Modern Physics From Scratch(theoreticalminimum.com)
theoreticalminimum.com
Modern Physics From Scratch
http://theoreticalminimum.com/
16 comments
Cool book. That's from where I learnt the Euler-Lagrange equations first.
Sussman also wrote a book, in his characteristic style, on Differential Geometry, that doubles as a possible introduction to special relativity, and bridge to the general theory.
http://groups.csail.mit.edu/mac/users/gjs/6946/calculus-inde...
Sussman also wrote a book, in his characteristic style, on Differential Geometry, that doubles as a possible introduction to special relativity, and bridge to the general theory.
http://groups.csail.mit.edu/mac/users/gjs/6946/calculus-inde...
And one on quantum mechanics, though by a different author:
http://www.amazon.com/The-Structure-Interpretation-Quantum-M...
I've read some of it, and it's not even in the same sport, much less league. SIQM has no code and uses all the handwavy notation you could read in better books (Landau, probably; or Feynmann, for an intro). It struck me as the Ford Fiesta to Sussman's 911. In fact, after that read, I was pissed at the author from riding the coat-tails of the Structure and Interpretation series.
This differential geometry book is convenient. If only someone could port this book into Python.
The Landau chapter (2nd on the "Mechanics book) demonstrating how conservation laws derive from symmetries (eg Energy conservation due to homogeneity of time) was really mind-blowing for me when I was starting out in college. I don't understand why I haven't seen this idea presented in other textbooks and I can't recommend it enough for anyone with an interest in physics or science.
Online: http://archive.org/stream/Mechanics_541/LandauLifshitz-Mecha...
Online: http://archive.org/stream/Mechanics_541/LandauLifshitz-Mecha...
It's also in the Feynman lectures (proved only for quantum mechanics) and Feynman's popularization The Character of Physical Law (proof sketch for classical mechanics). (I suppose the latter is also in the online videos for the lectures that book was made from -- IIRC the Messenger lectures. http://research.microsoft.com/apps/tools/tuva/)
It's funny you mention these two books in the same comment, since I always assumed Landau was one of the targets of Sussman and Wisdom's comment, "It is surprisingly easy to get the right answer with unclear and informal symbol manipulation." (See their paper, Functional differential geometry.) Sussman/Wisdom's book is, from a brief look, not 'rigorous' either, but the 'symbol manipulations' in Landau/Lifschitz's series are sometimes borderline insane!
This is perfect for me! As a physics/CS student I prefer to learn my physics from a computational perspective. It allows me to solve more interesting/complex problems as traditional problems tend to go for cookie cutter analytical solutions that are very restricted.
Thanks!
Thanks for the Landau recommendation. I'm finding I'm not progressing with Goldstein's Mechanics.
"A number of years ago I became aware of the large number of physics enthusiasts out there who have no venue to learn modern physics and cosmology. Fat advanced textbooks are not suitable to people who have no teacher to ask questions of, and the popular literature does not go deeply enough to satisfy these curious people."
It's as if he made the courses just for me! :) Thanks for sharing this.
It's as if he made the courses just for me! :) Thanks for sharing this.
In 2004, Roger Penrose published "The Road to Reality: A Complete Guide to the Laws of the Universe" which is 1100 pages long.
http://staff.washington.edu/freitz/penrose.pdf
"One of my mother’s closest friends, when she was a young girl, was among those who could not grasp fractions. This lady once told me so herself after she had retired from a successful career as a ballet dancer. I was still young, not yet fully launched in my activities as a mathematician, but was recognized as someone who enjoyed working in that subject. ‘It’s all that cancelling’, she said to me, ‘I could just never get the hang of cancelling.’ She was an elegant and highly intelligent woman, and there is no doubt in my mind that the mental qualities that are required in comprehending the sophisticated choreography that is central to ballet are in no way inferior to those which must be brought to bear on a mathematical problem. So, grossly overestimating my expositional abilities, I attempted, as others had done before, to explain to her the simplicity and logical nature of the procedure of ‘cancelling’."
