの結論にたどり着く。そんなことが教訓として語られなければならないほどに、今の理論物理はずれたものになっているのだろう。
ホッセンフェルダーは最後に「やるべきことが たくさんある」「物理学の次のブレイクスルーは、今世紀に起こるだろう」と書く。そしてこの本を「それは美しいだろう」という言葉で終える。
どんなに否定的なことを書いても、『Lost in Math』という本を出版しても、ホッセンフェルダーは物理学者であることを諦めてはいない。『Lost in Math』という本は、もしかしたら、とてもポジティブな本なのかもしれない。
個人的には、この本は救いだった。今までの長いあいだのモヤモヤが一気に晴れた。そんな気がした。ホッセンフェルダーがこの本を書いてくれたことに、心から感謝している。。。のだが、細かいことを言えば、突っ込みどころの多い本でもあった。
例えば、先ほども取り上げた「Preface」の「数十億ドル（数千億円）を使いながら、物理学者たちは もう何十年も「もうすぐ素晴らしい発見がある」と言い続けてきた。加速器を建設し、人工衛星を打ち上げ、地下や山頂に観測機器を据えてきたが、新しい事実が明らかになることはなかった」という部分。ALMA の建設費用だけで 14億ドル（2千億円）、CERN の LHR の建設費用にいたっては 90億ドル（1兆2千億円）とも 300億ドル（4兆円）とも言われていることを考えれば、物理学者たちが使ってきたお金は数千億ドル（数十兆円）に及ぶ。桁が二つも違うことに驚く。
ホッセンフェルダーだけでなく、多くの物理学者たちが、自分たちがどれだけのお金を使っているのかということについての意識に乏しい。ほとんどの物理学者たちは、自分たちにあてがわれた予算しか眼中にない。電気技術者の人件費やセキュリティーにいくらかかるかとか、施設の建設にいくらかかったとか、知っている物理学者は少ない。
この本の記述のなかには、物理学者たちの世間知らずのところとか常識のないところが垣間見られる。もっともそれは物理学者たちのいいところでもあるので、あまり突っ込まないでおいたほうがいいのだろう。
たとえ突っ込みどころが多くても、この本がいいことに変わりはない。何度も手に取って開く。そのたびに新しい発見がある。こんな本はめずらしい。
by Sabine Hossenfelder
In this “provocative” book (New York Times), a contrarian physicist argues that her field’s modern obsession with beauty has given us wonderful math but bad science.
Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades.
The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these “too good to not be true” theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.
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https://www.amazon.co.jp/Lost-Math-Beauty-Physics-Astray/dp/1978643381?asin=B0764BZW8S&revisionId=&format=2&depth=1
https://pdf.zlibcdn.com/dtoken/a488be776408bec6b578c35ed6482850/Lost_in_Math_How_Beauty_Leads_Physics_Astray_by_S_4999738_(z-lib.org).pdf
Preface
They were so sure, they bet billions on it. For decades physicists told us they knew where the next discoveries were waiting. They built accelerators, shot satellites into space, and planted detectors in underground mines. The world prepared to ramp up the physics envy. But where physicists expected a breakthrough, the ground wouldn’t give. The experiments didn’t reveal anything new.
What failed physicists wasn’t their math; it was their choice of math. They believed that Mother Nature was elegant, simple, and kind about providing clues. They thought they could hear her whisper when they were talking to themselves. Now Nature spoke, and she said nothing, loud and clear.
Theoretical physics is the stereotypical math-heavy, hard-to-understand discipline. But for a book about math, this book contains very little math. Strip away equations and technical terms and physics becomes a quest for meaning—a quest that has taken an unexpected turn. Whatever laws of nature govern our universe, they’re not what physicists thought they were. They’re not what I thought they were.
