big-bangcosmologyenergy-conservationuniverse
If the Universe is flat and the total energy of the universe can be zero (we don't know if it is, but many theorists support the idea, i.e. at BB initial conditions:
t = 0, V = 0, E = 0) then is it possible that all matter in the universe could have emerged from nothing? If so, that what is the total energy of the matter compensated by?
Edit: Yes, I've watched the lecture by Lawrence Krauss, and I know about his book. Haven't read it though (I guess it's too difficult for me).
First of all, Lawrence Krauss has nothing to do with the discovery of dark energy, cosmological constant, or any important discovery, for that matter. This doesn't prove that his ambiguous formulations to suggest otherwise were deliberately written as ambiguous - but it doesn't disprove it, either.
The cosmological constant was introduced by Einstein right after 1916 in an incorrect attempt to make the Universe static and it was observed - at a lower value - in the 1990s experimentally by experimenters which couldn't include Lawrence Krauss. A rather detailed history, explanations, and names of the discoverers of these advances may be found in the very book by Brian Greene, The Hidden Reality, that my Dopplegänger Sheldon Cooper downplayed in the video offered by Raskolonikov, and that I am just translating, in a parallel universe, to my native tongue. ;-)
Second, Einstein's $E=mc^2$ is not an equivalence of energy and matter. It is the equivalence of energy and mass (i.e. the number of kilograms). So a unit volume of the empty space carries some mass equivalent to the energy - it's a mass of a few protons per cubic meter. But the $E=mc^2$ equation does not imply, in any sense, that the mass equivalent to the energy has to take the form of localized particles. It may be dispersed, much like the cosmological constant - whose generalized form is also called dark energy. The main reason why the vacuum contains mass is that this mass contributes to the curvature of spacetime - the gravitational field of mass - and be sure that dark energy does. That is why it was introduced.
Dark energy, unlike mass, carries a negative pressure, and it's the real source of the accelerating expansion it induces. Ordinary matter has attractive gravity.
Third, physics can't label things by moral evaluations such as "worst possible" etc. Krauss probably meant that if the spatial slices of our spacetime are exactly flat - which is the boundary scenario in between the positive curvature and negative curvature - then we have no chance to ever experimentally find out what the magnitude of the curvature is because the sign may always be 0 or $\pm \epsilon$ where $\epsilon$ is sufficiently small relatively to the experimental resolution.
In some sense, the exact flat slices may also be viewed as an example of fine-tuning - something would be zero without any good reason. Some advanced cosmological considerations could imply that the spatial curvature is positive (we can swim around the Universe in principle, after some time), or negative (curved like the Lobachevsky plane, a saddle if you wish).
This question involves the concept of "virtual particle" which was discussed a few days ago here. In a nutshell, a particle is virtual when it is a connecting line in a Feynman diagram between two vertices. It has all the quantum numbers of its name ( photon, electron, etc.) but not the mass, which is the measure of the four vector describing it. In that sense energy is not conserved with a virtual particle.
A virtual particle may continue out of the vertex and become "real", but a search for corresponding Feynman diagrams for Hawking radiation does not give any clear ones.
I found this heuristic one:
These loops are handwaved as coming "from the strong gravitational field in the hole .
This is the Feynman diagram of how pair creation is in the lab
It is necessary to have a second interaction because the created pair has invariant mass while the photon has zero mass.
One can adapt the left diagram to the heuristic loops of the Hawking plot above.
As the unification of gravity with the other three forces is not done yet, the diagrams are a guess that is missing an incoming "photon, Z0, gluon .." and an outgoing "photon, Z0, gluon..." ( do not now if gravitons can make a pair directly, were they unified with the rest) as the real particle in the feynman graphs. We do not know whether this will really work, and thus it is heuristic. I did find a publication that states the problem of feynman graphs and gravity for Hawking radiation.Anyway lets call the particle a generic "graviton".
If we assume that the graphs work ,then a "graviton" creates an e+e- pair which recombines within the horizon to the same "graviton". For certain conditions at the horizon one of the pair interacts with another "graviton" which supplies the second vertex, and falls into the hole while the other continues free. In this sense virtual is the e+ of the picture, whose second vertex is a "graviton" in the hole while the electron goes on as real picking up the energy from the potential of the hole. Thus black holes evaporate eventually in this scenario. No need for negative energies.
Best Answer
The answer crucially depends on what is meant by nothing. From the philosopher's nothing, nothing comes.
But the physicist's nothing is something, i.e., there is at least physical law and whatever obeys it.
For example, matter and anti-matter can materialize from the "vacuum" and, in some sense, this is something (matter) from nothing (no matter). But this presupposes the existence of quantum fields and the laws that govern them.
So, your question is actually far more subtle (and ancient) than you might grasp at this moment.