Albert Einstein

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"How does it happen that a properly endowed natural scientist comes to concern himself with epistemology? Is there not some more valuable work to be done in his specialty? That's what I hear many of my colleagues ask, and I sense it from many more. But I cannot share this sentiment. When I think about the ablest students whom I have encountered in my teaching — that is, those who distinguish themselves by their independence of judgment and not just their quick-wittedness — I can affirm that they had a vigorous interest in epistemology. They happily began discussions about the goals and methods of science, and they showed unequivocally, through tenacious defense of their views, that the subject seemed important to them. Concepts that have proven useful in ordering things easily achieve such authority over us that we forget their earthly origins and accept them as unalterable givens. [Begriffe, welche sich bei der Ordnung der Dinge als nützlich erwiesen haben, erlangen über uns leicht eine solche Autorität, dass wir ihres irdischen Ursprungs vergessen und sie als unabänderliche Gegebenheiten hinnehmen.] Thus they might come to be stamped as "necessities of thought," "a priori givens," etc. The path of scientific progress is often made impassable for a long time by such errors. [Der Weg des wissenschaftlichen Fortschritts wird durch solche Irrtümer oft für längere Zeit ungangbar gemacht.] Therefore it is by no means an idle game if we become practiced in analysing long-held commonplace concepts and showing the circumstances on which their justification and usefulness depend, and how they have grown up, individually, out of the givens of experience. Thus their excessive authority will be broken. They will be removed if they cannot be properly legitimated, corrected if their correlation with given things be far too superfluous, or replaced if a new system can be established that we prefer for whatever reason."

- Albert Einstein

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"In the temple of science are many mansions, and various indeed are they that dwell therein and the motives that have led them thither. Many take to science out of a joyful sense of superior intellectual power; science is their own special sport to which they look for vivid experience and the satisfaction of ambition; many others are to be found in the temple who have offered the products of their brains on this altar for purely utilitarian purposes. Were an angel of the Lord to come and drive all the people belonging to these two categories out of the temple, the assemblage would be seriously depleted, but there would still be some men, of both present and past times, left inside. Our Planck is one of them, and that is why we love him. I am quite aware that we have just now lightheartedly expelled in imagination many excellent men who are largely, perhaps chiefly, responsible for the buildings of the temple of science; and in many cases, our angel would find it a pretty ticklish job to decide. But of one thing I feel sure: if the types we have just expelled were the only types there were, the temple would never have come to be, any more than a forest can grow which consists of nothing but creepers. For these people any sphere of human activity will do if it comes to a point; whether they become engineers, officers, tradesmen, or scientists depends on circumstances. Now let us have another look at those who have found favor with the angel. Most of them are somewhat odd, uncommunicative, solitary fellows, really less like each other, in spite of these common characteristics, than the hosts of the rejected. What has brought them to the temple? That is a difficult question and no single answer will cover it."

- Albert Einstein

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"Common to all these types is the anthropomorphic character of the idea of God. Only exceptionally gifted individuals or especially noble communities rise essentially above this level; in these there is found a third level of religious experience, even if it is seldom found in a pure form. I will call it the cosmic religious sense. This is hard to make clear to those who do not experience it, since it does not involve an anthropomorphic idea of God; the individual feels the vanity of human desires and aims, and the nobility and marvelous order which are revealed in nature and in the world of thought. He feels the individual destiny as an imprisonment and seeks to experience the totality of existence as a unity full of significance. Indications of this cosmic religious sense can be found even on earlier levels of development—for example, in the Psalms of David and in the Prophets. The cosmic element is much stronger in Buddhism, as, in particular, Schopenhauer's magnificent essays have shown us. The religious geniuses of all times have been distinguished by this cosmic religious sense, which recognizes neither dogmas nor God made in man's image. Consequently there cannot be a church whose chief doctrines are based on the cosmic religious experience. It comes about, therefore, that we find precisely among the heretics of all ages men who were inspired by this highest religious experience; often they appeared to their contemporaries as atheists, but sometimes also as saints. Viewed from this angle, men like Democritus, Francis of Assisi, and Spinoza are near to one another."

