(Part 2) Best products from r/AskPhysics

It's great that you want to study particle physics and String Theory! It's a really interesting subject. Getting a degree in physics can often make you a useful person so long as you make sure you get some transferable skills (like programming and whatnot). I'll reiterate the standard advice for going further in physics, and in particular in theoretical physics, in the hope that you will take it to heart. Only go into theoretical physics if you really enjoy it. Do it for no other reason. If you want to become a professor, there are other areas of physics which are far easier to accomplish that in. If you want to be famous, become an actor or a writer or go into science communication and become the new Bill Nye. I'm not saying the only reason to do it is if you're obsessed with it, but you've got to really enjoy it and find it fulfilling for it's own sake as the likelihood of becoming a professor in it is so slim. Then, if your academic dreams don't work out, you won't regret the time you spent, and you'll always have the drive to keep learning and doing more, whatever happens to you academically.

With that out of the way, the biggest chunk of learning you'll do as a theorist is math. A decent book (which I used in my undergraduate degree) which covers the majority of the math you need to understand basic physics, e.g. Classical Mechanics, Quantum Mechanics, Special Relativity, Thermodynamics, Statistical Mechanics and Electromagnetism. Is this guy: Maths It's not a textbook you can read cover to cover, but it's a really good reference, and undoubtably, should you go and do a physics degree, you'll end up owning something like it. If you like maths now and want to learn more of it, then it's a good book to do it with.

The rest of the books I'll recommend to you have a minimal number of equations, but explain a lot of concepts and other interesting goodies. To really understand the subjects you need textbooks, but you need the math to understand them first and it's unlikely you're there yet. If you want textbook suggestions let me know, but if you haven't read the books below they're good anyway.

First, particle physics. This book Deep Down Things is a really great book about the history and ideas behind modern particles physics and the standard model. I can't recommend it enough.

Next, General Relativity. If you're interested in String Theory you're going to need to become an expert in General Relativity. This book: General Relativity from A to B explains the ideas behind GR without a lot of math, but it does so in a precise way. It's a really good book.

Next, Quantum Mechanics. This book: In Search of Schrodinger's Cat is a great introduction to the people and ideas of Quantum Mechanics. I like it a lot.

For general physics knowledge. Lots of people really like the
Feynman Lectures They cover everything and so have quite a bit of math in them. As a taster you can get a couple of books: Six Easy Pieces and Six Not So Easy Pieces, though the not so easy pieces are a bit more mathematically minded.

Now I'll take the opportunity to recommend my own pet favourite book. The Road to Reality. Roger Penrose wrote this to prove that anyone could understand all of theoretical physics, as such it's one of the hardest books you can read, but it is fascinating and tells you about concepts all the way up to String Theory. If you've got time to think and work on the exercises I found it well worth the time. All the math that's needed is explained in the book, which is good, but it's certainly not easy!

Lastly, for understanding more of the ideas which underlie theoretical physics, this is a good book: Philsophy of Physics: Space and Time It's not the best, but the ideas behind theoretical physics thought are important and this is an interesting and subtle book. I'd put it last on the reading list though.

Anyway, I hope that helps, keep learning about physics and asking questions! If there's anything else you want to know, feel free to ask.

The books others have suggested here are all great, but if you've never seen physics with calculus before, you may want to begin with something more accessible. Taylor and Goldstein are aimed at advanced undergraduates and spend almost no time on the elementary formulation of Newtonian mechanics. They're designed to teach you about more advanced methods of mechanics, primarily the Lagrangian and Hamiltonian formulations.

Therefore, I suggest you start with a book that's designed to be introductory. I don't have a particular favorite, but you may enjoy Serway & Jewett or Halliday & Resnick.

Many of us learned out of K&K, as it's been something of a standard in honors intro courses since the seventies. (Oh my god, a new edition? Why?!) However, most of its readers these days have already seen physics with calculus once before, and many of them still find it a difficult read. You may want to see if your school's library has a copy so you can try before you buy.

