The Theoretical Minimum (2013)
theoreticalminimum.com
theoreticalminimum.com
As far as I am aware there are two ways to approach physics: basic algebra based (simplified) as its typically taught in high school and calculus based (the proper way).
Since I do have a solid grasp on linear algebra and calculus, are there good calculus based physics books that don't assume any previous exposure to high school type physics and are suited for self learning?
You aren't missing anything by not doing calculus based physics, you have to "learn" it again from scratch.
I actually first learned about calculus from this chapter :)
The Theoretical Minimum - https://news.ycombinator.com/item?id=14467181 - June 2017 (37 comments)
Modern Physics From Scratch - https://news.ycombinator.com/item?id=5702985 - May 2013 (49 comments)
I prefer this modern presentation (animations, simulations, plots) over the antiquated chalkboard presentation.
After trying to scour and even reading many books in this area, most that are either highly abstracted for the 'pop-sci' reader (like me, with no training in physics) or were all-out textbooks, I chanced upon Susskind's lectures and the Theoretical Minimum series. I started off right from the basics and IMHO, it has the right balance between introducing concepts and making sure you internalize them by having you actually work on problems (highly recommend that you don't skip these). I am nowhere near close to understanding any of this yet but it gave me at least an orientation for what to expect and how to prepare. Once I get a bit of time and the interest back again, I expect to go back to the other books in the series.
I went through the two courses on relativity and enjoyed them. They were super mathy, but I expected that going in. I had to stop them for a while and actually strengthen my math skills. I'd say my understanding is C+ at best, but like Isinlor's comment, I'm pretty sure all the relativity woo is out of my head.
Relativity does not have to be super mathy, special relativity is kind of just a postulation that maybe there's a different sort of Doppler shift in the world. In the normal Doppler shift, clocks moving towards you appear to tick fast and clocks moving away from you appear to tick slow. Relativity adds a universal effect where if you accelerate towards a clock, it will also appear to tick faster, in proportion to both your acceleration and its coordinate along that acceleration line. So it's just an anomalous Doppler shift, to first order. (And all higher-order behavior can be derived from that.)
So like in the twin paradox, it is resolved because one of the twins accelerates towards the other twin, and when that acceleration is happening the other twin gets much much older very quickly because they are far away and the twin is accelerating towards them.
Furthermore this makes it much easier to understand some aspects of general relativity quite quickly. For example you get gravitational time dilation without much effort, once you postulate that the state of nature is freefall and we are actually accelerating against that, in a constant acceleration g upwards, which is why things in the natural state of freefall appear to accelerate downwards with acceleration g, you immediately predict that relativity will tell you that you see clocks in the upper atmosphere tick faster than they do down here. Furthermore you predict that if you could see through the Earth, at some surface below you you would hypothetically see clocks stand still, leading into a quick intuition for black holes.
To give it some context: I watched classical mechanics a bit. Basically it's just math in the end, and to be honest after 50% of the lectures I had the feeling that the "practical" side or "intuition" is lacking. Especially in case of the conservation law's.
So maybe the question would be how much more do you get if you go through a true physics bachelor progamm?
I think you can learn here the core concepts in theorethical phisics even at the masters program level, but you will not go through the same "math muscle training" that college students go through, so you will have to supplement that from elsewhere.
Susskind's courses are very much overviews / appreciations. For each of these areas (GR, StatMech, Quantum etc.) you would expect several 30-hr lecturer courses + problem sheets (or equivalent working through a textbook) to gain a deep knowledge.
> how much more do you get if you go through a true physics bachelor program?
Every physics major will spend countless long nights working problems with pages and pages of algebraic manipulation and mathematical reasoning. It is (and must be) much more mathematical than what you see in the Susskind lectures. They're not intended to be an alternative to a traditional program, but IMHO, they do give a true understanding of the main concepts in physics.
Looking at Susskind's youtube, he has massive amount of content on Special Relativity (https://youtube.com/playlist?list=PLD9DDFBDC338226CA). Content-wise, it's the same as what a physics major would see, but without the many, many hours of problem solving exercises. The wonderful thing about Special Relativity is that it takes not a whole lot more than careful reasoning, a fair amount of algebra, and a little calculus to understand. The Susskind lectures actually go a bit farther, applying Special Relativity to Electro-Magnetism
One of the issues that Physics has (as a field) that others do not suffer, is a proliferation of cranks. I suspect that Susskind intends, in part, to counteract the cranks by providing solid, correct informational resources to the general public.
I really miss doing physics!