Does vacuum (empty space) exist? Added: 5 times down vote for now! Down voter is this religion or physics, please try to explain your decision.
I'm confused about this.
In physics we know for a vacuum, but I think that there is a contradiction in this term. The quantum fluctuations are the phenomena that  contradicts the vacuum existence because, according to them, the vacuum isn't the empty space. 
In vacuum the creation of particle-antiparticle pairs is allowed for small times and this is also proven in practice.
From the other side, the relativistic theory says about space-time that interactions like gravitation bend the vacuum (empty space). There seems to be a contradiction to me. If vacuum is an empty space then we can't bend it, because we can't bend something nonexistent. In other words: we can't bend 'nothing'.
Can empty space really exist in physics?
EDIT1: quote: Luboš Motl

"By definition, the space without
  energy is the space whose total value
  of energy is equal to 0."

But this space is nonexistent, so it is abstract and should exist only in our mind...
Why is so? My second statement of this post says that in physics we cant bend nothing because such a bending is only thinking and not physics!
Another possibility is that space is unknown kind of energy, but this is contradiction in modern physics!
EDIT2:
Can any physics believe that nothing exists?
By mathematical logic no! And mathematic is elementary tool in physics. Anything other than that is religion!
Nothing (empty space without energy) is only a logical state!
EDIT3: quote: Roy Simpson:

The General Relativity Vacuum is a
  space-time model region without
  matter.

and Luboš Motl says: "By definition, the space without energy is the space whose total value of energy is equal to 0."
Agree... 
But this is only mathematical Euclidean space + time so this is only a mathematic and not physics! With other words: this is only a method of mathematical mapping. But, in real (not theoretic) physics we can't mapping empty things. Empty is only a logical state!
EDIT4: 
Roy Simpsons argumentation seems to me acceptable. 
quote: Roy Simpson:

Einstein struggled with this too, and
  the problem has come to be known as
  the "Hole argument" within GR. You
  have to decide whether you are just
  interested in GR's vacuum (empty
  space) or the full physical vacuum
  which includes quantum aspects as
  well.

Thanks
 A: With the risk to repeat someone I'll say what I think. You shouldn't think of vacuum as empty space. Vacuum is the no particle state of a quantum field and no particle doesn't mean empty. The field is still there, it is just in a state we interpret as no particles. And particles are just a very convinced interpretation.   
A: 
"If we have two fundamental particles in space is there empty space between?"

I am no sure. Take a neutral atom. Outside it the space is empty, no force is acting on a probe particle. But it is because of neutralization of fields of positive and negative charges. Without neutralization the field is a long-range thing. So vacuum is such a combination of external forces that produces zero net effect.
A: Dear GJ, "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 $|0\rangle$. 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 $|0\rangle$ - 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.
A: The concept of vacuum in physics indeed comes from two different theories. 
The General Relativity Vacuum is a space-time model region without matter. In General Relativity all of space-time has a "curvature" which relates to the metric which can all have measurable effects, such as the bending of light rays (in the vacuum) near a massive object. One may wish to be a little careful of how one conceptualises the vacuum of empty space however since no events occur there since there is no interacting matter there. As soon as we have interacting matter we no longer just have a vacuum. Also General Relativity has introduced a term, called the Cosmological Constant $\Lambda$, which could be said to measure the curvature of the vacuum at the Cosmological level.
In Quantum Theory there is the concept of the "Vacuum State" which is a little different: it is the lowest possible energy state of a given quantum system. This lowest possible energy state has quantum fluctuations consistent with the $\Delta E \Delta t > h$ Uncertainty Principle.
Thus if we straightforwardly apply the "Vacuum State" concept to the space-time vacuum we get a conceptually different model, called the "Curved Space Vacuum". Some calculations show that this combined "Curved Space Vacuum" is rather different from the vacua of the two component theories: General Relativity and Quantum Mechanics. It has some interesting properties, like Temperature, that the component theories dont have and some calculations do suggest that the "Quantum Vacuum Energy" is different from the corresponding expected $\Lambda$ value by $10^{120}$. These results depend a little on what, if any, quantum fields uniformly pervade space and this aspect is not yet settled.
A: Numbers only exist in our minds.
Numbers, any number, only exist in our head and, in physics, must relate to some property of the outer physical world.
We measure the properties and we use numbers as a tool, or a language.
We use numbers to measure or classify properties, by comparison with selected references, and we use ratios of measures to obtain adimensional quantities.
A property belongs to an Entity 
When we measure a property we can not deny the existence of the underlying entity.
In this case the Aether, Vacuum, Field, Physical Space, ..., can not be empty because it has several properties:
$\epsilon_0, \mu_0, c^2=1/(\epsilon_0*\mu_0)$   c is the Impedance of Vacuum. The light speed is a property of space and not of the light. Gravitational waves also propagate at c speed.
philosophy or physics? Lets see:  
Where to goes the energy when exists destructive interference ?
Light can cancel light under appropriate conditions. This statement is backed by theory and by experiment (anti-laser discussion and paper). What is the nature of this destructive interference?  
The anti-laser experiment shows :  The outcome is 0 energy after the destructive interference of two beams of ligth,  each with energy content.
If energy is to be conserved then the vacuum must possess that energy after we lost it from sight.  
Photons are vacuum perturbations that propagate. (my friend Alf told me that long time ago)
This is a possible conclusion to maintain coherence with experiment.   
VACUUM IS ALL - is Spinosa(Baruch) view (in Ethics) and recently Israel Pérez: A physicist’s view of the universe: a philosophical approach
A: As strange as this object may feel to you, it is what it is: the empty space. As empty as it can. This is what happens when you take your room and get everything out.
