# Quotes & Sayings About Dirac

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Here the attention of the research workers is primarily directed to the problem of reconciling the claims of the special relativity theory with those of the quantum theory. The extraordinary advances made in this field by **Dirac** ... leave open the question whether it will be possible to satisfy the claims of the two theories without at the same time determining the Sommerfeld fine-structure constant. — **Werner Heisenberg**

A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. — **Paul Dirac**

I should like to suggest to you that the cause of all the economic troubles is that we have an economic system which tries to maintain an equality of value between two things, which it would be better to recognise from the beginning as of unequal value. — **Paul Dirac**

Well, in the first place, it leads to great anxiety as to whether it's going to be correct or not ... I expect that's the dominating feeling. It gets to be rather a fever ... At age 60, when asked about his feelings on discovering the **Dirac** equation. — **Paul Dirac**

There is in my opinion a great similarity between the problems provided by the mysterious behavior of the atom and those provided by the present economic paradoxes confronting the world. — **Paul Dirac**

Theoretical physicists accept the need for mathematical beauty as an act of faith ... For example, the main reason why the theory of relativity is so universally accepted is its mathematical beauty. — **Paul Dirac**

I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics. — **Paul Dirac**

I found the best ideas usually came, not when one was actively striving for them, but when one was in a more relaxed state ... I used to take long solitary walks on Sundays, during which I tended to review the current situation in a leisurely way. Such occasions often proved fruitful, even though (or perhaps, because) the primary purpose of the walk was relaxation and not research. — **Paul Dirac**

Living is worthwhile if one can contribute in some small way to this endless chain of progress. — **Paul A.M. Dirac**

All right," he said. "Since you asked, Webmind is an emergent quantum-computational system based on a stable null-sigma condensate that resists decoherence thanks to constructive feedback loops." He turned to the blackboard, scooped up a piece of chalk, and began writing rapidly. "See," he said, "using **Dirac** notation, if we let Webmind's default conscious state be represented by a bra of phi and a ket of psi, then this would be the einselected basis." His chalk flew across the board again. "Now, we can get the vector basis of the total combined Webmind alpha-state consciousness ... — **Robert J. Sawyer**

The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should take simplicity into consideration in a subordinate way to beauty ... It often happens that the requirements of simplicity and beauty are the same, but where they clash, the latter must take precedence. — **Paul Dirac**

**Dirac**'s equation not only accounted for the spin of the electron and its observed magnetic moment, but also correctly explained the fine structure of the hydrogen atom. If the derivation of the Sommerfeld-like formula for the spectrum of the hydrogen atom was one of the striking successes of the **Dirac** equation, some of its other features were very troublesome. — **Silvan S. Schweber**

The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed. There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with reasonable success. — **Paul Dirac**

It is more important to have beauty in one's equations than to have them fit experiment. — **Paul Dirac**

As time goes on, it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen. — **Paul Dirac**

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. — **Paul Dirac**

Following the path of earlier unificationists, one of Eddington's aims was to reduce the contingencies in the description of nature, for example, by explaining the fundamental constants of physics rather than accepting them as merely experimental data. One of these constants was the fine-structure constant ... , which entered prominently in **Dirac**'s theory and was known to be about 1/137. — **Helge Kragh**

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 ... If someone can hit on the right lines along which to make this development, it m may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply the ... My own belief is that this is a more likely line of progress than trying to guess at physical pictures. — **Paul Dirac**

I count Maxwell and Einstein, Eddington and **Dirac**, among "real" mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as "useless" as the theory of numbers. — **G.H. Hardy**

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. — **Paul A.M. Dirac**

I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it. — **Paul Dirac**

Hopes are always accompanied by fears, and, in scientific research, the fears are liable to become dominant. — **Paul Dirac**

The measure of greatness in a scientific idea is the extent to which it stimulates thought and opens up new lines of research. — **Paul A.M. Dirac**

When you ask what are electrons and protons I ought to answer that this question is not a profitable one to ask and does not really have a meaning. The important thing about electrons and protons is not what they are but how they behave, how they move. I can describe the situation by comparing it to the game of chess. In chess, we have various chessmen, kings, knights, pawns and so on. If you ask what chessman is, the answer would be that it is a piece of wood, or a piece of ivory, or perhaps just a sign written on paper, or anything whatever. It does not matter. Each chessman has a characteristic way of moving and this is all that matters about it. The whole game os chess follows from this way of moving the various chessmen. — **Paul A.M. Dirac**

What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating. — **Paul Dirac**

A book on the new physics, if not purely descriptive of experimental work, must essentially be mathematical. — **Paul Dirac**