Lost in Math is the story of how aesthetic judgment drives contemporary research. It is my own story, a reflection on the use of what I was taught. But it is also the story of many other physicists who struggle with the same tension: we believe the laws of nature are beautiful, but is not believing something a scientist must not do?
by ザビーネ・ホッセンフェルダー
translated by 吉田三知世
物理学の基盤的領域では30年以上も、既存の理論を超えようとして失敗し続けてきたと著者は言う。実験で検証されないまま理論が乱立する時代が、すでに長きに渡っている。それら理論の正当性の拠り所とされてきたのは、数学的な「美しさ」や「自然さ」だが、なぜ多くの物理学者がこうした基準を信奉するのか？ 革新的な理論の美が、前世紀に成功をもたらした美の延長上にあると考える根拠はどこにあるのか？ そして、超対称性、余剰次元の物理、暗黒物質の粒子、多宇宙……等々も、その信念がはらむ錯覚の産物だとしたら？研究者たち自身の語りを通じて浮かび上がるのは、究極のフロンティアに進撃を続けるイメージとは異なり、空振り続きの実験結果に戸惑い、理論の足場の不確かさと苦闘する物理学の姿である。「誰もバラ色の人生なんて約束しませんでしたよ。これはリスクのある仕事なのです」（ニマ・アルカニ=ハメド）、「気がかりになりはじめましたよ、確かに。たやすいことだろうなんて思ったことは一度もありませんが」（フランク・ウィルチェック）著者の提案する処方箋は、前提となっている部分を見つめ直すこと、あくまで観測事実に導かれること、それに、狭く閉じた産業の体になりつつあるこの分野の風通しをよくすることだ。しかし、争点はいまだその手前にある。物理学は「数学の美しさのなかで道を見失って」いるのだろうか？ 本書が探針を投じる。
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はじめに
確信に満ちて、彼らは数十億ドルを投じた。物理学者たちは、次に人類を待ち受けている発見がどこにあるのか自分たちは知っていると、もう何十年も言い続けてきた。彼らは加速器を建設し、人工衛星を打ち上げ、地下坑道に観測機器を埋め込んだ。ああ、もうすぐ、また一段と物理学を羨むようになるのかと世界は身構えた。しかし、物理学者らがブレイクスルーを期待していた場所で、地盤が割れて革新が起こることはなかった。これらの実験は、新事実など一切明らかにしなかったのだ。
物理学者らを裏切ったのは、数学ではなく、彼らの数学の選び方だった。彼らは、母なる自然はエレガントで、シンプルで、しかも優しく手掛かりを教えてくれていると信じていた。自分たちには母なる自然がささやく声が聞こえていると思っていたのだ。その間、同業どうしが互いに向かって話していたのだが。そしていまや母なる自然は語った──高らかで明瞭な、沈黙をもって。
理論物理学は、数学を多用する、理解するのが難しい分野の典型だ。だが本書は、数学を話題にする本にしては、数学はほとんど出てこない。方程式と専門用語をすべて取り去ると、物理学は意味の探求になる──だがその探究は、思わぬ方向へと向かってしまった。どんな法則が私たちの宇宙を支配していようが、それはかつて物理学者たちが期待していたものとは違っている。それは私が期待していたものとも違っている。
本書は、美意識に頼った判断がいかに現在の物理学の研究を推し進めているかという物語だ。それは、教わったものをいかに使ってきたかを省みる、私自身の物語でもある。しかしそれはさらに、私と同じく、「自然法則は美しいのだと私たちは信じているが、何かを信じ込むことは、科学者がやってはならないことではないのか？」という不安と闘っている、ほかの多くの物理学者たちの物語でもある。
Lost in Math: How Beauty Leads Physics Astray
by Moira I. Gresham
https://aapt.scitation.org/doi/full/10.1119/1.5086393
Lost in Math: How Beauty Leads Physics Astray, Hossenfelder Sabine
In brief. Read this book. It is fascinating. Don’t expect it to fit a mold of other books on theoretical physics for a popular audience. The core strand of this book is an insightful argument of import to philosophy of and best practices in physics. It also offers much more. Read it with good humor, generosity, skepticism, and care. Also read Frank Wilczek’s response in Physics Today.
Introduction. The author, Sabine Hossenfelder, is a German theoretical physicist who works on quantum gravity and physics beyond the standard model. She is also an excellent writer. She’s been funded through short-term research grants and postdoctoral appointments since she received her PhD in 2003. An impetus for her book is Hossenfelder’s self-admitted personal crisis: “And while I witnessed my profession slip into crisis, I slipped into my own personal crisis. I’m not sure anymore that what we do here, in the foundations of physics, is science. And if not, why am I wasting my time on it?” (p. 2). Hossenfelder goes on to explore, analyze, and generalize from the supposed crisis. In a style inspired by that of the book, I begin by describing my own personal micro-crisis in deciding whether to review it.
