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.)
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.
If you don’t mind, I have a question.
If I drive in a straight line on the Earth’s surface without stopping and I ignore mountains and oceans and other obstacles, then after 16 days, I will arrive at my starting point.
Why is this?
It’s because the Earth is a sphere.
This is a nice satisfying answer, whereas x^2+y^2+z^2=r^2, while perfectly accurate, is arguably less satisfying.
Given this context, my question is, for special relativity, why do time dilation and length contraction happen?
Ideally, I’m looking for an answer that has the same satisfying intuitive flavor as “Because the Earth is a sphere”, or at least is suggestive of that kind of answer.
Place two rulers right next to each other, and their length scales will agree. Now, place them at an angle, and have one ruler measure the other by orthogonal projection. Each of the observers represented by the rulers will conclude that the other one has 'contracted' by a factor given by the cosine of the angle.
Now, add a third ruler to complete the triangle. To go from one vertex to the opposite one, you can either follow along a single ruler, or via a bent path along two rulers. The symmetry has been broken, and the bent path will be objectively longer - that's the twin 'paradox'.
Things are more complicated than that because Minkowski space is non-Euclidean (for example, less time will pass for the travelling twin, ie the bent path will be the 'shorter' one), but if you want a simple analogy, I think that's a pretty decent one...
https://gravityandlevity.wordpress.com/2009/04/08/why-cant-i...
I guess a global object in spacetime analogous to a sphere in space is the hyperboloid t^2 - x^2 = r^2. Moving on this hyperboloid corresponds to changing boost velocity. But unlike a sphere, it is not closed, so moving in one direction does not get you back to the same point.
May add to this answer later.
For SR, I'm looking for an answer to "why?" that only has same satisfying flavor as the sphere question. I want the same "aha!" feeling.
For example, if I stand up from the sofa and walk across the room and come back and sit down next to my friend, I want a deep intuitive sense that of course it must be the case that less time has passed for me than the amount of time that my friend has experienced. Why does this happen?
An answer like "t'=t/sqrt(1-v^2/c^2) describes what happens", while correct, is not satisfying.
Similarly, if I wave my hand in front of my face, I want it to seem obvious to me that less time must have passed for my hand than for the rest of my body.
Given your experience writing the book, you must have developed an intuitive sense for the behavior of the effects of relativity and why they happen, so I am wondering how you would translate that into words for a general audience.
Imagine the context where a random person with a minimal math background at a party was to ask you why less time passes in the sofa scenario, using an actual sofa to demonstrate it.
They stand up and walk away from you and return and sit back down next to you and they want you to explain to them why less time has passed for them. They want you to explain why the room around them got shorter in the direction that they were walking.
These are effects that, while undetectably small, really happened.
They want to know why.
How would you answer their question?
https://en.m.wikipedia.org/wiki/Moving_magnet_and_conductor_...
I think a lot of avenues of core sciences need books like these that are deeper than popular science but are accessible to someone who is not doing it for a living.
It’s a compact book of essentials for mathematically minded people*. It’s not a shallower-than-textbooks accessible introduction one step up from pop science.
* If you only ever took some linear algebra and calculus for engineering students, this probably doesn’t describe you.
- rigorous treatment of the material
- no bullshit fluff
- exercises that you can do to think about the material and test your comprehension (often 50-100% of the answers are available online)
- systematic treatment used to train real physicists
In my experience, it's all about the homework. The rest just supports that.
Sure hope there's a similar primer on QFT.
The article https://people.carleton.edu/~nchriste/PTO000041.pdf gives an overview of the ways and books to learn GR. It does not cover some more recent intro books.
If you like "physics first" then I am a big fan of Hartle's book.
