“At first it might seem that quantum mechanics (QM), which began with Einstein's photon as the explanation for the photoelectric effect in 1905, goes further in the direction of discreteness. But the wave-particle duality discovered by de Broglie in 1925 is at the heart of QM, which means that this theory is profoundly ambiguous regarding the question of discreteness vs. continuity. QM can have its cake and eat it too, because discreteness is modeled via standing waves (eigenfunctions) in a continuous medium.”

— Gregory Chaitin

How real are real numbers? https://arxiv.org/abs/math/0411418 arXiv:math/0411418v3 (2004). p. 12

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Gregory Chaitin 5

Argentinian mathematician and computer scientist 1947

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“While the founding fathers agonized over the question 'particle' or 'wave', de Broglie in 1925 proposed the obvious answer 'particle' and 'wave'. Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored.”

John S. Bell (1928–1990) Northern Irish physicist

"Six Possible Worlds of Quantum Mechanics" (1986), included in Speakable and Unspeakable in Quantum Mechanics (1987), p. 191

“Quantum mechanics explains the physical stability of the atom by predicting its allowed discrete energy levels and defining the wave functions (also called atomic orbitals) associated with each energy level. The orbitals determine the probability density for finding the electrons at particular locations in the atom when the electrons are in a specific quantum state.”

David W. Oxtoby (1951) President of Pomona college

Principles of Modern Chemistry (7th ed., 2012), Ch. 5 : Quantum Mechanics and Atomic Structure

“Conventional wisdom, fooled by our misleading "physical intuition", is that the real world is continuous, and that discrete models are necessary evils for approximating the "real" world, due to the innate discreteness of the digital computer.”

Doron Zeilberger (1950) Israeli mathematician

"Real" Analysis is a Degenerate Case of Discrete Analysis. Appeared in the book "New Progress in Difference Equations"(Proc. ICDEA 2001), edited by Bernd Aulbach, Saber Elaydi, and Gerry Ladas, and publisher by Taylor & Francis, London, 2004.

“A new development began for relativity theory after 1925 with its absorption into quantum physics. The first great success was scored by Dirac's quantum mechanical equations of the electron, which introduced a new sort of quantities, the spinors, besides the vectors and tensors into our physical theories. …But difficulties of the gravest kind turned up when one passed from one electron or photon to the interaction among an indeterminate number of such particles. In spite of several advances a final solution of this problem is not yet in sight and may well require a deep modification of the foundation of quantum mechanics, such as would account in the same basic manner for the elementary electric charge e as relativity theory and our present quantum mechanics account for c and h.”

Hermann Weyl (1885–1955) German mathematician

Preface to the First American Printing (1950) Note: see Paul Dirac, The Principles of Quantum Mechanics (1947)
Space—Time—Matter (1952)

“Einstein had drawn attention to nonlocality in 1935 in an effort to show that quantum mechanics must be flawed. …Einstein proposed a thought experiment—now called the EPR experiment—involving two particles that spring from a common source and fly in opposite directions.
According to the standard model of quantum mechanics, neither particle has a definite position or momentum before it is measured; but by measuring the momentum of one particle, the physicist instantaneously forces the other particle to assume a fixed position… Deriding this effect as "spooky action at a distance," Einstein argued that it violated both common sense and his own theory of special relativity, which prohibits the propagation of effects faster than the speed of light; quantum mechanics must therefore be an incomplete theory. In 1980, however, a group of French physicists carried out a version of the EPR experiment and showed that it did indeed give rise to spooky action.”

John Horgan (journalist) (1953) American science journalist

The reason that the experiment does not violate special relativity is that one cannot exploit nonlocality to transmit information.
Source: The End of Science (1996), p. 83

“One thing leads to another, and soon you are searching for answers to basic questions.Another time during lectures on Classical Logic, we were introduced to an “experimentum crucis”. It was illustrated by the deciding experiment of Fizeau on the speed of light in water as compared to its speed in air. Since wave theory predicts that speed in water is less, and corpuscular theory (with point particles) predicts it would be faster, this is supposed to have selected the wave theory is correct. But then how would one accommodate the photoelectric effect? Then it turns out that if the “corpuscle” of light had a finite size, corpuscular theory also predicts lower speed of light in water. But then one can ask how come photoelectric emission being prompt even in feeble light, how could the energy of a photon spread over π(λ/2)2 act as a whole and liberate a single photoelectron! This leads us to question the square of the amplitude being interpreted as the probability of the particle being formed in the immediate vicinity. How do probabilities enter quantum mechanics? Thus the questions (and the quest) go on.”

E. C. George Sudarshan (1931–2018) Indian physicist

in A Glance Back at Five Decades of Scientific Research, published in Particles and Fields: Classical and Quantum, Journal of Physics: Conference Series 87 (2007), IOP Publishing, p. 1-2.

“Surely, after 62 years, we should have an exact formulation of some serious part of quantum mechanics? By 'exact' I do not of course mean 'exactly true'. I mean only that the theory should be fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist… until workable approximations are needed in applications. By 'serious' I mean that some substantial fragment of physics should be covered. Nonrelativistic 'particle' quantum mechanics, perhaps with the inclusion of the electromagnetic field and a cut-off interaction, is serious enough.”

John S. Bell (1928–1990) Northern Irish physicist

Against 'measurement' (1990)

“Most biologists," (says Vogel, 1981) "seem to have heard of the boundary layer, but they have a fuzzy notion that it is a discrete region, rather than the discrete notion that it is a fuzzy region.”

Bill Mollison (1928–2016) Australian permaculturist

quoting Vogel, Steven, Life in Moving Fluids; the Physical Biology of Flow, Willard Grant Press, Boston, 1981.
Source: Permaculture: A Designers' Manual (1988), chapter 4.4

“One God, multiple manifestations – in both the spiritual realm and the physical world – just as Albert Einstein wrote about the wave-particle duality of light.”

Newton Lee American computer scientist

Google It: Total Information Awareness, 2016

“Courts are the mere instruments of the law, and can will nothing. When they are said to exercise a discretion, it is a mere legal discretion, a discretion to be exercised in discerning the course prescribed by law; and, when that is discerned, it is the duty of the Court to follow it. Judicial power is never exericised for the purpose of giving effect to the will of the Judge; always for the purpose of giving effect to the will of the Legislature; or, in other words, to the will of the law.”

John Marshall (1755–1835) fourth Chief Justice of the United States

Osborn v. Bank of the United States, 22 U.S. (9 Wheaton) 738, 866 (1824)

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