See according to the uncertainty principle there is no such thing as empty space, space is always teeming with virtual particles popping in and out of existence. These virtual usually come in pairs and annihilate each other. So the question doesn't make sense when quantum mechanics is factored in.
Add to the matter that physicist don't even know if space and time are fundamental or if they come from a more fundamental concept. Really if you take relativity to it's logical conclusion the universe is block spacetime so there really is no objective flow of time, maybe this is the fundamental nature of spacetime.
So if you interpret "empty space" to be full of quantum foam, and you conclude that the question doesn't make sense, then perhaps a classical interpretation of "empty space" is in order?
No. If you look at it from the relativity equation, if there is no mass/energy in a "space" there is no curvature of that local spacetime and thus no attraction. As far as I know.
Robobop is right about the quantum foam of empty space but the energy of the fields is net 0 so as far as spacetime is concerned there's nothing there to make it bend.
But if curved space-time attracts curved space-time, what are the implications for flat space-time relative to flat space-time.
I think you should read up on the Casimir force...
In addition to photons other particles are relevant when discussing this... but it is important to remember that only the photon force is quantifiable at this time. All bosons result in an attractive force and fermions repulsive. In supersymmetric electromagnetism fermionic photinos would counter photons, thus the Casimir effect would not exist...
However, we know that the Casimir effect in fact does exist and there have been recent advancements made in quantifying this... thus we can assume that if supersymmetry exists it is not perfect symmetry...
theoretically the total zero point energy in the vacuum is infinite if summed across the total possible photon modes. The Casimir effect results from a difference of energies where those infinities cancel each other. Assigning energy to the vacuum is somewhat problematic in theories quantifying quantum gravity because it is expected to behave gravitationally and thus give a large cosmological constant that should produce a distortion in spacetime.
More info on this can be found here -
The Force of Empty Space | Physical Review Focus
I was already aware of the Casimir effect, and I understand most of the math...the regulator functions, I only have some idea of what they are.
But the Casimir effect is more about the attractive/repulsive forces of empty space acting on things like closely separated plates.
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My main thoughts are along the lines of perfectgirl, and involve simple classical non-relativistic principles.
In our universe, from a classical perspective, there is matter and empty space.
Imagine an area where there is both a lot of matter and empty space, like before the formation of a planet. The area is surrounded by empty space.
As the matter condenses into a planet, the empty space "bubbles out" to the empty space. So we can conclude that empty space does indeed attract empty space in our universe, because the opposite of it, matter, attracts the opposite of empty space.
Now does empty space repel matter? Perhaps. Matter does tend to expel empty space from itself, when only accounting for gravity.
I find this situation analogous to "holes" in a semiconductor. They represent an absence of electrons in a sea of electrons. Nevertheless, these holes act as positively charged particles.