Academics From Germany

"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."

"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."

"Can you, or anyone else, reach the central order of things or events, whose existence seems beyond doubt, as directly as you can reach the soul of another human being? I am using the term 'soul' quite deliberately so as not to be misunderstood. If you put your question like that, I would say yes. ... the word 'soul' refers to the central order, to the inner core of a being whose outer manifestations may be highly diverse and pass our understanding."

"The problem of values is nothing but the problem of our acts, goals and morals. It concerns the compass by which we must steer our ship if we are to set a true course through life. The compass itself has been given different names by various religions and philosophies: happiness, the will of God, the meaning of life-to mention just a few. The differences in the names reflect profound differences in the awareness of different human groups. I have no wish to belittle these differences, but I have the clear impression that all such formulations try to express man's relatedness to a central order."

"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."

"One evening I reached the point where I was ready to determine the individual terms in the energy table, or, as we put it today, in the energy matrix, by what would now be considered an extremely clumsy series of calculations. When the first terms seemed to accord with the energy principle, I became rather excited, and I began to make countless arithmetical errors. As a result, it was almost three o'clock in the morning before the final result of my computations lay before me. The energy principle had held for all terms, and I could no longer doubt the mathematical consistency and coherence of the kind of quantum mechanics to which my calculations pointed. At first, I was deeply alarmed. I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and I felt almost giddy at the thought that I now had to probe this wealth of mathematical structures nature had so generously spread out before me. I was far too excited to sleep, and so, as a new day dawned, I made for the southern tip of the island, where I had been longing to climb a rock jutting out into the sea. I now did so without too much trouble, and waited for the sun to rise."

"An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them."

"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."

"Every experiment destroys some of the knowledge of the system which was obtained by previous experiments."

"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."

"The more precise the measurement of position, the more imprecise the measurement of momentum, and vice versa."

"[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."

"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."

"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."

"Believe me,... the bitterness of life, or at least of mine, which runs through it like a strand of red, and becomes less and less endurable as I grow older, is not compensated in the hundredth part by the joy of life. I will freely admit that these burdens, which to me have been so grievous, would have been lighter to many another; but our temperament is part of ourselves, given to us by the Creator with our very existence, and we have very little power to change it. I find, on the other hand, in this very consciousness of the vanity of life, which nearly all men must confess to as they draw near the end, my strongest assurance of the approach of a more beautiful metamorphosis. In this, my dear friend, let us find comfort, and endeavour to call up calmness to bear life out to the end."

"May the dream which we call life be for you a happy dream, a foretaste of that true life which we shall inherit in our real home, when the awakened spirit shall labour no longer under the grievous bondage of the flesh, the fetters of space, the whips of earthly pain, and the sting of our paltry needs and desires. Let us carry our burdens to the end, stoutly and uncomplainingly, never losing sight of that higher goal. Glad then shall we be to lay down our weary lives, and to see the dropping of the curtain.""

""It is beyond doubt that the happiness which love can bestow on its chosen souls is the highest that can fall to mortal's lot. But when I imagine myself in the place of the man who, after twenty happy years, now in one moment loses his all, I am moved almost to say that he is the wretchedest of mortals, and that it is better never to have known such happy days. So it is on this miserable earth: 'the purest joy finds its grave in the abyss of time'. What are we without the hope of a better future?"

"There is in this world a joy of the intellect, which finds satisfaction in science, and a joy of the heart, which manifests itself above all in the aid men give one another against the troubles and trials of life. But for the Supreme Being to have created existences, and stationed them in various spheres in order to taste these joys for some 80 or 90 years — that were surely a miserable plan.... Whether the soul were to live for 80 years or for 80 million years, if it were doomed in the end to perish, such an existence would only be a respite. In the end it would drop out of being. We are thus impelled to the conclusion to which so many things point, although they do not amount to a coercive scientific proof, that besides this material world there exists another purely spiritual order of things, with activities as various, as the present, and that this world of spirit we shall one day inherit."

"The function just found cannot, it is true, express rigorously the probabilities of the errors: for since the possible errors are in all cases confined within certain limits, the probability of errors exceeding those limits ought always to be zero, while our formula always gives some value. However, this defect, which every analytical function must, from its nature, labor under, is of no importance in practice, because the value of our function decreases so rapidly... that it can safely be considered as vanishing. Besides, the nature of the subject never admits of assigning with absolute rigor the limits of error."

"Mathematics is the queen of the sciences."

"I will add that I have recently received from Hungary a little paper on non-Euclidean geometry in which I rediscover all my own ideas and results worked out with great elegance... The writer is a very young Austrian officer, the son of one of my early friends, with whom I often discussed the subject in 1798, although my ideas were at that time far removed from the development and maturity which they have received through the original reflections of this young man. I consider the young geometer J. Bolyai a genius of the first rank."