I do not see how a man can work on the frontiers of physics and write poetry at the same time. They are in opposition. — **Paul Dirac**

**Dirac** politely refused Robert's [Robert Oppenheimer] two proffered books: reading books, the Cambridge theoretician announced gravely, "interfered with thought." — **Luis Walter Alvarez**

**Dirac** found that the ratio of the electric force to the gravitational force of an electron-proton pair is roughly equal to the ratio of the age of the universe to the time it takes light to traverse an atom. — **Michael Flynn**

During the meeting in Delhi with **Dirac** on 12 January 1955, Nehru asked him if he had any recommendations for the future of the new republic of India. After his usual reflective pause, **Dirac** replied: 'A common language, preferably English. Peace with Pakistan. The metric system. — **Graham Farmelo**

The shortage of buyers, which the world is suffering from, is readily understood, not as due to people not wishing to obtain possession of goods, but as people being unwilling to part with something which might earn a regular income in exchange for those goods. — **Paul Dirac**

A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78. — **Paul Dirac**

A termination of one's life is necessary in the scheme of things to provide a logical reason for unselfishness ... The fact that there is an end to one's life compels one to take an interest in things that will continue to live after one is dead. — **Paul Dirac**

Despite the experimental success of the theory...the fact that the infinities occur at all continues to produce grumbling...**Dirac** in particular always referred to renormalization as sweeping the infinities under the rug. I disagreed with **Dirac** and argued the point with him at conferences at Coral Gables and Lake Constance. Taking account of the difference between the bare charge and mass of the electron and their measured values is not merely a trick that is invented to get rid of infinities; it is something we would have to do even if everything was finite. There is nothing arbitrary or ad hoc about the procedure; it is simply a matter of correctly identifying what we are actually measuring. — **Steven Weinberg**

Mathematical theories have sometimes been used to predict phenomena that were not confirmed until years later. For example, Maxwell's equations, named after physicist James Clerk Maxwell, predicted radio waves. Einstein's field equations suggested that gravity would bend light and that the universe is expanding. Physicist Paul **Dirac** once noted that the abstract mathematics we study now gives us a glimpse of physics in the future. In fact, his equations predicted the existence of antimatter, which was subsequently discovered. Similarly, mathematician Nikolai Lobachevsky said that "there is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world. — **Clifford A. Pickover**

The methods of theoretical physics should be applicable to all those branches of thought in which the essential features are expressible with numbers. — **Paul Dirac**

It was not until some weeks later that I realized there is no need to restrict oneself to 2 by 2 matrices. One could go on to 4 by 4 matrices, and the problem is then easily soluable. In retrospect, it seems strange that one can be so much held up over such an elementary point. The resulting wave equation for the electron turned out to be very successful. It led to correct values for the spin and the magnetic moment. This was quite unexpected. The work all followed from a study of pretty mathematics, without any thought being given to these physical properties of the electron. — **Paul Dirac**

Es gibt keinen Gott und **Dirac** ist sein Prophet. (There is no God and **Dirac** is his Prophet.)

{A remark made during the Fifth Solvay International Conference (October 1927), after a discussion of the religious views of various physicists, at which all the participants laughed, including **Dirac**, as quoted in Teil und das Ganze (1969), by Werner Heisenberg, p. 119; it is an ironic play on the Muslim statement of faith, the Shahada, often translated: 'There is no god but Allah, and Muhammad is his Prophet.'} — **Wolfgang Pauli**

In the history of science it happens not infrequently that a reductionist approach leads to a spectacular success. Frequently the understanding of a complicated system as a whole is impossible without an understanding of its component parts. And sometimes the understanding of a whole field of science is suddenly advanced by the discover of a single basic equation. Thus it happened that the Schrodinger equation in 1926 and the **Dirac** equation in 1927 brought a miraculous order into the previously mysterious processes of atomic physics. The equations of Erwin Schrodinger and Paul **Dirac** were triumphs of reductionism. Bewildering complexities of chemistry and physics were reduced to two lines of algebraic symbols. These triumphs were in Oppenheimer's mind when he belittled his own discovery of black holes. Compared with the abstract beauty and simplicity of the **Dirac** equation, the black hole solution seemed to him ugly, complicated, and lacking in fundamental significance. — **Freeman Dyson**

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. — **Paul Dirac**

The strength of the familiar electromagnetic force between two electrons, for example, is expressed in physics in terms of a constant known as the fine structure constant. The value of this constant, almost exactly 1/137, has puzzled many generations of physicists. A joke made about the famous English physicist Paul **Dirac** (1902-1984), one of the founders of quantum mechanics, says that upon arrival to heaven he was allowed to ask God one question. His question was: "Why 1/137? — **Mario Livio**

