Physicists From Germany

"It seems clear that [set theory] violates against the essence of the continuum, which, by its very nature, cannot at all be battered into a single set of elements. Not the relationship of an element to a set, but of a part to a whole ought to be taken as a basis for the analysis of a continuum."

"We cannot hope to give here a final clarification of the essence of fact, judgement, object, property; this task leads into metaphysical abysses; about these one has to seek advice from men whose name cannot be stated without earning a compassionate smile—e.g. Fichte."

"If I knew something about it, I wouldn’t lecture on it!"

"Zuko saysThermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, so it doesn't bother you any more."

"Modern positivism...expresses criticism against the naïve use of certain terms... by the general postulate that the question whether a given sentence has any meaning... should always be thoroughly and critically examined. This... is derived from mathematical logic. The procedure of natural science is pictured as an attachment of symbols to the phenomena. The symbols can, as in mathematics, be combined according to certain rules... However, a combination of symbols that does not comply with the rules is not wrong but conveys no meaning. The obvious difficulty in this argument is the lack of any general criterion as to when a sentence should be considered meaningless. A definite decision is possible only when the sentence belongs to a closed system of concepts and axioms, which in the development of natural science will be rather the exception than the rule. In some case the conjecture that a certain sentence is meaningless has historically led to important progress... new connections which would have been impossible if the sentence had a meaning. An example... sentence: "In which orbit does the electron move around the nucleus?" But generally the positivistic scheme taken from mathematical logic is too narrow in a description of nature which necessarily uses words and concepts that are only vaguely defined."

"From 1946 onward, as Germany's leading physicist, he had two disappointments. His efforts to bring scientists into government failed, and his scientific work, offering suggestions for a new unified field theory, was not generally accepted."

"In 1925, the world view of physics was a model of a great machine composed of separable interacting material particles. During the next few years, Schrodinger and Heisenberg and their followers created a universe based on superimposed inseparable waves of probability amplitudes. This new view would be entirely consistent with the Vedantic concept of All in One."

"Heisenberg in cattedra / spiegava il Principio di indeterminazione / a una platea di eletti. / In un angolo Fermi e Dirac / si guardarono un attimo sbigottiti / poi si scambiarono brevi formule / scritte sui palmi delle mani"

"We gaze continually at the world and it grows dull in our perceptions. Yet seen from the another's vantage point, as if new, it may still take our breath away. Come... dry your eyes, for you are life, rarer than a quark and unpredictable beyond the dreams of Heisenberg. Come, dry your eyes. And let's go home."

"In 1929, Heisenberg spent some time in India as the guest of the celebrated Indian poet Rabindranath Tagore, with whom he had long conversations about science and Indian philosophy. This introduction to Indian thought brought Heisenberg great comfort, he told me. 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. “After these conversations with Tagore,” he said, “some of the ideas that had seemed so crazy suddenly made much more sense. That was a great help for me.”"

"When he arrived he looked like a simple peasant boy, with short, fair hair, clear bright eyes and a charming expression. He took his duties as an assistant more seriously than Pauli and was a great help to me. His incredible quickness and acuteness of apprehension has always enabled him to do a colossal amount of work without much effort; he finished his hydrodynamic thesis, worked on atomic problems partly alone, partly in collaboration with me, and helped me to direct my research students."

"Heisenberg's name will always be associated with his theory of quantum mechanics, published in 1925, when he was only 23 years old. For this theory and the applications of it which resulted especially in the discovery of allotropic forms of hydrogen, Heisenberg was awarded the Nobel Prize for Physics for 1932. His new theory was based only on what can be observed, that is to say, on the radiation emitted by the atom. We cannot, he said, always assign to an electron a position in space at a given time, nor follow it in its orbit, so that we cannot assume that the planetary orbits postulated by Niels Bohr actually exist. Mechanical quantities, such as position, velocity, etc. should be represented, not by ordinary numbers, but by abstract mathematical structures called "matrices" and he formulated his new theory in terms of matrix equations."

"The first gulp from the glass of natural sciences will turn you into an atheist, but at the bottom of the glass God is waiting for her."

"I am the one who knocks."

"Reality is in the observations, not in the electron."

"Some subjects are so serious that one can only joke about them."

"[F]rom all that has been said about modern science... modern physics is just one... but... characteristic, part of a general historical process... toward a unification and a widening of our... world. This... would... lead to a diminution of... cultural and political tensions that create the great danger... But... forces in the existing cultural communities... try to ensure for their traditional values the largest... role in the final state of unification... and thereby adds to the instability of the transient state. Modern physics... shows that the use of arms... would be disastrous, and... through it openness for all... concepts it raises the hope that in the final state of unification many different cultural traditions may live together and... combine different human endeavors into a new... balance between thought and deed, between activity and meditation."