I was approached about this book review late last summer. After using my superior research skills to locate and read the blurb, “A contrarian argues that modern physicists’ obsession with beauty has given us wonderful math but bad science,” the table of contents, e.g., “Chap. 5: Ideal Theories:… In which… I fly to Austin, let Steven Weinberg talk at me, and realize just how much we do to avoid boredom,” and the first part of the preface, “They were so sure, they bet billions on it… But where physicists expected a breakthrough, the ground wouldn’t give. The experiments didn’t reveal anything new,” I started freaking out a little bit. I can’t believe she just painted the LHC as a waste of money. The politicians are going to run with this and use it as ammunition against science. And how could she speak so apparently irreverently about an interaction with Steven Weinberg? This is really going to piss some people off, and if I’m associated with it in any way, I could be kicked off the island.
However—I thought, after having calmed down—even the table of contents is hilarious. I’ve heard that Hossenfelder’s blog is one of the best written and most read in the business. (Although I don’t read it, nor do I regularly read any blogs.) I’m nervous about the time this could take from precious research hours, but it could be intellectually stimulating. I’m on sabbatical this fall, and if I don’t say yes to a review like this now, I never will. Okay, I’ll do it.
What is this book and should I read it? Lost in Math is organized around about a dozen captivating interviews with physicists—mostly theoretical physicists. Several of the interviewees are acknowledged luminaries, while a few are working on their own at the fringes of science. Hossenfelder describes why and how she interviews each physicist. The interviewees reveal interesting ideas and insights. They also provide a window on the way theoretical physicists think and work. She weaves in impressively clear, concise, and untechnical explanations of the theoretical physics topics referenced in the interviews. Hossenfelder also weaves in histories of physics. While the physics ideas and histories are interesting on their own—and could serve as a nonspecialist-appropriate introduction to a slew of contemporary theoretical physics topics—they are not the main point of the book. Though entertaining, the table of contents and “In Brief” summaries at the end of each chapter give no real clue to the physics described in any given chapter. They’re not designed to. To satisfy your curiosity, in the table below, I have summarized the physics topics discussed along with physicists interviewed, by chapter.
Hossenfelder highlights social elements of physicists’ interactions, along with her own and other physicists’ feelings. She also weaves some of her personal story throughout the book, including how and why she got into the business of theoretical physics, and difficult realities that she faces due to the structure of her employment. Some physics students might particularly benefit from reading and thinking about these human aspects of being a physicist. But Hossenfelder spends substantial space addressing human aspects of doing theoretical physics for reasons other than entertainment value and outreach: she thinks that our failure to recognize and address our social/human biases (related to factors that almost kept me from writing this review) is hurting the science we do. She also demonstrates some of the kinds of metacognition that might help to keep our human biases from hurting progress in science.
One might rightly point out—as Frank Wilczek does in his Physics Today review of the book—that Hossenfelder paints an overly dire picture of the state of foundational physics as a whole (encompassing high energy physics, cosmology, quantum gravity, and foundations of quantum mechanics). She omits details in her accounts of the contemporary history of various physics subfields that might paint a more optimistic picture. Chapter 8 provides a key that alerts us to these choices. In it, she presents two histories of string theory—one pessimistic history and one romantic history of similar length. Then, she writes, “Both stories are true. But it’s more fun if you pick one and ignore the other,” (p. 176). Hint: Hossenfelder generally chooses one. We should not lose sight of this. I think that we should not be too upset about the pessimistic choices, either. (I was upset, at first—especially in Chap. 9.) First, she’s providing a counterpoint to the romantic stories that most other physicists tell (at least in public), where they typically leave out a different set of details. Second, she’s trying to create a productive tension that might move some of us scientists to do better science. Hossenfelder delivers some heavy blows, but they are moderated by sarcasm, witticisms, expressions of self-doubt, and (more rarely) glimmers of optimism.
