An idea I had a while ago, I don't know if it's wrongheaded or not but it's a fun thought anyway.
Imagine a bed of nails in the middle of empty space. The nails are very thin, but very massive, and very densely packed.
Consider a point next to the flat side of the board, the side opposite the nails. Now compare it to a point just the other side of the board, amongst the nails. The point on the nailed side is nearer to more massive objects, thus has more gravitational spacetime stretching. The space on the nailed side is ever so slightly bigger than the space on the flat side.
Now consider the density of virtual particles. If the density is constant, then there will be more virtual particles where there is more space. So there's more virtual particles on the nailed side of the board than the flat side. This would cause a tiny pressure, pushing the board in the direction of the flat side.
Yes, there would have to be many many nails, short, massive, and thin, and the pressure would still be infinitesimal. But... if the density of virtual particles is indeed constant over all space, there would be some pressure.
If anyone has information about virtual particle density, I'd be interested to hear it - /msg me.