E2 - p2c2 = m2c4 - Meaning of symbols

[JesseM]

From that quotation we can draw the conlusion that the solutions of the relativistic energy equation E² = m²c⁴+p²c² are as follows: (1) in classical physics we could keep the positive values separate from the negative ones, (2) in quantum mechanics the positive and negative values do not tend to separate neatly; each of the two roots has to be considered as a possibility, so even an “unphysical negative energy” has to be considered as a physical possibility (3) in relativity we do not have a clear cut procedure for ruling out negative square root.

(3) should say that in relativistic quantum mechanics we do not have a clear-cut procedure. In the non-quantum version of relativity we do--that's what he meant by "classical physics" here.

Even Dirac when he took antiparticle to solve the problem, he obliged to introduce the concept of “the ocean of occupied negative energy states” which is now referred to as the Dirac Sea (the same book p. 624-625).

My understanding is that the modern version of quantum field theory basically gets rid of the whole "Dirac Sea" idea, antiparticles are no longer viewed as "holes" but as particles in their own right. See this section of the wikipedia article, or this thread from physicsforums, or the last paragraph before "Free Space Solutions" in this google books result.

 

[aeon.rs]

(3) should say that in relativistic quantum mechanics we do not have a clear-cut procedure. In the non-quantum version of relativity we do--that's what he meant by "classical physics" here.

My understanding is that the modern version of quantum field theory basically gets rid of the whole "Dirac Sea" idea, antiparticles are no longer viewed as "holes" but as particles in their own right. See this section of the wikipedia article, or this thread from physicsforums, or the last paragraph before "Free Space Solutions" in this google books result.

Thank you, you are right. The original text of the quotation was written within the context of quantum mechanics. But the bottom line I would like to express is that we can not take the possibility of the existence of such negative energies very lightly. For me the presence of this symmetry, the pairing of these opposite energies and their interplay will substantially enrich the relativity theory and empower it to resolve the troubles we have both at the cosmic and quantum levels.