University Of Cambridge Faculty

"The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation."

"If we are honest — and scientists have to be — we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can't for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as why God allows so much misery and injustice, the exploitation of the poor by the rich and all the other horrors He might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards — in heaven if not on earth — all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins."

"One possibility in this direction is to regard, classically, an electron as the end of a single Faraday line of force. The electric field in this picture from discrete Faraday lines of force, which are to be treated as physical things, like strings. One has then to develop a dynamics for such a string like structure, and quantize it.... In such a theory a bare electron would be inconceivable, since one cannot imagine the end of a piece of string without having the string."

"The latest and most successful creation of theoretical physics, namely Quantum Mechanics, is fundamentally different in its principles from the two programmes which we will briefly call Newton's and Maxwell's. For the quantities that appear in its laws make no claim to describe Physical Reality itself, but only the probabilities for the appearances of a particular physical reality on which our attention is fixed. Dirac, to whom, in my opinion, we owe the most logically perfect presentation of this theory, rightly points out that it appears, for example, to be by no means easy to give a theoretical description of a photon that shall contain within it the reasons that determine whether or not the photon will pass a polarizator set obliquely in its path."

"I have trouble with Dirac. This balancing on the dizzying path between genius and madness is awful."

"Regardless of the prophetic value of Dirac’s description [on interference] his was probably the first discussion... including a coherent beam of light. In other words, Dirac wrote the first chapter in laser optics."

"Dirac was the strangest man who ever visited my institute. […] During one of Dirac’s visits I asked him what he was doing. He replied that he was trying to take the square-root of a matrix, and I thought to myself what a strange thing for such a brilliant man to be doing. Not long afterwards the proof sheets of his article on the equation arrived, and I saw he had not even told me that he had been trying to take the square root of the unit matrix!"

"Perhaps the most distinguished of 'why botherers has been Dirac (1963 Sci. American 208 May 45). He divided the difficulties of quantum mechanics into two classes, those of the first class and those of the second. The second-class difficulties were essentially the infinities of relativistic quantum field theory. Dirac was very disturbed by these, and was not impressed by the 'renormalisation' procedures by which they are circumvented. Dirac tried hard to eliminate these second-class difficulties, and urged others to do likewise. The first-class difficulties concerned the role of the 'observer', 'measurement', and so on. Dirac thought that these problems were not ripe for solution, and should be left for later. He expected developments in the theory which would make these problems look quite different. It would be a waste of effort to worry overmuch about them now, especially since we get along very well in practice without solving them."

"Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future. A good many people are working on the mathematical basis of quantum theory, trying to understand the theory better and to make it more powerful and more beautiful. If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them."

"It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better."

"It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory."

"{\int _{-\infty }^{\infty }{\delta \left({x}\right){d{x}}}}=1 \delta \left({x}\right)=0 \text{ for } x\not= 0"

"... people have tried to establish analogies with systems in classical mechanics, such as vibrating strings or membranes... Such analogies have led to the name 'Wave Mechanics' being sometimes given to quantum mechanics. It is important to remember, however, that the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation. The analogies are thus liable to be misleading."

"The nature of the relationships which the superposition principle requires to exist between the states of any system is of a kind that cannot be explained in terms of familiar physical concepts. One cannot in the classical sense picture a system being partly in each of two states and see the equivalence of this to the system being completely in some other state. There is an entirely new idea involved, to which one must get accustomed and in terms of which one must proceed to build up an exact mathematical theory, without having any detailed classical picture."

"... we cannot observe a small system with that amount of detail which classical theory supposes. The limitation in the power of observation puts a limitation on the number of data that can be assigned to a state... A state of a system may be defined as an undisturbed motion that is restricted by as many conditions or data as are theoretically possible without mutual interference or contradiction."