"Cautious deliberation based on purely rational arguments can save us from many errors and dangers. ...But ...there will always be a fundamental complementarity between deliberation and decision. ...The decision finally... pushing away all the arguments... The decision may be the result of deliberation, but it is... complementary... it excludes deliberation. Even the most important decisions... contain this inevitable element of irrationality. ...[I]t cannot be avoided that some real or apparent truth form the basis of life; and this fact should be acknowledged with regard to those groups... whose basis is different from our own."

"[U]ncomprimising belief carries much more weight than some special philosophical notions... [T]he great majority... can scarcely have any well-founded judgement concerning the correctness of certain important general ideas or doctrines. ...[T]he word "belief" can for this majority not mean "perceiving the truth of something" but... only... as "taking this as the basis for life." ...[T]his second kind of belief is much firmer... much more fixed... it can persist even against immediate contradicting experience... not... shaken by added scientific knowledge... sometimes... to the point where it seems completely absurd, and ends... only with the death of the believer. Science and history can teach us that this... may become a great danger... [S]uch belief has always belonged to the great forces in human history."

"I remember discussions with Bohr which went through many hours till very late at night and 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?"

"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."

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

"[E]ven in the most precise part of science, in mathematics, we cannot avoid using concepts that involve contradictions. ...[I]t is well known that the concept of infinity leads to contradictions... but it would be practically impossible to construct... mathematics without this concept."

"The way in which the convergent mathematical schemes did not fulfill the requirements of relativity and quantum theory was... interesting. ...[O]ne scheme ...interpreted in terms of actual events in space and time, led to a...time reversal... The physicists are convinced... that the processes... do not occur in nature... if... separated by measurable distance in space and time. ...If we assume that the laws of nature do contain a third universal constant... of the order of 10-13 cm, then... our usual concepts... apply only to regions in space and time that are large compared to the universal constant. We should... be prepared for phenomena of a qualitatively new character when we... approach regions... smaller than the nuclear radii. The phenomenon of time reversal... might therefore belong to these smallest regions."

"[S]ets of concepts... defined in physics. ...[F]our systems... have ...attained ...final form. The first ...Newtonian mechanics ...for the description of all mechanical systems, ...motion of fluids and ...elastic ..; it comprises , , aerodynamics. The second closed system of concepts... the theory of heat. Though... connected with mechanics through... statistical mechanics, it... [is] not... a part of mechanics. ...[T]he phenomenological theory of heat uses ...[some] concepts that have no [physics] counterpart ...like: , specific heat, entropy, free energy, etc. ...[F]rom ...phenomenological ...to a statistical interpretation ...considering heat as energy, distributed statistically among ...many degrees of freedom due to ...atomic structure... heat is no more connected with mechanics than with electrodynamics or other ...physics. The central concept ...is ...probability, closely connected with ...entropy ...Besides this ...the statistical theory of heat requires the concept of energy. But any coherent set ...in physics will ...contain ...concepts of energy, and and the law that these ...be conserved. This follows if the ...set is ...to describe ...features ...correct at all times and everywhere; ...[i.e.,] features that do not depend on space and time ...[i.e.,] are invariant under arbitrary translations in space and time, rotations in space and the Galileo— or Lorentz—transformation. Therefore, the theory of heat can be combined with any of the other closed systems of concepts. The third... electricity and magnetism... reached... final form... through... Lorentz, Einstein and Minkowski. It comprises electrodynamics, special relativity, optics, magnetism, and one may include the de Broglie theory of s of all different sorts of elementary particles, but not the wave theory of Schrodinger. [F]ourth... the quantum theory... Its central concept is the probability function, or... "statistical matrix"... It comprises quantum and wave mechanics, the theory of atomic spectra, chemistry, and the theory of other properties... like electric conductivity, , etc. ...The first set is contained in the third as the limiting case where the velocity of light can be considered as infinitely big, and is contained in the fourth as the limiting case where of action can be considered as infinitely small. The first and partly the third set belong to the fourth as a priori for the description of the experiments. The second set can be connected with any of the other three sets without difficulty and is especially important in its connection with the fourth. The independent existence of the third and fourth sets suggests the existence of a fifth set, of which one, three, and four are limiting cases. This fifth set will probably be found someday in connection with the theory of the elementary particles."

"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. This is actually the fact when the concepts become part of a system of axioms and definitions which can be expressed consistently by a mathematical scheme. Such 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."

