How Can Himanshu Master Relativity and Quantum Physics with a Background in IT?

[himanshu2004@]

Hello all,

I want to understand the Theory of Relativity (Special and General) and Quantum physics. I also want to understand the general problems faced with their unification.

My background:
I have studied up to high school level Physics and Maths. In addition I have also studied a very little amount of graduate level Maths while doing my degree in Computer Science.
I've been corrupted by 4 years of an IT job since then.

I have recently only started revisiting Physics, the subject I have most loved exploring.

So, how would you suggest I go about this? Any books, online material etc that is recommended? How much time would this reasonably require assuming I spend around 3-4 hours a day?

Thanks,
Himanshu

 

[Uglybb]

Books like "The Fabric of the Cosmos: Space, Time, and the Texture of Reality" from Brian Greene are probably a good place to start.

Goes from Newtonian physics right through to string theory.

Recommended read if you don't have an in depth knowledge and work out what areas you want to go into from there.

 

[himanshu2004@]

Thanks. From the reviews on Amazon, this seems like a popular science book without much Math. While I am going going to order it anyway, I was hoping for something more mathematical as well (if this is not so).
I had a good grip on high school level Physics including the basics of Special Relativity and Quantum mechanics. I am now looking to do deeper into these topics while also working out the accompanying mathematics.
I've actually taken myself an year off and am pursuing random things that interest me :)

 

[capandbells]

Do you know calculus (up to Stoke's theorem)? If you don't, learn it. Then pick up any good freshman level textbook and start studying it. Once you've gotten through that (as in, you can do most or all of the problems for each chapter), you can move on. At this point, if you don't know ordinary differential equations or linear algebra, you should learn them. Picking up Fourier analysis and partial differential equations at this point would be a good idea. Now move on to mechanics (Taylor; make sure to do all the sections, you will need them), E&M (Griffiths) and quantum mechanics (Griffths and Liboff are just a few choices). Once you've done these (again, you should be able to do almost all of the exercises in whatever book you're using), you can move on to more advanced mechanics (Goldstein), electrodynamics (Jackson), and quantum mechanics (Sakurai). Eventually you can learn about relativistic quantum mechanics and quantum field theory, as well as general relativity (someone who knows better than me can recommend books). Once you are at this point, you can finally get started. It takes most people several years of full-time study to get there.

 

[himanshu2004@]

Okay, that seems quite intimidating... err.. thanks

 

[yenchin]

Do you know calculus (up to Stoke's theorem)? If you don't, learn it. Then pick up any good freshman level textbook and start studying it. Once you've gotten through that (as in, you can do most or all of the problems for each chapter), you can move on. At this point, if you don't know ordinary differential equations or linear algebra, you should learn them. Picking up Fourier analysis and partial differential equations at this point would be a good idea. Now move on to mechanics (Taylor; make sure to do all the sections, you will need them), E&M (Griffiths) and quantum mechanics (Griffths and Liboff are just a few choices). Once you've done these (again, you should be able to do almost all of the exercises in whatever book you're using), you can move on to more advanced mechanics (Goldstein), electrodynamics (Jackson), and quantum mechanics (Sakurai). Eventually you can learn about relativistic quantum mechanics and quantum field theory, as well as general relativity (someone who knows better than me can recommend books). Once you are at this point, you can finally get started. It takes most people several years of full-time study to get there.

That reminds me of this: http://abstrusegoose.com/272 (Continue to click on the comic for a few times)

 

[Pengwuino]

How much detail do you want? You could study for years and still only have a vague idea about the issues at play in a grand unified theory. As capandbells noted, you pretty much need an undergrad education to even begin to have an idea of what's going on. Hell, you probably need a Masters level education to actually understand any current research on the concept.

 

[Nabeshin]

Hell, you probably need a Masters level education to actually understand any current research on the concept.

This is quite true. An undergraduate degree gets you familiar with QM, classical field theories, maybe a spat of GR, and classical mechanics. Then you really need to move on to QFT and rigorous GR, which are certainly masters level subjects. Even after that it probably takes a year or so of reading post-graduate literature to get to the point where you can understand how the field is progressing.

 

[capandbells]

Okay, that seems quite intimidating... err.. thanks

The bottom line is that it takes a lot of time and work to even get started learning about modern developments in physics, and even more time after that to go through the literature, digest other people's ideas, and start developing your own. This doesn't mean you shouldn't try, and it shouldn't discourage you if you are genuinely interested. Certainly if you're willing to spend time learning, then you should go ahead and do it. But if you're going to do it, do it right. There are plenty of crackpots on the internet who are willing to give you their theory of quantum gravity that they developed after a week's worth of watching YouTube videos on general relativity and quantum mechanics, but couldn't even write out a Lagrangian for a free classical particle if you asked.