- Albert Einstein

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"It is, therefore, quite natural that the churches have always fought against science and have persecuted its supporters. But, on the other hand, I assert that the cosmic religious experience is the strongest and noblest driving force behind scientific research. No one who does not appreciate the terrific exertions, and, above all, the devotion without which pioneer creations in scientific thought cannot come into being, can judge the strength of the feeling out of which alone such work, turned away as it is from immediate practical life, can grow. What a deep faith in the rationality of the structure of the world and what a longing to understand even a small glimpse of the reason revealed in the world there must have been in Kepler and Newton to enable them to unravel the mechanism of the heavens in long years of lonely work! Any one who only knows scientific research in its practical applications may easily come to a wrong interpretation of the state of mind of the men who, surrounded by skeptical contemporaries, have shown the way to kindred spirits scattered over all countries in all centuries. Only those who have dedicated their lives to similar ends can have a living conception of the inspiration which gave these men the power to remain loyal to their purpose in spite of countless failures. It is the cosmic religious sense which grants this power. A contemporary has rightly said that the only deeply religious people of our largely materialistic age are the earnest men of research."

- Albert Einstein

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"I just want to explain what I mean when I say that we should try to hold on to physical reality. We are ... all aware of the situation regarding what will turn out to be the basic foundational concepts in physics: the point-mass or the particle is surely not among them; the field, in the Faraday-Maxwell sense, might be, but not with certainty. But that which we conceive as existing ("real") should somehow be localized in time and space. That is, the real in one part of space, A, should (in theory) somehow "exist" independently of that which is thought of as real in another part of space, B. If a physical system stretches over A and B, then what is present in B should somehow have an existence independent of what is present in A. What is actually present in B should thus not depend the type of measurement carried out in the part of space A; it should also be independent of whether or not a measurement is made in A. If one adheres to this program, then one can hardly view the quantum-theoretical description as a complete representation of the physically real. If one attempts, nevertheless, so to view it, then one must assume that the physically real in B undergoes a sudden change because of a measurement in A. My physical instincts bristle at that suggestion. However, if one renounces the assumption that what is present in different parts of space has an independent, real existence, then I don't see at all what physics is supposed to be describing. For what is thought to be a "system" is after all, just conventional, and I do not see how one is supposed to divide up the world objectively so that one can make statements about parts."

- Albert Einstein

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"The reciprocal relationship of epistemology and science is of noteworthy kind. They are dependent on each other. Epistemology without contact with science becomes an empty scheme. Science without epistemology is — insofar as it is thinkable at all — primitive and muddled. However, no sooner has the epistemologist, who is seeking a clear system, fought his way through to such a system, than he is inclined to interpret the thought-content of science in the sense of his system and to reject whatever does not fit into his system. The scientist, however, cannot afford to carry his striving for epistemological systematic that far. He accepts gratefully the epistemological conceptual analysis; but the external conditions, which are set for him by the facts of experience, do not permit him to let himself be too much restricted in the construction of his conceptual world by the adherence to an epistemological system. He therefore must appear to the systematic epistemologist as a type of unscrupulous opportunist: he appears as realist insofar as he seeks to describe a world independent of the acts of perception; as idealist insofar as he looks upon the concepts and theories as free inventions of the human spirit (not logically derivable from what is empirically given); as positivist insofar as he considers his concepts and theories justified only to the extent to which they furnish a logical representation of relations among sensory experiences. He may even appear as Platonist or Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensible and effective tool of his research."

- Albert Einstein

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"Even though the realms of religion and science in themselves are clearly marked off from each other, nevertheless there exist between the two strong reciprocal relationships and dependencies. Though religion may be that which determines the goal, it has, nevertheless, learned from science, in the broadest sense, what means will contribute to the attainment of the goals it has set up. But science can only be created by those who are thoroughly imbued with the aspiration toward truth and understanding. This source of feeling, however, springs from the sphere of religion. To this there also belongs the faith in the possibility that the regulations valid for the world of existence are rational, that is, comprehensible to reason. I cannot conceive of a genuine scientist without that profound faith. The situation may be expressed by an image: science without religion is lame, religion without science is blind. Though I have asserted above that in truth a legitimate conflict between religion and science cannot exist, I must nevertheless qualify this assertion once again on an essential point, with reference to the actual content of historical religions. This qualification has to do with the concept of God. During the youthful period of mankind's spiritual evolution human fantasy created gods in man's own image, who, by the operations of their will were supposed to determine, or at any rate to influence, the phenomenal world. Man sought to alter the disposition of these gods in his own favor by means of magic and prayer. The idea of God in the religions taught at present is a sublimation of that old concept of the gods. Its anthropomorphic character is shown, for instance, by the fact that men appeal to the Divine Being in prayers and plead for the fulfillment of their wishes."

