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Interpretation of solutions with negative energies was such that charge, rather then probability, density was assumed. When inserting charge of a particle negative sign is then obviously due to charge. How did the equation know this? Maybe it is a stupid question, but how did the equation know our convention regarding different kinds of charges?

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marked as duplicate by Sofia, Kyle Kanos, ACuriousMind, Community Mar 13 '15 at 15:51

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  • $\begingroup$ It is not quite clear what you are asking, but I think you are asking about the "negative probability" problem in QM. In that case, have a look at e.g. this question - the answer is that "relativistic quantum mechanics" is a "hack", and full QFT has no such problem because the equations are for operator-valued fields, not wavefunctions, then. $\endgroup$ – ACuriousMind Mar 13 '15 at 14:08
  • $\begingroup$ Well, negative probabilities are solved by assuming it is actually a charge density. Actually it is assumed that this was an indication of existence of antiparticles. $\endgroup$ – Žarko Tomičić Mar 13 '15 at 15:47