- #1
exmarine
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In Dirac’s QM book, Revised Fourth Edition (~1967), Chapter XI Relativistic Theory of the Electron, page 262, he reaches the conclusion that “…a measurement of a component of the velocity of a free electron is certain to lead to the result ±c.”
Is this still the current thinking? (He is talking about the instantaneous velocity.)
He then goes on to “verify” that by using the uncertainty principle later on the same page. “The great accuracy with which the position of the electron is known (my edit: in order to measure instantaneous velocity) during the time interval must give rise, according to the principle of uncertainty, to an almost complete indeterminacy in its momentum. This means that almost all values of the momentum are equally probable, so that the momentum is almost certain to be infinite. An infinite value for a component of momentum corresponds to the value ±c for the corresponding component of velocity.” (my italics)
Equally probable values of momentum mean it is almost certain to be infinite? I don’t understand that. Any help appreciated.
Well I see it didn't hold my italics, but you can still understand my question.
Is this still the current thinking? (He is talking about the instantaneous velocity.)
He then goes on to “verify” that by using the uncertainty principle later on the same page. “The great accuracy with which the position of the electron is known (my edit: in order to measure instantaneous velocity) during the time interval must give rise, according to the principle of uncertainty, to an almost complete indeterminacy in its momentum. This means that almost all values of the momentum are equally probable, so that the momentum is almost certain to be infinite. An infinite value for a component of momentum corresponds to the value ±c for the corresponding component of velocity.” (my italics)
Equally probable values of momentum mean it is almost certain to be infinite? I don’t understand that. Any help appreciated.
Well I see it didn't hold my italics, but you can still understand my question.