If you do enjoy the level of K&K, then I strongly encourage you to find a copy of Purcell when you get to studying electricity and magnetism. If you are confident with the math, it is far and away the best book for introductory E&M—there's no substitute! (And personally, I'd strongly suggest you get the original or the second edition used. The third edition made the switch to SI units, which are not well-suited to electromagnetic theory.)

By the way: if you don't care what edition you're getting, and you're okay with international editions, you can get these books really cheaply. For instance: Goldstein, S&J, K&K, Purcell.

Finally, if you go looking for other books or asking other people, you should be aware that "analytical mechanics" often means those more advanced methods you learn in a second course on mechanics. If you just say "mechanics with calculus", people will get the idea of what you're looking for.

There's a lot of fun and interesting physics and astronomy that can be understood with little more than solid algebra skills. Add a little bit of introductory calculus, and there's a lot to keep you busy. If you're brave enough to dive into calc, I recommend this book.

Since you expressed particular interest in Astronomy, I would suggest using that as an anchor point. Get a good Astrophysics text like An Introduction to Modern Astrophysics by Carroll and start there. Inevitably, you will come upon concepts that you're shaky on-- luckily this is the age of the internet! I find HyperPhysics is a great resource (which appears to be down at the moment).

If you find that Newtonian physics is tripping you up, I recommend Basic Physics: A Self-Teaching Guide to fill in the gaps.

What level E&M? If it is intro physics 2 then look for AP physics B/C stuff in addition to what you would normally look for since that's the same level.

If it is an upper division E&M class then I will recommend a book you can probably find in most of your professors offices somewhere: Div, Grad, Curl, and All That. Older editions are much cheaper even and archive.org has a PDf of the 3rd edition. I have no idea what the differences are, but I have the 4th and it is just great.

I have yet to find an E&M textbook I like. Griffiths is alright and when paired with Div, Grad, Curl and maybe a Schaum's outline on E&M it forms what I think should just be one textbook.

As for online resources I think The Mechanical Universe about Maxwell does a great job at covering Maxwell's laws, especially the bit starting around 15 minutes in

I've never used this site but it looks like it has a bunch of solved problems as well.

Brian Cox writes some good books like this. The only one I can think of off the top of my head is Why does E=MC2

But following the links of related titles will probably help you a lot.

The elegant universe is also a really good book... somebody else mentioned it, just want to say that I support that thought. :)

Actually, I would disagree with /u/Metlover: Newton's Principia is a terrible place to start: we've had a few hundred years to absorb Newtonian physics and figure out how best to study it. Going back to the source material is only a good idea once you already know it, or if the field has jumped ahead of textbooks.

I would recommend a modern mechanics textbook instead. In fact, my strongest recommendation would be to get hold of a general first year physics textbook along the lines of Young and Freedman second-hand, and learn the mathematics required to understand that (single and multi-variate calculus, solutions of equations etc). I have no experience of online courses so can't say which of those are good.

The most valuable experience I had from undergraduate onwards was trying to solve problems with other people: if you can find other motivated people to study with, it will make a huge difference.

+1 for Taylor. I haaaaated the Thornton and Marion text. Taylor's book really helped me connect all the concepts that were floating untethered in my brain.

When you get to quantum, get this text as a supplement if it's not what your professor uses. It's so well and humorously written, that I read the unassigned chapters for fun.

YouTube was another valuable resource for me. If I still didn't understand something after finishing a problem with my professor, I would find a similar problem worked out on YouTube. More often than not, it really helped everything sink in more clearly.

Most of my upper level professors made us write solutions in complete sentences with every step explained. I highly recommend this if it's not already required of you. It improved my ability to recall information later and my understanding of the problems. One professor always complained how students would come back to him with their graded assignment and say "Well, you know what I meant." His response was, "No, actually. I don't know what you mean. The burden of expressing what you mean lies with you, the author of the assignment, not me." That really stuck with me and made me a much better student/scientist in several ways.

Good luck!

Edit: forgot to add that I found a pdf of Taylor's text online for free. If you have trouble finding it, let me know. I'll see if I can find the link.

Read this book.
http://www.amazon.com/Thermodynamics-Enrico-Fermi/dp/1607962381

It's very short and introduces all the fundamental principles of thermodynamics.

