Dirac's c-number Time-energy uncertainty RelationThere exists an uncertainty relation between time and energy variable. This relation makes it possible for an electron jump from one energy level to a lower level by emitting a photon. However, there are no quantum excitations along the time variable.
- 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).
Dirac could have said the following, but he did not. He could have said:
- The Gaussian distribution along the time axis is a representation
of the c-number time-energy uncertainty relation he mentioned
in his 1927 paper.
- The space-time variables measure space-time separation of
two point particles.
- He could have said how his Gaussian form looks to a moving
- In 1949, Dirac published a paper entitled "Forms of Relativistic
Dynamics in the Reviews of Modern Physics:
- 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.
- His instant form calls for the elimination of time-like excitations.
This is consistent with his c-number time-energy uncertainty relation.
- 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 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.
- 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.
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