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).
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.
You open a box and say "there is nothing inside". In a strict mathematical (math-logic) language what you mean is: $$!\,\exists x\in ObjectsCouldBeInTheBox: InABox(x) $$ What you do next is just a "linguistic trap" -- you take a word "nothing" out your sentence. Which roughly corresponds to a "$!\exists$" part of your statement. And it's not an object. It's not even a predicate.
But "nothing" is a noun, so it feels like you can operate with it as it was an object. Well, that is a wrong feeling.
Just try to formulate the statement "Universe could emerge from nothing" strictly. I can only get something like: $$\exists x\in SetOfNothings: UniverseEmergesFrom(x) $$ And I don't know what $SetOfNothings$ is...
Because there is a law such as gravity, the universe can and will create itself from nothing. Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist,
Hawking writes.
http://www.phenomenica.com/2010/09/hawking-god-did-not-create-universe.html
but another question is why our universe has laws of physics?
No. The Friedmann equation says that the fractional expansion rate grows with energy density. If the energy density were really zero and there were no curvature, then the universe (or the lack thereof) would simply sit still.
Quantum fluctuations (antimatter + matter annihilations) of the vacuum are not zero energy. In fact, they act like a cosmological constant or dark energy. One of the mysteries of modern physics is why the vacuum energy is so much smaller than what we expect. If we set the planck length as the UV cutoff scale, the vacuum energy would be roughly 120 orders of magnitude denser than the observed amount of dark energy. So there must be something (a symmetry, holography, etc) that reduces this to within observation constraints.
Much of the idea of "a universe emerging from nothing" relies on a naive sense of how time should behave. In a recent work by Yasunori Nomura, he describes how the multiverse can be viewed as intrinsically static. The waveform of the multiverse is completely stationary with no evolution.
He describes that the concept of "time" (and related notions of causality) are tied up with the concept of ordered vs. disordered states (look at the chair example on page 8). The entire multiverse as a whole doesn't need to evolve, only the probabilities within a single universe.
Looking at previous answers to this question, I decided to lend my support to those of Alfred Centauri and hwlin, and I made a couple of critical remarks elsewhere. However I think nobody answered well the energy aspect of the original question, so I will do that.
The basic idea is that owing to gravitational attraction to one another the stars and galaxies etc. have a form of binding energy which can be said to be negative potential energy, and this could conceivably balance the amount of rest energy and kinetic energy in the universe, so the total comes out zero. In a simple classical picture, look at the situation of two point masses $M$ and $m$, moving away from one another. The total energy is
$E_{\rm tot} = \frac{1}{2} M v_1^2 + \frac{1}{2} m v_2^2 - \frac{G M m}{r}$
It can happen that this total is zero. When that happens, we say the relative velocity of the masses is just equal to the escape velocity associated with their initial separation $r$. Now of course the cosmology of the early universe has to invoke general relativity and quantum physics, but nevertheless this is essentially what the claims about energy are asserting. The main new ingredient is rest energy, so we get something like
$E_{\rm tot} = \gamma_1 M c^2 + \gamma_2 m c^2 - (\mbox{G.R. version of}) \frac{G M m}{r}$
and again this total can be zero. In the early universe the gravitational part goes to negative infinity if you let $r$ go to zero, but of course this formula is not the fully correct one. A calculation invoking quantum physics could in principle handle the singularity but now we are venturing into topics where our knowledge is far from confident (popular books tend to be too confident here; this is unhelpful in my opinion).
I would say that it would be interesting if such an energy calculation came out zero for the universe as a whole. But surely this is a VERY long way from any sort of solution of the origin of the universe. In this context, the statement "the total energy is zero" is just a way of saying "the rest energy and kinetic energy is just enough to allow the various items of stuff to move a long way away from one another against their long-range gravitational attraction".
Once one sees this, the issue I find myself drawn to ask next is, "why this state of affiars? why this configuration?" It is a configuration with extraordinarily low entropy.
To conclude, there are several issues all bound up together here. One is energy, another is entropy, and a third is care and attention to philosophical language when we invoke metaphysical terms such as "nothing" and "existence".
There is really no answer to the question asked as yet because the laws of Quantum gravity are not known. So We really dont know what happened.
You say that
If so, then what is the total energy of the matter compensated by?
then you say that
Yes, I've watched the lecture by Lawrence Krauss
My point is that if you watch even one of his full lectures on this topic like this one, you would have your answer.
then is it possible that all matter in the universe could have emerged from nothing?
The answer to above is YES as already summarised by @juanrga
As Prof.Krauss says not only matter even space-time itself can pop up into existence if we mix gravity with quantum mechanics
As of right now, there is no physical theory able to demonstrate the creation of universe out of nothing; even worse, there is no theory able to pass before the big bang (if there is anything or nothing there). The general relativity gives a very mathematical solution to the question, in terms of existence of solutions to the Einstein's equation; but that hardly provides any physical insight. However, there is hope, that String theory can surpass the difficulties raised by the singularities (in the General Relativistic sense of the word) at the big bang and go before that. But even if that happens and String theory provides some descriptions for the universe before the big bang, the issue of going back in time, until some beginning or something, will remain as puzzling unless String theory has more interesting things to say.
As a very amateur and very patient physicist, I believe we have to wait for the new ideas about spacetime (including the "emergent spacetime" notions, that are supported by the String theoretic investigations) to become more mature and hopefully then we will have our knives sharpened enough to analyse the difficult problems concerning the creation/existence of the universe.
It is possible albeit speculative. This is the free-lunch cosmology model. In such model it is supposed that the positive energy of the matter is compensated by the negative energy of the gravitational 'field' to give total zero energy.