- Albert Einstein

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"If it is one of the goals of religion to liberate mankind as far as possible from the bondage of egocentric cravings, desires, and fears, scientific reasoning can aid religion in yet another sense. Although it is true that it is the goal of science to discover rules which permit the association and foretelling of facts, this is not its only aim. It also seeks to reduce the connections discovered to the smallest possible number of mutually independent conceptual elements. It is in this striving after the rational unification of the manifold that it encounters its greatest successes, even though it is precisely this attempt which causes it to run the greatest risk of falling a prey to illusions. But whoever has undergone the intense experience of successful advances made in this domain is moved by profound reverence for the rationality made manifest in existence. By way of the understanding he achieves a far-reaching emancipation from the shackles of personal hopes and desires, and thereby attains that humble attitude of mind toward the grandeur of reason incarnate in existence, and which, in its profoundest depths, is inaccessible to man. This attitude, however, appears to me to be religious, in the highest sense of the word. And so it seems to me that science not only purifies the religious impulse of the dross of its anthropomorphism but also contributes to a religious spiritualization of our understanding of life. The further the spiritual evolution of mankind advances, the more certain it seems to me that the path to genuine religiosity does not lie through the fear of life, and the fear of death, and blind faith, but through striving after rational knowledge."

- Albert Einstein

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"Even when I was a fairly precocious young man the nothingness of the hopes and strivings which chases most men restlessly through life came to my consciousness with considerable vitality. Moreover, I soon discovered the cruelty of that chase, which in those years was much more carefully covered up by hypocrisy and glittering words than is the case today. By the mere existence of his stomach everyone was condemned to participate in that chase. Moreover, it was possible to satisfy the stomach by such participation, but not man in so far as he is a thinking and feeling being. As the first way out there was religion, which is implanted into every child by way of the traditional education-machine. Thus I came—despite the fact that I was the son of entirely irreligious (Jewish) parents—to a deep religiosity, which, however, found an abrupt ending at the age of 12. Through the reading of popular scientific books I soon reached the conviction that much in the stories of the Bible could not be true. The consequence was a positively fanatic [orgy of] freethinking coupled with the impression that youth is intentionally being deceived by the state through lies; it was a crushing impression. Suspicion against every kind of authority grew out of this experience, a skeptical attitude towards the convictions which were alive in any specific social environment—an attitude which has never again left me, even though later on, because of a better insight into the causal connections, it lost some of its original poignancy."

- Albert Einstein

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"A wonder of such nature I experienced as a child of 4 or 5 years, when my father showed me a compass. That this needle behaved in such a determined way did not at all fit into the nature of events, which could find a place in the unconscious world of concepts (effect connected with direct "touch"). I can still remember—or at least believe I can remember—that this experience made a deep and lasting impression upon me. Something deeply hidden had to be behind things. What man sees before him from infancy causes no reaction of this kind; he is not surprised over the falling of bodies, concerning wind and rain, nor concerning the moon or about the fact that the moon does not fall down, nor concerning the differences between living and non-living matter. At the age of 12 I experienced a second wonder of a totally different nature: in a little book dealing with Euclidean plane geometry, which came into my hands at the beginning of a schoolyear. Here were assertions, as for example the intersection of the three altitudes of a triangle in one point, which—though by no means evident—could nevertheless be proved with such certainty that any doubt appeared to be out of the question. This lucidity and certainty made an indescribable impression upon me. That the axioms had to be accepted unproved did not disturb me. In any case it was quite sufficient for me if I could peg proofs upon propositions the validity of which did not seem to me to be dubious."

- Albert Einstein

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"I now imagine a quantum theoretician who may even admit that the quantum-theoretical description refers to ensembles of systems and not to individual systems, but who, nevertheless, clings to the idea that the type of description of the statistical quantum theory will, in its essential features, be retained in the future. He may argue as follows: True, I admit that the quantum-theoretical description is an incomplete description of the individual system. I even admit that a complete theoretical description is, in principle, thinkable. But I consider it proven that the search for such a complete description would be aimless. For the lawfulness of nature is thus constituted that the laws can be completely and suitably formulated within the framework of our incomplete description. To this I can only reply as follows: Your point of view — taken as theoretical possibility — is incontestable. For me, however, the expectation that the adequate formulation of the universal laws involves the use of all conceptual elements which are necessary for a complete description, is more natural. It is furthermore not at all surprising that, by using an incomplete description, (in the main) only statistical statements can be obtained out of such description. If it should be possible to move forward to a complete description, it is likely that the laws would represent relations among all the conceptual elements of this description which, per se, have nothing to do with statistics."

