[danbruc]

That is actually wrong, the equivalence principle requires careful wording. Imagine a point mass. Gravitational forces will always point directly towards it and therefore the direction of the force you measure within the elevator will vary a tiny bit in order to point exactly towards the point mass. It will also vary a tiny bit in strength because of the varying distance to the point mass depending on where you measure it within the elevator. On the other hand normal acceleration of the elevator will not show any dependence on where you measure the force.

[stolio]

Right. So sorry. "Constant" gravitational field. Happy?

But I agree, if you put the box within the event horizon of a black hole (aka near a point mass) the person inside the box might be able to tell, if they and the box were still intact. What I don't agree with is that splitting hairs on the divergence of the gravitational field is productive.

[danbruc]

But that's an important point, there is no such thing as a constant gravitational field besides no gravity at all. I only used a point mass because it is easier to visualize but the actual mass distribution does not matter. Therefore the simple statement that it is impossible to distinguish gravitational and normal acceleration is not true unless you restrict yourself to an infinitesimal small volume.

[stolio]

The comment you jumped in to "correct" was based on the equivalence of inertial reference frames which you can take up with Newton, and the equivalence of force-accelerated and gravity-accelerated reference frames which you can take up with Einstein.

If you don't like the thought experiment commonly used to give people an intuition about the Equivalence Principle then come up with a better one. I don't think yours holds up either, I'm guessing that thanks to the Uncertainty Principle you'll also need infinities to generalize it.

[danbruc]

The original comment correctly pointed out that you can make fictitious forces vanish by selecting a suitable frame of reference (which will not be a inertial frame of reference), he incorrectly stated that you can do the same with gravitational forces which you can not because they will at best vanish locally.

The response to my fist comment I could not fully understand but the last part of it sounds to me like it implied that a frame of reference only comprises a single point in space which of course is not true.

All in all my objection was the you can not treat gravity like fictitious forces which is an understandable and easy to make mistake if you base your reasoning on the simple elevator gedankenexperiment. I have absolutely no objections to the way the equivalence principle is introduced to people. So I am not really sure what we are arguing about, it seems to me that we - at least mostly - agree on the matter.

[stolio]

What I object to is this statement:

> And you don't have to leave your frame of reference to see a difference between acceleration and gravity, they are distinguishable in any frame of reference.

You're clearly presenting an idealized situation, which is fine. You've chosen a non-idealized (or less idealized) gravitational field, which is also fine. But the convention when talking about this particular subject is to also idealize gravity and take it as being the same everywhere. If somebody reads this statement with the usual definition of gravity, they might get the wrong idea.

All it needs is some signal that the gravity you're using is different (less symmetric) than usual. It is an interesting idea, I'm just saying maybe present it a little differently so people like me don't get confused.

[bashinator]

There are a lot of planetary science (née geological) experiments using various instrumentation to figure out variations in the force of gravity over land masses. I wonder if they account for what you're describing?