I'm not sure who this is supposed to be useful to; I'm not sure how anybody can understand it unless they have completed an undergraduate degree in math AND already have a solid conceptual understanding of relativity.
It is extremely dense.
It is extremely dense.
The prerequisites are clearly listed:
> Prerequisites: vector calculus and classical mechanics
Do you not find this accurate?
(Note that classical mechanics means the typical physics undergrad classical mechanics - where you know diff eq and things like Lagrangians and calculus of variations).
It works well as an outline from my point of view, but I think you have to assume the reader already understands the Lagrangian in classical physics (which is a stretch for even the comparatively well-educated Hacker News audience). Also, somewhere around 3.5 it gets too dense with material I don't already know. (Christoffel symbols? Riemann curvature tensor?)
And then in the General Relativity section, there's simply too much material covered for any of it to be explained in depth beyond the necessary equations. I would drop the fluids (at a minimum) to give more space for other topics.
For relativity with more explanation and not much math I suggest
Relativity (The Special and the General Theory) by Albert Einstein, 1916. Translated to English: ISBN 0-517-029618
I think the book is still in print, and new and used copies are cheap if you shop around.
It is good reading if you want the details explained step by step.
The reason for time dilation and the other facets of relativity pretty much come down to the fact that objects either move or change, but cannot do both simultaneously. One can think of time passing inside a spacecraft or object as internal movement, as oppose to the external movement of the spacecraft throughout the cosmos. Each bit of energy provides h (Planck's constant) action, a measure of change of state. The more the object allocates toward external movement in space, the less it can allocate for internal movement / internal changes, which is what observer time really is. Even though I say external vs internal, I am not violating relativity. The reference frames are relative, we do not need an absolute reference frame.
Doubly special relativity deduces most of these elegant derivations by assuming there is a smallest quanta of energy possible, but nonetheless, these concepts can be derived just by understanding the role of mass as loops of energy, energy as an allowance for change of state, and time as the usage of energy for internal change of state, and movement as the usage of energy for external change of state.
Relativity is just the consequence of energy's connection to information and movement.
An interesting (if unusual) viewpoint; I wonder if this could lead to (a more realistic) quantum gravity.
> objects either move or change, but cannot do both simultaneously
This does make time slowing down inside a moving object kind of obvious. (I wonder if this description based on action/energy quantization turns out to be equivalent, at a certain level, to the essentially geometric picture of the classical relativity.)
Gravity being quantum would most likely indicate that position is also discrete.
Since all energy, being allocated for external movement or just internal time, produces the same amount of gravity, it appears that the act of any state change induces gravity. Einstein never really gave a physically understandable reason for why all change causes gravitation, but it's likely similar to a ship in water. If the ship is rocking really fast, the waves that emanate from it can pull objects towards it. The rocking is just state change and even for a rest mass, we know that it's a loop of energy, there really is no static storage of mass.. it's a process of energy containment and cyclic change.
For instance, your second paragraph: No, objects move or change at the same time, just at different rates. And an object can be moving in one frame of reference, and only "changing" (time passing) in another.