Dirac’s Paradox


Paul Dirac 1902-84

Dirac, after completing the write up of his equations generalising Schrödinger’s equation to fit with special relativity, boldly stated:

  • The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known. 

But then Dirac quickly added:

  • The difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.

This gives the paradoxical situation, from scientific point of view, that the physical laws expressed by Dirac’s equations are viewed to be “known completely”, but since the equations cannot be solved there is no way to check if solutions agree with observed physics and thus that the equations express true physical laws.

Dirac then turned his hope to approximate solutions:

  • 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.

Today 90 years later, Dirac’s equations are as uncomputable as ever, and the actual truth of all the physics and chemistry claimed to be completely known, is still written in the sky.

This makes Dirac’s model into an unsolvable riddle for which the answer is hidden in an approximation of unknown accuracy, as unclear as an answer by the Oracle of Delphi:

Pythia Aegeus Themis Delphi[1]