- Albert Einstein

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"The theory of relativity is a beautiful example of the basic character of the modern development of theory. That is to say, the hypotheses from which one starts become ever more abstract and more remote from experience. But in return one comes closer to the preeminent goal of science, that of encompassing a maximum of empirical contents through logical deduction with a minimum of hypotheses or axioms. The intellectual path from the axioms to the empirical contents or to the testable consequences becomes, thereby, ever longer and more subtle. The theoretician is forced, ever more, to allow himself to be directed by purely mathematical, formal points of view in the search for theories, because the physical experience of the experimenter is not capable of leading us up to the regions of the highest abstraction. Tentative deduction takes the place of the predominantly inductive methods appropriate to the youthful state of science. Such a theoretical structure must be quite thoroughly elaborated in order for it to lead to consequences that can be compared with experience. It is certainly the case that here, as well, the empirical fact is the all-powerful judge. But its judgment can be handed down only on the basis of great and difficult intellectual effort that first bridges the wide space between the axioms and the testable consequences. The theorist must accomplish this Herculean task with the clear understanding that this effort may only be destined to prepare the way for a death sentence for his theory. One should not reproach the theorist who undertakes such a task by calling him a fantast; instead, one must allow him his fantasizing, since for him there is no other way to his goal whatsoever. Indeed, it is no planless fantasizing, but rather a search for the logically simplest possibilities and their consequences."

- Albert Einstein

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"We all know, from what we experience with and within ourselves, that our conscious acts spring from our desires and our fears. Intuition tells us that that is true also of our fellows and of the higher animals. We all try to escape pain and death, while we seek what is pleasant. We are all ruled in what we do by impulses; and these impulses are so organized that our actions in general serve for our self preservation and that of the race. Hunger, love, pain, fear are some of those inner forces which rule the individual’s instinct for self preservation. At the same time, as social beings, we are moved in the relations with our fellow beings by such feelings as sympathy, pride, hate, need for power, pity, and so on. All these primary impulses, not easily described in words, are the springs of man’s actions. All such action would cease if those powerful elemental forces were to cease stirring within us. Though our conduct seems so very different from that of the higher animals, the primary instincts are much alike in them and in us. The most evident difference springs from the important part which is played in man by a relatively strong power of imagination and by the capacity to think, aided as it is by language and other symbolical devices. Thought is the organizing factor in man, intersected between the causal primary instincts and the resulting actions. In that way imagination and intelligence enter into our existence in the part of servants of the primary instincts. But their intervention makes our acts to serve ever less merely the immediate claims of our instincts."

- Albert Einstein

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"Professor Smith has kindly submitted his book to me before publication. After reading it thoroughly and with intense interest I am glad to comply with his request to give him my impression. The work is a broadly conceived attempt to portray man's fear-induced animistic and mythic ideas with all their far-flung transformations and interrelations. It relates the impact of these phantasmagorias on human destiny and the causal relationships by which they have become crystallized into organized religion. This is a biologist speaking, whose scientific training has disciplined him in a grim objectivity rarely found in the pure historian. This objectivity has not, however, hindered him from emphasizing the boundless suffering which, in its end results, this mythic thought has brought upon man. Professor Smith envisages as a redeeming force, training in objective observation of all that is available for immediate perception and in the interpretation of facts without preconceived ideas. In his view, only if every individual strives for truth can humanity attain a happier future; the atavisms in each of us that stand in the way of a friendlier destiny can only thus be rendered ineffective. His historical picture closes with the end of the nineteenth century, and with good reason. By that time it seemed that the influence of these mythic, authoritatively anchored forces which can be denoted as religious, had been reduced to a tolerable level in spite of all the persisting inertia and hypocrisy. Even then, a new branch of mythic thought had already grown strong, one not religious in nature but no less perilous to mankind — exaggerated nationalism. Half a century has shown that this new adversary is so strong that it places in question man's very survival. It is too early for the present-day historian to write about this problem, but it is to be hoped that one will survive who can undertake the task at a later date."

