Adam Brown: evaluation

Transcript context

…o make some gravito-magnetic theory that makes Newton’s second law an approximation that’s ultimately consistent with special relativity. In some grand sense, that is what we’re going to end up doing. That is what Einstein’s going to end up doing. But it’s going to be a much more radical departure than the Maxwell generalization of electrostatics. There’s really two hints, both of which are visible in this formula, that we’re going to have to do something slightly different than we did for electrostatics. The first difference between the electrostatic force law and Newton’s law of gravity is this sign difference. There is a big difference, which is that here it is a minus sign, and here it is a plus sign. That is reflected in the fact that if you have two positive masses—the Earth and the Sun—they gravitationally attract each other. Conversely, if you have two like charges, they electrostatically repel each other, which is why that’s a minus sign and that’s a plus sign. That means that you cannot do literally the same thing for gravity that you did for electromagnetism, because otherwise, if you did mathematically the same trick, you’d end up with mathematically the same result, which is that you would find that like masses would repel rather than attract. Not to get ahead of ourselves, but ultimately that’s because electrostatics is mediated by a spin-1 particle, the photon, and gravity is going to be mediated by a spin-2 particle, and that’s responsible for the change in that sign there. That’s why you can’t do exactly the same thing as electrostatics. So Einstein had to look for something else. He had to look for some other way to try and lift this to a relativistically invariant theory. In doing that, he had one clue. There’s lots of stuff going on. It’s part of Einstein’s central genius to focus on this as a highly significant clue of where he should look. It’s sometimes described as his most beautiful thought, that’s how he would describe it. The clue is this. There is another difference between the gravitational force law and the electrostatics, and that is the object that plays the analog of the charge in electrostatics, for gravity. It’s the fact that it’s the mass sitting here. That’s a strange coincidence from Newtonian physics. Mass, in electrostatic forces and accelerations, plays exactly one role. It’s sitting here. It’s the inertia of the object, and it’s what is resisting being accelerated. This is sometimes called the inertial mass. And then the charge is completely different and unrelated to the mass. You can have heavy objects that have no charge, like the neutron. You can have light objects, like the electron, that have high charge. There is no necessary relation between the charge of a particle and its mass. They’re just two entirely separate things. Not true in gravity. In gravity, this mass that’s sitting here in Newton’s second law—the inertial mass that’s resisting the force—is exactly equal to the mass that’s sitting here in Newton’s gravitational law, that’s telling you how much you’re pulled along. It’s the same mass. So this is sometimes called the gravitational mass, and this is sometimes called the inertial mass. in Newton’s gravitational law, that’s telling you how much you’re pulled along. It’s the same mass. So this is sometimes called the gravitational mass, and this is sometimes called the inertial mass. Unlike in electrostatics, the gravitational mass that appears in this formula is equal to what’s sometimes called the inertial mass that sits in this formula. This equation is already true in Newtonian physics. Newton noticed it, in fact, and did a number of experiments to confirm that this was true to one part in 1,000 or so. By the time of Einstein, we knew it was true to one part in a billion, and now we know it’s true to one part in 1015. It’s striking that these two—which in Newtonian physics is just a complete coincidence, essentially, that they’re the same thing—nevertheless were observed to be exactly the same thing. Einstein honed in on this fact, and it was his central clue for what to do next. This is sometimes called the equivalence principle. It’s responsible for the fact that if you take a feather and a brick in a vacuum chamber and drop them both, they will both fall and hit the ground at the same time. They’ll fall and hit the ground at the same time because even though the force on the brick is much stronger than the force on the feather because it’s heavier, that exactly cancels out the fact that the resistance to acceleration of the brick is larger than the resistance to acceleration of the feather, and they fall exactly at the same rate. The equality of those two is responsible for that exact equality. Einstein’s genius was to hone in on this as a central clue for how he is going to end up replacing Newton’s law. A reason it’s a central clue is because there is, in fact, another class of forces—not fundamental forces like electromagnetism or gravity, but a set of emergent forces—that exactly have this property baked into them, that’s guaranteed in those theories. To explain that, we’re now going to move over to the experimental section of this discussion. So here’s a bucket. Here’s some water filling the bucket. You better know your physics, Adam. Otherwise you’ll destroy the studio.…

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