物理硏究中的理論與實驗 / 觀察 ( i.e. 科學方法 )

物理硏究中的理論與實驗/觀察(i.e.科學方法) 王子敬中央研究院物理研究所中研院物理所高中生物理培育計畫 2008/5/10

Scientific Methods : Binding together of Facts by Ideas 科學方法 :事實與思維的互動 History of Science : Perpetual Sequence of Conjectures and Refutations 科學史 :假設的提出與推翻

問題是甚麼、為甚麼重要 • 歸納與演繹、理論與實驗的互動 • 物理進展的標準與流程 • 理論與實驗方法的限制 • 物理與數學 : 工具還是目標 ? • 科學方法以外 • “ Punch Lines ”

藝術家眼中的科學研究工作： Picasso’s Don Quixote Rodin’s Thinker

科學方法 (Vs 科學內容) : • 討論 “How Science ought to be done” • 科學研究的特性、步驟、標準 • “Nature of Truth” (Vs “Truth of Nature” ) • Operating System (Vs Software)

理論以論理 • (原理、道理、真理…) • 實驗以驗實 • (事實、實體、實踐…)

“ A Man of Science is distinguished not by What he believes but by Why and How he believes them .”（Bertrand Russell ) • What –知道是甚麼【現象的描述】 • Why –瞭解為甚麼【現象的理論解釋】 • How –憑甚麼相信【現象的實驗證據】數學+數字物理的研究精神：

研究如下棋(e.g Mastermind) 科學發展理論實驗相輔相成

硏究如瞎子摸象……… • Theory Observation : one-to-one • Observation  Theory : one-to-many

歸納 Induction (1) 解釋性原理 (2) 觀察 (3) 演繹 Deduction 歸納─演繹方法:亞里斯多德後續的科學哲學家 :Pythagorus, Galileo, Descartes, Newton, Bacon, Herschel, Whewell, Berkeley, Mach, Popper,Feyerabend, Lakatos, Kuhn ……..

Experimental/Observational Tests Same Kind Different Kind Predictions Problems, Puzzles, Anomalies, Crises deduction Theories Laws of Phenomena induction ElementaryFacts Concepts Insights, Ideas, Axioms, Postulate, Hypothesis …. NewFacts Imagination, “Flash of Genius”……. 科學方法 (“Anything that works”以外) consistent contradictory

Induction(歸納)Vs Axiomatic(公設) Approaches : • e.g. Newton’s Theory of Light (I) Vs Newton’s Laws of Motion (A) • emphasis on data/facts (I) Vs creative imagination (A) • Common objectives : explain known phenomena and make predictions of new ones • Modern language : “Bottom-Up” (I) Vs “Top-Down” (A)

Induction • Axioms of Newtons’s Theory of Mechanics: • Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it. • The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. • To every action there is always opposed an equal reaction: or, the mutual actions on two bodies upon each other are always equal, and directed to contrary parts.

Law (定律) & Theory (理論) : • no clear border-line ; in general • descriptive “see that”(Law) Vs explanatory “see as”(Theory) • Theories incorporate Laws via deduction • Laws can outlive Theories • e.g. Boyle’s Law to Kinetic Theory ; Kepler’s Law to Newton’s theory of Gravitation • “effective” theory (a la onion) – explain & predict at certain scale without understanding of underlying mechanism , using theoretically non-derivable “fundamental constants” to parametrize our ignorance • e.g. fluid mechanics (viscosities, densities …etc as fundamental variables, without involving molecular physics) • i.e. all scientific theory are “effective” at present.

