Supposing I take some object which is made up out of something which is very unrigid. Just a collection of point masses. Maybe let’s even say they’re not even exerting any forces on each other. It’s a cloud, a very diffuse cloud of particles and we watch it fall. Now, let’s suppose we start each particle from rest, not all at the same height, and we let them all fall. Some particles are heavy, some particles are light, some of them may be big, some of them may be small. How does the whole thing fall? And the answer is, all of the particles fall at exactly the same rate. The consequence of it is that the shape of this object doesn’t deform as it falls. It stays absolutely unchanged. The relationship between the neighboring parts are unchanged. There are no stresses or strains which tend to deform the object. So even if the object were held together by some sort of struts or whatever, there would be no forces on those struts because everything falls together.
The consequence of that is that falling in the gravitational field is undetectable. You can’t tell that you’re falling in a gravitational field by — when I say you can’t tell, certainly you can tell the difference between free fall and standing on the earth. That’s not the point. The point is that you can’t tell by looking at your neighbors or anything else that there’s a force being exerted on you and that that force that’s being exerted on you is pulling downward. You might as well, for all practical purposes, be infinitely far from the earth with no gravity at all and just sitting there because as far as you can tell there’s no tendency for the gravitational field to deform this object or anything else. You cannot tell the difference between being in free space infinitely far from anything with no forces and falling freely in a gravitational field. That’s another statement of the equivalence principle.
Question: You say not mechanically detectable?
Leonard Susskind: Well, in fact, not detectable, period. But so far not mechanically detectable.
Question: Well, would it be optically detectable?
Leonard Susskind: No. No. For example, these particles could be equipped with lasers. Lasers and optical detectors of some sort. What’s that? Oh, you could certainly tell if you were standing on the floor here, you could tell that there was something falling toward you. But the question is, from within this object by itself, without looking at the floor, without knowing that the floor was—
Question: Something that wasn’t moving.
Leonard Susskind: Well, you can’t tell whether you’re falling and it’s, uh — yeah. If there was something that was not falling it would only be because there was some other force on it like a beam or a tower of some sort holding it up. Why? Because this object, if there are no other forces on it, only the gravitational forces, it will fall at the same rate as this.
All right. So, that’s another expression of the equivalence principle, that you cannot tell the difference between being in free space far from any gravitating object versus being in a gravitational field. Now, we’re going to modify this. This, of course, is not quite true in a real gravitational field, but in this flat space approximation where everything moves together, you cannot tell that there’s a gravitational field. At least, you cannot tell the difference — not without seeing the floor in any case. The self-contained object here does not experience anything different than it would experience far from any gravitating object standing still or in uniform motion.
Leonard Susskind: What’s that? Yeah.
Question: We can tell where we’re accelerating.
Leonard Susskind: No, you can’t tell when you’re accelerating.
Question: Well, you can — you can’t feel — isn’t that because there’s no connection between objects?
Leonard Susskind: Okay. Here’s what you can tell. If you go up to the top of a high building and you close your eyes, and you step off, and go into free fall, you will feel exactly the same — you will feel weird. I mean, that’s not the way you usually feel because your stomach will come up and do some funny things. You know, you might lose it. But the point is, you would feel exactly the same discomfort in outer space far from any gravitating object just standing still. You’ll feel exactly the same peculiar feelings.
Okay? What are those peculiar feelings due to? They’re not due to falling. They’re due to not fall – well they’re due to the fact that when you stand on the earth here, there are forces on the bottom of your feet which keep you from falling and if the earth suddenly disappeared from under my feet, sure enough, my feet would feel funny because they’re used to having those forces exerted on their bottoms. You get it. I hope. So, the fact that you feel funny in free fall is because you’re not used to free fall. It doesn’t matter whether you’re infinitely far from any gravitating objects standing still or freely falling in the presence of a gravitational field.
Now, as I said, this will have to be modified in a little bit. There are such things as tidal forces. Those tidal forces are due to the fact that the earth is curved and that the gravitational field is not the same in — the same direction in every point, and that it varies with height. That’s due to the finiteness of the earth. But, in the flat space of the — in the flat earth approximation where the earth is infinitely big pulling uniformly, there is no other effect of gravity that is any different than being in free space. Okay. Again, that’s known as the equivalence principle.