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• The more precise the measurement of position, the more imprecise the measurement of momentum, and vice versa.
  • Initial statement of the Uncertainty principle in "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik" in Zeitschrift für Physik, 43 (1927)
  • Variant translation: The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.
    • As quoted in "The Uncertainty Principle" at the American Institute of Physics

• Light and matter are both single entities, and the apparent duality arises in the limitations of our language. It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme — the quantum theory — which seems entirely adequate for the treatment of atomic processes; for visualisation, however, we must content ourselves with two incomplete analogies — the wave picture and the corpuscular picture.
  • "Introductory" in The Physical Principles of the Quantum Theory (1930) as translated by Carl Eckhart and Frank C. Hoyt, p. 10

• Every experiment destroys some of the knowledge of the system which was obtained by previous experiments.
  • "Critique of the Physical Concepts of the Corpuscular Theory" in The Physical Principles of the Quantum Theory (1930) as translated by Carl Eckhart and Frank C. Hoyt, p. 20; also in "The Uncertainty Principle" in The World of Mathematics : A Small Library of the Literature of Mathematics (1956) by James Roy Newman, p. 1051

• An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them.
  • Physics and Beyond : Encounters and Conversation (1971)

• Quantum theory provides us with a striking illustration of the fact that we can fully understand a connection though we can only speak of it in images and parables.
  • Physics and Beyond : Encounters and Conversation (1971)

• In general, scientific progress calls for no more than the absorption and elaboration of new ideas— and this is a call most scientists are happy to heed.
  • Physics and Beyond : Encounters and Conversation (1971)

• There is a fundamental error in separating the parts from the whole, the mistake of atomizing what should not be atomized. Unity and complementarity constitute reality.
  • As quoted in Physics from Wholeness : Dynamical Totality as a Conceptual Foundation for Physical Theories (2005) by Barbara Piechocinska

• After these conversations with Tagore some of the ideas that had seemed so crazy suddenly made much more sense. That was a great help for me.
  • On conversations with Rabindranath Tagore, as quoted in Uncommon Wisdom: Conversations With Remarkable People (1988) by Fritjof Capra, who states that after these "He began to see that the recognition of relativity, interconnectedness, and impermanence as fundamental aspects of physical reality, which had been so difficult for himself and his fellow physicists, was the very basis of the Indian spiritual traditions."
  • Variant: After the conversations about Indian philosophy, some of the ideas of Quantum Physics that had seemed so crazy suddenly made much more sense.
    • As quoted in Pride of India (2006) by Samskrita Bharati. p. 56

• I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.
  • As quoted in The New York Times Book Review (8 March 1992)

The Development of Quantum Mechanics (1933)

Nobel lecture (11 December 1933) Full text online (PDF)

• The interest of research workers has frequently been focused on the phenomenon of regularly shaped crystals suddenly forming from a liquid, e.g. a supersaturated salt solution. According to the atomic theory the forming force in this process is to a certain extent the symmetry characteristic of the solution to Schrödinger's wave equation, and to that extent crystallization is explained by the atomic theory. Nevertheless this process retains a statistical and — one might almost say — historical element which cannot be further reduced: even when the state of the liquid is completely known before crystallization, the shape of the crystal is not determined by the laws of quantum mechanics. The formation of regular shapes is just far more probable than that of a shapeless lump. But the ultimate shape owes its genesis partly to an element of chance which in principle cannot be analysed further.

• However the development proceeds in detail, the path so far traced by the quantum theory indicates that an understanding of those still unclarified features of atomic physics can only be acquired by foregoing visualization and objectification to an extent greater than that customary hitherto. We have probably no reason to regret this, because the thought of the great epistemological difficulties with which the visual atom concept of earlier physics had to contend gives us the hope that the abstracter atomic physics developing at present will one day fit more harmoniously into the great edifice of Science.

Physics and Philosophy (1958)

Physics and Philosophy: The Revolution in Modern Science (1958) Lectures delivered at University of St. Andrews, Scotland, Winter 1955-56

• We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning.
  • This has also appeared in the alternate form: "What we observe is not nature itself, but nature exposed to our method of questioning."

• In the philosophy of Democritus the atoms are eternal and indestructible units of matter, they can never be transformed into each other. With regard to this question modern physics takes a definite stand against the materialism of Democritus and for Plato and the Pythagoreans. The elementary particles are certainly not eternal and indestructible units of matter, they can actually be transformed into each other. As a matter of fact, if two such particles, moving through space with a very high kinetic energy, collide, then many new elementary particles may be created from the available energy and the old particles may have disappeared in the collision. Such events have been frequently observed and offer the best proof that all particles are made of the same substance: energy. 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 Greek philosophers thought of static forms and found them in the regular solids. Modern science, however, has from its beginning in the sixteenth and seventeenth centuries started from the dynamic problem. The constant element in physics since Newton is not a configuration or a geometrical form, but a dynamic law. 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. This is a problem which has not yet been solved.

• The existing scientific concepts cover always only a very limited part of reality, and the other part that has not yet been understood is infinite.

• Whenever we proceed from the known into the unknown we may hope to understand, but we may have to learn at the same time a new meaning of the word "understanding."

• The physicist may be satisfied when he has the mathematical scheme and knows how to use for the interpretation of the experiments. But he has to speak about his results also to non-physicists who will not be satisfied unless some explanation is given in plain language. Even for the physicist the description in plain language will be the criterion of the degree of understanding that has been reached.

• I remember discussions with Bohr which went through many hours till very late at night an ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighbouring park I repeated to myself again and again the question: Can nature possibly be so absurd as it seemed to us in these atomic experiments?

• Any concepts or words which have been formed in the past through the interplay between the world and ourselves are not really sharply defined with respect to their meaning: that is to say, we do not know exactly how far they will help us in finding our way in the world. We often know that they can be applied to a wide range of inner or outer experience, but we practically never know precisely the limits of their applicability. This is true even of the simplest and most general concepts like "existence" and "space and time". Therefore, it will never be possible by pure reason to arrive at some absolute truth.
  The concepts may, however, be sharply defined with regard to their connections... a group of connected concepts may be applicable to a wide field of experience and will help us to find our way in this field. But the limits of the applicability will in general not be known, at least not completely...

Misattributed

• Some subjects are so serious that one can only joke about them.
  • Sometimes attributed to Heisenberg, this was actually a statement made by Niels Bohr, as quoted in The Genius of Science: A Portrait Gallery (2000) by Abraham Pais, p. 24
  • Some things are so serious that one can only joke about them.
    • Variant without any citation as to author in Denial is not a river in Egypt (1998) by Sandi Bachom, p. 85.