Adam Brown – A deep but accessible introduction to general relativity

**Dwarkesh Patel** (0:00)
I'm back with Adam Brown. You currently need Blueshift at Google Deep Mind, which is cracking science and reasoning. In a previous life, Adam was a prolific physicist, taught at Stanford, and did research on everything from cosmology to string theory to general relativity.
It's said that general relativity is the most beautiful thing the human mind has ever conceived or seen. And I was curious if there's a way that ordinary people like me could understand what is happening or have some vintage on why it's beautiful without taking your 20-lecture graduate course. So, that was the prompt for this lecture, and I appreciate you being willing to do it.

**Adam Brown** (0:31)
Super exciting to be here, and yes, I think the answer is yes, yes, we can. Yeah, so, I mean, general relativity, Einstein's theory of gravity is, I think, as you say, like the most beautiful product of a single mind that we've ever created. It's one of the two great theories of 20th century physics, along with quantum mechanics. And unlike quantum mechanics, it was basically Einstein, he had a little help, but basically one person doggedly pursuing this idea for 10 years, and then wrote down this theory that ends up describing the motion of planets in the solar system, and also the origin and fate of the universe, and it's pretty extraordinary. And it took Einstein, one of the most famous minds in history, about a decade to figure it out. But, you know, when I teach it, I'll do a 10 week course, and so in 10 weeks, people will get a better idea of general relativity than Einstein really had in 10 years. And that's kind of because we have an advantage that Einstein didn't have, which is that we have Einstein, and many others like him going before us, who were able to take these super complicated ideas that were understood at the time as being totally incomprehensible by anybody with a sub-Einstein level of intelligence, and boil them down to their essentials, and not make many of the same mistakes that were made by our forebearers. I think in 10, 20 minutes, I can't give you a better idea of general relativity than Einstein had, but we can get to the core insight. What Einstein said was his most beautiful idea, and push through it to try and understand what the central idea of this theory is. Okay, let's go. Before general relativity, there was special relativity. So special, meaning it doesn't apply everywhere. That was also invented by Einstein 10 years earlier, in 1905, during his Annus Mirabilis.
And if you want to sloganize special relativity, you would start with the observation or the hypothesis that nothing can go faster than light. Special relativity takes that observation, promotes it to a principle, takes that principle extremely seriously, as the sort of central observation of our understanding of space-time. And you arrive at special relativity. Special relativity applies to electromagnetism. It applies, though Einstein didn't even know about these at the time, it applies straightforwardly to the strong and weak nuclear forces, to the other fundamental forces that we know about. It does not obviously apply to gravity. And so that was corrected 10 years later by Einstein.
In his general theory of relativity, a theory more general, because it includes gravity, completes the set of fundamental forces. Again invented by Einstein after 10 years of dogged pursuit in 1950 If you wanted to sloganize general relativity, you might say, not even gravity. Nothing can go faster than light, not even gravity. There's much more to it than that, but it's going to complete this arc of the centrality of nothing being able to go faster than the speed of light.
Okay, so to see some background here, we're going to have to rewind.
We're going to have to rewind all the way back to the theory of gravity that existed before Einstein. The reigning theory of gravity at the time of Einstein stretches all the way back to Newton in the late 17th century. So, let's talk about that. So, Newton's laws in his Principia in 1687 Newton's laws, well, he had a few. And, you know, maybe the one that we most talk about today is two of them, which is his famous second law that says the acceleration, A, caused by a force, is given by the formula MA equals F, that if you have a force F, it will cause an acceleration on an object given by A, where the mass tells you how much an object resists being accelerated. The bigger the mass, the bigger the force you need to do to cause a given acceleration.
And this law, his second law, will turn out to be still true once we come to general relativity. We'll have to have a more sophisticated understanding of what we mean by force and acceleration, but this will be preserved by general relativity. A special case of the second law is Newton's first law. Newton's first law says that if the force is zero, then the acceleration is zero. If the force is zero, then objects continue to move on a straight line at all times. And that will also continue to be true in general relativity, that if not subject to an external force, objects move along straight lines. However, we'll have to upgrade our understanding of what we mean by force and what we mean indeed by straight line. Okay, that's going to keep being true. The one that's not going to keep being true is Newton's law of gravity. So Newtonian gravity, this tells you what the acceleration is in response to a force, you need to know what the force is to be able to do anything with that. And Newton's law of gravity says that the force caused by the gravitational interaction of two bodies is what's called Newton's constants, just some constant of nature, times the mass of one body, times the mass of the other body, the mass of the sun, times the mass of the earth, divided by the distance between them squared, his famous inverse square law. And it points, it's a vector that points in the direction of separation, and it's attractive. So there's a minus sign there.