One of the most famous equations in mathematics comes from special relativity. The equation — E = mc2 — means “energy equals mass times the speed of light squared.” It shows that energy (E) and mass (m) are interchangeable; they are different forms of the same thing.

What is general relativity? Essentially, it’s a theory of gravity. The basic idea is that instead of being an invisible force that attracts objects to one another, gravity is a curving or warping of space. The more massive an object, the more it warps the space around it.

The theory explains the behavior of objects in space and time, and it can be used to predict everything from the existence of black holes, to light bending due to gravity, to the behavior of the planet Mercury in its orbit. The implications of Einstein’s most famous theory are profound.

Albert Einstein, in his theory of special relativity, determined that the laws of physics are the same for all non-accelerating observers, and he showed that the speed of light within a vacuum is the same no matter the speed at which an observer travels.

While relativity has a reputation for being intimidatingly difficult, it’s a peculiar kind of difficulty. Coming at the subject without any preparation, you hear all kinds of crazy things about time dilating and space stretching, and it seems all very recondite and baffling.

General Relativity is more mathematically difficult than non-relativistic quantum mechanics (which is what most people mean when they say “quantum mechanics”). Special Relativity. (non-relativistic) Quantum Mechanics. General Relativity.

In February 2016, the Advanced LIGO team announced that they had directly detected gravitational waves from a black hole merger. This discovery, along with additional detections announced in June 2016 and June 2017, tested general relativity in the very strong field limit, observing to date no deviations from theory.

Most self-contained courses or texts on general relativity teach the necessary differential geometry to understand how gravitation works. Otherwise, a little multivariable calculus and some linear algebra are probably all that you need as a prerequisite.

The best way to learn General Relativity and Gravity are to watch these video lectures on YouTube from The WE-Heraeus International Winter School on Gravity and Light 2015 Central Lectures. Schuller has the best and most clear and mathematically rigorous (and he teaches it very well) exposition on the subject.

At the time he was conceiving the General Theory of Relativity, he needed knowledge of more modern mathematicss: tensor calculus and Riemannian geometry, the latter developed by the mathematical genius Bernhard Riemann, a professor in Göttingen. These were the essential tools for shaping Einstein’s thought.

It takes about 10 minutes to understand General Relativity. Einstein thought of it very quickly, but it took Einstein eight years to do the math and that was with a lot of help, so it’s going to take a long time for most anyone to understand the math.

Here you have it:

1. Start with the old edition of the small Schaum book ‘Vector Calculus’ by Murray M.
2. After the Schaum, study the book “The Meaning of Relativity” (1922) by Einstein.

You need to learn:

1. Calculus (to a very high standard)
2. Linear Algebra.
3. Tensor Analysis.
4. Classical Mechanics (yes, really)
5. Electromagnetism.
6. Special Relativity (and you need to know this until your eyes bleed 4-vectors)
7. Differential Geometry.

Tachyons are hypothetical particles that travel faster than light. According to Einstein’s special theory of relativity – and according to experiment so far – in our ‘real’ world, particles can never travel faster than light.