 

[zif.]

So, how would you suggest I go about this? Any books, online material etc that is recommended? How much time would this reasonably require assuming I spend around 3-4 hours a day?

Physics I & II are 4 credits a piece (not including lab) so approximately 12 hours per week on physics.

Calc I & II are the same, so another 12 hours per week from them.


Around 28 weeks in an academic year - not including christmas break or finals time.

24 hours/week * 28 weeks = 672 hours

672 hours / 4 hours/day = 168 days


So, working 4 hours per day at this, it should take you 168 days to get to the level (in just physics and math) of someone that has completed the first year of a science program. This is pretty much in line with someone in university.

However, this estimate is based off the number of hours a student in a university setting would be spending on the class every week. A student that would be attending lectures (huge advantage), surrounded by classmates learning the same material (even bigger advantage), and have a prof or TA available to answer questions.

As you move up, the number of courses in math and physics will increase and self-studying at only 4 hours per day will mean you could take a decade to finish just an undergraduate degree in physics.


There's a reason people go to university.

 

[himanshu2004@]

Well thanks for all the input guys. I do understand that I'd actually need to go to university to do this properly.

But that's not an option; at least not right now.

Right now I have a few months available, and want to do what I can. I don't want it to be a watered down discovery channel type version, so I wanted some mathematical treatment as well. At the same time, I don't think I have the time to try out all problems in a textbook and see if I am able to work them out, as someone suggested, so that might save some time. Anyways, I have always felt really understanding a mathematical concept does not need you to solve tonnes of problems, which is the approach I have seen some people adopt; they can really only get a grip on the theory after they have solved many problems. My style has been to try and spend more time understanding what the math/theory really means to begin with and then am satisfied to try out a few problems to see how it goes, but I find it saves me some time overall. Its just that everyone has different learning styles. Anyway, being very skilled at solving really different problems in maths is different from understanding the maths behind it really well, though obviously they are related.
So anyway, I am not looking to come up with any new theories or become an expert solver of all kinds of problems :) but understand these theories with as much maths as time permits right now.

I have studied calculus, differential equations and some linear algebra and Fourier analysis as well (up till my engineering degree), and I enjoyed these so I think I should be fine with maths.

So finally, for my stated goal, if someone could recommend specific books I'd really appreciate that. And if I should just pick up an under-graduate level Physics textbook, I'd still appreciate if you could tell me which one would be good for me.

 

[Nabeshin]

Anyways, I have always felt really understanding a mathematical concept does not need you to solve tonnes of problems, which is the approach I have seen some people adopt; they can really only get a grip on the theory after they have solved many problems. My style has been to try and spend more time understanding what the math/theory really means to begin with and then am satisfied to try out a few problems to see how it goes, but I find it saves me some time overall. Its just that everyone has different learning styles.

As good as this sounds on paper, I don't think I know anyone who's been able to make it work. Everything sounds fine and you think you understand when the professor explains a concept or does an example on the board, or similarly while reading through a book. But there really is a big difference between following someone else's work and creating your own... If you're not actually doing problems, you're not doing physics, you're just sort of... musing.

So finally, for my stated goal, if someone could recommend specific books I'd really appreciate that. And if I should just pick up an under-graduate level Physics textbook, I'd still appreciate if you could tell me which one would be good for me.

Well, to start learning GR, you might try picking up Hartle's Gravity. (Presumably you already have an understanding of QM at the level of, say, Griffiths? If not, this would be a good place to start.)

 

[MissSilvy]

It sounds like you're looking for a shortcut to get to a place in a year that hundreds of smart people have taken a decade or more to get to, from your position. What exactly is this burning desire to do relativity and QM when it sounds like the most math you've had is calculus and the most physics is high school level? I won't discourage you from exploring (it's a very fascinating subject), however, I would pare down your ambitions a bit. To be blunt, just READING a physics textbook won't do squat for you, anymore than watching a football game would get me closer to the NFL. Physics is learned by doing problems, period. If you don't want to do the problems, don't even bother with a mathematical treatment and turn on the Discovery channel.

 

[Pengwuino]

As good as this sounds on paper, I don't think I know anyone who's been able to make it work. Everything sounds fine and you think you understand when the professor explains a concept or does an example on the board, or similarly while reading through a book. But there really is a big difference between following someone else's work and creating your own... If you're not actually doing problems, you're not doing physics, you're just sort of... musing.

