In the Dirac's old attempt of relativistic quantum mechanics, a hole in the $E'$ level of the Dirac sea was interpreted as a particle of opposite charge and positive energy. I do get why it can be seen as having opposite charge but I don't get why it can be interpreted as having opposite energy. Any ideas?
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$\begingroup$ The equation produces solutions with negative eigenvalues, so it's an unfortunate/unwanted mathematical feature, rather than a matter of interpretation. $\endgroup$– CuriousOneSep 18, 2014 at 8:26
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$\begingroup$ @CuriousOne Why would negative eigenvalues be 'unwanted'? $\endgroup$– my2ctsFeb 26, 2021 at 16:48
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$\begingroup$ There is no such thing as the Dirac sea. The closest thing is a valence band in a semiconductor or metal. $\endgroup$– my2ctsFeb 26, 2021 at 16:53
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2 Answers
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The ground state of Dirac sea is full of particles with negative energy, according to Dirac equation. When a particle/electron absorbs energy and excites to a positive energy state with energy level $E$, it will leave a hole with energy $E-E\prime$ (if the total energy absorbed is $E$) , which is positive according to energy conservation. So the hole seems to have positive energy.
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$\begingroup$ The Dirac Sea does not exist. It is an untenable idea. Pure fantasy. $\endgroup$– my2ctsFeb 26, 2021 at 16:49
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The hole has to have positive energy because if we want to make it disappear we would have to add an electron with negative energy to the system.