"The words "position" and "velocity" of an electron... seemed perfectly well defined... and in fact they were clearly defined concepts within the mathematical framework of Newtonian mechanics. But actually they were not well defined, as seen from the relations of uncertainty. One may say that regarding their position in Newtonian mechanics they were well defined, but in their relation to nature, they were not. This shows that we can never know beforehand which limitations will be put on the applicability of certain concepts by the extension of our knowledge into the remote parts of nature, into which we can only penetrate with the most elaborate tools. Therefore, in the process of penetration we are bound sometimes to use our concepts in a way which is not justified and which carries no meaning. Insistence on the postulate of complete logical clarification would make science impossible. We are reminded... of the old wisdom that one who insists on never uttering an error must remain silent."

"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."

"J. Robert Oppenheimer: You're talking about turning theory into a practical weapons system faster than the Nazis. Leslie Groves: Who have a twelve month head start. J. Robert Oppenheimer: Eighteen. Leslie Groves: How could you possibly know that? J. Robert Oppenheimer: Our fast neutron research took six months. The man they've undoubtedly put in charge will have made that leap instantly. Leslie Groves: Who do you think they put in charge? J. Robert Oppenheimer: Werner Heisenberg. He has the most intuitive understanding of atomic structure I've ever seen. Leslie Groves: You know his work? J. Robert Oppenheimer: I know him. Just like I know Walter Bothe, von Weizsäcker, Diebner... In a straight race, the Germans win. We've got one hope. Leslie Groves: Which is? J. Robert Oppenheimer: Antisemitism. Leslie Groves: What? J. Robert Oppenheimer: Hitler called quantum physics "Jewish science", said it right to Einstein's face. Our one hope is that Hitler is so, so blinded by hate that he's denied Heisenberg proper resources, because it'll take vast resources."

"If one finds a difficulty in a calculation which is otherwise quite convincing, one should not push the difficulty away; one should rather try to make it the centre of the whole thing."

"[I]n the Copenhagen interpretation of quantum theory we can indeed proceed without mentioning ourselves as individuals, but we cannot disregard the fact that natural science is formed by men. Natural science does not simply describe and explain nature; it is part of the interplay between nature and ourselves; it describes nature as exposed to our nature of questioning. This was a possibility of which Descartes could not have thought, but it makes a sharp separation between the world and the I impossible. If one follows the great difficulty which even eminent scientists like Einstein had in understanding and accepting the Copenhagen interpretation... one can trace the roots... to the Cartesian partition....it will take a long time for it [this partition] to be replaced by a really different attitude toward the problem of reality."

"There is an enormous difference between modern science and Greek philosophy, and that is just the empiristic attitude... Since the time of Galileo and Newton, modern science has been based upon a detailed study of nature and upon the postulate that only such statements should be made, as have been verified or at least can be verified by experiment. The idea that one can single out some events from nature by an experiment... to find out what is the constant law in the continuous change, did not occur to the Greek philosophers. Therefore, modern science has from its beginning stood on a much more modest, but at the same time much firmer, basis than ancient philosophy. Therefore, the statements of modern physics are in some way meant much more seriously than the statements of Greek philosophy."

"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."

"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."

"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."

"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."

"The atoms in the philosophy of do not move merely by chance. Leucippus seems to have believed in complete determinism, since he is known to have said: "Naught happens for nothing, but everything from a ground and of necessity." The atomists did not give any reason for the original motion of the atoms, which just shows that they thought of a causal description of the atomic motion; causality can only explain later events by earlier events, but it can never explain the beginning."

"We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning."

"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."

"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."

"If nature leads us to mathematical forms of great simplicity and beauty... that no one has previously encountered, we cannot help thinking that they are "true", that they reveal a genuine feature of nature... You must have felt this too: the almost frightening simplicity and wholeness of the relationships which nature suddenly spreads out before us and for which none of us was in the least prepared."

"I was lucky enough to look over the good Lord's shoulder while He was at work."

"After a great war, history is written by the victors and legends develop which glorify them."

"The great scientific contribution in theoretical physics that has come from Japan since the last war may be an indication of a certain relationship between philosophical ideas in the tradition of the Far East and the philosophical substance of quantum theory."

"Of course, we all know that our own reality depends on the structure of our consciousness; we can objectify no more than a small part of our world. But even when we try to probe into the subjective realm, we cannot ignore the central order…In the final analysis, the central order, or 'the one' as it used to be called and with which we commune in the language of religion, must win out."

"If nature leads us to mathematical forms of great simplicity and beauty—by forms I am referring to coherent systems of hypothesis, axioms, etc.—to forms that no one has previously encountered, we cannot help thinking that they are "true," that they reveal a genuine feature of nature. It may be that these forms also cover our subjective relationship to nature, that they reflect elements of our own thought economy. But the mere fact that we could never have arrived at these forms by ourselves, that they were revealed to us by nature, suggests strongly that they must be part of reality itself, not just of our thoughts about reality. ... You must have felt this too: The almost frightening simplicity and wholeness of relationships which nature suddenly spreads out before us and for which none of us was in the least prepared."

"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."

"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."

"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."