It's reasonable to believe that our universe started with the Big Bang about 15 billion years ago. This event was initiated from a state where all matter in (our) universe was 'on top of itself'. In this 'small' ball of matter, the density would have been infinite, breaking all our laws of physics (singularity). It thus is not useful to talk about sizes, matter, energy nor time (at the time of this event). 

Of course, there are a theories which add phenomena like repulsive universes (Bondi, Gold, and Hoyle), imaginary time (Hartle, Hawking) and other mind-bending phenomena to describe the 'universe' before the big bang. None of these theories however, provides an answer to the question on how the first particle/energy in our (or any) universe was created. Instead, they 'transfer' the problem to 'higher dimensions', 'other universes' or 'infinite loops'. However, the 'small' ball of matter, the repulsive universe, or any other particle or energy-form must have some origin from where they started (evolving). It don't seem very logical that a complete 'ball' of matter/energy suddenly popped-up out of nothing. So whatever there was first, it probably started small. Still, we have to extend, modify or disprove the first law of thermodynamics (the conservation of energy principle).

The least mind-bending theory for this problem, probably is the one which uses negative gravitational energy (Borde, Guth and Vilenkin) to explain how something (e.g. a universe) can be made out of nothing. Still, this theory takes a not very well understood concept (gravity) and adds some hocus-pocus (negative gravity) to 'explain' something which should be very simple. It's not sufficient and probably not efficient neither, to spent time on solving this by maths. 

In the beginning, there was absolutely nothing, so it should be the most simple, basic theory... ever (like the curved space paradigm-shift of Einstein). Moreover it should be 'easy' to verify; If we come up with a theory which can create something out of nothing, we should be able to perform (or discover) the reverse operation as well: Break-down something into nothing.

Defining the playfield

In summary, it seems we need to combine these clues:

1. It must be possible to create something from nothing (main hypothesis, described above)

2. We're looking for a paradigm shift in our understanding of energy / matter (mass)

Together with the current (lack of) knowledge:

3. E=mc^2 (Einstein)
Note that this formula implies that heating up an object, increases its mass (although the only change is/seems the increase in particle motion). 

4. It is impossible to find a general definition for a system's total mass (or energy) in the general relativity theory (ref.: http://en.wikipedia.org/wiki/Mass_in_general_relativity)

5. Quantum Mechanics / Electrodynamics (QED) fails totally to explain why particles such as the electron have the masses they do. "There is no theory that adequately explains these numbers [mass]. We use the numbers in all our theories, but we don't understand them – what they are, or where they come from. I believe that from a fundamental point of view, this is a very interesting and serious problem." (Feynman, ref. http://en.wikipedia.org/wiki/Quantum_electrodynamics)

6. (Long) distance 'communication' of entangled particles (e.g. photons). (ref. http://en.wikipedia.org/wiki/EPR_paradox)

7. All matter (e.g. photons, electrons, protons, molecules) behave as particle (having mass) and wave (which transfer energy and interfere)  (ref. http://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality) 

Where to go from here?

It seems we need a paradigm shift for the way we define mass (before we're able to search for a theory to create something out of nothing). Or is mass a non-existing property which we used in Newtonian mechanics to describe gravitational forces? 

How is the electron mass measured?

Thijs Bressers