"One of my mother’s closest friends, when she was a young girl, was among those who could not grasp fractions. This lady once told me so herself after she had retired from a successful career as a ballet dancer. I was still young, not yet fully launched in my activities as a mathematician, but was recognized as someone who enjoyed working in that subject. ‘It’s all that cancelling’, she said to me, ‘I could just never get the hang of cancelling.’ She was an elegant and highly intelligent woman, and there is no doubt in my mind that the mental qualities that are required in comprehending the sophisticated choreography that is central to ballet are in no way inferior to those which must be brought to bear on a mathematical problem. So, grossly overestimating my expositional abilities, I attempted, as others had done before, to explain to her the simplicity and logical nature of the procedure of ‘cancelling’."
Penrose, huh. I was reading the intro to Scott Aaronson's new book on quantum computing, and in it he says,
> More pointedly, one wonders who the audience for this book is supposed to be. On the one hand, it has way too much depth for a popular book. Like Roger Penrose’s _The Road to Reality_ – whose preface promises an accessible adventure even for readers who struggled with fractions in elementary school, but whose first few chapters then delve into holomorphic functions and fiber bundles – _Quantum Computing since Democritus_ is not for math-phobes.
> More pointedly, one wonders who the audience for this book is supposed to be. On the one hand, it has way too much depth for a popular book. Like Roger Penrose’s _The Road to Reality_ – whose preface promises an accessible adventure even for readers who struggled with fractions in elementary school, but whose first few chapters then delve into holomorphic functions and fiber bundles – _Quantum Computing since Democritus_ is not for math-phobes.
There is a book that comes with the course: http://www.amazon.com/gp/product/046502811X
The intro chapter is quite good ... very condensed material, but could be very interesting read.
The intro chapter is quite good ... very condensed material, but could be very interesting read.
I worked through the entire core sequence over about 18 months, along with texts recommended by friends and on forums. In particular, Shankar's Quantum Mechanics, and Taylor's Classical Mechanics were great supplements to the first two courses. I recommend that approach because, while it is great to have the "theoretical minimum" delivered in lecture format, its also nice to have a more thorough text on hand for the topics that really get you interested.
With that said, I hadn't even heard of the official text book AFAICR Susskind never mentioned it in any of the lectures.
With that said, I hadn't even heard of the official text book AFAICR Susskind never mentioned it in any of the lectures.
What about the math background ? Is someone who barely touched calculus able to follow through the classical mechanics course ?
Approximately speaking, first year undergraduate maths level is assumed, but no more. Most topics are elaborated on as required to teach the content.
You'll need to understand calculus, i.e. understand the principles behind derivatives and integrals. You certainly won't need to be proficient in manipulating them. A brief book, like Martin Gardner's updated edition of Calculus Made Easy, is the type of background that you need. A bit more specifically, having an intuition for vector calculus and partial differential equations is important.
For QM, you will need to understand what linear algebra is for, and how it uses abstraction to simplify certain types of operations. Here's a good introduction: http://betterexplained.com/articles/linear-algebra-guide/
Honestly, I can't think of anything else that you would necessarily need to know before starting, but to get the most out of it you WILL need to follow along with his working in pen-and-paper, and get used to rewatching, or looking up topics that you struggle with.
You'll need to understand calculus, i.e. understand the principles behind derivatives and integrals. You certainly won't need to be proficient in manipulating them. A brief book, like Martin Gardner's updated edition of Calculus Made Easy, is the type of background that you need. A bit more specifically, having an intuition for vector calculus and partial differential equations is important.
For QM, you will need to understand what linear algebra is for, and how it uses abstraction to simplify certain types of operations. Here's a good introduction: http://betterexplained.com/articles/linear-algebra-guide/
Honestly, I can't think of anything else that you would necessarily need to know before starting, but to get the most out of it you WILL need to follow along with his working in pen-and-paper, and get used to rewatching, or looking up topics that you struggle with.
> Martin Gardner's updated edition of Calculus Made Easy
I've seen several (quite a few actually) books with this title on Amazon. Some of them written by Martin Gardner and Silvanus P. Thompson, others written by Thompson alone. Do you recommend a particular edition? (and what's the deal with the plethora of different editions?)