"The reader.. may argue that a very strange idea has been introduced — the possibility of a photon being partly in each of two states of polarization, or partly in each of two separate beams — but even with the help of this strange idea no satisfying picture of the fundamental single-photon processes has been given... it may be remarked that the main object of physical science is not the provision of pictures, but is the formulation of laws governing phenomena and the application of these laws to the discovery of new phenomena. If a picture exists, so much the better; but whether a picture exists or not is a matter of only secondary importance. In the case of atomic phenomena no picture can be expected to exist in the usual sense of the word 'picture', by which is meant a model functioning essentially on classical lines. One may, however, extend the meaning of the word 'picture' to include any way of looking at the fundamental laws which makes their self-consistency obvious. With this extension, one may gradually acquire a picture of atomic phenomena by becoming familiar with the laws of the quantum theory."

"We may define an object to be big when the disturbance accompanying our observation of it may be neglected, and small when the disturbance cannot be neglected... In order to give an absolute meaning to size, such as is required for any theory of the ultimate structure of matter, we have to assume that there is a limit to the fineness of our powers of observation and the smallness of the accompanying disturbance... If the object under observation is such that the unavoidable limiting disturbance is negligible, then the object is big in the absolute sense and we may apply classical mechanics to it. If, on the other hand, the limiting disturbance is not negligible, then the object is small in the absolute sense and we require a new theory for dealing with it."

"Classical mechanics has been developed continuously from the time of Newton and applied to an ever-widening range of dynamical systems, including the electromagnetic field in interaction with matter. The underlying ideas and the laws governing their application form a simple and elegant scheme, which one would be inclined to think could not be seriously modified without having all its attractive features spout. Nevertheless it has been found possible to set up a new scheme, called quantum mechanics, which is more suitable for the description of phenomena on the atomic scale and which is in some respects more elegant and satisfying than the classical scheme. This possibility is due to the changes which the new scheme involves being of a very profound character and not clashing with the features of the classical theory that make it so attractive, as a result of which all these features can be incorporated in the new scheme."

"I have the best of reasons for being an admirer of Werner Heisenberg. He and I were young research students at the same time, about the same age, working on the same problem. Heisenberg succeeded where I failed. There was a large mass of spectroscopic data accumulated at that time and Heisenberg found out the proper way of handling it. In doing so he started the golden age in theoretical physics, and for a few years after that it was easy for any second rate student to do first rate work."

"If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics led me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress."

"I was taught at school never to start a sentence without knowing the end of it."

"The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible."

"When I was a young man, Dirac was my hero. He made a breakthrough, a new method of doing physics. He had the courage to simply guess at the form of an equation, the equation we now call the Dirac equation, and to try to interpret it afterwards. Maxwell in his day got his equations, but only in an enormous mass of 'gear wheels' and so forth."

"In the fight between you and the world, back the world."

"Dirac’s relationship with quantum electrodynamics was not an easy one. On the one hand, the theory owes to him much more than to anybody else, especially if one considers the years crucial for its emergence, the late 1920s and early 1930s, when practically all its main concepts, except for that of renormalization, were developed. After this period Dirac also wrote a number of important papers, specifically, on indefinite metrics and quantum dynamics with constraints. On the other hand, since the early 1930s he was an active critic of the theory and tried to develop alternative schemes. He did not become satisfied with the later method of renormalization and regarded it as a mathematical trick rather than a fundamental solution, and died unreconciled with what, to a large extent, was his own brainchild. …"

"Dirac has done more than anyone this century, with the exception of Einstein, to advance physics and change our picture of the universe. He is surely worthy of the memorial in Westminster Abbey. It is just a scandal that it has taken so long."

"Dirac, in his first paper, in contrast to what his “hole”-theory implied, had identified the positively charged particle corresponding to the electron also with the proton. However, after Weyl had pointed out that Dirac’s hole theory led to equal masses, he changed his mind and gave the new particle the same mass as the electron."

