Quotes

The beauty of Physics

$$ \Large i \hbar \frac{\partial \psi}{\partial t} = {\hat{H}} \psi \qquad \nabla ^{2} \Phi -{\frac {1}{v^{2}}}{\frac {\partial ^{2} \Phi}{\partial t^{2}}} = 0 \qquad {\frac {\partial \Phi }{\partial t } } = k \nabla ^{2} \Phi $$

$$ \Large R_{\mu \nu} - {1 \over 2}R g_{\mu \nu} + \Lambda g_{\mu \nu}= {8 \pi G \over c^4} T_{\mu \nu} \qquad \left( i \gamma^{\mu}\partial_{\mu} - m \right)\psi = 0 $$

All Science is either Physics or a stamp collection

Ernst Rutherford, quoted by John D. Bernal in The Social Function of Science (1939)

If I were obliged to summarize in one sentence what the Copenhagen interpretation [of quantum mechanics] suggests to me this might be “shut up and calculate!”

N. David Mermin, What’s Wrong with this Pillow?, Physics Today, April 1989 https://physicstoday.scitation.org/doi/10.1063/1.2810963

The behavior of large and complex aggregates of elementary particles, it seems, is not to be understood in terms of simply extrapolating a few particles. Instead, entirely new properties appear at each level of complexity, and understanding new behaviors requires research which I think is as fundamental in its nature as any other.

PPhilip W. Anderson, More is different. Science 177 (4047): 393-396, (1972)

Most misunderstandings about physics are about science (and often technology) in general, but they are more obvious in the case of physics, because of all the sciences it is the most foreign to most people, because it seems to be less related to daily events. In fact, the opposite is true, as physics applies to everything, while the other sciences are more specialized. …

The common man’s view of physics is usually far from reality. In fact, the common man’s view of reality is often far from reality: physics is the study of the fundamental properties of the Universe; but the average person understands little physics, at least not the way a physicist does. Thus, most people have little understanding of the world in which they live, except for things limited to humanity, which tends to have a small influence on the Universe as a whole. Of course, if people understood each other better, the world would be a better place to live, but that’s another story.

Warren Siegel, Common misconceptions , in http://insti.physics.sunysb.edu/~siegel/warning.html

In a long time from now–say, ten thousand years from now–there is no doubt that the discovery of Maxwell’s equations [ed., describing electromagnetic waves] will be judged the most significant event of the 19th century. The American Civil War will appear insignificant and provincial when compared to this important scientific event that occurred in the same decade.

Richard Feynman, (Lectures on Physics, vol. II) (1965)

It is very interesting, in this regard, that the survival of species depends in some respects on nuclear fission, in others on sex, and people are equally reluctant to talk about either.

John Archibald Wheeler, interview 5/4/1967, https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4958

Between Mathematics and Physics

No certainty is where one of the mathematical sciences cannot be applied, that is, which are not united with them mathematical, and yet, O scholars, study the mathematical, and do not build without foundations

Leonardo da Vinci, cited in Selected Writings,ed.2009, pg.614

  … It seems to me, in addition to this, to discern in Sarsi firm belief, that in philosophizing it is necessary to lean on the opinions of some celebrated author, so that our mind, when not marrying itself to the discourse of another, should in everything remain sterile and fruitless; and perhaps estimates that philosophy is a book and a man’s fantasy, like the Iliad and ‘Orlando furioso, books in which the least important thing is that what is written in them is true. Mr. Sarsi, this is not the case. philosophy is written in this very great book that continually stands open before our eyes (I say the universe), but it cannot be understood unless we first learn to understand the language, and know the characters, in which it is written. he is written in the mathematical language, and the characters are triangles, circles, and other geometrical figures, without which means it is impossible to humanly understand a word of it; without these it is a vain wandering through a dark labyrinth.

Galileo Galilei (The Assayer, ch. VI, 1623)

the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious for which there is no rational explanation… It is difficult to avoid the impression that we are facing a miracle, comparable in its startling nature to the miracle that the human mind manage to put thousands of arguments in a row without falling into contradiction, or to the two miracles of the laws of nature and the ability of the human mind to intuit them…. The miracle of the appropriateness of the language of mathematics for formulating the laws of physics is a wonderful gift that we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and which will extend, for better or worse, at our pleasure, though perhaps also to our disturbance, to the broader branches of knowledge.

Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” Communications on Pure and Applied Mathematics, vol. XIII, 001-014 (1960), translated 2017

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether, say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.

Richard W. Hamming

In my work [as a mathematician and physicist] I always try to combine truth with beauty, but when I have to choose between one or the other, I generally choose beauty

Hermann Weyl, quoted in Beauty as Method by Paul A.M. Dirac.

To those who do not know mathematics, it is difficult to get an idea of the beauty, the deeper beauty, of nature. … If you want to know nature, to appreciate nature, you must understand the language in which it speaks.

Richard Feynman - The Physical Law - II The relationship of mathematics to physics

The best mathematicians think secretly like physicists, and only after working out the general idea of a demonstration they cover it with ( \epsilon ) and ( \Delta )

Anomymous Fields medal winner, quoted by Anthony Zee in QFT in a nutshell (2010)

Mathematics is a part of physics.Physics is a science experimental, part of the natural sciences.Mathematics is that part of physics where experiences are cheap. Jacobi’s identity (which forces the heights of a triangle to meet at one point) is an experimental fact in the same way in to which the earth is round (i.e., homeomorphic to a sphere). But it can be discovery at less expense. In the mid-20th century, attempts were made to divide physics and mathematics.The consequences proved catastrophic. Entire generations of mathematicians were formed without knowing half of the their science and, of course, in total ignorance of any other science. they began by teaching their ugly scholastic pseudomathematics to their students, and then to schoolchildren (forgetting Hardy’s warning that for bad math does not there is permanent place under the sun). Since school mathematics cut off from physics is not suitable neither for teaching nor for application to any other science, the result has been universal hatred of mathematicians-both by the poor pupils (some of whom have since become ministers) than of users

Vladimir I. Arnold , On the Teaching of Mathematics, Russian Mathematical Surveys,vol. 53, no. 1, 1998, pp. 229-234, transl.it. in CRITICAL POINTS No. 3 (MAY 2000) On the teaching of mathematics