Albert Einstein

"Before the development of the theory of relativity it was known the principle of energy and momentum could be expressed in a differential form for the electromagnetic field. The four-dimensional formulation of these principles leads to an important conception, that of the energy tensor, which is important of the further development of the theory of relativity."

"A little reflection will show that the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, it is: (Inertial mass) \cdot (Acceleration) = (Intensity of the gravitational field) \cdot (Gravitational mass). It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body."

"A material particle upon which no force acts moves, according to the principle of inertia, uniformly in a straight line. In the four-dimensional continuum of the special theory of relativity (with real time co-ordinate) this a real straight line. The natural, that is, the simplest, generalization of the straight line which is meaningful in the system of concepts of the general (Riemannian) theory of invariants is that of the straightest, or geodesic, line."

"The theory of relativity is intimately connected with the theory of space and time. I shall therefore begin with a brief investigation of the origin of our ideas of space and time, although in doing so I know that I introduce a controversial subject. The object of all science, whether natural science or psychology, is to co-ordinate our experiences and to bring them into a logical system. How are our customary ideas of space and time related to the character of our experience?"

"In May 1921 Albert Einstein delivered a series of lectures at Princeton University on the broad topic of relativity. The lectures form a unified survey of the basic concepts of relativity. Beginning with the pre-relativity physics of Newton (or perhaps, more correctly, the "three dimensional" relativity of Newton) Einstein lays the foundation for "four dimensional" relativity primarily from the postulational standpoint. The development of special relativity is followed by the formulation of the general theory leading up to the Schwarzschild line element and the cosmological problem."

"Some try to explain Hubble's shift of spectral lines by means other than the Doppler effect. There is, however, no support for such a conception in the known physical facts."

"It is the essential achievement of the general theory of relativity that it has freed physics from the necessity of introducing the "inertial system" (or inertial systems). This concept is unsatisfactory for the following reason: without any deeper foundation it singles out certain co-ordinate systems among all conceivable ones. It is then assumed that the laws of physics hold only for such inertial systems (e.g. the law of inertia and the law of the constancy of the velocity of light). Thereby, space as such is assigned a role in the system of physics that distinguishes it from all other elements of physical description. It plays a determining role in all process, without in its turn being influenced by them. Though such a theory is logically possible, it is on the other hand rather unsatisfactory. Newton had been fully aware of this deficiency, but he had also clearly understood that no other path was open to physics in his time. Among the later physicians it was above all Ernst Mach who focussed attention on this point."

"One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seem to be in accordance with a continuum theory, and must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the basis of such a theory."

"Exile in Switzerland brought Kahler and Thomas Mann together as friends, and it was at Thomas Mann's suggestion that Kahler and his family settled in Princeton, New Jersey, in 1938. Once again, Kahler's presence was magnetic: Albert Einstein, Wolfgang Pauli Ernst Kantorowicz, Ben Shahn, and Roger Sessions were frequent visitors ..."

"Austrian-born Antoinette von Kahler and her son Erich Kahler (1885–1970) fled Nazi-occupied Germany in 1933. They arrived in the United States in 1938 and settled in Princeton, New Jersey, where their friend Thomas Mann (1875–1955) had also taken up residence. The Kahler’s Princeton home at One Evelyn Place became known as Kahler-Kreis (Kahler-Circle) where German intellectuals gathered, including Albert Einstein, Mann, Erwin Panofsky, Ben Shahn, and Hermann Broch. Early in the 20th century, Antoinette Von Kahler wrote a number of children’s books (several are in the Cotsen children’s book collection). After settling in Princeton, she took up embroidery and designed a number of silks with biblical themes and Jewish iconography. Ben Shahn, an artist and family friend, is said to have been an admirer of her work."

"At Evelyn Place once a fortnight a group of men—the composer Roger Sessions, the mathematician Hermann Weyl, the philosopher David Bowers, the economist Friedrich Lutz, as well as Richard and John—met for an evening of serious conversation. The subject might be the poetry of Hölderlin, the works of Kierkegaard (which were beginnning to appear in Walter Lowrie's translation), the economy of postward Europe or the form of punishment that should be meted out to the Nazis."

"... My wife and I were good friends of the Kahlers and were invited to social gatherings at their home, but we did not belong to their intellectual circle. We never heard the words "Kahler Kreis" and never read their writings. The most memorable part of our relationship was the kitchen-friendship between my wife Imme and Lily Kahler. The two of them would prepare delicious German pastries in the kitchen while the husbands discussed German philosophy in the living-room. I remember only the pastries."

"If you wish to learn from the theoretical physicist anything about the methods which he uses... Don't listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities."

"[S]cientists of those times were for the most part convinced that the basic concepts and laws of physics... were derivable by abstraction, i.e. by a logical process, from experiments. It was the general Theory of Relativity which showed in a convincing manner the incorrectness of this view. ...quite apart from the question of comparative merits, the fictitious character of the principles is made quite obvious by the fact that it is possible to exhibit two essentially different bases, each of which in its consequences leads to a large measure of agreement with experience. This indicates that any attempt logically to derive the basic concepts and laws of mechanics from the ultimate data of experience is doomed to failure."

