# Frases de Paul Dirac

## Paul Dirac

**Data de nascimento:** 8. Agosto 1902**Data de falecimento:** 20. Outubro 1984

Paul Adrien Maurice Dirac OM, FRS foi um físico teórico britânico.

Estudou engenharia elétrica na Universidade de Bristol, completando o curso em 1921. Em 1923 se formou em matemática e recebeu uma bolsa de pesquisa no St John's College, na Universidade de Cambridge.

Fez contribuições fundamentais para o desenvolvimento da Mecânica Quântica e Eletrodinâmica Quântica. Foi Professor lucasiano de Matemática da Universidade de Cambridge e passou os últimos dez anos da sua vida na Florida State University. Entre outras descobertas, formulou a Equação de Dirac, que descreve o comportamento do férmion e que o levou à previsão da existência da antimatéria.

Em sua tese, defendida em 1926, desenvolveu uma versão da Mecânica Quântica incorporando a “Mecânica Matricial” de Werner Heisenberg com a “Mecânica Ondulatória” de Erwin Schrödinger num único formalismo matemático.

Em 1928, desenvolveu a chamada Equação de Dirac, que descreve o comportamento relativístico do elétron. Esta teoria o levou a prever a existência do pósitron, a antipartícula do elétron, que foi observado experimentalmente em 1932 por Carl David Anderson.

Recebeu em 1933, junto com Erwin Schrödinger, o Nobel de Física .

Participou da 5ª, 6ª, 7ª e 8ª Conferência de Solvay.

Faleceu aos 82 anos e foi sepultado em Roselawn Cemetery, Tallahassee, Flórida no Estados Unidos.

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### Citações Paul Dirac

### „The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are“

— Paul Dirac

Context: 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.
Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 123, No. 792 http://doi.org/10.1098/rspa.1929.0094 (6 April 1929)

### „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.“

— Paul Dirac

Context: 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“

— Paul Dirac

Context: 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.

### „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

Context: 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.

### „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.“

— Paul Dirac

Context: 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.
Remarks made during the Fifth Solvay International Conference (October 1927), as quoted in Physics and Beyond: Encounters and Conversations (1971) by Werner Heisenberg, pp. 85-86; these comments prompted the famous remark later in the day by Wolfgang Pauli: "Well, our friend Dirac, too, has a religion, and its guiding principle is "God does not exist and Dirac is His prophet." Variant translations and paraphrases of that comment are listed in the "Quotes about Dirac" section below.

### „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

Context: 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.

### „If you are receptive and humble, mathematics will lead you by the hand.“

— Paul Dirac

Context: 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.
As quoted in The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom (2009) by Graham Farmelo, p. 435

### „The interpretation of quantum mechanics has been dealt with by many authors, and I do not want to discuss it here. I want to deal with more fundamental things“

— Paul Dirac

Context: The interpretation of quantum mechanics has been dealt with by many authors, and I do not want to discuss it here. I want to deal with more fundamental things.
P. A. M. Dirac, The inadequacies of quantum field theory, in Paul Adrien Maurice Dirac, B. N. Kursunoglu and E. P. Wigner (Cambridge University, Cambridge, 1987) p. 194

### „It seems clear that the present quantum mechanics is not in its final form.“

— Paul Dirac

Context: 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.
"The Early Years of Relativity" in Albert Einstein : Historical and Cultural Perspectives : The Centennial Symposium in Jerusalem (1979) edited by Gerald James Holton and Yehuda Elkana, p. 85

### „I don't suppose that applies so much to other physicists; I think it’s 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.“

— Paul Dirac

Interview with Dr. P. A. M. Dirac by Thomas S. Kuhn at Dirac's home, Cambridge, England, May 7, 1963 http://www.aip.org/history/ohilist/4575_3.html

### „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.“

— Paul Dirac

Bombay Lectures (1955)

### „math>{\int _{-\infty }^{\infty }{\delta \left({x}\right){d{x}}}}=1

\delta \left({x}\right)=0 \text{ for } x\not= 0</math“

— Paul Dirac

III. Representation - 15. The δ function

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

— Paul Dirac

http://www-history.mcs.st-and.ac.uk/Printonly/Dirac.html

### „Causality applies only to a system which is left undisturbed. If a system is small, we cannot observe it without producing a serious disturbance and hence we cannot expect to find any causal connexion between the results of our observations. Causality will still be assumed to apply to undisturbed systems and the equations which will be set up to describe an undisturbed system will be differential equations expressing a causal connexion between conditions at one time and conditions at a later time. These equations will be in close correspondence with the equations of classical mechanics, but they will be connected only indirectly with the results of observations.“

— Paul Dirac

I. The Principle of Superposition - 1. The Need for a Quantum Theory

### „The measure of greatness in a scientific idea is the extent to which it stimulates thought and opens up new lines of research.“

— Paul Dirac

The scientific work of Georges Lemaître (1968), P.A.M. Dirac, Commentarii (Pontifical Academy of Sciences), vol 2, 11, pp. 1–18.