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
Answer
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.
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