P. A. M. Dirac: Some strangeness in the proportion

This quote is by Francis Bacon and is taken from

Graham

Farmelo

, (, , ), p. .

Farmelo obtained this anecdote from

Kurt

 

Gottfried

, e-print arXiv:quant-ph/0302041v1. Gottfried heard it directly from Bohr.

F.

 

Conway

and

J.

 

Siegelman

, (, , ).

See, for example,

Hazel

 

Muir

, “,” New Scientist, Magazine Issue No. 2393 (03 May ).

See, for example,

Brian

 

Silver

, (, , ), p. .

Another biography of Dirac is by

Helge

 

Kragh

, (, , ). The two biographies are in a sense complementary. As the title of Kragh’s book suggests the emphasis is on Dirac’s science and has many valuable insights. Farmelo is more focused on Dirac the man.

Reference 1, p. .

The amplitudes depend on which energy levels they refer to. If a transition is from a level characterized by the integer $n$ to one characterized by an integer $m$⁠, then the amplitude $Anm$ is a function of these levels. It is the multiplication of these amplitudes that does not in general commute.

Reference 1, p. .

English translations of this paper and that of Born and Jordan as well as the paper of Dirac can be found in , edited by

B. L.

 

Van der Waerden

(, , ).

Reference 1, p. .

$A$ and $B$ are dynamical variables that are functions of the position $q$ and the momentum $p$⁠. For simplicity I will take these to be one dimensional. Dirac assumed that $AB−BA=iℏ(∂A/∂q∂B∂p−∂B/∂q∂A/∂p)$⁠. The quantity in the parentheses is the Poisson bracket of $A$ and $B$⁠. If you take $A=q$ and $p=B$⁠, the canonical commutator follows. Notice that this assumption cannot be derived from classical physics.

P. A. M.

 

Dirac

, “,”  , – ().

Reference 1, p. .

A. M.

 

Dirac

, “,”  , – ().

A. M.

 

Dirac

, (, , ).

For example, Dirac notes that a necessary part of a quantum mechanical measurement is the collapse of the wave function. He does not mention that this process cannot be described by the formalism he is about to introduce.

See, for example,

Jeremy

 

Bernstein

, “,”  , – ().

This paper minus an appendix to which Dirac refers is held at the Public Records Office at Kew, London. The status of the appendix is unknown.