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. — **Paul Dirac**

It also predicted that the electron should have a partner: an antielectron, or positron. The discovery of the positron in 1932 confirmed **Dirac**'s theory and led to his being awarded the Nobel prize for physics in 1933. — **Stephen Hawking**

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. — **Richard P. Feynman**

Quantum mechanics has explained all of chemistry and most of physics. — **Paul Dirac**

It seems clear that the present quantum mechanics is not in its final form. Some further changes will be needed, just about as drastic as the changes made in passing from Bohr's orbit theory to quantum mechanics. Some day a new quantum mechanics, a relativistic one, will be discovered, in which we will not have these infinities occurring at all. It might very well be that the new quantum mechanics will have determinism in the way that Einstein wanted. — **Paul Dirac**

Maybe I'm being a bit harsh on philosophers, but they have not been very kind to me ... I have been variously called nominalist, an instrumentalist, a positivist, a realist, and several other ists. The technique seems refutation by denigration: If you can attach a label to my approach, you don't have to say what is wrong with it ... I am sure that Einstein, Heisenberg and **Dirac** didn't worry about whether they were realists or instrumentalists. — **Stephen Hawking**

I am not, however, militant in my atheism. The great English theoretical physicist Paul **Dirac** is a militant atheist. I suppose he is interested in arguing about the existence of God. I am not. It was once quipped that there is no God and **Dirac** is his prophet. — **Linus Pauling**

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. — **Paul Dirac**

Quantum field theory was originally developed for the treatment of electrodynamics, immediately after the completion of quantum mechanics and the discovery of the **Dirac** equation. — **David Gross**

The successful development of science requires a proper balance to be maintained between the method of building up from observations and the method of deducing by pure reasoning from speculative assumptions. — **Paul A.M. Dirac**

People who equate all the different kinds of human activity to money are taking too primitive a view of things. — **Paul A.M. Dirac**

In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite. — **Paul A.M. Dirac**

Renormalization is just a stop-gap procedure. There must be some fundamental change in our ideas, probably a change just as fundamental as the passage from Bohr's orbit theory to quantum mechanics. When you get a number turning out to be infinite which ought to be finite, you should admit that there is something wrong with your equations, and not hope that you can get a good theory just by doctoring up that number. — **Paul Dirac**

I admired Bohr very much. We had long talks together, long talks in which Bohr did practically all the talking. — **Paul Dirac**

A great deal of my work is just playing with equations and seeing what they give. — **Paul Dirac**

I think it is a peculiarity of myself that I like to play about with equations, just looking for beautiful mathematical relations which maybe don't have any physical meaning at all. Sometimes they do.

At age 60. — **Paul Dirac**

In his 1930 book, **Dirac** took for granted that measurements could be made, but was very vague about what was actually involved. — **Willis Lamb**

The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved. — **Paul Dirac**

If one is working from the point of view of getting beauty into one's equation, ... one is on a sure line of progress. — **Paul A.M. Dirac**

There are always more people who prefer to speak than to listen. — **Paul Dirac**

Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field. — **Paul Dirac**

Lying there, I thought of my own culture, of the assembly of books in the library at Alexandria; of the deliberations of Darwin and Mendel in their respective gardens; of the architectural conception of the cathedral at Chartres; of Bach's cello suites, the philosophy of Schweitzer, the insights of Planck and **Dirac**. Have we come all this way, I wondered, only to be dismantled by our own technologies, to be betrayed by political connivance or the impersonal avarice of a corporation? — **Barry Lopez**

Pick a flower on Earth and you move the farthest star. — **Paul A.M. Dirac**

It is quite clear that beauty does depend on one's culture and upbringing for certain kinds of beauty, pictures, literature, poetry and so on ... But mathematical beauty is of a rather different kind. I should say perhaps it is of a completely different kind and transcends these personal factors. It is the same in all countries and at all periods of time. — **Paul Dirac**

I think it is the general rule that the originator of a new idea is not the most suitable person to develop it, because his fears of something going wrong are really too strong ... At age 69. — **Paul Dirac**

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 — **Paul Dirac**

The only object of theoretical physics is to calculate results that can be compared with experiment ... it is quite unnecessary that any satisfactory description of the whole course of the phenomena should be given. — **Paul Dirac**

No. I had successfully solved the difficulty of finding a description of the electron which was consistent with both relativity and quantum mechanics. Of course, when you solve one difficulty, other new difficulties arise. You then try to sove them. You can never solve all difficulties at once. — **Paul Dirac**

God used beautiful mathematics in creating the world. — **Paul Dirac**