Now, I don’t know. Maybe the doge or whoever they called the guy at the time said, no, no Galileo. You can’t drop things from the tower. You’ll kill somebody. So, maybe he didn’t. He must have surely thought of it.
All right. So, the result, had he done it, and had he not had to worry about such spurious effects as air resistance would be that a cannon ball and a feather would fall in exactly the same way, independent of the mass, and the equation would just say, the acceleration would first of all be downward, that’s the minus sign, and equal to this constant G. Excuse me. Now, G is a number, it’s 10 meters per second per second at the surface of the earth. At the surface of the moon it’s something smaller. On the surface of Jupiter it’s something larger. So, it does depend on the mass of the planet but the acceleration doesn’t depend on the mass of the object you’re dropping. It depends on the mass of the object you’re dropping it onto but not the mass of the object stopping it. That fact, that gravitational motion, is completely independent of mass is called or it’s the simplest version of something that’s called the equivalence principle. Why it’s called the equivalence principle we’ll come to later. What’s equivalent to what. At this stage we can just say gravity is equivalent between all different objects independent of their mass. But that is not exactly what the equivalence – an equivalence principle was about. That has a consequence. An interesting consequence.
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.