> For QM, you will need to understand what linear algebra is for, and how it uses abstraction to simplify certain types of operations. Here's a good introduction: http://betterexplained.com/articles/linear-algebra-guide/
Could you recommend a wood-pulp version of this kind of material?
I've seen several (quite a few actually) books with this title on Amazon. Some of them written by Martin Gardner and Silvanus P. Thompson, others written by Thompson alone. Do you recommend a particular edition? (and what's the deal with the plethora of different editions?)
> For QM, you will need to understand what linear algebra is for, and how it uses abstraction to simplify certain types of operations. Here's a good introduction: http://betterexplained.com/articles/linear-algebra-guide/
Could you recommend a wood-pulp version of this kind of material?
Griffith's QM is an excellent intro textbook that also reviews/teaches the necessary parts of linear algebra: http://www.amazon.com/Introduction-Quantum-Mechanics-David-G...
(despite being a math major in undergrad, I didn't really appreciate linear algebra until I saw it used in QM when in grad school... linear algebra is a very dry subject by itself, but incredibly useful when applied to various other fields).
(despite being a math major in undergrad, I didn't really appreciate linear algebra until I saw it used in QM when in grad school... linear algebra is a very dry subject by itself, but incredibly useful when applied to various other fields).
> Calculus Made Easy
Thompson wrote the original edition a century ago. It is now Public Domain.
http://www.gutenberg.org/ebooks/33283
Gardner's revised edition adds introductory material, a problem set, and updates the language to keep it roughly in line with what is taught now. I can't speak to the differences between modern editions, but I have this one:
http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/d...
> linear algebra
To be honest, all abstract algebra is tough on new-comers. Compared to undergraduate calculus, the "aha" moments have more pay-off, but usually take a lot more time. The significance and power of vector spaces is just not something that is easily learnt, other than by working through problems with pen-and-paper math, and while doing so, constantly asking yourself "why do mathematicians do things this way, rather than some other way?"
I bought a copy of Gilbert Strang's Linear Algebra And It's Applications when I was an undergrad, and still refer to it now. It's brilliant, but it's a traditional text book, and definitely not a "primer".
It's not the type of maths you would call "hard" (integral calculus can be infuriatingly "hard") but it's the type that takes time and work to understand. Once you understand vector spaces, QM is surprisingly straight-forward.
Thompson wrote the original edition a century ago. It is now Public Domain.
http://www.gutenberg.org/ebooks/33283
Gardner's revised edition adds introductory material, a problem set, and updates the language to keep it roughly in line with what is taught now. I can't speak to the differences between modern editions, but I have this one:
http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/d...
> linear algebra
To be honest, all abstract algebra is tough on new-comers. Compared to undergraduate calculus, the "aha" moments have more pay-off, but usually take a lot more time. The significance and power of vector spaces is just not something that is easily learnt, other than by working through problems with pen-and-paper math, and while doing so, constantly asking yourself "why do mathematicians do things this way, rather than some other way?"
I bought a copy of Gilbert Strang's Linear Algebra And It's Applications when I was an undergrad, and still refer to it now. It's brilliant, but it's a traditional text book, and definitely not a "primer".
It's not the type of maths you would call "hard" (integral calculus can be infuriatingly "hard") but it's the type that takes time and work to understand. Once you understand vector spaces, QM is surprisingly straight-forward.
I haven't seen the updated version, but the one on gutenberg is gold. The old language is comical on its own: he cracks jokes and it is funny because of the jokes //and// because of the old language.
This book is so good, that gutenbeg volunteers took the time to typeset all the math in latex so the PDFs are very good for reading or printing out.
excerpt:
This book is so good, that gutenbeg volunteers took the time to typeset all the math in latex so the PDFs are very good for reading or printing out.
excerpt:
PROLOGUE.
Considering how many fools can calculate,
it is surprising that it should be thought
either a difficult or a tedious task for any
other fool to learn how to master the same tricks.
