# General Relativity General relativity is a specific theory that lives within the framework of [Special Relativity](Special%20Relativity.md). It is more specific than special relativity. It is the theory of special relativity when you let spacetime be curved and you give it a specific way of being curved and you call that gravity. In curved spacetime objects want to move on the closest thing they can to a straight line. So the motion of the earth around the sun, *in spacetime*, is the best it can do to move around a straight line. It doesn't seem straight to us because there are no absolutely straight lines, because spacetime is curved. That is [the big idea of general relativity](https://youtu.be/353lEB63iyg?t=1620). Gauss and reimann said that if you go to small regions of space things look euclidean. But einstein said if you go to small regions of spacetime things look minkowskian. We can chose coordinates in which the metric looks like flat minkowski space at one point. That is the mathematical translation of the [Principle of Equivalence](Principle%20of%20Equivalence.md). Differential geometry says that we can make the metric look minkowskian in a small region of spacetime. The curvature tensor tells you the geometry of space, but we derive that from the metric. General relativity is the theory of dynamical spacetime, in which curvature gives rise to gravity. A great video detailing the **metric tensor** in is [here](https://www.youtube.com/watch?v=Hf-BxbtCg_A). * So in the train cars frame, which is accelerating forward, it is as if there is an additional gravitational field which points backward https://youtu.be/NblR01hHK6U?t=222 * So accelerated frames of reference mimic a gravitational field in the opposite direction of the frames acceleration * An interesting way to think about this is that there is "artificial gravity". We can combine it with real gravity to result in gravity that will point down and back * For all you know you could be completely at rest, tilted upward, in a completely inertial frame * Einstein asked, what if gravity was also fake? In other words, what if the gravity on earth was generated because earths surface was really accelerating upward? TODO: Add deutsch's commentary: [David Deutsch - What is Truth? - YouTube](https://youtu.be/3eEffbjzNwE?t=303) --- Date: 20221228 Links to: Tags: #review References: * [Demystifying The Metric Tensor in General Relativity - YouTube](https://www.youtube.com/watch?v=Hf-BxbtCg_A) * [The Biggest Ideas in the Universe | 16. Gravity - YouTube](https://youtu.be/353lEB63iyg?t=1620)