- Albert Einstein

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"The boys, who cannot grow up to adult human nature, are beating the prophets of the ancient race — Marx, Freud, Einstein — who have been tearing at our social, personal and intellectual roots, tearing with an objectivity which to the healthy animal seems morbid, depriving everything, as it seems, of the warmth of natural feeling. What traditional retort have the schoolboys but a kick in the pants? ... To our generation Einstein has been made to become a double symbol — a symbol of the mind travelling in the cold regions of space, and a symbol of the brave and generous outcast, pure in heart and cheerful of spirit. Himself a schoolboy, too, but the other kind — with ruffled hair, soft hands and a violin. See him as he squats on Cromer beach doing sums, Charlie Chaplin with the brow of Shakespeare... So it is not an accident that the Nazi lads vent a particular fury against him. He does truly stand for what they most dislike, the opposite of the blond beast — intellectualist, individualist, supernationalist, pacifist, inky, plump... How should they know the glory of the free-ranging intellect and soft objective sympathy to whom money and violence, drink and blood and pomp, mean absolutely nothing? Yet Albert and the blond beast make up the world between them. If either cast the other out, life is diminished in its force. When the barbarians destroy the ancient race as witches, when they refuse to scale heaven on broomsticks, they may be dooming themselves to sink back into the clods which bore them."

- Albert Einstein

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"I tried to persuade him to give up his determinism, which amounted to the view that the world was a four-dimensional Parmenidean block universe in which change was a human illusion, or very nearly so. (He agreed that this had been his view, and while discussing it I called him "Parmenides".) I argued that if men, or other organisms, could experience change and genuine succession in time, then this was real. It could not be explained away by a theory of the successive rising into our consciousness of time slices which in some sense coexist; for this kind of "rising into consciousness" would have precisely the same character as that succession of changes which the theory tries to explain away. ... I tried to present to Einstein-Parmenides as strongly as I could my conviction that a clear stand must be made against any idealistic view of time. And I also tried to show that, though the idealistic view was compatible with both determinism and indeterminism, a clear stand should be made in favor of an "open" universe — one in which the future was in no sense contained in the past or the present, even though they do impose severe restrictions on it. I argued that we should not be swayed by our theories to give up realism (for which the strongest arguments were based on common sense), though I think that he was ready to admit, as I was, that we might be forced one day to give it up if very powerful arguments (of Gödel's type, say) were to be brought against it. I therefore argued that with regard to time, and also to indeterminism (that is, the incompleteness of physics), the situation was precisely similar to the situation with regard to realism. Appealing to his own way of expressing things in theological terms, I said: if God had wanted to put everything into the world from the beginning, He would have created a universe without change, without organisms and evolution, and without man and man's experience of change. But He seems to have thought that a live universe with events unexpected even by Himself would be more interesting than a dead one."

- Albert Einstein

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"In considering the structure of the universe... Einstein assumed... the irregularities in the distribution of matter can be neglected [i.e., the universe is homogeneous]. ...he noted that the largest velocities then assigned to the stars and nebulae were very small compared with the velocity of light. In 1917... the immense red-shifts of the farther nebulae were unknown. Einstein, therefore, considered a model of the universe in which matter was distributed in a uniform and continuous manner, the relative motion of the various parts being negligible [i.e., a static universe]. Following Seeliger, he found it impossible to regard the system as filling the whole of [infinite] Euclidean space. Also he could not regard the universe as an island in infinite space. For, in applying a well-known theorem of Boltzmann relating the densities at various points of space in which a distribution of particles is moving at random, he showed that zero density at the boundary would necessitate zero density at all points inside. Thus it appeared to Einstein that the universe as a whole could be neither infinite nor have a finite boundary. Hence space as a whole could not be Euclidean. ...In the classical picture time and space are distinct, time being infinite in duration and space Euclidean. In devising an alternative model Einstein retained this world-wide separation of time and space, despite the fusion of the two concepts in General Relativity, but he assumed that space as a whole was of the type known as spherical."

- Albert Einstein

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"We may... be treating merely as physical variations effects which are really due to changes in the curvature of our space; whether, in fact, some or all of those causes which we term physical may not be due to the geometrical construction of our space. There are three kinds of variation in the curvature of our space which we ought to consider as within the range of possibility. (i) Our space is perhaps really possessed of a curvature varying from point to point, which we fail to appreciate because we are acquainted with only a small portion of space, or because we disguise its small variations under changes in our physical condition which we do not connect with our change of position. The mind that could recognise this varying curvature might be assumed to know the absolute position of a point. For such a mind the postulate of the relativity of position would cease to have a meaning. It does not seem so hard to conceive such a state of mind as the late Professor Clerk-Maxwell would have had us believe. It would be one capable of distinguishing those so-called physical changes which are really geometrical or due to a change of position in space. (ii) Our space may be really same (of equal curvature), but its degree of curvature may change as a whole with the time. In this way our geometry based on the sameness of space would still hold good for all parts of space, but the change of curvature might produce in space a succession of apparent physical changes. (iii) We may conceive our space to have everywhere a nearly uniform curvature, but that slight variations of the curvature may occur from point to point, and themselves vary with the time. These variations of the curvature with the time may produce effects which we not unnaturally attribute to physical causes independent of the geometry of our space. We might even go so far as to assign to this variation of the curvature of space 'what really happens in that phenomenon which we term the motion of matter.'"