Starting from certain principles, NO arbitrary/non-derivable numbers, everything predictable in principle • A candidate : Superstring Theory • NOT proven yet ! Physics’ Holy Grail : “Theory of Everything” (ToE)

“ All Theories are False ; Some Theories are More False than the Others .” (Karl Popper) • But ………. • “refutation (否定) rejection (摒棄)” • i.e. Theories approach but cannot, in principle, achieve "necessary truth“ : • " that which is, is, and cannot not be " • (Aristotle)

Criteria of Acceptance / Gauge of Progress of Theory : BOTTOM LINE – • Facts (experimental/observational confirmations), facts, more facts ………! • Survival of the “Fittest”

Confirmation weights: • Reproducibility • Internal consistency • Unversality • Testability/Falsifiable – range of possibilities of falsification • Predictive power, esp. to the extreme range • Extension of understanding to new regions • Knowledge of boundaries (limits of validity) • “crucial experiments” : differentiate competing theories • Progress of Science : Progressive incorporation of past knowledge into new framework • New theory converges to old ones in asymptotic region • “River-tributary , with rapids” analogy • e.g. Newton’s Theory included Kepler’s Law, Galileo’s Law of free fall, motions of tides ….. etc • A continuing process with occasional revolutions • Normal Vs Revolution Science

Limitations in Experiments/Observations : • Finite statistics • Hardware imperfections • Complexities of real configurations : Are all relevant parameters been taken into account ?? • Experimental Errors : statistical + systematic e.g. Uncorrelated Gaussian errors : • Statistical statements can be misleading e.g. mean Vs median • Only probabilistic statements possible from “ x = A  B “

Poisson : discrete N Gaussian : Large N or continuous x

10-9 !!!!!!!

Limitations in Theory : • Are they reality, final, complete, and permanent ? (NO) • Hypothesis, Laws, Theories, Realities: not distinct(e.g. atoms) • Idealized/Simplified : give predictions (real world) only after modelling/making assumptions , and specify initial/boundary conditions ( from mathematical forms to numbers !! ) • Sometimes based on “first-principles/axioms” which cannot be proven. • Chaos System: unpredictable – infinitely sensitive to initial conditions • Quantum cosmology: “Only One Universe to Observe” Can it be investigated with Scientific Methods ? • Facts cannot prove a theory to be completely and absolutely true. Theories can only be shown to be “empirically adequate”.

Role of Mathematics in Physics : • Ends or Means ?? Discovery or Inventions ?? • “Pythagorean” : the necessary truth is the mathematical harmony present in nature, and that can be discovered by reason, and is the starting point of all investigations. • “Instrumentalist” : physical laws are computational device for the explanation and prediction of the phenomena Galileo:“Philosophy is written in this grand book, the universe, which stands continually open to our gaze. ….. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it….” Mach:“ …in the investigation of nature, we have to deal only with knowledge of the connexion of appearances with one another. What we represent to ourselves behind the appearances exists only in our understanding, and has for us only the value of a memoria technica or formula, whose form, because it is arbitrary and irrelevant, varies very easily with the standpoint of our culture.”

Physics  Mathematics e.g.Are “Feynman diagrams” realities ?? If so, physics or mathematics ? ……. i.e.agreement between ideas & facts to 6+ digits (parts per million…)!!!!

Beyond Scientific Methods ……. • 科學方法以外 ……… “ ……. if a thing is not a Science, it is not necessarily bad. For example, Love is not a Science. So if something is said not to be a Science, it does not mean there is something wrong with it; it just means it is not a Science. ” ( Richard Feynman )

Distinguish / Identify / 區分 : • “Science” Vs “Non-Science” • “Good Science” Vs “Bad Science” • “Genuine Science” Vs “Pseudo-Science”

現實生活的科學研究工作：

Scientific Trainings (科學訓練) , • At the End of the Day , are ……….. A Signal-to-Noise Problem : Judgement & Differentiation 『訊噪比』的判斷與區分

“ Science has only One Command : Contributions ! ” Bertolt Brecht’s Galileo 『科學的唯一戒律，就是貢獻 !』布萊希特 -- 伽利略傳

物理硏究中的理論與實驗 / 觀察 ( i.e. 科學方法 )