How did Einstein (invent? Discover?) that gravity is the geometry of spacetime and that mass bends spacetime?


How did Einstein (invent? Discover?) that gravity is the geometry of spacetime and that mass bends spacetime?

In: 7

He actually first conceptualized it by considering the case of light in an accelerating room. Because the light isn’t immediately connected to the room, it would appear to bend and move towards the floor, while the floor would actually be the thing accelerating into the light. Except, gravity works exactly like a constant acceleration upwards. So why wouldn’t it work the same way for light. And it turns out that it does work the same way.

The derivation and analysis took 8 years, but its also just a lot of really hard tensor mathematics, so I don’t have a complete grasp on it. Unsurprisingly, Einstein was a genius.

At the time, we had a theory of gravity from Newton (mass attracts mass) which had a property that troubled Einstein. He called it “spooky action at a distance”, where a sensitive gravity detector could measure a change if a planet vanished in a distant solar system before a sensitive telescope could see it. He wanted to produce a better theory that explained this more logically.

This got him considering the math of moving near the speed of light, which produced special relativity and then led to more math and general relativity. It’s all a theory, invented by a person, which made a number of predictions which subsequent scientists have discovered to be correct.

So…a lot of people kind of forget the context of state of physics in Einstein’s time.

Back then, there were observed issues with the Newtonian view of how gravity works (e.g. the motion of the planet Mercury didn’t *quite* follow what Newton said it should). This led to a lot of researchers looking for something that eventually got called the Luminiferous Aether, which was thought of as this invisible kind of matter that existed basically everywhere in the universe, and which only interacted with light. The search for the aether eventually led to the Michelson-Morley experiment, which basically shattered the idea of Aether theory by showing that the speed of light doesn’t change, no matter your reference frame.

Einstein basically took the result of Michelson-Morley (among a ton of other work being done at the time) and followed it. In doing so, he basically cast away what would be called “common sense” as Michelson-Morley had obviously blasted a massive hole through what was common sense in physics at the time.

From that he worked out Relativity, and after he published it a separate group of researchers tested it during the [1919 solar eclipse.]( Lo and behold, it was correct.

Einstein suspected that gravity is a fictitious force, and derive a theory based on that idea.

What’s a fictitious force? In the context of Newtonian physics, it’s a force that we only “see” because we choose a wrong frame of reference, an accelerating one. A famous example is centrifugal force: a force we feel if we sit on a merry-go-round. From our perspective, there is a force pushing us away from the center. From a perspective of a stationary observer outside, there are no such forces, we are pushed away through our own inertia. Our own frame of reference is accelerating compared to the stationary frame of reference, so things that are not accelerating in the stationary frame of reference looks like it’s accelerating, to us. We attributes this mysterious acceleration to a force, and that force is a fictitious force.

How would one begin to suspect that certain force is fictitious? After all, we can’t know if we are in an accelerating frame of reference or not: the earth moves around the sun, the sun moves around the galaxy, and even the galaxy also moves, so there is no ways to decide which frame of reference is stationary. But there is one way to infer. Let’s imagine we are in an accelerating frame of reference. Then it must cause all non-accelerating objects to be accelerated the same way, or more generally, all objects gain an additional acceleration that are all the same. The fictitious force that we use to account for this acceleration must act in such a way that all acceleration are the same; which means the fictitious force is proportional to mass. Knowing this, it’s very reasonable to assume that, a force that is always proportional to the object’s mass is likely to be a fictitious force. And in Newtonian physics, gravity is indeed proportional to the object’s mass.

From there, we are lead to Einstein’s elevator thought experiment. If you’re stuck in a small elevator, without seeing outside, can you tell if you’re accelerating in free space, or you’re being pulled by a planet? The answer is no, you can’t tell. (don’t take this thought experiment too literally though; this thought experiment’s elevator is supposed to be infinitesimally small)

Once we had accepted the idea that gravity is a fictitious force, then the next thing to do is to describe it not as a force, but rather, in term of how it causes objects to move. Previously, from his work on special relativity (as well as other scientists building up on it, particularly Minkowski), Einstein had known that constant motion can be described as a straight line in a 4 dimensional space called Minkowski’s spacetime. If constant motion result in straight line, and gravity is fictitious, then that means whatever path an object moves caused only by gravity must be a straight line (even if it looks bent to us). In order for a straight line to be to looks bent from the wrong perspective, spacetime must have curvature.

As for how Einstein knew that mass causes this curvature, it just comes from Newton, again. In Newtonian physics, gravity is dependent on mass of other objects, so obviously mass of other objects have to factor in.