- Theory of relativity

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"The modern world began on 29 May 1919 when photographs of a solar eclipse, taken on the island of Principe off West Africa and at Sobral in Brazil, confirmed the truth about a new theory of the universe. It had been apparent for half a century that the Newtonian cosmology, based upon the straight lines of Euclidean geometry, and Galileo's notions of absolute time, was in need of serious modification. It had stood for more than two hundred years. It was the framework within which the European Enlightenment, the Industrial Revolution, the vast expansion of human knowledge, freedom, and prosperity which had characterized the nineteenth century, had taken place. But increasingly powerful telescopes were revealing anomalies. In particular, the motions of the planet Mercury deviated by forty-three seconds of an arc a century from its predictable behavior under Newtonian laws of physics. Why? In 1905, a twenty-six-year old German Jew, Albert Einstein, then working in the Swiss patent office in Berne, had published a paper, 'On the electrodynamics of moving bodies,' which became known as the Special Theory of Relativity. Einstein's observations on the way in which, in certain circumstances, lengths appeared to contract and clocks to slow down, are analogous to the effects of perspective in painting. In fact the discovery that space and time are relative rather than absolute terms of measurement is comparable, in its effect on our perception of the world, to the first use of perspective in art, which occurred in Greece in the two decades c.500-480 BC."

- Theory of relativity

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"After the doctor figured out the special idea, he started thinking about weight. Things with weight pull on each other. Earth pulls things down toward it, which is why you can’t jump to space. Earth also pulls on the moon, keeping it near us, and the sun pulls on Earth in the same way. It turns out that light gets pulled by weight, too. (People weren’t sure about this for a while, because it moves so fast that it only gets pulled a little.) Someone very careful might notice that this gives us a new problem: How can light turn? The numbers that explain how light moves also say that it can only go forward. It can’t change direction in empty space. That’s just what the numbers for light say—the same numbers that say it always moves a certain distance every second. If a light wave is pulled down, it has to turn to point down, since it can’t travel to the side. To turn, the bottom part of the wave has to go slower than the top part, since it’s going a shorter distance in the same time. But that can’t be right, because the numbers say that light can’t go faster or slower. We’re in trouble again. And, once again, the space doctor has an answer. The space doctor figured out that to explain how weight pulls things like light, we have to play around with time again. He showed that if time itself goes slower near heavy things, then the side of the light near the heavy thing won’t go as far every second. This lets the light turn toward the heavy thing. The doctor’s idea was that weight slows down time, and it explained how light could bend. But to figure out how much light bends, we need to look at the other part of the doctor’s big idea. To talk about that part, let’s forget about light and instead visit another world."

- Theory of relativity

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"This is the mathematical formulation of the theory of relativity. The metric properties of the four-dimensional continuum are described... by a certain number (ten, in fact) of quantities denoted by gαβ, and commonly called "potentials." The physical status of matter and energy, on the other hand, is described by ten other quantities, denoted by Tαβ, the set of which is called the "material tensor." This special tensor has been selected because it has the property which is mathematically expressed by saying that its divergence vanishes, which means that it represents something permanent. The fundamental fact of mechanics is the law of inertia, which can be expressed in its most simple form by saying that it requires the fundamental laws of nature to be differential equations of the second order. Thus the problem was to find a differential equation of the second order giving a relation between the metric tensor gαβ and the material tensor Tαβ. This is a purely mathematical problem, which can be solved without any reference to the physical meaning of the symbols. The simplest possible equation (or rather set of ten equations, because there are ten gs) of that kind that can be found was adopted by Einstein as the fundamental equation of his theory. It defines the space-time continuum, or the "field." The world-lines of material particles and light quanta are the geodesics in the four-dimensional continuum defined by the solutions gαβ of these field-equations. The equations of the geodesic thus are equivalent to the equations of motion of mechanics. When we come to solve the field-equations and substitute the solutions in the equations of motion, we find that in the first approximation, i.e. for small material velocities (small as compared with the velocity of light), these equations of motion are the same as those resulting from Newton's theory of gravitation. The distinction between gravitation and inertia has disappeared; the gravitational action between two bodies follows from the same equations, and is the same thing, as the inertia of one body. A body, when not subjected to an extraneous force (i.e. a force other than gravitation), describes a geodesic in the continuum, just as it described a geodesic, or straight line, in the absolute space of Newton under the influence of inertia alone. The field-equations and the equations of the geodesic together contain the whole science of mechanics, including gravitation."

