How to learn physics?

Question

I am an engineering student (CSE) in India..But recently I have developed a strong love to physics..I want to learn physics and understand it in deep..I know physics is the search of deep fundamental laws of nature.That means I need to start from first principles and extrapolate from it?How should i learn physics?

Answer 1

The resources you use actually don't matter as much as how you study them -- the best way to understand stuff in physics (and also math) is to look at a variety of sources and figure out the basic insights/axioms -- often empirically rooted insights -- that lead to the subject, then derive the entire subject for yourself. This means you stumble across all the insights that the guy who first discovered it came into, and you have a complete intuition (and the formalisation of this intuition) of the entire structure of the field. Then you go back, and think about how you could have come up with those initial insights yourself.

For instance -- if you're learning special relativity, you first have a scattered understanding of a bunch of seemingly (somewhat) disconnected laws and theorems in the theory -- you've got the dynamics equations someplace, then you see the Lorentz transformations, etc. You know something about how $c$ is the "speed of things in spacetime", and different speeds are just different angles in spacetime, yada yada. So you start drawing these spacetime diagrams, seeing what results you can get from them -- you realise you're dealing with linear transformations, and you spend some time determining exactly what the transformation is (it's a skew), and reconcile this with what you earlier thought (that it's a rotation). This allows you to come up with rapidities, and you discover things like Minkowski dot products and the Lorentz group.

Now you have a complete theory of spacetime, and can figure all sorts of things from it. But then you realise -- you can't figure out everything from it. From what you've already skimmed from some sources, you know things about how momentum transforms, and how mass transforms. You try to derive these, but keep encountering circularities in proofs you find online. Then you realise, the issue is really a definitional one -- how do you define momentum in relativity? How do you define energy in relativity? The natural way to define these comes to you in the form of conservation laws, so you immediately start formulating some thought experiments, and after some trial and error, you have discovered a completely non-circular series of arguments that allow you to define dynamics in relativity. And then you look closely at the expressions you've derived for energy and momentum -- and voila! They seem to follow the exact same relationship as time and space do. So you've stumbled across four-vectors, and you have a complete theory of relativistic mechanics, and your understanding of it is so deep you can solve seemingly any problem with it.

The reason this skim-and-discover method works so effectively, is that you can rediscover all the important insights for yourself, but do it without taking centuries, because you already have the starting point, but can still develop the experience of having discovered them via the "think about how you could've discovered the starting point yourself" stuff. It's also important to study mathematics alongside physics -- there are often extremely strong connections -- almost equivalences -- between certain areas of math and certain areas of physics (perhaps it's because the math was developed for the physics). E.g. special relativity and linear algebra (the basic geometric stuff), quantum mechanics and linear algebra (the more abstract, general stuff), general relativity and differential (at least Riemannian) geometry, etc. Learning them side-by-side helps you get the full set of insights, it's like learning two similar languages (or languages that share a similar script) side-by-side.

With that said, resources still do matter, and the best resources are those which derive things fully, giving close attention to avoid circularity. It's also useful to have good exercises, but sometimes you can make these up yourself. Definitely avoid popular science ("math-free" books), and in the same spirit avoid any texts that claim to specifically avoid a certain mathematical formalism (e.g. "non-calculus-based" mechanics), because usually this formalism is the best, most appropriate and relevant formalism for the task (avoiding it because you don't understand the formalism is like using a glue-stick to assemble your home because you're out of nails).

It's also important to learn roughly "in order" -- you don't need to be very steadfast about this, you can learn general relativity before statistical physics, but you probably shouldn't learn string theory before statistical physics (even though technically "you can", you won't learn to think like a physicist if you do).

Here's a reasonable ordering, with good resources that satisfy the description I mentioned:

1. Newtonian mechanics, classical gravity -- Jewett & Serway Learn alongside single-variable calculus and differential equations.
2. Electromagnetism -- you actually don't need to know this in full detail before going to special relativity, but you need a theoretical understanding of the Maxwell equations and how they predict a wave if you want to understand the empirical motivations behind relativity. You should also have a good understanding of basic stuff like polarisation before learning quantum mechanics (it's one of the justifications for Born's law). Learn alongside multivariable calculus.
3. Analytical mechanics, at least basic Lagrangian -- The IITs in India have a very nice lecture series on this, google "V Balakrishnan NPTEL classical mechanics". Learn alongside calculus of variations.
4. Special relativity -- learn from all over the place, if you ever get really stuck (for a week or so), consult the Feynman lectures (I don't like some of his dynamics proofs, though), or better Einstein's original paper (there's a good translation with comments from Stephen Hawking in "A stubbornly persistent illusion"). Learn alongside first-year linear algebra.
5. Thermodynamics, statistical physics -- there are many good books on the subject, but I'd recommend you pick up a graduate-level text right away, at least if you know all the undergrad stuff (it's impossible not to). Learn alongside statistics (distributions and stuff).
6. Quantum mechanics -- NPTEL is good again, but there are other sources too (you can start with the wikipedia article on matrix mechanics, and a recent 3blue1brown video called "some light on quantum mechanics"). Learn while discovering abstract linear algebra for yourself.
7. General relativity -- Schutz is your god, it's a wonderful textbook, much better than any of the overrated pap from Zee. Learn alongside Riemannian geometry.
8. Quantum field theory and related -- this is extensive, it's what much of the mid-20th century was about. There are many standard texts, I think Tom Banks has a good book on this, and Zee actually has a reasonable book here. But Weinberg's volumes are the most extensive, you should at least use these to fall back on.

Then of course you'll be ready for the really advanced stuff -- string theory and all -- I could recommend some stuff, but there are mathematical prerequisites, and frankly I don't feel like adding too much new content to this answer.