Some calculus-tricks are quite easy. Some are
enormously difficult. The fools who write the
textbooks of advanced mathematics—and they are
mostly clever fools—seldom take the trouble to
show you how easy the easy calculations are.
On the contrary, they seem to desire to impress
you with their tremendous cleverness by going about
it in the most difficult way.
Being myself a remarkably stupid fellow, I have had
to unteach myself the difficulties, and now beg to
present to my fellow fools the parts that are not hard.
Master these thoroughly, and the rest will follow.
What one fool can do, another can.Thank you for your answer, I'll have a look into Calculus Made Easy.
I'm the OP and originally posted the link and a brief review here: http://www.latestlesson.org/the-theoretical-minimum-modern-p.... If anyone has other suggested physics materials for those who are not professional physicists, I would be interested in reviewing them for our site. We're trying to create a comprehensive list of resources for STEM learners.
I can recommend this soil physics script:
http://www.iup.uni-heidelberg.de/institut/forschung/groups/t...
It needs some basic math (for a physicist) and some other basics (it won't explain the many things physicists take for basic knowledge, such as the existence of electrons etc), but most concepts are explained well, IMHO.
Same for this book on isotopic tracers in the hydrological cycle:
http://www-naweb.iaea.org/napc/ih/IHS_resources_publication_...
(better if you have the basics of radioactivity etc down)
Also, here's a good book about physical oceanography:
http://oceanworld.tamu.edu/home/course_book.htm
Hm.. that's that off the top of my head.. there might be some more (also other areas); I can look if you're interested.
http://www.iup.uni-heidelberg.de/institut/forschung/groups/t...
It needs some basic math (for a physicist) and some other basics (it won't explain the many things physicists take for basic knowledge, such as the existence of electrons etc), but most concepts are explained well, IMHO.
Same for this book on isotopic tracers in the hydrological cycle:
http://www-naweb.iaea.org/napc/ih/IHS_resources_publication_...
(better if you have the basics of radioactivity etc down)
Also, here's a good book about physical oceanography:
http://oceanworld.tamu.edu/home/course_book.htm
Hm.. that's that off the top of my head.. there might be some more (also other areas); I can look if you're interested.
Someone linked on HN this webpage by a theoretical physicist on how to become one and all the things you need to learn:
http://www.staff.science.uu.nl/~hooft101/theorist.html
http://www.staff.science.uu.nl/~hooft101/theorist.html
SICM belongs in that category!
http://en.wikipedia.org/wiki/Structure_and_Interpretation_of...
http://en.wikipedia.org/wiki/Structure_and_Interpretation_of...
Absolutely agree and it will be added to the list. Initially, we're interested in K-12 resources and something that might be a little bit easier for students still in school (although SICP can be used by advanced high school students). There do not seem to be that many good cs books for younger students, so any ideas on that front would be especially useful.
If you want to approach physics from a mathematical background I strongly recommend Peter Szekeres' book 'A Course in Modern Mathematical Physics'
http://www.amazon.co.uk/gp/aw/d/0521829607/ref=redir_mdp_mob...
http://www.amazon.co.uk/gp/aw/d/0521829607/ref=redir_mdp_mob...
I've watched a few of these just for fun. They are very watchable even if, like me, you don't have the first clue about the actual mathematics he uses. He explains enough of the physics in words that you can just let the forumlae wash over you and not worry about it.
The maths is kept into self-contained bits, so a lecture will typically be 40 minutes of words and pictures, then 20 minutes of calculation. I'm sure if you do get the maths then it will be perfect for you, but I encourage you to watch it anyway.
Overall, highly recommended, especially the cosmology ones.
EDIT: actually my memory is probably biased towards the cosmology course. I imagine the classical/statistical mechanics stuff does have a lot more maths running through each lecture.
The maths is kept into self-contained bits, so a lecture will typically be 40 minutes of words and pictures, then 20 minutes of calculation. I'm sure if you do get the maths then it will be perfect for you, but I encourage you to watch it anyway.
Overall, highly recommended, especially the cosmology ones.