- Theory of relativity

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"Two points should be specially emphasized in connection with the general theory of relativity. First, it is a purely physical theory, invented to explain empirical physical facts, especially the identity of gravitational and inertial mass, and to coordinate and harmonize different chapters of physical theory, especially mechanics and electromagnetic theory. It has nothing metaphysical about it. Its importance from a metaphysical or philosophical point of view is that it aids us to distinguish in the observed phenomena what is absolute, or due to the reality behind the phenomena, from what is relative, i.e. due to the observer. Second, it is a pure generalization, or abstraction, like Newton's system of mechanics and law of gravitation. It contains no hypothesis, as contrasted with the atomic theory or the theory of quanta, which are based on hypothesis. It may be considered as the logical sequence and completion of Newton's Principia. The science of mechanics was founded by Archimedes, who had a clear conception of the relativity of motion, and may be called the first relativist. Galileo, who was inspired by the reading of the works of Archimedes, took the subject up where his great predecessor had left it. His fundamental discovery is the law of inertia, which is the backbone of Newton's classical system of mechanics, and retains the same central position in Einstein's relativistic system. Thus one continuous line of thought can be traced through the development of our insight into the mechanical processes of nature... characterized by the sequence... Archimedes, Galileo, Newton, Einstein."

- Theory of relativity

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"With the new views advocated by Riemann... the texture, structure or geometry of space is defined by the metrical field, itself produced by the distribution of matter. Any non-homogeneous distribution of matter would then entail a variable structure of geometry for space from place to place. ... Riemann's exceedingly speculative ideas on the subject of the metrical field were practically ignored in his day, save by the English mathematician Clifford, who translated Riemann's works, prefacing them to his own discovery of the non-Euclidean Clifford space. Clifford realised the potential importance of the new ideas and suggested that matter itself might be accounted for in terms of these local variations of the non-Euclidean space, thus inverting in a certain sense Riemann's ideas. But in Clifford's day this belief was mathematically untenable. Furthermore, the physical exploration of space seemed to yield unvarying Euclideanism. ...it was reserved for the theoretical investigator Einstein, by a stupendous effort of rational thought, based on a few flimsy empirical clues, to unravel the mystery and to lead Riemann's ideas to victory. (In all fairness to Einstein... he does not appear to have been influenced directly by Riemann.) Nor were Clifford's hopes disappointed, for the varying non-Euclideanism of the continuum was to reveal the mysterious secret of gravitation, and perhaps also of matter, motion, and electricity. ... Einstein had been led to recognize that space of itself was not fundamental. The fundamental continuum whose non-Euclideanism was fundamental was... one of Space-Time... possessing a four-dimensional metrical field governed by the matter distribution. Einstein accordingly applied Riemann's ideas to space-time instead of to space... He discovered that the moment we substitute space-time for space (and not otherwise), and assume that free bodies and rays of light follow geodesics no longer in space but in space-time, the long-sought-for local variations in geometry become apparent. They are all around us, in our immediate vicinity... We had called their effects gravitational effects... never suspecting that they were the result of those very local variations in the geometry for which our search had been in vain....the theory of relativity is the theory of the space-time metrical field."

- Theory of relativity

0 likesTheoretical physicsAlbert Einstein
"Einstein's definition... does not differ in spirit from the definitions in classical science; its sole advantage is that it entails a minimum of assumptions, and is susceptible of being realised in a concrete way permitting a high degree of accuracy in our measurements. Einstein's definition, is then, as follows: If we consider a ray of light passing through a Galilean frame, its velocity in the frame will be the same regardless of the relative motion of the luminous source and frame, and regardless of the direction of the ray. ...when it was found that contrary to the anticipations of classical science not the slightest trace of anisotropy could be detected even by ultra-precise experiment, the objections which classical science may might have presented... lost all force. ...ether drift appeared to exert no influence one way or the other. ... Isotropy signifies that the velocity of light is the same in all directions. And how can we ascertain the equality of a velocity in all directions when we do not yet know how to measure time? Experimenters solved the difficulty by appealing to the observation of coincidences. ... Waves of light leaving the centre of a sphere simultaneously are found to return to the centre also in concidence, after having suffered a reflection against a highly polished inner surface of the sphere. ...the light waves have thus covered equal distances in the same time; whence we conclude that their speed is the same in all directions. Inasmuch as this experiment has been performed, yielding the results we have just described, even though the ether drift caused by the earth's motion should have varied in direction and intensity, the isotropy of space to luminous propogations was thus established. (The experiment described constitutes but a schematic form of Michelson's.) It is to be noted that in this experiment the observation of coincidences is alone appealed to (even spatial measurements can be eliminated). This is because in Michelson's experiment it is not necessary to consider a sphere. The two arms of the apparatus may be of different lengths; and all that is observed is the continued coincidence of the interference-bands with markings on the instrument. When it is realised that coincidences constitute the most exact form of observation, we understand why it is that Einstein's definition is justified"