The first two laws:
dU = dQ - dW. The change in energy of a system is equal to the amount of heat you put in (dQ) minus the amount of work the system does on its environment (dW).

Clausius statement for the second law:
"Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time." Basically a cooler object cannot spontaneously warm a hotter object (cooler and hotter described by something called temperature).

Then you have PV = nRT for an ideal gas, and W = integral P * dV.
S = entropy = integral dQ/T, and you can prove that entropy is a description of the state of a system using basic properties of differential equations (basically, if you take a closed integral of dQ/T, you'll get 0).

Also if you had a physics test coming up, wouldn't your physics classes have taught it? Or are you talking about some sort of standardized test? If it's the latter, you're better off getting a practice book and chugging away. I know at least for the physics SAT subject tests, the thermodynamics you need is not thermodynamics in the classical sense, but more about heat transfer and the like.

There's a reason whole semesters are devoted to thermodynamics and kinetic theory; it's a very broad topic.

>and the uncertainty principal imposes limits on what we can know through measurement.

Not what we can know, but that a particle's state at any time isn't given by a precise position and momentum (state of a classical particle). This sort of information doesn't exist. Instead the state of the particle is a wave function. The wave function gives probabilities to measure the particle to be in a certain position or alternatively to have a certain momentum. The probabilities for the two quantities are dependent on each other (via fourier transform). The uncertainty principle just says that any wave function can't both be precisely localised in momentum and position space. The best you can do is a bell shaped (gaussian) distribution in both position and momentum that have some nonzero width.

After measurement of position the particle is then in an eigenstate of definite position. That kind of state gives a uniform probability distribution for the momentum measurement (ie all momenta are equally likely, momentum can be anything if you measure that afterwards).

>In doing so, we are assuming space is a continuous object, there are particles in space that occupy a single point, and once measured, a particle has a well defined location even if we cannot entirely know that location.

In that instance we have just measured it so we do know it.

>If we still assume space is continuous but particles had some size and shape which is able to move in a non-uniform manner (different parts moving in different speeds or directions)

We can detect internal structure of particles in experiments. This is how we know the from is fundamental and the proton isn't. There's no evidence otherwise (though having an internal structure doesn't change much for the proton, it's also a quantum object) and there is no incentive of getting rid of what you call "weirdness", on the contrary, quantum theory gives the most accurate predictions we've ever had.

Describing the state of a particle by a wave function psi(t) instead of a pair of values (x(t), p(t)) is a more accurate description.

Your suggestion is literally choosing something that disagrees with experiments over something that agrees with them.

>our inability to measure its position could be related to how we try and collapse this into a single positional value. Or, what if particles are just bigger than what we would expect and in doing a measurement, we are only seeing a given piece a particle?

I agree with /u/cantgetno197 (who isn't a troll, he just told you something that's accurate but you didn't want to hear). I think your view might have to do with not knowing quantum theory very well yet. In that case I would be trying to learn about it (textbooks), not trying to get rid of it. https://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/1107179866

Yes books do teach you. They teach you intuition too, contrary to what you say (again you haven't read any quantum theory books but have already an opinion). How is anyone supposed to take someone saying he is learning seriously if he is dismissive of reading educational material?

>Besides, those who don't ask questions generally don't understand as well as they think, or they are unimaginative...

Those who don't read books are worse off, they don't ask very useful questions to begin with and don't make progress.

I recently read The Hunt for Vulcan, a book about the history of astronomy between Newton and the 20th century, describing scientists noticing slight eccentricities in Mercury's orbit, and trying to explain it with a hypothetical planet "Vulcan", and then constantly adjusting their theories when "Vulcan" never actually appears, and how the problem is eventually solved with relativity.

Great book about the history of science, and gives a really good idea of the relation between theory and experiment, and older versus more modern theories (classical gravity vs relativity) without assuming any actual physics background. IMO, it's the best "non-technical" physics book I've come across.

