So You Want to Learn Physics

Really recommend it to anybody who's interested in that part of history. Amazing writing, and an incredible story. (You know it's gripping when you read about some of the experiments and feverishly hope they don't blow themselves up, nevermind knowing the outcome)

https://www.amazon.com/End-Physics-Myth-Unified-Theory/dp/04...

Once you understand the maths clearly, it becomes much easier to understand the failures of the past. For example, reading Newton and Leibniz on calculus makes it clear that it was epsilon/delta waiting to get out.

On the other hand, it would have been intellectually pleasing(at least for me) to know how Physicists came with it, what's the motivation behind 1/d(A,B)^3, how did people come up with G, how it was measured, etc.

But physics is different. Physics is about the question whether those assumption (including many hidden assumption) can be wrong and how to interpret the mathematical equation even when the equation gives confirmed results. So Maxwell's equations is not a clear picture on what the light is. Maxwell's equation just describes one aspect of how light behave under one set of assumptions. There are other aspects of light and there are different set of maths that physicists tried to describe them. There are physics intuition on what light is, but that is subjectively dependent on which physicist you are asking. In physics, there is simply no mathematically equivalent of "clear picture" where you simply just accept what is given and go from there. In physics, it is "what is given" in question.

Often times, there are no "failed theoretical frameworks", it's not like special relativity is "right" and newtonian mechanics is "wrong", they are right in different physical regimes. If they are down right wrong, then they wouldn't be known to us anyway.

If you stick to parts where theoretical physicists live, it's easier to find mathematical consistency and coherence, like QFT. Outside of that region, what things are and what approximations you use really come down to "what matches experiment best" at best and "what people will allow me to publish with" at worst.

There are two kinds of people that fight actual Physics from within, those that say Math is not important: physical intuition "has to" be enough, and those that say that it's just Math, so they are equally happy with perfectly reasonable correct models and completely absurd correct models. They churn out both, usually more of the latter. Both schools of opinionated thought miss that wherever you go you have to learn the trade and be humble.

They should have told you that we don't know what things are, we just deal with how they do their thing.

It's a wave, it's a particle... it's a state, a linear combination of the eigenstates of the EM Hamiltonian, which span a Hilbert space. That's what we got and every physicist knows it, they are just being polite. If they told you that, your next question would be: why on Earth would you think that? why not just [random brainstorming here]? I don't think you're really interested in the really long answer, but it has to do with the boring fact that Physics is, above all, an experimental science.

Later, when I realized what I was missing out on, I tried to teach myself the missing concepts. I failed, until I found H.M. Schey's "Div, Grad, Curl, and All That: An Informal Text on Vector Calculus." It's a pragmatic, friendly, slim little math book that reads more like lecture notes than a classic textbook, and I can fairly say it's taught me everything I know about those operators (which isn't much).

So if you are like me, and got to calc III, vector math, and/or liner algebra without learning div, grad, curl and partial differential equations... check out the book. it's great: https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161

Also: can we get three cheers for HYPERPHYSICS?? http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html

> There are two ways to teach quantum mechanics. The first way -- which for most physicists today is still the only way -- follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then you learn about the "blackbody paradox" and various strange experimental results, and the great crisis these things posed for physics. Next you learn a complicated patchwork of ideas that physicists invented between 1900 and 1926 to try to make the crisis go away. Then, if you're lucky, after years of study you finally get around to the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes that can be positive, negative, or even complex.

> Today, in the quantum information age, the fact that all the physicists had to learn quantum this way seems increasingly humorous. For example, I've had experts in quantum field theory -- people who've spent years calculating path integrals of mind-boggling complexity -- ask me to explain the Bell inequality to them. That's like Andrew Wiles asking me to explain the Pythagorean Theorem.

> As a direct result of this "QWERTY" approach to explaining quantum mechanics - which you can see reflected in almost every popular book and article, down to the present -- the subject acquired an undeserved reputation for being hard. Educated people memorized the slogans -- "light is both a wave and a particle," "the cat is neither dead nor alive until you look," "you can ask about the position or the momentum, but not both," "one particle instantly learns the spin of the other through spooky action-at-a-distance," etc. -- and also learned that they shouldn't even try to understand such things without years of painstaking work.

> The second way to teach quantum mechanics leaves a blow-by-blow account of its discovery to the historians, and instead starts directly from the conceptual core -- namely, a certain generalization of probability theory to allow minus signs. Once you know what the theory is actually about, you can then sprinkle in physics to taste, and calculate the spectrum of whatever atom you want. This second approach is the one I'll be following here.

Here's the full lecture.[0] The approach was interesting enough that I bought his full book[1], but unfortunately it was a little over my head.

[0] http://www.scottaaronson.com/democritus/lec9.html [1] https://www.amazon.com/Quantum-Computing-since-Democritus-Aa...