"Let me backtrack... to the 1920s when quantum mechanics was created. ...[O]ne of the things that the originators of quantum mechanics... were very unhappy about was that quantum mechanics was not compatible with the special theory of relativity. ...Attempts were made to create a theory of the electron that is consistent with relativity, and one person made such a theory, but it was inconsistent with the electron spin. Another person made a theory that was consistent with electron spin, but not consistent with relativity. Until finally... a then young man... Paul Dirac created the theory of an equation that correctly describes the electron, and is relativistic, and also includes the description of spin... [T]hat was the beginning of the marriage that would take place between quantum mechanics and relativity. ...He originally noticed that the equation had too many solutions... He thought the negatively charged solutions would be electrons and the positive charge solutions would be s... He realized that this made no sense and the two things had to have the same , and finally... realized that he was... predicting [the positively charged electron,] the , just shortly before the positron was... independently and serendipitously discovered."

"Here we find a man with an almost miraculous apprehension of the structure of the physical world, coupled with gentle incomprehension of that less logical, messier world, the world of other people."

"Before World War II there had been considerable theoretical effort directed towards the question of the self-energy of the electron. However, because of the war, interest had remained dormant. Now, the stimulus of results of Lamb and Retherford the latent interest developed into a major attack by theoretical physicists, and within a few years the problem was solved to the satisfaction of nearly everyone. (To the end of his life, however, Dirac maintained that any theory involving the subtraction of infinities was ugly, unsatisfactory and surely incomplete.)"

"The attitude to sexual love in the 'pop' song is so ugly and mechanical as to seem schizoid, and psychopathological. Exposed as they are to such powerful cultural statements, young people are being encouraged to forfeit genuine commitment in love in favour of depersonalised sexual activity, with an undercurrent of violence, and to take false solutions in which they must deny their deepest needs, by hate."

"I think that it's important for scientists to explain their work, particularly in cosmology. This now answers many questions once asked of religion."

"Evolution has ensured that our brains just aren't equipped to visualise 11 dimensions directly. However, from a purely mathematical point of view it's just as easy to think in 11 dimensions, as it is to think in three or four."

"I'm sorry to disappoint science fiction fans, but if information is preserved, there is no possibility of using black holes to travel to other universes. If you jump into a black hole, your mass energy will be returned to our universe but in a mangled form which contains the information about what you were like but in a state where it can not be easily recognized. It is like burning an encyclopedia. Information is not lost, if one keeps the smoke and the ashes. But it is difficult to read. In practice, it would be too difficult to re-build a macroscopic object like an encyclopedia that fell inside a black hole from information in the radiation, but the information preserving result is important for microscopic processes involving virtual black holes."

"The life we have on Earth must have spontaneously generated itself. It must therefore be possible for life to generate spontaneously elsewhere in the universe."

"My expectations were reduced to zero when I was 21. Everything since then has been a bonus."

"I am discounting reports of UFOs. Why would they appear only to cranks and weirdos?"

"Life would be tragic if it weren't funny."

"I have no idea. People who boast about their IQ are losers."

"[on the possibility of contact with an alien civilization]: I think it would be a disaster. The extraterrestrials would probably be far in advance of us. The history of advanced races meeting more primitive people on this planet is not very happy, and they were the same species. I think we should keep our heads low."

"We shouldn't be surprised that conditions in the universe are suitable for life, but this is not evidence that the universe was designed to allow for life. We could call order by the name of God, but it would be an impersonal God. There's not much personal about the laws of physics."

"I don't think the human race will survive the next thousand years, unless we spread into space. There are too many accidents that can befall life on a single planet. But I'm an optimist. We will reach out to the stars."

"Although September 11 was horrible, it didn't threaten the survival of the human race, like nuclear weapons do."

"One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?"

"The world has changed far more in the past 100 years than in any other century in history. The reason is not political or economic but technological — technologies that flowed directly from advances in basic science."

"Thus it seems that even God is bound by the uncertainty principle, and can not know both the position, and the speed, of a particle. So God does play dice with the universe. All the evidence points to him being an inveterate gambler, who throws the dice on every possible occasion."

"All my life, I have been fascinated by the big questions that face us, and have tried to find scientific answers to them."

"Einstein was confused, not the quantum theory."

"It is not clear that intelligence has any long-term survival value."

"I think computer viruses should count as life … I think it says something about human nature that the only form of life we have created so far is purely destructive. We've created life in our own image."