Physicists From Germany

"I must give some attention to the delicate question of religion, on which I have touched already. In my father's generation this question still was discussed with passion. Since then a sort of truce has existed in the countries of the West, while in the communist states of the East atheism has been made into the State religion. It is not advisable to blow on the embers of such controversies. But as I am talking about the limitations of our physical world picture I cannot but say that I do not believe in transgressions of the laws of nature. As these laws are of a statistical nature, and therefore allow deviations from the norm, I must define more clearly what I mean. The statistical deviations themselves obey certain laws. The miraculous events of religious tradition, however, are of a different kind, they lie on a different plane altogether; they are meant to prove something lying entirely beyond scientific consideration, such as the power of prayer, the intervention of divine power for or against certain men or nations."

"It is true that many scientists are not philosophically minded and have hitherto shown much skill and ingenuity but little wisdom."

"I... refer to the... Waynflete Lectures given by... E. D. Adrian, on The Physical Background of Perception because the results of physiological investigations seem... in perfect agreement with my suggestion about the meaning of reality in physics. The messages which the brain receives have not the least similarity with the stimuli. They consist in pulses of given intensities and frequencies, characteristic for the transmitting nerve-fiber, which ends in a definite place in the cortex. All the brain 'learns' (I use... the objectionable language of the 'disquieting figure of a little hobgoblin sitting... aloft in the ') is a distribution or a 'map' of pulses. From this information it produces the image of the world by a process which can metaphorically be called a consummate place of combinatorial mathematics: it sorts out of the maze of indifferent and varying signals invariant shapes and relations which form the world of ordinary experience."

"The belief that there is only one truth and that oneself is in possession of it, seems to me the deepest root of all that is evil in the world."

"There are metaphysical problems, which cannot be disposed of by declaring them meaningless. For, as I have repeatedly said, they are "beyond physics" indeed and demand an act of faith. We have to accept this fact to be honest. There are two objectionable types of believers: those who believe the incredible and those who believe that "belief" must be discarded and replaced by "the scientific method.""

"The scientist's urge to investigate, like the faith of the devout or the inspiration of the artist, is an expression of mankind's longing for something fixed, something at rest in the universal whirl: God, Beauty, Truth. Truth is what the scientist aims at. He finds nothing at rest, nothing enduring, in the universe. Not everything is knowable, still less predictable. But the mind of man is capable of grasping and understanding at least a part of Creation; amid the flight of phenomena stands the immutable pole of law."

"The dance of atoms, electrons and nuclei, which in all its fury is subject to God's eternal laws, has been entangled with another restless Universe which may well be the Devil's: the human struggle for power and domination, which eventually becomes history. My optimistic enthusiasm about the disinterested search for truth has been severely shaken. I wonder at my simplemindedness when I re-read what I said on the modern fulfilment of the alchemists dream: "Now however, the motive is not the lust for gold, cloaked by the mystery of magic arts, but the scientists' pure curiosity. For it is clear from the beginning that we may not expect wealth too." Gold means power, power to rule and to have a big share in the riches of this world. Modern alchemy is even a short-cut to this end, it provides power directly; a power to dominate and to threaten and hurt on a scale never heard of before. And this power we have actually seen displayed in ruthless acts of warfare, in the devastation of whole cities and the destruction of their population."

"America has grown by expansion in a practical vacuum; the pioneers of the West had to overcome terrific natural obstacles, but negligible human resistance. The Russia of today had to conquer not only natural but human difficulties: she had to break up the rotten system of the Czars and to assimilate backward Asiatic tribes; now she has set herself the task of bringing her brand of modernization to the ancient civilizations of the Far East. For this purpose it is indispensable to have a well-defined doctrine full of slogans, which appeals to the needs and instincts of the poverty-stricken masses. Thus one understands the power which Marx's philosophy has gained in the East. What can we scientists do in this conflict? We can join the spiritual, religious, philosophical forces, which reject war on ethical grounds. We can even attack the ideological foundations of the conflict itself. For science is not only the basis of technology but also the material for a sound philosophy."

