Paul Dirac: Theory

“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

The Evolution of the Physicist's Picture of Nature (1963)
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.

Law , Beauty , Mathematics , Nature

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

Paul Dirac

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)
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.

Law , Mathematics , Parting

“I want to emphasize the necessity for a sound mathematical basis for any fundamental physical theory. Any philosophical ideas that one may have play only a subordinate role. Unless such ideas have a mathematical basis they will be ineffective.”

Paul Dirac

The Mathematical Foundations of Quantum Theory (1978)

Mathematics , Idea

“At the beginning of time the laws of Nature were probably very different from what they are now. Thus we should consider the laws of Nature as continually changing with the epoch, instead of as holding uniformly throughout space-time. This idea was first put forward by Milne, who worked it out on… assumptions… not very satisfying… we should expect them also to depend on position in space, in order to preserve the beautiful idea of the theory of relativity [that] there is fundamental similarity between space and time.”

Paul Dirac

The Relation between Mathematics and Physics http://www.damtp.cam.ac.uk/events/strings02/dirac/speach.html (Feb. 6, 1939) Proceedings of the Royal Society (Edinburgh) Vol. 59, 1938-39, Part II, pp. 122-129.

Law , Beauty , Idea , Nature

“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.”

Paul Dirac book Principles of Quantum Mechanics

I. The Principle of Superposition - 1. The Need for a Quantum Theory
The Principles of Quantum Mechanics (4th ed. 1958)

Law , Idea , Thinking , Change

“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)

Imagination