Physicist,
In an effort to more reliably condemn the error of Luther, we found ourselves stumped by this.
We know that, according to the general relativity, an observer in a car accelerating at a constant rate will not be able to distinguish between the effect of his acceleration and a certain gravitational pull emerging behind the trunk of his car. We know that this equivalence between a constantly accelerated frame of reference and a gravitational pull of a fixed mass reflects the equivalence between a timespace warp of the frame of reference fixed on the car, either effected by the acceleration or by a mass.
But let us imagine a car that is first stationary and then accelerated. Now acceleration is not constant but rather has increased from zero to A. The surface of a cup of coffee on the dashboard of that car will not merely tilt consistent with the cumulative gravity of the earth and the pseudogravity of the inertial force due to the acceleration, but it will splash out before it steadies at an angle. It seems that this effect cannot be equivalently understood in terms of mass, while it is easily understood in terms of inertia.
The question is, does the equivalence principle break for frames of reference with varied acceleration, and if not, how can an observer in the variedly accelerated car interpret his observations as gravity effects?
My theory is that the observer will conclude that a mass grew (or a fixed mass came closer) behind his car. But Stripes1776 theorizes that if a mass had grown behind the car, the coffee would not spill out of the cup, yet if the car jerks forward the coffee will spill.
Tell us what General Relativity teaches.
I'm not exactly clear on why the coffee would splash out, but if you arrange everything just right so that the final, tilted surface is just at the lip of the cup, then the surface should act as a damped pendulum, and slop a bit on the first few cycles of its oscillation. Is this what you had in mind?
The situation where the car "jerks forward" sounds different. It sounds as if the acceleration of the car is not constant (which is how real cars accelerate). But that's not a fair test of the equivalence principle, that's just a test of the mechanics of the car and driver.
In order to compare this to the gravitational field case, you'd have to have some way of "turning on" the mass behind the car. I don't know of any way to do this, so yes, the fact that you can turn a dynamic acceleration on and off rapidly would probably be a good indication that the acceleration was not gravitational in nature. But this isn't a violation of the equivalence principle: the equivalence principle is a statement about constant, uniform accelerations.
The damped oscillations of the coffee surface wouldn't constitute a violation of the equivalence principle, because that just tells you that the surface of the coffee was tilted somehow with respect to vertical in the recent past. If you tilted it somehow by the same amount in a gravitational field, and then let it go to find its equilibrium state, it would behave in precisely the same way, and slop the same amount.
In a real experiment, there would be better ways to distinguish between the car's acceleration and the gravitational field. For example, any real gravitational field will have some measurable divergence--the tidal force--whereas the car's acceleration will not. But this also is not considered a violation of the equivalence principle. It's just a feature of the specific experimental geometry, an "in practice" distinction rather than an "in principle" distinction.