|MadSci Network: Physics|
You pose interesting questions. What you need to keep in mind is that when Dirac posed the idea of a filled sea of negative/energy electrons in 1927, the concept of antimatter did not exist (the positron was discovered in 1933 by Carl Anderson, who was unaware of Dirac's prediction). Dirac's "sea of electrons" was a way to save his equation from the unexpected negative energy solutions that it allowed.
While it is possible to explain the production of particle-antiparticle pairs using Dirac's picture (not just electrons, but any other electrically charged particle!), there are other, more useful models which have been developed over the years that have much farther-reaching predictive powers, such as Feynman calculus. As you can gather from this link, here we can see that the positron can be described as an electron travelling backwards in time!
In any case, I don't think that there is anything particularly profound with the Dirac picture, although many of your fundamental questions about gravitation and the vacuum energy are major points of interest and debate among cosmologists. While I am not a cosmologist myself, Ned Wright's Cosmology Tutorial is an extremely informative website, and may be of interest to you.
I will try now to respond to your specific questions:
1. The total amount of gravitation in the universe is not actually changed by pair production. Photons, too, can cause gravity. If you had a box with mirrors on the inside, it would weigh more if there were a lot of photons trapped inside than if it were dark.
2. You do create mass with pair production. In Dirac's picture, you have a hole where there used to be negatively charged negative energy. This lack of negatively charged negative energy is seen as a positively charged particle with the mass of the electron. But this is just saying that a photon is transformed into an electron-positron pair.
3. Pair production can only occur in the presence of another particle or particles. This is due to conservation of momentum. A frame of reference exists where the center-of-mass of the final electron-positron pair is stationary. But if there was only the initial photon taking part in the interaction, there is no frame of reference where the photon could have been stationary too (light speed is constant in all reference frames). Therefore at least one other particle must be included in the system to balance out the photon momentum.
I hope this is helpful to you. Please feel free to email me at email@example.com if you need more information.
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