EDIT: actually my memory is probably biased towards the cosmology course. I imagine the classical/statistical mechanics stuff does have a lot more maths running through each lecture.
I have been following his lectures for quite some time. Hat's off to Leonard Suskind.
I did Quantum Mechanics, Classical Mechanics, and now General Relativity. All of them enlightening, provides pure joy that only science can. And he is incredibly easy to follow, despite being a leading and esteemed Physicist of modern times - falls in similar class as Hawking. (The holographic principle anyone?)
I did Quantum Mechanics, Classical Mechanics, and now General Relativity. All of them enlightening, provides pure joy that only science can. And he is incredibly easy to follow, despite being a leading and esteemed Physicist of modern times - falls in similar class as Hawking. (The holographic principle anyone?)
For those interested in QM I highly recommend this intro
Quantum Mechanics for Engineers
http://www.eng.fsu.edu/~dommelen/quantum/
I've been reading this and it's fantastic - approaching the subject from the tools needed to understand the way the material works mathematically (Lagrangians etc) rather than as a series of separate physical problems is an excellent idea.
The video lectures in combination with the text would, I think, be a great subject for a regular meet up - its dense enough that there's lots to discuss but doesn't have too many prereqs. Anyone in London interested? Shoot me an email if so (Thomas dot m dot McGrath at gmail dot com)
The video lectures in combination with the text would, I think, be a great subject for a regular meet up - its dense enough that there's lots to discuss but doesn't have too many prereqs. Anyone in London interested? Shoot me an email if so (Thomas dot m dot McGrath at gmail dot com)
This is interesting, I've watched Professor Susskind's lectures on Quantum Mechanics and they were very good. Was able to understand how QM actually works for the first time.
I'm going to check this out, but the cadence of the lectures (just by looking at Classical Mechanics) seems pretty high for a 1.5 hour lecture, getting to Lagrangians in the third lecture seems pretty advanced for a survey of the subject especially targeted at enthusiasts.
A lot of the stuff covered in this series of courses wouldn't even be touched in a lot of undergrad Physics programs, outside of a small survey/project as part of a more broad course.
A lot of the stuff covered in this series of courses wouldn't even be touched in a lot of undergrad Physics programs, outside of a small survey/project as part of a more broad course.
From another point of view, the lectures are purely focused on giving an intuition behind concepts in modern theoretical physics, which is only a very small part of what is taught in an undergraduate program.
Lagrangians are a difficult, and abstract concept, but they doesn't mean that they can't be communicated in 3-4 hours by a skilled educator.
Lagrangians are a difficult, and abstract concept, but they doesn't mean that they can't be communicated in 3-4 hours by a skilled educator.
For the 300-400 page version see: "Classical Mechanics" by Goldstein.
I highly recommended this book. The first four chapters are a solid treatment of everything you learned in first year physics. For example, you will understand that the angular velocity \omega is actually \vec{\omega}.
Okay, so the gist of the whole Hamiltonian/Lagrangian is you we can solve problems by using energy calculations. The //Hamiltonian// describes the total energy in a system H = K + V. The Lagrangian is a bit f-up because, apparently, all the information you will ever need about the system can also be computed[1] from the Lagrangian L = K - V. The relation between H and L is called the Legendre transformation.
But the fun doesn't stop there. We have three different ways to solve physics problems until now (1) Newton (dynamics->a->kinematics), (2) Lagrangian + L-eqns, and (3) Hamiltonian + H-eqns. You would think physicists would stop at this point. Be like "OK we got three now, done!", but no they thought of an even more general way to think about the world.
The Hamilton-Jacobi equation is the final piece of the classical mechanics puzzle. In the last three chapters of Goldstein, you will learn about the connection between the Hamilton-Jacobi and Schrodinger's equation. Essentially, if you take the limit $\hbar \to 0$ in the main equation of QM, it simplifies to the Hamilton-Jacobi equation. Read JJ.Sakurai's ``Modern QM'' to continue.
[1] http://en.wikipedia.org/wiki/Hamiltonian_mechanics#Calculati...
[2] http://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi_equatio...
