Richard Feynman quote: “So far as we know, all the fundamental laws of physics, like Newton’s equations, are reversible.”

“The Gordon Equation is as close as being a physical law, like gravitation or planetary motion, as we will ever encounter in finance.”

William J. Bernstein (1948) economist

Source: The Four Pillars of Investing (2002), Chapter 2, Measuring The Beast, p. 54.

“There is one alternative to dark matter, and that is the assumption that Newton's laws don't hold over distances as great as galaxies. But we know that Newton's laws hold over a very large domain. And virtually one hundred percent of the physics and astronomy community believes that there is matter in the universe that does not radiate.”

Vera Rubin (1928–2016) American astronomer

As quoted in [Astronomer Vera Rubin—The Doyenne of Dark Matter, Discover Magazine, http://discovermagazine.com/2002/jun/breakdialogue] (1 June 2002)

“Fabricating astronomical data going back thousands of years calls for knowledge of Newton’s Law of Gravitation and the ability to solve differential equations.”

N. S. Rajaram (1943–2019) Indian mathematician

N.S. Rajaram: The Politics of History, p.47.

“The physicist needs a facility in looking at problems from several points of view. The exact analysis of real physical problems is usually quite complicated, and any particular physical situation may be too complicated to analyze directly by solving the differential equation. But one can still get a very good idea of the behavior of a system if one has some feel for the character of the solution in different circumstances. Ideas such as the field lines, capacitance, resistance, and inductance are, for such purposes, very useful. … On the other hand, none of the heuristic models, such as field lines, is really adequate and accurate for all situations. There is only one precise way of presenting the laws, and that is by means of differential equations. They have the advantage of being fundamental and, so far as we know, precise. If you have learned the differential equations you can always go back to them. There is nothing to unlearn.”

Richard Feynman (1918–1988) American theoretical physicist

volume II; lecture 2, "Differential Calculus of Vector Fields"; section 2-1, "Understanding physics"; p. 2-1
The Feynman Lectures on Physics (1964)

“No one hangs himself by the rope of a physical law. The equations fall tirelessly into themselves.”

Octavio Paz (1914–1998) Mexican writer laureated with the 1990 Nobel Prize for Literature

The Clerk's Vision (1949)
Context: The world stretches out before me, the vast world of the big, the little, and the medium. Universe of kings and presidents and jailors, of mandarins and pariahs and liberators and liberated, of judges and witnesses and the condemned: stars of the first, second, third and nth magnitudes, planets, comets, bodies errant and eccentric or routine and domesticated by the laws of gravity, the subtle laws of falling, all keeping step, all turning slowly or rapidly around a void. Where they claim the central sun lies, the solar being, the hot beam made out of every human gaze, there is nothing but a hole and less than a hole: the eye of a dead fish, the giddy cavity of the eye that falls into itself and looks at itself without seeing. There is nothing with which to fill the hollow center of the whirlwind. The springs are smashed, the foundations collapsed, the visible or invisible bonds that joined one star to another, one body to another, one man to another, are nothing but a tangle of wires and thorns, a jungle of claws and teeth that twist us and chew us and spit us out and chew us again. No one hangs himself by the rope of a physical law. The equations fall tirelessly into themselves.
And in regard to the present matter, if the present matters: I do not belong to the masters. I don't wash my hands of it, but I am not a judge, nor a witness for the prosecution, nor an executioner. I do not torture, interrogate, or suffer interrogation. I do not loudly plead for leniency, nor wish to save myself or anyone else. And for all that I don't do and for all that they do to us, I neither ask forgiveness nor forgive. Their piety is as abject as their justice. Am I innocent? I'm guilty. Am I guilty? I'm innocent. (I'm innocent when I'm guilty, guilty when I'm innocent. I'm guilty when … but that is another song. Another song? It's all the same song.) Guilty innocent, innocent guilty, the fact is I quit.

“Our knowledge of physics only takes us back so far. Before this instant of cosmic time, all the laws of physics or chemistry are as evanescent as rings of smoke.”

Joseph Silk (1942) British-American astronomer

The Infinite Cosmos, Page 3

“So we have these wide principles which sweep across all the different laws, and if one takes too seriously its derivations, and feels that this is only valid because this [assumed more fundamental principle] is valid, you cannot understand the interconnections of the different branches of physics. Some day, when physics is complete, then maybe with this kind of argument we'll know all the laws, then we can start with some axioms (and no doubt somebody will figure out a particular way of doing it) and then all the deductions will be made. But while we don't know all the laws, we can use some to make guesses at theorems which extend beyond the proof.”

Richard Feynman book The Character of Physical Law

Source: The Character of Physical Law (1965), chapter 2, “The Relation of Mathematics to Physics”

“The minimum principle that unified the knowledge of light, gravitation, and electricity of Hamilton's time no longer suffices to relate these fundamental branches of physics. Within fifty years of its creation, the belief that Hamilton's principle would outlive all other physical laws of physics was shattered. Minimum principles have since been created for separate branches of physics… but these are not only restricted… but seem to be contrived…
A single minimum principle, a universal law governing all processes in nature, is still the direction in which the search for simplicity is headed, with the price of simplicity now raised from a mastery of differential equations to a mastery of the calculus of variations.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 442.

“The more important fundamental laws and facts of physical science have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote.”

Albert A. Michelson (1852–1931) American physicist

Light Waves and Their Uses. By Albert A. Michelson. Published by The University of Chicago Press, 1903, pp 23-25.
Context: Before entering into these details, however, it may be well to reply to the very natural question: What would be the use of such extreme refinement in the science of measurement? Very briefly and in general terms the answer would be that in this direction the greater part of all future discovery must lie. The more important fundamental laws and facts of physical science have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i. e., whenever the circumstances of experiment are such that extreme cases can be examined. Such examination almost surely leads, not to the overthrow of the law, but to the discovery of other facts and laws whose action produces the apparent exceptions.As instances of such discoveries, which are in most cases due to the increasing order of accuracy made possible by improvements in measuring instruments, may be mentioned: first, the departure of actual gases from the simple laws of the so-called perfect gas, one of the practical results being the liquefaction of air and all known gases; second, the discovery of the velocity of light by astronomical means, depending on the accuracy of telescopes and of astronomical clocks; third, the determination of distances of stars and the orbits of double stars, which depend on measurements of the order of accuracy of one-tenth of a second—an angle which may be represented as that which a pin's head subtends at a distance of a mile. But perhaps the most striking of such instances are the discovery of a new planet by observations of the small irregularities noticed by Leverier in the motions of the planet Uranus, and the more recent brilliant discovery by Lord Rayleigh of a new element in the atmosphere through the minute but unexplained anomalies found in weighing a given volume of nitrogen. Many instances might be cited, but these will suffice to justify the statement that "our future discoveries must be looked for in the sixth place of decimals." It follows that every means which facilitates accuracy in measurement is a possible factor in a future discovery, and this will, I trust, be a sufficient excuse for bringing to your notice the various methods and results which form the subject matter of these lectures.

“It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power”

Paul Dirac (1902–1984) theoretical physicist

The Evolution of the Physicist's Picture of Nature (1963)
Context: It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

“So far as we know, all the fundamental laws of physics, like Newton’s equations, are reversible.”

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