Exactly, this is key. Hell, the very basis of quantum mechanics makes no sense conceptually. Vector calculus is nice because it has such a great grounding in the real world. However, the infinite dimensional hilbert space for QM? SO(2), SU(3)? Variational principles? At some point you're 1) going to run into a topic that makes absolutely no sense without actually working problems out with it or 2) not going to understand a huge subject simply because the foundation of that subject is rooted in a mathematical problem, not a conceptual one.

 

[himanshu2004@]

No no, if you read what I'd said, I certainly want to do the maths myself, what I'd said was I don't want to get overly concerned with solving lots of mathematical problems. For example if I was learning calculus I'd want to understand truly mathematically deeply :) the whole idea behind, and the precise mathematical formulations of, the concepts of limits/differentiation/integration/differential equations etc but I wouldn't, right now, really care about solving tonnes of really challenging calculus problems, because I think *really* understanding calculus and being very skilled at solving calculus problems are two different things, though certainly one would expect a correlation between the two abilities. I have seen personally that some people cannot really "understand" let's say integration, till they have solved several integration problems on their own; I have found I tend to spend more time actually understanding a mathematical concept, followed by working through a couple of basic examples, before I even start solving problems and thereafter I need to solve a lesser number of problems than most students I have known (and this comparison may or may not apply to the average amongst you guys).

If you're not actually doing problems, you're not doing physics, you're just sort of... musing.

Physics is learned by doing problems, period. If you don't want to do the problems, don't even bother with a mathematical treatment and turn on the Discovery channel.

I don't know where you guys got that I didn't want to do any maths at all, but like I said above I do want to do the maths myself, and also solve a few problems on my own. But I don't mind just "musing", if that is all I can do in the given time; I just want the musing to be a tad more mathematically based than the musing I do when watching discovery channel physics.
"Doing physics", I will leave to more competent people... at least till I have substantially raised my levels of competency.

Anyways, thanks guys for all the textbook recommendations. I will explore a bit more, and decide which ones I want to get right now. The other positive takeaway from this thread has been to tone down my expectations of what I can accomplish in the given time period. But I am looking forward to this nonetheless. Thanks for now

 

[yenchin]

Anyways, thanks guys for all the textbook recommendations. I will explore a bit more, and decide which ones I want to get right now. The other positive takeaway from this thread has been to tone down my expectations of what I can accomplish in the given time period. But I am looking forward to this nonetheless. Thanks for now

By the way check out the recommendations by t' Hooft http://www.staff.science.uu.nl/~hooft101/theorist.html. Also you can learn some great stuffs from Susskind lectures on YouTube.

 

[Ryker]

No no, if you read what I'd said, I certainly want to do the maths myself, what I'd said was I don't want to get overly concerned with solving lots of mathematical problems. For example if I was learning calculus I'd want to understand truly mathematically deeply :) the whole idea behind, and the precise mathematical formulations of, the concepts of limits/differentiation/integration/differential equations etc but I wouldn't, right now, really care about solving tonnes of really challenging calculus problems, because I think *really* understanding calculus and being very skilled at solving calculus problems are two different things, though certainly one would expect a correlation between the two abilities. I have seen personally that some people cannot really "understand" let's say integration, till they have solved several integration problems on their own; I have found I tend to spend more time actually understanding a mathematical concept, followed by working through a couple of basic examples, before I even start solving problems and thereafter I need to solve a lesser number of problems than most students I have known (and this comparison may or may not apply to the average amongst you guys).

I don't know, I'm big against the grind your life away by doing thousands of problems mantra, but I really wonder how many problems you intend to solve. Personally, I've found that with Maths doing hard examples does make you think about the stuff in ways you haven't while reading the textbook or lecture notes, even though at the time you thought you got the material. There's also a difference between being able to do hard problems that are merely calculational in their nature and those that aren't. Have you done any proof-based stuff? Because if not, I don't think being able to do a hard integral faster than your peers is much of an indicator of how well you understand the actual concept of integration.

Again, I don't think you need to do tons of problems, but if you do only a select few you need to do the challenging ones that differ from one another in their approach. There's nothing easier than saying "I get the concept, but just can't do this particular problem", but ultimately that's just fooling yourself. I'm not implying you're doing that, but if you are, don't

Anyway, no one knows how much work you plan on doing, so perhaps you already do plan on doing enough by people's standards, and they're just worried because you say you don't want to do tons of problems. But tons of problems is an empty concept, because what might feel like a lot for one person is little for another.

