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On Lorentz invariance in the quantum theory

Published online by Cambridge University Press:  24 October 2008

P. A. M. Dirac ,
R. Peierls  and
M. H. L. Pryce
P. A. M. Dirac
Affiliation:
St John's CollegeCambridge
R. Peierls
Affiliation:
The UniversityBirmingham
M. H. L. Pryce
Affiliation:
The UniversityLiverpool
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Extract

In a recent paper, Eddington raises an objection against the customary use of the Lorentz transformation in quantum mechanics, as for instance when applied to the theory of the hydrogen atom or the behaviour of a degenerate gas. This objection seems to us to be mainly based on a misunderstanding, and our purpose here is to show that the practice of theoretical physicists on this point is quite consistent. The issue is a little confused because Eddington's system of mechanics is in many important respects completely different from quantum mechanics, and although Eddington's objection is to an alleged illogical practice in quantum mechanics he occasionally makes use of concepts which have no place there. Such arguments will not have any bearing on the question whether or not the practice in quantum mechanics is logically consistent—although they may have bearing on which of the two systems describes physical phenomena better.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 2 , April 1942 , pp. 193 - 200
Copyright
Copyright © Cambridge Philosophical Society 1942

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References

* Proc. Cambridge Phil. Soc. 35 (1939), 186.Google Scholar

† In a note on p. 190 of the paper referred to above Eddington objects to the statement that the uncertainty of the position of the proton is negligible. His objection is based on assuming the total linear momentum to be zero. There is, however, no need to choose the frame in which this is the case. All that is necessary is that the momentum shall be small enough for the velocity of the proton to be negligible compared with the distances and times involved in the problem. This is obviously compatible with the uncertainty principle if the mass of the proton is assumed to be very large.

* § 3, loc. cit.

† ν 2 stands for the quantal mean value.