"The world of Man's experience is infinitely rich and manifold, but chaotic and involved with the experiencing being. This being strives to arrange his impressions and to agree with others concerning them. Language and art, with their numerous modes of expression, are such ways of transmission from mind to mind, complete in their way where objects of the sense-world are concerned, but not well suited to the communication of exact ideas concerning the outer world. This marks the beginning of the task of science. From the multitude of experiences it selects a few simple forms, and constructs from them, by thought, an objective world of things. In physics, all 'experience' consists of the activity of constructing apparatus and of reading pointer instruments. Yet the results thereby obtained suffice to re-create the cosmos by thought. At first images are formed which are much influenced by observation; gradually, the conceptions become more and more abstract, old ideas are rejected and replaced by new ones. But, however far the constructed world of things departs from observation, nevertheless it is indissolubly linked at its boundaries to the perceptions of the sense, and there is no statement of the most abstract theory that does not express, ultimately, a relation between observations. That is why each new observation shakes up the entire structure, so that theories seem to rise and fall. This, however, is precisely what charms and attracts the scientist. The creation of his mind would be a melancholy thing, did it not die and come to life once more."

"He [Einstein] calls my way of describing the physical world 'incomplete'; in his eyes this is a flaw which he hopes to see removed, while I am prepared to put up with it. I have in fact always regarded it as a step forward, because an exact description of the state of a physical system presupposes that one can make statements of infinite precision about it, and this seems absurd to me. It seems to me that I have followed Einstein's own way of thinking in accordance with his theory of relativity, which recognizes the impossibility of locating any point in time and space absolutely, and therefore concludes that the concept of absolute place and time determination does not make sense. This is at the base of the whole of his mighty edifice. But he did not want to acknowledge the analogy of the situation in the quantum theory."

"While Born evidently realised that our extended order no longer gratified primitive instincts, he too failed to examine closely the structures that create and maintain this order, or to see that our instinctual morals have over the past five thousand years or more gradually been replaced or restrained. Thus, although perceiving that 'science and technology have destroyed the ethical basis of civilisation, perhaps irreparably', he imagines that they have done so by the facts they have uncovered rather than by their having systematically discredited beliefs that fail to satisfy certain 'standards of acceptability' demanded by constructivist rationalism (see below). While admitting that `no one has yet devised a means of keeping society together without traditional ethical principles', Born yet hopes that these can be replaced 'by means of the traditional method used in science'. He too fails to see that what lies between instinct and reason cannot be replaced by 'the traditional method used in science'."

"He felt that what is called “Copenhagen interpretation” should be called “Göttingen interpretation,” and was a bit hurt that he got the Nobel rather late."

"In the realm of physics it is perhaps only the theory of relativity which has made it quite clear that the two essences, space and time, entering into our intuition, have no place in the world constructed by mathematical physics. Colours are thus "really" not even æther-vibrations, but merely a series of values of mathematical functions in which occur four independent parameters corresponding to the three dimensions of space, and the one of time."

"Quantum theory does not trouble me at all. It is just the way the world works. What eats me, gets me, drives me, pushes me, is to understand how it got that way. What is the deeper foundation underneath it? Where does it come from? So that we won’t see it as something that is unwelcome by friends that we admire—John Bell and many others—it will be something that will make you say, ‘It couldn’t have been otherwise.’ We haven’t gotten to that stage yet, and until we do, we have not met the challenge that is right there. I continue to say that the quantum is the crack in the armor that covers the secret of existence. To me it’s a marvelous stimulus, hope, and driving force. And yet I am afraid that just the word—‘hope’—is what does not eat, or possess, or drive so many of our colleagues in the field. They’re content to take the theory for granted, rather than to find out where it comes from. But you would hardly feel the drive to find out where from if you don’t feel that the theory is utterly right. I have been brought up from ‘childhood’ to feel that it is utterly right. Here I was, reading that book of Weyl’s at the age of eighteen and just crazy about it."

"He realized that formal mathematics might even have an advantage over immediately insightful ("phenomenological") mathematics, because in its conceptual constitution it was free from the restrictions of the latter. I will call this view the symbolic realism of the "mature" Weyl."

"Weyl never became a devoted adherent to any single philosophy. He rather was a wanderer through the philosophical fields differing with the changes in his scientific view..."

