hossi said:
I understand the equivalent principle this way: locally physics is as in special relativity.
This means, if I understand correctly, that locally, (apart from tidal effects), you cannot observe any gravitational field to distinguish it from a uniformly accelerating frame, right ? So it is sufficient to "accelerate in the other direction", in other words, to "fall along", and everything should happen AS IF THERE WAS NO GRAVITY, right ?
Now, consider a local inertial frame initially "falling along" with your anti-gravity particle, towards the sun, say. It will have, at a certain point, a certain position and momentum, so we can define a "tangent" inertial frame. In this frame, initially, your anti-gravity particle is at rest, right ? But it won't stay that way ! It will start accelerating in your local inertial frame! On the other hand, a normal particle, initially at rest in your inertial frame, will stay at rest - by definition of it being an inertial frame.
So your inertial frame is only an inertial frame for "normal" particles, and not for "antigravity" particles ? But then locally, physics is NOT as in special relativity, no ? Where particles, free of interactions, should follow a uniform motion (and in particular, when initially at rest, should stay at rest). Some do, and others don't. And from this difference, we can then find out, locally, that the "inertial frame" is falling in a gravity field.
Let's now go to outer space, far away from our galaxy, and put ourselves in a rocket, floating freely. We now put our anti-gravity particle at rest in our rocket: it stays at rest. And so does the normal particle.
So we succeeded in making a difference between a free falling frame in a gravity field, and a "true" inertial frame in outer space. Exactly what was forbidden, no ? The entire idea of the equivalence principle was that this was impossible, I thought. I don't see how you can *partially* relax this. Something is impossible in principle, or not. For instance, in special relativity, it is in principle impossible to distinguish one inertial frame from another, by just doing local experiments. That's the entire contents of the relativity principle (which is already present in Galilean relativity). From the moment that there is ONE single way to do so, the entire structure of special relativity falls apart ; or even, galilean relativity falls apart (that was exactly what happened when the Maxwell equations defined a single velocity c which could be locally measured: the effect of having a way of locally establishing an absolute velocity killed off Galilean relativity, and hence the group of galilean transformations and introducing the ether ; only to be replaced by special relativity and the Lorentz group). There was no way to partially relax galilean relativity: after having an absolute c, it was dead.
What's supposed to be impossible, by the equivalence principle, is to make a distinction between a free-falling frame in a uniform gravity field, and an inertial frame "in outer space". At least, that's how I understand it.
With my normal particle / anti-gravity particle set, I can make the difference ; I can even find out the absolute acceleration of the gravitational field that way, and hence the "background" inertial frame in which this gravitational field is present. And if that's the case, then the entire geometrical picture of gravity as a curved 4-dim spacetime manifold falls apart, no ? Because we now have a NON-CURVED background spacetime on which we have gravity as a field, like any other.
And once we have that, to me, the equivalence principle and from it, the requirement of general covariance, are dead. In the same way as galilean relativity, and its related group, were dead after having a fixed c.
The referee reports on the other one were pretty weird btw. For some reason I got 4 of them at once. They all said, its obvious. Then I wrote back, yeah, well, might not be obvious for everybody and that was it.
look what I just found 
Hey, I am serious about my anti-gravitation stuff. The cosmological implications are quite interesting. There is nothing spiritual about it, it's just a GR-extension. I don't think that is weirder than http://en.wikipedia.org/wiki/Quintessence_(physics)" .
Of course, my fqxi application (which I never intended accepting) was rejected. I regret deleting the letter I received, which contained some very flowery language and proudly informed me that I was now on their mailing list. Until then I wasn't quite sure whether to think of fqxi as another ordinary research institute, or not.