The central strand of Lost in Math is an argument that (some) theoretical physicists and philosophers of science have lost the track of where science ends and philosophy begins. This is potentially damaging. This is not to say that physicists ought not value philosophy, do philosophy, or engage with philosophers. In fact, we theoretical physicists could use philosophers’ help in thoroughly understanding the subtle boundary between philosophical assumptions, mathematics, and scientific reasoning at the foundations of physics. Hossenfelder argues that one mechanism by which (some) physicists’ delusions developed is through the mathematical formalization of aesthetic ideals over the past several decades. Particular ideals of beauty have become entrenched and even elevated in some circles to constituting solid scientific criteria—able to justify rather than merely to guide scientific work, even in the absence of observational evidence. Furthermore, even if serving merely as guides, Hossenfelder worries that entrenchment and uniformity of aesthetic ideals and ideas, more generally, could stifle innovation and lead us astray. At various points throughout the book and in advertising it, she makes the stronger assertion that the field as a whole has been led astray. Whether or not Hossenfelder’s characterization of exactly who has been led astray is correct, her arguments deserve serious attention. Hossenfelder argues that other important factors in the entrenchment and elevation of aesthetic ideals and ideas within theoretical physics (and other sciences) are rooted in cognitive biases that have been exacerbated by recent shifts in the way science is funded, disseminated, and done. That it’s always worked out in the past shouldn’t give us too much comfort. The final chapter ends with a summary of three main lessons for theoretical physicists to draw from her arguments. Appendix C contains further recommendations relevant to all of science—written for scientists, administrators, editors, and others—all of which seem sensible to me.
Going back to my initial anxieties, I still worry that politicians might be emboldened to further cut science funding after misunderstanding this book or accounts of it, but I’m glad that Hossenfelder wrote it. (If you are a politician, please read rather than skim, or skip to Appendix C.) She is insightful and makes arguments that deserve careful attention. She makes it easy to give that attention by writing so well and humorously. I’m no longer worried about being kicked off the island.
To conclude, you should read this book. And don’t give it short shrift. Nor should you take it entirely at its word. Recommend Lost in Math to your philosophically inclined physics students—especially those interested in theoretical physics. Also recommend it to any critical reader interested in the philosophy of science or science policy.
1
The Hidden Rules of Physics
In which I realize I don’t understand physics anymore. I talk to friends and colleagues, see I’m not the only one confused, and set out to bring reason back to Earth.
The Conundrum of the Good Scientist
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After twenty years in theoretical physics, most people I know make a career by studying things nobody has seen. They have concocted mind-boggling new theories, like the idea that our universe is but one of infinitely many that together form a “multiverse.” They have invented dozens of new particles, declared that we are projections of a higher-dimensional space and that space is spawned by wormholes that tie together distant places.
These ideas are highly controversial and yet exceedingly popular, speculative yet intriguing, pretty yet useless. Most of them are so difficult to test, they are practically untestable. Others are untestable even theoretically. What they have in common is that they are backed up by theoreticians convinced that their math contains an element of truth about nature. Their theories, they believe, are too good to not be true.
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第１章 物理学の隠れたルール
この章で私は、自分はもはや物理学が理解できていないことに気づく、友だちや同僚と話、とまどっているのは自分だけではないことを知り、理性を地上に取り戻そうと決意する。
善良なる科学者が抱える難問
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二〇年間理論物理学に取り組んできたが、私の知人のほとんどは、誰も見たことがないものを研究して身を立てている。彼らはたとえば、この宇宙は「多宇宙」を形成する無限に多くの宇宙のひとつでしかないというような、奇抜な新理論をこしらえている。あるいは、数十種類の新しい素粒子を作り出し、私たちはより高次元の宇宙の投影にすぎないと主張したり、宇宙には遠く離れた場所どうしをつなぐワームホールがたくさんあるなどと説いている。
これらの概念はかまびすしい論争を起こしている一方で、非常に人気があり、推測の域を出ないのに魅力的で、恰好はよいが使い物にはならない。大半は検証が非常に困難で、事実上検証不可能だ。理論的にすら検証不可能なものもある。これらの理論に共通するのは、どれも、自分たちの数学には自然に関する真実がひとかけらは含まれていると確信している理論家たちに支持されているということだ。自分たちの理論は、大変うまくできているので、正しくないはずがないというわけである。
When Beauty Gets in the Way of Science
Insisting that new ideas must be beautiful blocks progress in particle physics.
by Sabine Hossenfelder
https://nautil.us/issue/71/flow/why-beauty-is-fatal-to-physics
**
The biggest news in particle physics is no news. In March, one of the most important conferences in the field, Rencontres de Moriond, took place. It is an annual meeting at which experimental collaborations present preliminary results. But the recent data from the Large Hadron Collider (LHC), currently the world’s largest particle collider, has not revealed anything new.