"It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible..."

"Have we any right to hope that experience will guide us aright, when there are theories (like classical mechanics) which agree with experience to a very great extent, even without comprehending the subject in its depths? ...there is the correct path and, moreover... it is in our power to find it. ...in Nature is actualized the ideal of mathematical simplicity. ...pure mathematical construction enables us to discover the concepts and the laws..."

"Conclusions obtained by purely rational processes are, so far as Reality is concerned, entirely empty. It was because he recognized this, and especially because he impressed it upon the scientific world that Galileo became the father of modern physics and in fact of the whole of modern natural science."

"[I]n order to include the atomistic character of electricity, the field equations only need to involve that a three-dimensional volume of space on whose boundary the electrical density vanishes everywhere, contains a total electrical charge of an integral amount. Thus in a continuum theory, the atomistic character could be satisfactorily expressed by integral propositions without localizing the particles which constitute the atomistic system. Only if this sort of representation of the atomistic structure be obtained could I regard the quantum problem within the framework of a continuum theory as solved."

"On the other hand... we have to give up the notion of an absolute localization of the particles in a theoretical model. This seems to me to be the correct theoretical interpretation of Heisenberg's indeterminacy relation. And yet a theory may perfectly well exist, which is in a genuine sense an atomistic one (and not merely on the basis of a particular interpretation), in which there is no localizing of the particles in a mathematical model."

"[E]xperience... remains the sole criterion of the serviceability of a mathematical construction for physics, but the truly creative principle resides in mathematics. ...pure thought is competent to comprehend the real, as the ancients dreamed."

"Newton felt by no means comfortable about the concept of absolute space, which embodied that of absolute rest; for he was alive to the fact that nothing in experience seemed to correspond to this latter concept. He also felt uneasy about the introduction of action at a distance. But the enormous practical success of his theory may well have prevented him and the physicists of the eighteenth and nineteenth centuries from recognizing the fictitious character of the principles of his system."

"In the paucity of the mathematically existent simple field-types and of the relations between them, lies the justification for the theorist's hope that he may comprehend reality in its depths. The most difficult point for such a field-theory at present is how to include the atomic structure of matter and energy. For the theory in its basic principles is not an atomic one in so far as it operates exclusively with continuous functions of space, in contrast to classical mechanics whose most important feature, the material point, squares with the atomistic structure of matter."

"[I]f we conceive Euclidean geometry as the science of the possibilities of the relative placing of actual rigid bodies and accordingly interpret it as a physical science, and do not abstract from its original empirical content, the logical parallelism of geometry and theoretical physics is complete."

"I want... to glance... at the development of the theoretical method, and... especially to observe the relation of pure theory to the totality of the data of experience. Here is the eternal antithesis of the two inseparable constituents of human knowledge, Experience and Reason, within the sphere of physics. We honour ancient Greece as the cradle of western science. She for the first time created the intellectual miracle of a logical system, the assertions of which followed one from another with such rigor that not one of the demonstrated propositions admitted of the slightest doubt—Euclid's geometry. This marvellous accomplishment of reason gave to the human spirit the confidence it needed for its future achievements. ...But yet the time was not ripe for a science that could comprehend reality... until a second elementary truth had been realized, which only became the common property of philosophers after Kepler and Galileo. Pure logical thinking can give us no knowledge whatsoever of the world of experience; all knowledge about reality begins with experience and terminates in it."

"We have now assigned to reason and experience their place within the system of theoretical physics. Reason gives the structure to the system; the data of experience and their mutual relations are to correspond exactly to consequences in the theory. On the possibility alone of such a correspondence rests the value and the justification of the whole system, and especially of its fundamental concepts and basic laws. But for this, these latter would simply be free inventions of the human mind which admit of no a priori justification..."

"The modern quantum theory, as associated with the names of de Broglie, Schrödinger, and Dirac, which of course operates with continuous functions, has overcome this difficulty by means of a daring interpretation, first given in a clear form by Max Born:-the space functions which appear in the equations make no claim to be a mathematical model of atomic objects. These functions are only supposed to determine... the probabilities of encountering those objects in a particular place or in a particular state of motion... This conception... forces us to employ a continuum of which the number of dimensions is not that of previous physics, namely 4, but which has dimensions increasing without limit as the number of the particles... increases. ...I ...accord to this interpretation no more than a transitory significance. I still believe in the possibility of giving a model of reality, a theory, that is to say, which shall represent events themselves and not merely the probability..."

"A complete system of theoretical physics consists of concepts and basic laws to interrelate those concepts and of consequences to be derived by logical deduction."

"The conception... of the purely fictitious character of the basic principles of theory was in the eighteenth and nineteenth centuries still far from being the prevailing one. But it continues to gain more and more ground because of the everwidening logical gap between the basic concepts and laws on the one side and the consequences to be correlated with our experiences on the other—a gap which widens progressively with the developing unification of the logical structure, that is with the reduction in the number of the logically independent conceptual elements required for the basis of the whole system."

"I very much enjoyed your delightful explanation of the formation of meanders. It just happens that my wife had asked me about the “teacup phenomenon” a few days earlier, but I did not know a rational explanation. She says that she will never stir her tea again without thinking of you."