Quoting Feynman www.feynmanlectures.caltech.edu/II_02.html

> The physicist needs a facility in looking at problems from several points of view. The exact analysis of real physical problems is usually quite complicated, and any particular physical situation may be too complicated to analyze directly by solving the differential equation. But one can still get a very good idea of the behavior of a system if one has some feel for the character of the solution in different circumstances. Ideas such as the field lines, capacitance, resistance, and inductance are, for such purposes, very useful. So we will spend much of our time analyzing them. In this way we will get a feel as to what should happen in different electromagnetic situations. On the other hand, none of the heuristic models, such as field lines, is really adequate and accurate for all situations. There is only one precise way of presenting the laws, and that is by means of differential equations. They have the advantage of being fundamental and, so far as we know, precise. If you have learned the differential equations you can always go back to them. There is nothing to unlearn.

> It will take you some time to understand what should happen in different circumstances. You will have to solve the equations. Each time you solve the equations, you will learn something about the character of the solutions. To keep these solutions in mind, it will be useful also to study their meaning in terms of field lines and of other concepts. This is the way you will really “understand” the equations. That is the difference between mathematics and physics. Mathematicians, or people who have very mathematical minds, are often led astray when “studying” physics because they lose sight of the physics. They say: “Look, these differential equations—the Maxwell equations—are all there is to electrodynamics; it is admitted by the physicists that there is nothing which is not contained in the equations. The equations are complicated, but after all they are only mathematical equations and if I understand them mathematically inside out, I will understand the physics inside out.” Only it doesn’t work that way. Mathematicians who study physics with that point of view—and there have been many of them—usually make little contribution to physics and, in fact, little to mathematics. They fail because the actual physical situations in the real world are so complicated that it is necessary to have a much broader understanding of the equations.

> What it means really to understand an equation—that is, in more than a strictly mathematical sense—was described by Dirac. He said: “I understand what an equation means if I have a way of figuring out the characteristics of its solution without actually solving it.” So if we have a way of knowing what should happen in given circumstances without actually solving the equations, then we “understand” the equations, as applied to these circumstances. A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist.

From personal experience, there are such mathematics-oriented people in physics too, not just mathematicans. And some of them push a lot of papers, typically by applying the same method over and over again in different subfields, resulting in infinitesimal incremental "advances".

Or, you can start from the bottom. For the latter this should be a good place to start:https://www.staff.science.uu.nl/~gadda001/goodtheorist/

If you don't want the physical intuition, then you don't want the physics at all; You should stop claiming to want to learn physics and never stray further from the one true path than the applied mathematics building.

I will agree there are lots of bad textbooks, but the best-in-class textbooks are better than any self-learning guide you could make up yourself (within categories).

For those wanting a more mathematical perspective (versus engineering/applied science), there's Axler's Linear Algebra Done Right.

For the programmers in the audience, another fun and illuminating (and cheap!) text is Klein's Coding the Matrix.

A very important development in my understanding of mathematics was developing an intuition of when something is worth visualizing. Sometimes visualization is extremely helpful. Sometimes it just makes understanding the problem more difficult (looking at you quaternions).

> One problem I have often had is that in a long derivation my brain will be so fried on the mathematics that I eventually forget what the terms in the equations actually represent. I'm like "what is q again? oh yeah it's a generalised coordinate".

I had a professor who said something along the lines of "a good notation liberates the mind while a poor one clutters it." I suspect he was quoting a famous mathematician (as he was wont to do), but I cannot remember who (Whitehead?).

I didn't assert that, so you can't disagree with it :-) I think the how-we-know and the what-it-means should both precede the math, but I don't have a strong opinion on which of those should come first.

I have not read Griffiths, but I took a quick look at:

http://www.fisica.net/quantica/Griffiths%20-%20Introduction%...

and I was not impressed. It seems like a completely traditional presentation, and like all traditional presentations it completely misses the absolutely central role that entanglement plays in the conceptual foundations of QM. (In fact, the word "entanglement" does not even appear in the table of contents! Alas, the on-line text I found at the above link is not searchable so I can't tell you if he doesn't address it at all.)

[EDIT] I've now read more of Griffiths and I would like to revise and extend my above remarks :-) My original criticism still stands, but aside from that the book is actually quite good.

I've always looked for more effective ways to study. And to counter your suggestion you can definitely fully understand the principles of an equation without being able to remember the equation itself. A simple example of this would be the Laplacian in spherical coordinates. It is easy to understand what is being done and the Cartesian form is trivial (most people have this memorized even) and the spherical can be derived from it simply. Problem is this takes way too much time. I don't think an example like this you could argue that there isn't an understanding of what is going on, just a familiarity issue. And thus how the information was stored. I'd argue that most of those that know this off the top of their head do so from repetition and not because of a better understanding than their Cartesian only counterparts.

As for testing, when I was in school most classes didn't allow me to have a formula sheet. And anyone that does the physics GRE knows how much has to be remembered. But to me it is more about quick and easy access. Motivation isn't about some test.