Dirac's c-number Time-energy uncertainty Relation

• In 1927, Dirac noticed this point and stated this space-time asymmetry makes it difficult for us to make quantum mechanics consistent with special relativity. He said this clearly in his paper
  • P. A. M. Dirac, Proc. Roy. Soc. (London) A114, 243 (1927).

• In 1945, Dirac published a paper where he wrote down a Gaussian form form for three space coordinate variables and the time variable. In so doing his Gaussian form
  • P. A. M. Dirac, Proc. Roy. Soc. (London) A183 , 284 (1945).

  The content of this paper can be summarized in this figure. Dirac's Gaussian form tells the wave function is localized within a circular region around the origin of space and time axis.

  Dirac could have said the following, but he did not. He could have said:

  1. The Gaussian distribution along the time axis is a representation of the c-number time-energy uncertainty relation he mentioned in his 1927 paper.

  2. The space-time variables measure space-time separation of two point particles.

  3. He could have said how his Gaussian form looks to a moving observer.

• In 1949, Dirac published a paper entitled "Forms of Relativistic Dynamics in the Reviews of Modern Physics:
  • Rev. Mod. Phys. 21 , 392 (1949).
  1. In this paper, Dirac introduces the light cone coordinate system in which the Lorentz boost takes the form of a rectangular squeeze along the light cones.

  2. His instant form calls for the elimination of time-like excitations. This is consistent with his c-number time-energy uncertainty relation.

  3. He said we can construct quantum mechanics relativistic by constructing a representation of the Poincaré' group. However, he forgot to mention his 1945 paper where he attempted the representation using harmonic oscillators.

• In 1962, I was fortunate enough to have an audience with Dirac. The issue was how to make quantum mechanics consistent with relativity. Since then, I spent many years to find out what he meant by reading his papers. I can summarize what I did with the following illustration.

  

• Click here Dirac and Feynman.