Maybe try applied math programs. Some of them seem to have astrophysics faculty https://www.princeton.edu/gradschool/about/catalog/fields/applied_mathematics/. You'll probably have an easier time getting in with your background and can take the math GREs. In a physics BS you would at least have the knowledge of these books:

http://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X,

http://www.amazon.com/Introduction-Electrodynamics-4th-David-Griffiths/dp/0321856562/ref=sr_1_1?s=books&ie=UTF8&qid=1396384599&sr=1-1&keywords=griffiths,

http://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927/ref=sr_1_2?s=books&ie=UTF8&qid=1396384599&sr=1-2&keywords=griffiths,

http://www.amazon.com/Introduction-Thermal-Physics-Daniel-Schroeder/dp/0201380277/ref=sr_1_1?s=books&ie=UTF8&qid=1396384625&sr=1-1&keywords=schroeder+statistical+physics.

The more you know from those books, the better. Although an applied math program, probably wouldn't expect you to have read all of them. Also try x-posting to /r/askacademia. I'm sure someone there could be more helpful.

Most of the topics you mentioned were what I would call algebra or single-variable calculus. I would start learning some linear algebra and multivariable/vector calculus first - the latter should be available in any good calculus text anyways. Besides these, you should at least know some basic probability and maybe a little about complex numbers. With this amount of math you could probably get through most of a "basic" physics degree, but you'll probably want to learn much more math if that's what you're into.

Many people on Reddit have glowing reviews for Boas' mathematical physics text (haven't read it myself though). Looking at the table of contents, I think it's a good overview of topics useful for an undergrad curriculum.

Most physics undergrads take a class called "Mathematics for Physics" or something similar which uses a book like this. It will help you cut to the chase and is a good reference for the math you haven't studied in detail.

As for where you are right now, you should be okay with ODE, multivariable/vector calc, and linear algebra. Those you probably want to devote considerable time learning.

I don't think this is a pop math book, but I really like this book as an introduction to math for aspiring physicists:

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https://www.amazon.com/Mathematics-Physics-Calculus-Biman-Das/dp/0131913360

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Not stupid expensive like a textbook, costs 10-20 bucks and has good examples from actual physics scenarios for each math point. Goes through basic units, geometry, vectors, and calculus.

IMO they're good, but there've been advances in physics pedagogy since they were written.

My favorite intro physics course is this, which comes in a separate edition as well. If you already have taken some physics and know trig, I don't see why you couldn't start there.

Griffiths Electrodynamics would be a good thing to look at. It's surprisingly readable, and it could possibly wind up being your E&M textbook. In my undergrad, E&M was the "weed out" course, where those who weren't up to scratch lost interest in the physics degree, so it's good to get a head start. I wish I had started on it sooner. Maybe I'd have gotten more out of E&M as an undergrad and then Jackson in grad school wouldn't have been so hard.

I haven't read this, but this is from the Kip Thorns, the science adviser on the film

http://www.amazon.com/The-Science-Interstellar-Kip-Thorne/dp/0393351378

Also if it is half as good as his previous book, you're in for a treat

www.amazon.com/Black-Holes-Time-Warps-Commonwealth/dp/0393312763/

Something doesn't seem right. This is saying that at 10' pitch height, the ball would land 32" to the right of his left knee. From the knee point, it would travel 21.5" down, but 32" to the right? Seems to me at that angle, horizontal distance should be less than the vertical distance or maybe close to the same.

The flight time must also be off. It doesn't take 9 seconds to throw a ball 50' with a height of 10'.

I do like your A,B,C points. There is one other point and that's the apogee (Z, 120) - maybe it's accounted for but I don't spot it.

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I found this graph that may help, but it uses a 12' maximum height - what the rule used to be.

https://i.imgur.com/iFjnvlz.png

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It is from page 61 of this book. https://www.amazon.com/Physics-Baseball-Softball-Rod-Cross/dp/1441981128 Use "Search inside this book" for "Some pitched ball trajectories".

Griffith's Electrodynamics has a decent introduction to special relativity. Otherwise, Hartle's book is geared towards the advanced undergrad. Also, Schultz is good too.

The textbooks recommended in the intro Astronomy class here are An Introduction to Modern Astrophysics by Carroll & Ostlie and Foundations of Astrophysics. I've never read through either, but apparently the first one is much more detailed.

