Is the vacuum empty? Are virtual particles in the vacuum? Is the vacuum non-zero? I have read a lot about this stuff. 


*

*Is the vacuum empty? How is it not-empty? 


But nobody can it explain serious and simple that I can fully understand it.
Some physicists tell may that virtual particles were a big lie. 


*There don't arises in the vacuum? 

*What is the truth about the vacuum?
I found this: 

Is the Universe a Vacuum Fluctuation?
EDWARD P. TRYON
1.Department of Physics and Astronomy, Hunter College of the City University of New York, New York, New York 10021
Top of page
  Abstract
The author proposes a big bang model in which our Universe is a fluctuation of the vacuum, in the sense of quantum field theory. The model predicts a Universe which is homogeneous, isotropic and closed, and consists equally of matter and anti-matter. All these predictions are supported by, or consistent with, present observations.
Nature 246, 396-397 (14 December 1973) | doi:10.1038/246396a0



*What does this paper tells us? 

*Is the vacuum empty or not? 

*Are virtual particles in the vacuum? 

*Can a universe arise from nothing?
 A: I will quote from the answer by Lubos Motl to a similar question "does vacuum , empty space ,exist" which has been closed . If Lubos answers here I will delete this:

"vacuum" and "empty space" is always the same thing, but one must always be careful what these two synonymous terms mean.
General relativity implies that the only "information" that the vacuum carries at each point is the so-called "metric tensor" - a set of numbers that allow one to calculate the distance between any two nearby points. This is enough for the vacuum to be able to bend - much like any material. One doesn't need any atomic constituents to be able to talk about geometry of the space, and to guarantee that the environment is able to get curved (and to distinguish a flat region of the vacuum from a curved one).
Quantum field theory implies that the vacuum is full of virtual particles that emerge and quickly disappear. Those virtual particles make their impact on other objects - for example, they make the electromagnetism a little bit weaker at long distances (and stronger at very short distances) than what one expects from the classical Coulomb's law etc.
However, quantum mechanics implies that the vacuum corresponds to a very particular "state" - a vector on the Hilbert space - called |0⟩. It is completely unique and as empty as you can get. In particular, it is the eigenstate of the energy operator with the minimum allowed energy - essentially zero. (More precisely, the vacuum energy density is nothing else than the magnitude of dark energy but this energy only becomes sizable for huge, cosmological volumes of space.)
The uncertainty principle of quantum mechanics implies that when one measures things such as the intensity of the electric field in the vacuum - i.e. when the physical system is found in the state |0⟩ - one may get many random values. It is not allowed for the electric and magnetic fields to be exactly zero, much like a particle can't have a well-defined position and velocity in the quantum mechanics of one particle.
So even though the vacuum has a well-defined (minimal) energy and it is as low as we can get, so the vacuum is as empty as we can get, and there are no particular "atoms" or other particles sitting in the vacuum, there's a lot of activity going on in the vacuum which can be seen by the fact that the measurements of various things, such as the density of energy at a given point, will lead to random results that are not strictly zero.
Now, the picture of the vacuum as a "literally empty space" that only has the metric tensor at each point; and the quantum picture with all the activity of virtual particles are actually fully compatible with one another. The statement of general relativity that the metric tensor has particular values at a given point should be viewed as a classical approximation, however: when we look at it precisely, the metric tensor is a set of operators, too. They will inevitably have variable and chaotic values if they're measured - that are just "approximately zero" if they're averaged over large enough volumes.

So with this background your final questions:

1.Is the vacuum empty or not?

Not empty because in the universe we exist in there exists dark energy, but the numbers are so small that it can be considered empty, in the sense of almost 0 energy content.

2.Are virtual particles in the vacuum?

Only if interactions happen, then the virtual particles affect measurable values. Otherwise they are  a mathematical abstraction

3.Can a universe arise from nothing?

We do not know how or observable universe arouse. Various models are proposed as in the one you quote. Our observable universe is mostly composed of particles, and this asymmetry of particle antiparticle is not explainable within current theories (CP violation in particle physics is too small to explain it) . The models I am aware of start with equal numbers of particles antiparticles and presume that by the hydrogen age an unknown yet CP violation gave the asymmetry we observe.
A: 
Is the vacuum empty? 

No. Space isn't nothing. See Einstein talking about it here: "This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that "empty space" in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gmn), has, I think, finally disposed of the view that space is physically empty."

Are virtual particles in the vacuum? 

No. Virtual particles are virtual, as in not real. It's a popscience myth that space is full of virtual particles popping in and aout of existence like magic. Vacuum fluctuations are real. They're the electromagnetic equivalent of little ripples on the surface of the sea. But don't think they account for spatial energy. A gravitational field is a place where the spatial energy-density varies, and it isn't because there's more vacuum fluctuations near a star.   

Is the vacuum non-zero?

Vacuum energy is non zero. 

Is the vacuum empty? How is it not-empty? 

It isn't empty because a field has energy, and a field is a state of space. See Einstein talking about that here: "The two types of field are causally linked in this theory, but still not fused to an identity. It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric". 

But nobody can it explain serious and simple that I can fully understand it.

I think it's simpler than you think. Just take a look at the stress-energy-momentum tensor: 
Public domain image by Maschen, see Wikipedia 
Note the shear stress and the pressure, and remember things like "curved spacetime". General relativity kind of treats space like it's some kind of gin-clear ghostly elastic continuum. When you add energy to create a gravitational field, it's a bit like pushing space outwards. IMHO it's like space and energy are the same thing. 

Some physicists tell may that virtual particles were a big lie. 

They're not a lie, they're just virtual. The lie is the idea that space is full of virtual particles popping in and out of existence. 

There don't arises in the vacuum? 

No, they're field quanta used to model fields and interactions. See anna's answer to this question. Virtual particles exist only in the mathematics of the model.

What is the truth about the vacuum?

It isn't nothing. Space sustains fields and waves. 

What does this paper tells us? 

Nothing much. It's speculative.  

Is the vacuum empty or not? 

No. 

Are virtual particles in the vacuum? 

No. Just in the maths. 

Can a universe arise from nothing?

No. Because even when people say our universe arose from a vacuum fluctuation, something fluctuated.   