"Weyl considered an aspect about general relativity... the nonpreservation of direction in a curved space. ...[He] decided to consider the possibility that length was also not preserved. ...To effect this change mathematically, Weyl had to make a slight modification in the structure of general relativity. He assumed that in addition to the usual metric (set of numbers or variables) that described the gravitational field, there was another one related to length. ...amazingly when the result was analyzed Maxwell's equations mysteriously appeared. It almost seemed as if a bit of magic had occurred and scientists quickly became interested in the miracle. ...but with detailed analysis the theory was shown to be flawed. Einstein was the first to put his finger on the flaw. ...Weyl soon acknowledged the flaw and laid his theory to rest. It may have been a failure (actually it was not an entire failure; a similar idea is used today in modern field theory), but it did accomplish something important: it got people interested in the possibility that the electromagnetic and gravitational field could be unified. Einstein soon began working on an alternative theory, as did others."

"I inquired of Dyson whether Weyl had given an example of his having sacrificed truth for beauty. I learned that the example which Weyl gave was his gauge theory of gravitation which he had worked out in his Raum-Zeit-Materie. Apparently, Weyl became convinced that this theory was not true as a theory of gravitation; but still it was so beautiful that he did not wish to abandon it and so he kept it alive for the sake of beauty. But much later, it did turn out that Weyl's instinct was right after all, when the formalism of gauge invariance was incorporated into quantum electrodynamics."

"In the first attempt to introduce gauge theories in physics, Hermann Weyl, around the 1920s, proposed certain scale transformations to be a fundamental symmetry of nature."

"Hermann Weyl was both a mathematician and a mathematical physicist. Weyl wrote on mathematics, general relativity... quantum mechanics... art and philosophy. His smaller book on philosophy is entitled The Open World. It is made up of lectures... in 1932 at Yale University. In the philosophy of science, according to Weyl, complexity is essential in understanding the concept of a law of nature. If laws of nature may be arbitrarily complex, he argued, the very concept... becomes vacuous. What difference would remain... if the laws meant to explain them were as complex as the phenomena they are meant to explain? Laws of nature must be simple."

"Hermann Weyl’s 1918 text Das Kontinuum... investigates how much of the mathematical corpus can be retained if we restrict ourselves to predicative definitions and methods of proof. He presents a foundational system in which it is impossible to perform an impredicative definition. ...It is an excellent example of a fully developed non-mainstream foundational system for mathematics."

"The scene of action of reality is not a three-dimensional Euclidean space but rather a four-dimensional world, in which space and time are linked together indissolubly. However deep the chasm may be that separates the intuitive nature of space from that of time in our experience, nothing of this qualitative difference enters into the objective world which physics endeavors to crystallize out of direct experience. It is a four-dimensional continuum, which is neither "time" nor "space". Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it as history, that is, as a process that is going forward in time and takes place in space."

"Above all, the ominous clouds of those phenomena that we are with varying success seeking to explain by means of the quantum of action, are throwing their shadows over the sphere of physical knowledge, threatening no one knows what new revolution."

"After Riemann had made known his discoveries, mathematicians busied themselves with working out his system of geometrical ideas formally; chief among these were Christoffel, Ricci, and Levi-Civita. Riemann... clearly left the real development of his ideas in the hands of some subsequent scientist whose genius as a physicist could rise to equal flights with his own as a mathematician. After a lapse of seventy years this mission has been fulfilled by Einstein."

"Consciousness spreads out its web, in the form of time, over reality."

"All characteristics of material things as they are presented to us in the acts of external perception (e.g. colour) are endowed with the separateness of spatial extension, but it is only when we build up a single connected real world out of all our experiences that the spatial extension, which is a constituent of every perception, becomes a part of one and the same all-inclusive space. … every material thing can, without changing content, equally well occupy a position in Space different from its present one. This immediately gives us the property of the homogeneity of space which is the root of the conception, Congruence."

"Time is the primitive form of the stream of consciousness. ...If we project ourselves outside the stream of consciousness and represent its content as an object, it becomes an event happening in time, the separate stages of which stand to one another in the relations of earlier and later."

"It is the nature of a real thing to be inexhaustible in content; we can get an ever deeper insight into this content by the continual addition of new experiences, partly in apparent contradiction, by bringing them into harmony with one another. In this interpretation, things of the real world are approximate ideas. From this arises the empirical character of all our knowledge of reality."

"In the field of philosophy Kant was the first to take the next decisive step towards the point of view that not only the qualities revealed by the senses, but also space and spatial characteristics have no objective significance in the absolute sense; in other words, that space, too, is only a form of our perception."

"Recognition of the subjectivity of the qualities of sense is found in Galilei (and also in Descartes and Hobbes) in a form closely related to the principle underlying the constructive mathematical method of our modern physics which repudiates" qualities"."