 

[Pengwuino]

No no, if you read what I'd said, I certainly want to do the maths myself, what I'd said was I don't want to get overly concerned with solving lots of mathematical problems. For example if I was learning calculus I'd want to understand truly mathematically deeply :) the whole idea behind, and the precise mathematical formulations of, the concepts of limits/differentiation/integration/differential equations etc but I wouldn't, right now, really care about solving tonnes of really challenging calculus problems, because I think *really* understanding calculus and being very skilled at solving calculus problems are two different things, though certainly one would expect a correlation between the two abilities. I have seen personally that some people cannot really "understand" let's say integration, till they have solved several integration problems on their own; I have found I tend to spend more time actually understanding a mathematical concept, followed by working through a couple of basic examples, before I even start solving problems and thereafter I need to solve a lesser number of problems than most students I have known (and this comparison may or may not apply to the average amongst you guys).

Come to think of it, there's actually some good news and some bad news for you. In your calculus and linear algebra courses, there are typically dozens if not hundreds of problems per chapter you can do. When you start getting into advanced undergrad courses, you may have a couple dozen problems. Beyond that, some texts may have only 5-10 questions! And those questions are LONG. So you won't be doing 50 problems in a week, but you'll be spending hours if not days on a single problem.

To add to that, the more advanced texts take sometimes HUGE leaps in their arguments which actually requires you to pull out pen and paper and do a mini-problem just while reading. So what you don't need to worry about is having to do 50 problems at the end of the chapter, but it's going to come back to you in the form of just 1 problem taking days to do and if you don't do those problems, you'll have little understanding of what's really going on.

 

[himanshu2004@]

@Ryker and Pengwuino
Ryker, I agree with everything you say, it makes sense. (In fact, I am one of those people who is generally slow at solving problems but I generally understand the concept pretty well. I don't say this as a compliment at all, for in many ways it is not one, but more matter-of-factly.)
Pengwuino, thanks for the input, certainly useful to know, and will help approach these problems with the right attitude and not give up if I am taking too long.

Also, thanks to you both for pointing out stuff in a non-presumptuous and non-overbearing way and generally being constructive, unlike some of the other posts.

@yenchin
Thanks for the link to t' Hooft's website and letting me know about Susskind's videos on youtube. I've just seen the website and it seems super awesome with lots of resources. I haven't seen the videos yet but hopefully they will be at a level not too far beyond my current capability. Thanks a ton!

 

[himanshu2004@]

Any reviews for Roger Penrose's The Road to Reality? From online reviews it seems to me to be a book that deals largely with Quamtum Mechanics and Relativity, and attempts at unification, with the first half of the book teaching all the maths required for the second half.
It seems to be somewhat like a popular science book but with (decent?) mathematical treatment. Sounds like exactly what I need?

 

[yenchin]

Any reviews for Roger Penrose's The Road to Reality? From online reviews it seems to me to be a book that deals largely with Quamtum Mechanics and Relativity, and attempts at unification, with the first half of the book teaching all the maths required for the second half.
It seems to be somewhat like a popular science book but with (decent?) mathematical treatment. Sounds like exactly what I need?

I would not recommend it. Go for proper textbooks. You might refer to Penrose's book but you still need the textbooks. I think Penrose greatly overestimate the intended readers - he wanted any layman to read his book, as he claimed early on in the book that even if one doesn't know fractions one can understand his book! And then he quickly teaches the readers how fractions are equivalent classes... In short, condensed in this book, in each and every chapter, is probably a semester worth of stuffs, good to read for review or from another perspective once you know the material, but not to actually learn from scratch from the book itself.

 

[WannabeNewton]

The problem with popular books is that they sometimes distort characteristics of various physics being described that only a firm mathematical treatment can resolve. I think with your knowledge of linear algebra, calculus, and freshman physics you could easily delve into an undergraduate GR textbook like Hartle's Gravity or Schutz's First Course in General Relativity so like the poster above said don't waste your time with popular books.

 

[Disinterred]

IMO, You should start your study off with

John R Taylor - Classical Mechanics

This is one of the clearest undergraduate Classical Mechanics textbooks ever written. Taylor accentuates understanding over anything else. This textbook will give you a great understanding of Classical Mechanics, you will need this.

Then after you have completed Taylor, you should read the popular Griffith's E&M and QM textbooks, which aren't very large, but are very good.

Once you have done that, you should then be able to tackle GR, you could try the very popular Hartle textbook on GR, which has great reviews on amazon.

This is just how I would self-study if I was not in university, but it might not be for everyone.

That would give you a very solid undergraduate understanding of physics. You would obtain the fundamentals of CM, EM, QM and GR.