Okay, so the gist of the whole Hamiltonian/Lagrangian is you we can solve problems by using energy calculations. The //Hamiltonian// describes the total energy in a system H = K + V. The Lagrangian is a bit f-up because, apparently, all the information you will ever need about the system can also be computed[1] from the Lagrangian L = K - V. The relation between H and L is called the Legendre transformation.
But the fun doesn't stop there. We have three different ways to solve physics problems until now (1) Newton (dynamics->a->kinematics), (2) Lagrangian + L-eqns, and (3) Hamiltonian + H-eqns. You would think physicists would stop at this point. Be like "OK we got three now, done!", but no they thought of an even more general way to think about the world.
The Hamilton-Jacobi equation is the final piece of the classical mechanics puzzle. In the last three chapters of Goldstein, you will learn about the connection between the Hamilton-Jacobi and Schrodinger's equation. Essentially, if you take the limit $\hbar \to 0$ in the main equation of QM, it simplifies to the Hamilton-Jacobi equation. Read JJ.Sakurai's ``Modern QM'' to continue.
[1] http://en.wikipedia.org/wiki/Hamiltonian_mechanics#Calculati...
[2] http://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi_equatio...
Agreed that these are geared towards intuition. Though for reference: in my undergraduate degree, Lagrangian Dynamics and Hamiltonian Dynamics were each given semester long treatments.
That's interesting. In my undergraduate degree (which I believe to be fairly standard for the US), Lagrangian and Hamiltonian dynamics were both part of a one-semester classical mechanics course, along with much else. I'm quite envious, though---both Lagrangian and Hamiltonian dynamics are beautiful, and I need a better background.
If you don't mind my asking, where did you do undergrad?
If you don't mind my asking, where did you do undergrad?
The University of Edinburgh, Scotland. They were two of my favourite courses, I was amazed at how simple some classes of problems became with the techniques. You should be able to find the course notes somewhere, but I'm not sure if they'd be much value without the lectures.
Ditto for me, though we spent quite a bit of time on Lagrangians and Hamiltonians in that semester.
Video lectures allow you to pause and rewind at will and I guess that enables the authors to have greater information density than conventional lectures. So they maybe just require different study methods to get the best results.
Oh my, this is exactly what I was looking for. I'm going to dive in into this but does anyone maybe know about similar online resources you could learn some more advanced physics topics? Btw, Susskind is such a great man, love his way of work and persistence.
See also: http://motionmountain.com/
The author seems to have some non-mainstream views on physics/cosmology:
http://motionmountain.com/research.html
I'm not really sure what to make of it.
http://motionmountain.com/research.html
I'm not really sure what to make of it.
Hmm I never got that far to be honest. But it does seem a bit out there.
[deleted]
You can probably do better by going through Feynman's lectures. And maybe also his QED.
Or perhaps by folowing the reading suggested by Gerard 't Hooft: http://www.staff.science.uu.nl/~hooft101/theorist.html
Although they give excellent physical intuition, Feynman's lectures don't exactly cover any "theoretical physics," they're more of an intensive introductory course to physics as a whole.
His QED in some sense helps you understand how QED works, but obviously one wants to learn the mathematics behind QFT, and QED is quite qualitative in nature.
This is very interesting
As someone that has studied physics in an undergrad course, and who has learned a lot, but is disappointed that these courses don't go very far, this is very interesting.
As someone that has studied physics in an undergrad course, and who has learned a lot, but is disappointed that these courses don't go very far, this is very interesting.
http://mitpress.mit.edu/sites/default/files/titles/content/s...
The idea behind the book is to make the "mathematical notations be explicit and precise enough that they can be interpreted automatically, as by a computer." Since Sussman is involved, that means that they (and you, when you do the problems) write scheme programs.
In a more traditional vein, _Mechanics_ by Landau and Lifshitz is (in my view) among the 2 or 3 best physics textbooks available. It's a great supplement for two reasons: (1) it takes a somewhat different approach to the material than most other textbooks (emphasizing the consequences of symmetries from the very beginning) (2) it's quite short, which I find to be very helpful when self-learning.