"I do not know how the Third World War will be fought, but I can tell you what they will use in the Fourth — rocks!"

"Never do anything against conscience even if the state demands it."

"Many persons have inquired concerning a recent message of mine that "a new type of thinking is essential if mankind is to survive and move to higher levels." Often in evolutionary processes a species must adapt to new conditions in order to survive. Today the atomic bomb has altered profoundly the nature of the world as we know it, and the human race consequently finds itself in a new habitat to which it must adapt its thinking. In light of new knowledge…an eventual world state is not just desirable in the name of brotherhood, it is necessary for survival... Today we must abandon competition and secure cooperation. This must be the central fact in all our considerations of international affairs; otherwise we face certain disaster. Past thinking and methods did not prevent world wars. Future thinking must prevent wars."

"Had I known that the Germans would not succeed in producing an atomic bomb, I would not have lifted a finger."

"You cannot simultaneously prevent and prepare for war. The very prevention of war requires more faith, courage and resolution than are needed to prepare for war. We must all do our share, that we may be equal to the task of peace."

"I agree with your remark about loving your enemy as far as actions are concerned. But for me the cognitive basis is the trust in an unrestricted causality. "I cannot hate him, because he must do what he does." That means for me more Spinoza than the prophets."

"As the issues are greater than men ever sought to realize before, the recriminations will be fiercer and pride more desperately hurt. It may help to recall that many recognized before the bomb ever fell that the time had already come when we must learn to live in One World. The stakes are immense, the task colossal, the time is short. But we may hope — we must hope — that man’s own creation, man’s own genius, will not destroy him. Scholars, indeed all men, must move forward in the faith of that philosopher who held that there is no problem the human reason can propound which the human reason cannot reason out."

"It is easier to denature plutonium than it is to denature the evil spirit of man."

"Our world faces a crisis as yet unperceived by those possessing power to make great decisions for good or evil. The unleashed power of the atom has changed everything save our modes of thinking and we thus drift toward unparalleled catastrophe."

"A new type of thinking is essential if mankind is to survive and move toward higher levels."

"As long as there are sovereign nations possessing great power, war is inevitable."

"I am an adherent of the ideal of democracy, although I well know the weaknesses of the democratic form of government. Social equality and economic protection of the individual appeared to me always as the important communal aims of the state.Although I am a typical loner in daily life, my consciousness of belonging to the invisible community of those who strive for truth, beauty, and justice has preserved me from feeling isolated."

"There is separation of colored people from white people in the United States. That separation is not a disease of colored people. It is a disease of white people. I do not intend to be quiet about it."

"The position in which we are now is a very strange one which in general political life never happened. Namely, the thing that I refer to is this: To have security against atomic bombs and against the other biological weapons, we have to prevent war, for if we cannot prevent war every nation will use every means that is at their disposal; and in spite of all promises they make, they will do it. At the same time, so long as war is not prevented, all the governments of the nations have to prepare for war, and if you have to prepare for war, then you are in a state where you cannot abolish war. This is really the cornerstone of our situation. Now, I believe what we should try to bring about is the general conviction that the first thing you have to abolish is war at all costs, and every other point of view must be of secondary importance."

"The prestige of government has undoubtedly been lowered considerably by the prohibition law. For nothing is more destructive of respect for the government and the law of the land than passing laws which cannot be enforced. It is an open secret that the dangerous increase of crime in the United States is closely connected with this."

"My passionate sense of social justice and social responsibility has always contrasted oddly with my pronounced lack of need for direct contact with other human beings and human communities."

"I am strongly drawn to the simple life and am often oppressed by the feeling that I am engrossing an unnecessary amount of the labour of my fellow-men. I regard class differences as contrary to justice and, in the last resort, based on force. I also consider that plain living is good for everybody, physically and mentally."

"This topic brings me to that worst outcrop of the herd nature, the military system, which I abhor. That a man can take pleasure in marching in formation to the strains of a band is enough to make me despise him. He has only been given his big brain by mistake; a backbone was all he needed. This plague-spot of civilization ought to be abolished with all possible speed. Heroism by order, senseless violence, and all the pestilent nonsense that goes by the name of patriotism — how I hate them! War seems to me a mean, contemptible thing: I would rather be hacked in pieces than take part in such an abominable business."

"My passion for social justice has often brought me into conflict with people, as did my aversion to any obligation and dependence I do not regard as absolutely necessary. I always have a high regard for the individual and have an insuperable distaste for violence and clubmanship.All these motives made me into a passionate pacifist and anti-militarist. I am against any nationalism, even in the guise of mere patriotism. Privileges based on position and property have always seemed to me unjust and pernicious, as did any exaggerated personality cult."

"The release of atomic energy has not created a new problem. It has merely made more urgent the necessary solving of an existing one. One could say it has affected us quantitatively, not qualitatively."

"I gang my own gait and have never belonged to my country, my home, my friends, or even my immediate family, with my whole heart; in the face of all these ties I have never lost an obstinate sense of detachment, of the need for solitude — a feeling which increases with the years."