Duhoc said:
There is obviously a distinction between space and space time. But even so, if spacetime is curved it must have a physical nature because only a physical think can curve.
No, it doesn't. There are several misconceptions here.
One problem is that you are implicitly looking at things from a perspective of Newton's absolute space and absolute time as if that is the "correct" way to view things. Physicists have known for over a century that that view is only approximately correct, and then only when objects are moving very slowly compared to the speed of light, and distances between objects are very large compared to the Schwarzschild radii of those objects. When velocities become large or distances become small you have to completely abandon those Newtonian notion. They aren't even approximately correct to any reasonable definition of "approximate". They are just wrong.
Forgot gravity for a bit. (I'll get back to it later.) I'll start with special relativity. Stealing an idea from the new Cosmos series, let's suppose we have a ship of the imagination, but one that is a bit more bound to reality than Tyson's. Our ship can't go faster than light, it can't backwards or forwards in time. What our ship can do is accelerate wildly (1000 m/s
2, or a bit over 100 g), and without rockets. By our watch, our ship will leave the Milky Way behind in a couple of months. In ten more days we'll have reached the Andromeda galaxy. In just three more days we'll have left the Local Group behind. Along the way, we'll see something funny happening to the stars to the side of us and behind us. They'll start migrating towards our front. By the time we've left the Local Group behind, almost all of the observable universe will appear to be directly in front of us, and what was visible light will have become very deadly gamma radiation. (Our ship needs some good shielding, which it has. It's made of unobtainium.)
Are the stars and galaxies truly moving from our rear to in front of us as we get ever closer to the speed of light? It certainly is what we see. If we turn our ship around accelerate in the other direction for 72 days they'll appear to have moved moved back to their rightful places, just shifted by 10 million light years. And how can we have gone 10 million light years in 144 days when the speed of light is the ultimate speed limit of the universe?
If we reverse this process and return home, we'll find a very different solar system and a very different Earth compared how they were when we departed. The solar system will be in a different part of the galaxy, and the continents will have moved. Our 288 day trip will have taken us 20 million years into the future. We haven't done any time traveling. Our little jaunt was the twin paradox, gone wild.
Until we develop that unobtainium-based shell and space drive, our spaceship will have to remain in the realm of the imagination. However, the mathematics and physics of that trip are very real. You have to discard your Newtonian worldview if you want to understand relativity theory.
Another problem with your view is your thinking that something physical must be happening to space-time, that space-time is a physical thing.
All of modern physics has a base below which there are no answers, just descriptions. In quantum theory that base is pretty deep, but it's still there. What does the Higgs exist? What are electrons and quarks, really? Good question. Physics doesn't have an answer. The standard model of physics is just that, a model or map to the world of the very small. In relativity theory, the base is fairly shallow. It's the Einstein field equation. General relativity is the physicist's mathematical description of what happens to moving objects with mass-energy. What makes general relativity happen? Physics doesn't have an answer. General is a map that describes what happens the world of moving objects.
The territories that those maps describe are distinct from those maps. A physicists job is mapping those territories. Don't confuse the maps for the territories.