- Theory of relativity

0 likesTheoretical physicsAlbert Einstein
"The most precise experiments have proved the correctness of the Einsteinian laws of mechanics and...Bucherer's experiment proving the increase in mass of an electron in rapid motion is a case in point. Very important differences distinguish the theory of Einstein from that of Lorentz. Lorentz also had deduced from his theory that the mass of the electron should increase and grow infinite when its speed neared that of light; but the speed in question was the speed of the electron through the stagnant ether; whereas in Einstein's theory it is merely the speed with respect to the observer. According to Lorentz, the increase in mass of the moving electron was due to its deformation or Fitzgerald contraction. The contraction modified the lay of the electromagnetic field round the electron; and it was from this modification that the increase in mass observed by Bucherer was assumed to arise. In Einstein's theory, however, the increase in mass is absolutely general and need not be ascribed to the electromagnetic field of the electron in motion. An ordinary unelectrified lump of matter like a grain of sand would have increased in mass in exactly the same proportion; and no knowledge of the microscopic constitution of matter is necessary in order to predict these effects, which result directly from the space and time transformations themselves. Furthermore, the fact that this increase in mass of matter in motion is now due to relative motion and not to motion through the stagnant ether, as in Lorentz's theory, changes the entire outlook considerably. According to Lorentz, the electron really increased in mass, since its motion through the ether remained a reality. According to Einstein, the electron increases in mass only in so far as it is in relative motion with respect to the observer. Were the observer to be attached to the flying electron no increase in mass would exist; it would be the electron left behind which would now appear to have suffered the increase. Thus mass follows distance, duration and electromagnetic field in being a relative and having no definite magnitude of itself and being essentially dependent on the conditions of observation. Owing to the general validity of the Lorentz-Einstein transformations, it becomes permissible to apply them to all manner of phenomena.. ...temperature, pressure and many other physical magnitudes turned out to be relatives. ...entropy, electric charge and the velocity of light in vacuo were absolutes transcending the observer's motion. ...a number of other entities are found to be absolutes, the most important of which is that abstract mathematical quantity called the Einsteinian interval, which plays so important a part in the fabric of the new objective world of science, the world of four-dimensional space-time."

- Theory of relativity

0 likesTheoretical physicsAlbert Einstein
"In contemplating the papers Einstein wrote in 1905, I often find myself wondering which of them is the most beautiful. It is a little like asking which of Beethoven’s symphonies is the most beautiful. My favorite, after years of studying them, is Einstein’s paper on the blackbody radiation. [...] Part of being a great scientist is to know—have an instinct for—the questions not to ask. Einstein did not try to derive the Wien law. He simply accepted it as an empirical fact and asked what it meant. By a virtuoso bit of reasoning involving statistical mechanics (of which he was a master, having independently invented the subject over a three-year period beginning in 1902), he was able to show that the statistical mechanics of the radiation in the cavity was mathematically the same as that of a dilute gas of particles. As far as Einstein was concerned, this meant that this radiation was a dilute gas of particles—light quanta. But, and this was also characteristic, he took the argument a step further. He realized that if the energetic light quanta were to bombard, say, a metal surface, they would give up their energies in lump sums and thereby liberate electrons from the surface in a predictable way, something that is called the photoelectric effect. [...] In the first place, not many physicists were even interested in the subject of blackbody radiation for at least another decade. Kuhn has done a study that shows that until 1914 less than twenty authors a year published papers on the subject; in most years there were less than ten. Planck, who was interested, decided that Einstein’s paper was simply wrong."

- Photoelectric effect

0 likesQuantum mechanicsAlbert Einstein