"The rapid development of science... has, as it were, burst its old shell, now become too narrow."

"First, the physicists in the persons of Faraday and Maxwell, proposed the "electromagnetic field" in contradistinction to matter, as a reality of a different category. Then, during the last century, the mathematicians, … secretly undermined belief in the evidence of Euclidean Geometry. And now, in our time, there has been unloosed a cataclysm which has swept away space, time, and matter hitherto regarded as the firmest pillars of natural science, but only to make place for a view of things of wider scope and entailing a deeper vision. This revolution was promoted essentially by the thought of one man, Albert Einstein."

"The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. and certainty Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church... had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science "more geometrico". Matter... could be measured as a quantity and... its characteristic expression as a substance was the Law of Conservation of Matter... This, which has hitherto represented our knowledge of space and matter, and which was in many quarters claimed by philosophers as a priori knowledge, absolutely general and necessary, stands to-day a tottering structure."

"Space and time are commonly regarded as the forms of existence of the real world, matter as its substance. A definite portion of matter occupies a definite part of space at a definite moment of time. It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship."

"With Mie's view of matter there is contrasted another, according to which matter is a limiting singularity of the field, but charges and masses are force-fluxes in the field. This entails a new and more cautious attitude towards the whole problem of matter."

"A new theory by the author has been added, which draws the physical inferences consequent on the extension of the foundations of geometry beyond Reimann... and represents an attempt to derive from world-geometry not only gravitational but also electromagnetic phenomena. Even if this theory is still only in its infant stage, I feel convinced that it contains no less truth than Einstein's Theory of Gravitation—whether this amount of truth is unlimited or, what is more probable, is bounded by the Quantum Theory."

"To gaze up from the ruins of the oppressive present towards the stars is to recognise the indestructible world of laws, to strengthen faith in reason, to realise the "harmonia mundi" that transfuses all phenomena, and that never has been, nor will be, disturbed."

"It was my wish to present this great subject as an illustration of the itermingling of philosophical, mathematical, and physical thought, a study which is dear to my heart. This could be done only by building up the theory systematically from the foundations, and by restricting attention throughout to the principles. But I have not been able to satisfy these self-imposed requirements: the mathematician predominates at the expense of the philosopher."

"Einstein's theory of relativity has advanced our ideas of the structure of the cosmos a step further. It is as if a wall which separated us from Truth has collapsed. Wider expanses and greater depths are now exposed to the searching eye of knowledge, regions of which we had not even a presentiment. It has brought us much nearer to grasping the plan that underlies all physical happening."

"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."

"In my work, I have always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful."

"This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind."

"Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect."

"[Physicists and philosophers] stick stubbornly to the principles of a mechanistic interpretation of the world after physics has, in its factual structure, already outgrown the latter. They have the same excuse as the inhabitant of the mainland who for the first time travels on the open sea: he will desperately try to stay in sight of the vanishing coast line, as long as there is no other coast in sight, towards which he steers."

"We now come to a decisive step of mathematical abstraction: we forget about what the symbols stand for... [The mathematician] need not be idle; there are many operations which he may carry out with these symbols, without ever having to look at the things they stand for."

"In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain."

"The introduction of numbers as coordinates by reference to the particular division scheme of the open one dimensional continuum is an act of violence whose only practical vindication is the special calculatory manageability of the ordinary number continuum with its four basic operations. The topological skeleton determines the connectivity of the manifold in the large."

"On a certain level of generality A which I call the ground level, you have certain theorems that have been proved and certain unsolved problems P of recognised interest. Suppose you discover a generalisation of one of these theorems and thereby rise to a higher level of generality A. Write it up, but lock it away in a drawer - unless or until it serves to solve one of the problems P on the ground level... But the deeper one drives the spade the harder the digging gets; maybe it has become too hard for us unless we are not given some outside help, be it even by such devilish devices as high-speed computing machines."

"Cartan developed a general scheme of infinitesimal geometry in which Klein's notions were applied to the tangent plane and not to the n-dimensional manifold M itself."

"Important though the general concepts and propositions may be with which the modern industrious passion for axiomatizing and generalizing has presented us, in algebra perhaps more than anywhere else, nevertheless I am convinced that the special problems in all their complexity constitute the stock and core of mathematics; and to master their difficulties requires on the whole the harder labor."