Forty years ago, particle physicists thought themselves close to a final theory for the structure of matter. At that time, they formulated the Standard Model of particle physics to describe the elementary constituents of matter and their interactions. After that, they searched for the predicted, but still missing, particles of the Standard Model. In 2012, they confirmed the last missing particle, the Higgs boson.
The Higgs boson is necessary to make sense of the rest of the Standard Model. Without it, the other particles would not have masses, and probabilities would not properly add up to one. Now, with the Higgs in the bag, the Standard Model is complete; all Pokémon caught.
The Standard Model may be physicists’ best shot at the structure of fundamental matter, but it leaves them wanting. Many particle physicists think it is simply too ugly to be nature’s last word. The 25 particles of the Standard Model can be classified by three types of symmetries that correspond to three fundamental forces: The electromagnetic force, and the strong and weak nuclear forces. Physicists, however, would rather there was only one unified force. They would also like to see an entirely new type of symmetry, the so-called “supersymmetry,” because that would be more appealing. Oh, and additional dimensions of space would be pretty. And maybe also parallel universes. Their wish list is long.
It has become common practice among particle physicists to use arguments from beauty to select the theories they deem worthy of further study. These criteria of beauty are subjective and not evidence-based, but they are widely believed to be good guides to theory development. The most often used criteria of beauty in the foundations of physics are presently simplicity and naturalness.
By “simplicity,” I don’t mean relative simplicity, the idea that the simplest theory is the best (a.k.a. “Occam’s razor”). Relying on relative simplicity is good scientific practice. The desire that a theory be simple in absolute terms, in contrast, is a criterion from beauty: There is no deep reason that the laws of nature should be simple. In the foundations of physics, this desire for absolute simplicity presently shows in physicists’ hope for unification or, if you push it one level further, in the quest for a “Theory of Everything” that would merge the three forces of the Standard Model with gravity.
As an ex-particle physicist, I understand the desire to have an encompassing theory for the structure of matter.
The other criterion of beauty, naturalness, requires that pure numbers that appear in a theory (i.e., those without units) should neither be very large nor very small; instead, these numbers should be close to one. Exactly how close these numbers should be to one is debatable, which is already an indicator of the non-scientific nature of this argument. Indeed, the inability of particle physicists to quantify just when a lack of naturalness becomes problematic highlights that the fact that an unnatural theory is utterly unproblematic. It is just not beautiful.
Anyone who has a look at the literature of the foundations of physics will see that relying on such arguments from beauty has been a major current in the field for decades. It has been propagated by big players in the field, including Steven Weinberg, Frank Wilczek, Edward Witten, Murray Gell-Mann, and Sheldon Glashow. Countless books popularized the idea that the laws of nature should be beautiful, written, among others, by Brian Greene, Dan Hooper, Gordon Kane, and Anthony Zee. Indeed, this talk about beauty has been going on for so long that at this point it seems likely most people presently in the field were attracted by it in the first place. Little surprise, then, they can’t seem to let go of it.
Trouble is, relying on beauty as a guide to new laws of nature is not working.
**
Since the 1980s, dozens of experiments looked for evidence of unified forces and supersymmetric particles, and other particles invented to beautify the Standard Model. Physicists have conjectured hundreds of hypothetical particles, from “gluinos” and “wimps” to “branons” and “cuscutons,” each of which they invented to remedy a perceived lack of beauty in the existing theories. These particles are supposed to aid beauty, for example, by increasing the amount of symmetries, by unifying forces, or by explaining why certain numbers are small. Unfortunately, not a single one of those particles has ever been seen. Measurements have merely confirmed the Standard Model over and over again. And a theory of everything, if it exists, is as elusive today as it was in the 1970s. The Large Hadron Collider is only the most recent in a long series of searches that failed to confirm those beauty-based predictions.
