Werner Heisenberg quote: “In modern quantum theory there can be no doubt that the elementary particles will finally also be mathematical forms”

“The elementary particles in Plato's Timaeus are finally not substance but mathematical forms. "All things are numbers" is a sentence attributed to Pythagoras.”

Werner Heisenberg (1901–1976) German theoretical physicist

Physics and Philosophy (1958)
Context: But the resemblance of the modern views to those of Plato and the Pythagoreans can be carried somewhat further. The elementary particles in Plato's Timaeus are finally not substance but mathematical forms. "All things are numbers" is a sentence attributed to Pythagoras. The only mathematical forms available at that time were such geometric forms as the regular solids or the triangles which form their surface. In modern quantum theory there can be no doubt that the elementary particles will finally also be mathematical forms but of a much more complicated nature.

“The law of causality is no longer applied in quantum theory and the law of conservation of matter is no longer true for the elementary particles.”

Werner Heisenberg (1901–1976) German theoretical physicist

Physics and Philosophy (1958)
Context: The law of causality is no longer applied in quantum theory and the law of conservation of matter is no longer true for the elementary particles. Obviously Kant could not have foreseen the new discoveries, but since he was convinced that his concepts would be "the basis of any future metaphysics that can be called science" it is interesting to see where his arguments have been wrong.

“Therefore, the mathematical forms that represent the elementary particles will be solutions of some eternal law of motion for matter.”

Werner Heisenberg (1901–1976) German theoretical physicist

Physics and Philosophy (1958)
Context: The equation of motion holds at all times, it is in this sense eternal, whereas the geometrical forms, like the orbits, are changing. Therefore, the mathematical forms that represent the elementary particles will be solutions of some eternal law of motion for matter. Actually this is a problem which has not yet been solved.<!-- p. 72

“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)

“The development of quantum mechanics in the 1920s was the greatest advance in physical science since the work of Isaac Newton. It was not easy; the ideas of quantum mechanics present a profound departure from ordinary human intuition. Quantum mechanics has won acceptance through its success. It is essential to modern atomic, molecular, nuclear, and elementary particle physics, and to a great deal of chemistry and condensed matter physics as well.”

Steven Weinberg (1933) American theoretical physicist

Preface
Lectures on Quantum Mechanics (2012, 2nd ed. 2015)

“A truly rational theory would allow us to deduce the elementary particles (electron, etc.) and not be forced to state them a priori.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

Letter to Michele Besso (10 September 1952), Letter n°190, Correspondance, 1903-1955 (1972), by Pierre Speziali and Michele Angelo Besso
1950s

“The quantum theory, as it is now constituted, presents us with a very great challenge, if we are at all interested in such a venture, for in quantum physics there is no consistent notion at all of what the reality may be that underlies the universal constitution and structure of matter. Thus, if we try to use the prevailing world view based on the notions of particles, we discover that the 'particles' (such as electrons) can also manifest as waves, that they move discontinuously, that there are no laws at all that apply in detail to the actual movements of individual particles and that only statistical predictions can be made about large aggregates of such particles. If on the other hand we apply the world view in which the world is regarded as a continuous field, we find that this field must also be discontinuous, as well as particle-like, and that it is as undermined in its actual behaviour as is required in the particle view of relation as a whole.”

David Bohm book Wholeness and the Implicate Order

Wholeness and the Implicate Order (1980)

“Replacing particles by strings is a naive-sounding step, from which many other things follow. In fact, replacing Feynman graphs by Riemann surfaces has numerous consequences: 1. It eliminates the infinities from the theory. …2. It greatly reduces the number of possible theories. …3. It gives the first hint that string theory will change our notions of spacetime. Just as in QCD, so also in gravity, many of the interesting questions cannot be answered in perturbation theory. In string theory, to understand the nature of the Big Bang, or the quantum fate of a black hole, or the nature of the vacuum state that determines the properties of the elementary particles, requires information beyond perturbation theory… Perturbation theory is not everything. It is just the way the [string] theory was discovered.”

Edward Witten (1951) American theoretical physicist

"The Past and Future of String Theory" in The Future of Theoretical Physics and Cosmology: Celebrating Stephen Hawking's Contributions to Physics (2003) ed. G.W. Gibbons, E.P.S. Shellard & S.J. Rankin

“The concept of a random walk is simple but rich for its many applications, not only in finance but also in physics and the description of natural phenomena. It is arguably one of the most founding concepts in modern physics as well as in finance, as it underlies the theories of elementary particles, which are the building blocks of our universe, as well as those describing the complex organization of matter around us.”

Didier Sornette (1957) French scientist

Source: Why Stock Markets Crash - Critical Events in Complex Systems (2003), Chapter 2, Fundamentals Of Financial Markets, p. 38.

“The classical concept of 'physical entity', be it particle, wave, field or system, has become a problematic concept since the advent of relativity theory and quantum mechanics. The recent developments in modern quantum mechanics, with the performance of delicate and precise experiments involving single quantum entities, manifesting explicit non-local behavior for these entities, brings essential new information about the nature of the concept of entity.”

Diederik Aerts (1953) Belgian theoretical physicist

Aerts, D. (1998). " The entity and modern physics: the creation-discovery view of reality. http://www.vub.ac.be/CLEA/aerts/publications/1998EntModPhys.pdf" In E. Castellani (Ed.), Interpreting Bodies: Classical and Quantum Objects in Modern Physics (pp. 223-257). Princeton: Princeton University Press.

“In modern quantum theory there can be no doubt that the elementary particles will finally also be mathematical forms”

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