The older edition of Modern Astrophysics is significantly cheaper and will fit your purposes just as well: 1st Edition Carroll

A relatively new book (McIntyre, 2012) that my university used to teach upper-division quantum mechanics this year actually starts with the Stern-Gerlach.

It was actually really well-received, and I liked it a lot. It introduces Stern-Gerlach and Dirac notation immediately (four pages in and you're already using bra-ket notation to talk about Stern-Gerlach).

I recommend it highly.

You should probably start by cracking open a copy of a good E&M book, like this one, and learning the science, rather than relying on Einstein quotations.

Of course, that assumes you've already learned integral and differential calculus (which any 19-year-old science or engineering student has).

How to Teach Relativity to Your Dog is a good one that explains the concepts by less abstract analogies. You might like it: http://www.amazon.com/How-Teach-Relativity-Your-Dog/dp/0465023312

I hadn't taken a math class in over 5 years when I enrolled in Calc I. This book https://www.amazon.com/gp/aw/d/0471827223/ref=mp_s_a_1_1?ie=UTF8&qid=1524052149&sr=8-1&pi=AC_SX236_SY340_FMwebp_QL65&keywords=quick+calculus was a perfect precursor for the class if you're pressed for time.

Goldstein is good.

I learned the basics from Shutz (which I liked a lot). I don't remember it requiring Lagrangian/Hamiltonian stuff.

The book is Mr. Tompkins in Wonderland.

If I had to make my own suggestion for a book, it would be How to Teach Relativity to Your Dog. Each chapter starts off as a conversation between the author and his dog, where the dog has heard some random fact about physics and is trying to exploit it for her own gains(catching squirrels, infinite bacon, etc..). Then the second part of each chapter is a more rigorous(but still easy to follow) mathematical explanation.

Books like Griffiths quantum or Nielsen and Chuang quantum information? From the sounds of your post you have some large gaps in your understanding.

Haven't used it myself, but you might want to check out Div,Grad,Curl by Schey.

This should keep you busy, but I can suggest books in other areas if you want.

Math books:
Algebra: http://www.amazon.com/Algebra-I-M-Gelfand/dp/0817636773/ref=sr_1_1?ie=UTF8&s=books&qid=1251516690&sr=8
Calc: http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?s=books&ie=UTF8&qid=1356152827&sr=1-1&keywords=spivak+calculus
Calc: http://www.amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X
Linear algebra: http://www.amazon.com/Linear-Algebra-Modern-Introduction-CD-ROM/dp/0534998453/ref=sr_1_4?ie=UTF8&s=books&qid=1255703167&sr=8-4
Linear algebra: http://www.amazon.com/Linear-Algebra-Dover-Mathematics-ebook/dp/B00A73IXRC/ref=zg_bs_158739011_2

Beginning physics:
http://www.amazon.com/Feynman-Lectures-Physics-boxed-set/dp/0465023827

Advanced stuff, if you make it through the beginning books:
E&M: http://www.amazon.com/Introduction-Electrodynamics-Edition-David-Griffiths/dp/0321856562/ref=sr_1_1?ie=UTF8&qid=1375653392&sr=8-1&keywords=griffiths+electrodynamics
Mechanics: http://www.amazon.com/Classical-Dynamics-Particles-Systems-Thornton/dp/0534408966/ref=sr_1_1?ie=UTF8&qid=1375653415&sr=8-1&keywords=marion+thornton
Quantum: http://www.amazon.com/Principles-Quantum-Mechanics-2nd-Edition/dp/0306447908/ref=sr_1_1?ie=UTF8&qid=1375653438&sr=8-1&keywords=shankar

Cosmology -- these are both low level and low math, and you can probably handle them now:
http://www.amazon.com/Spacetime-Physics-Edwin-F-Taylor/dp/0716723271
http://www.amazon.com/The-First-Three-Minutes-Universe/dp/0465024378/ref=sr_1_1?ie=UTF8&qid=1356155850&sr=8-1&keywords=the+first+three+minutes