These decades of failure show that postulating new laws of nature just because they are beautiful according to human standards is not a good way to put forward scientific hypotheses. It’s not the first time this has happened. Historical precedents are not difficult to find. Relying on beauty did not work for Kepler’s Platonic solids, it did not work for Einstein’s idea of an eternally unchanging universe, and it did not work for the oh-so-pretty idea, popular at the end of the 19th century, that atoms are knots in an invisible ether. All of these theories were once considered beautiful, but are today known to be wrong. Physicists have repeatedly told me about beautiful ideas that didn’t turn out to be beautiful at all. Such hindsight is not evidence that arguments from beauty work, but rather that our perception of beauty changes over time.
Physicists must, first and foremost, learn from their failed predictions. So far, they have not.
That beauty is subjective is hardly a breakthrough insight, but physicists are slow to learn the lesson—and that has consequences. Experiments that test ill-motivated hypotheses are at high risk to only find null results; i.e., to confirm the existing theories and not see evidence of new effects. This is what has happened in the foundations of physics for 40 years now. And with the new LHC results, it happened once again.
The data analyzed so far shows no evidence for supersymmetric particles, extra dimensions, or any other physics that would not be compatible with the Standard Model. In the past two years, particle physicists were excited about an anomaly in the interaction rates of different leptons. The Standard Model predicts these rates should be identical, but the data demonstrates a slight difference. This “lepton anomaly” has persisted in the new data, but—against particle physicists’ hopes—it did not increase in significance, is hence not a sign for new particles. The LHC collaborations succeeded in measuring the violation of symmetry in the decay of composite particles called “D-mesons,” but the measured effect is, once again, consistent with the Standard Model. The data stubbornly repeat: Nothing new to see here.
Of course it’s possible there is something to find in the data yet to be analyzed. But at this point we already know that all previously made predictions for new physics were wrong, meaning that there is now no reason to expect anything new to appear.
Yes, null results—like the recent LHC measurements—are also results. They rule out some hypotheses. But null results are not very useful results if you want to develop a new theory. A null-result says: “Let’s not go this way.” A result says: “Let’s go that way.” If there are many ways to go, discarding some of them does not help much.
To find the way forward in the foundations of physics, we need results, not null-results. When testing new hypotheses takes decades of construction time and billions of dollars, we have to be careful what to invest in. Experiments have become too costly to rely on serendipitous discoveries. Beauty-based methods have historically not worked. They still don’t work. It’s time that physicists take note.
And it’s not like the lack of beauty is the only problem with the current theories in the foundations of physics. There are good reasons to think physics is not done. The Standard Model cannot be the last word, notably because it does not contain gravity and fails to account for the masses of neutrinos. It also describes neither dark matter nor dark energy, which are necessary to explain galactic structures.
So, clearly, the foundations of physics have problems that require answers. Physicists should focus on those. And we currently have no reason to think that colliding particles at the next higher energies will help solve any of the existing problems. New effects may not appear until energies are a billion times higher than what even the next larger collider could probe. To make progress, then, physicists must, first and foremost, learn from their failed predictions.
So far, they have not. In 2016, the particle physicists Howard Baer, Vernon Barger, and Jenny List wrote an essay for Scientific American arguing that we need a larger particle collider to “save physics.” The reason? A theory the authors had proposed themselves, that is natural (beautiful!) in a specific way, predicts such a larger collider should see new particles. This March, Kane, a particle physicist, used similar beauty-based arguments in an essay for Physics Today. And a recent comment in Nature Reviews Physics about a big, new particle collider planned in Japan once again drew on the same motivations from naturalness that have already not worked for the LHC. Even the particle physicists who have admitted their predictions failed do not want to give up beauty-based hypotheses. Instead, they have argued we need more experiments to test just how wrong they are.
Will this latest round of null-results finally convince particle physicists that they need new methods of theory-development? I certainly hope so.
As an ex-particle physicist myself, I understand very well the desire to have an all-encompassing theory for the structure of matter. I can also relate to the appeal of theories such a supersymmetry or string theory. And, yes, I quite like the idea that we live in one of infinitely many universes that together make up the “multiverse.” But, as the latest LHC results drive home once again, the laws of nature care heartily little about what humans find beautiful.
物理学で最も頻繁に使用される
美しさ（beauty）
の基準は
単純さ（simplicity）
と
自然さ（naturalness）
Lost in Math – Archive.org
https://ia903102.us.archive.org/3/items/lostinmath/LostInMath.pdf