Say I’m in a box the size of the Pontiac Silverdome. I am feeling a force that is pulling me downward. It feels like gravity. Is the Silverdome big enough for me to determine if 1) I’m dealing with gravity or 2) the entire house that Barry built is hurtling through space at 9.8 m/s^2?
Nope. If the box is sealed, i.e. you have no reference frame beyond the box, then you cannot determine whether the force to which you are subject results from gravity or acceleration from the rocket thrusters under the Silverdome.
That’s what I thought, but Lance and the Good Doctor’s statements clearly imply that that only holds true inside a “small enough” box. I’m very curious to find out what that implication means.
If the box were large enough to include an object such as the earth, it would be rather apparent that the force to which you are subject would be gravitational in nature (assuming the object is present). It’s all a matter of the construct of the box and what is thereby permitted in your reference frame. Conversely, if a box were very large, but didn’t enclose a massive object at a great distance, you would not be able to discern if you were subject to a weak gravitational field or accelerating independently (assuming your rocket thruster is outside the box). BTW, freefall is being subject to a gravitational field, weak or otherwise.
I belive that the “small enough” caveat is in place because gravitational force decreases as you move away from the source. Therefore, if you measure gravitational pull at the top and bottom of your Silverdome box, and the value at the top is less than the value at the bottom, you’re in a gravitational field. If they’re the same, you’re accelerating.
zut is correct, but that is not exactly what I was thinking. If you are in a gravitational field, the path of dropped objects will converge toward your feet. In order to detect the convergence, the box would have to be wide enough. There are also tidal effects that could be used.
Nen’s point is also relevent. If the box contains the source of the gravity, you know the force is not from acceleration.
Actually, come to think of it, both the explanation that I posted and the one that Dr. Matrix posted require that there be acceleration or gravitational pull. What about the second part of the OP, i.e., Lance Turbo’s
If the box in free-fall is big enough, can you measure the “tidal effects” that you referred to, Dr. Matrix?
I guess the centre of gravity of the box will actually be in freefall. The parts of the box closer to the planet will be fractionally slower than true freefall, and the parts of the box further from the planet will be moving faster than true freefall.
So, if you have a big enough box, you can tell whether you’re in freefall or zero gravitational field by putting objects near the box walls and seeing if they move closer or further away! Might have to wait a few weeks to be sure. Although if you’re in ballistic freefall rather than orbital, you’ll find out rather soon.
The issue of a large box versus a small box is whether or not you can actually perform the experiment, and whether or not you can visualize the experiment.
As has been noted, in the radially-oriented field of a real “massive body”, generating gravitational force that decreases with distance from the body, you can detect the difference between gravity and straight-line acceleration inside a box by the convergence or non-convergence of the paths of free-falling objects or the presence or lack of “tidal” effects. In principle, this can be done no matter what the relative sizes of the box and the body are. In practice and in thought experiments, these effects are ignorable and indetectable if the box is very small relative to the massive body and the distance from the massive body.
The General Theory of Relativity allows for space to be warped in such a manner that the “force vectors” of the gravitational field are truly parallel and their magnitude does not depend on the observer’s position in space. There is no way in principle to tell the difference between straight line acceleration and such a gravitiational field from the inside of any box, no matter how large. But it’s hard to visualize how such a field would arise, and we haven’t a clue how to actually create such a field.