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The Theoretical Minimum
Special Relativity and Classical Field Theory: The Theoretical Minimum
The third volume in the bestselling physics series cracks open Einstein's special relativity and field theory
Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any armchair physicist who wants to improve their knowledge of physics' deepest truths.
Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any armchair physicist who wants to improve their knowledge of physics' deepest truths.
448 pages, Hardcover
First published September 26, 2017
398 people are currently reading
4189 people want to read
About the author
Leonard Susskind
18 books802 followersLeonard Susskind is the Felix Bloch Professor of Theoretical Physics at Stanford University. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology. He is a member of the National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics, and a distinguished professor of the Korea Institute for Advanced Study.
read more: http://en.wikipedia.org/wiki/Leonard_...
read more: http://en.wikipedia.org/wiki/Leonard_...
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Displaying 1 - 30 of 65 reviews
April 8, 2021
This is the third Volume in The Theoretical Minimum book series. The previous Volume was about quantum mechanics. This one goes back to classical physics, introducing both special relativity and classical field theory, while showing how these are deeply connected.
Years ago when I learned electromagnetism Maxwell’s equations were only briefly mentioned and we never derived them in class, so this was the first time I saw their derivation. Susskind first introduces two of the four equations through vector identities and in a later chapter he derives the remaining equations using the Lagrangian and Euler-Lagrange equations. And he does so in a brilliant way, with every step being easy to follow and perceptible. I had also learned some special relativity in engineering school, though from a simplified point of view. The sections on special relativity were excellent and they compose the three initial chapters, but my favourite lectures from this Volume were actually the ones related to classical field theory, even if they were much more demanding mathematically.
In one of the best sections of the whole book, Susskind points out the four fundamental principles underlying all of physics. These are the action principle, locality, Lorentz invariance and gauge invariance. He then explains the ideas, before using them mathematically to produce results. Another highlight was that many of the different concepts we previously learned, such as the action principle, Lagrangian, Euler-Lagrange equations, Hamiltonian and Noether’s theorem, among others, play a major role in classical field theory. It all comes together in the end.
This is my favourite book in the series. It is better edited and I also believe the authors have learned with the previous Volumes and improved upon their work. The explanations are even better this time around and there are many reviewing sections reminding the readers of concepts which were introduced earlier in the book. Leonard Susskind and Art Friedman deserve all the praise, as they have written a brilliant book.
Note: I would also like to mention the opening sections in each lecture, which feature Art and Lenny (both authors) having a relaxed conversation. These were just great fun and I’ve come to enjoy them each time more as the series goes on. As Groucho himself might have said: “Humor is reason gone mad”.
Years ago when I learned electromagnetism Maxwell’s equations were only briefly mentioned and we never derived them in class, so this was the first time I saw their derivation. Susskind first introduces two of the four equations through vector identities and in a later chapter he derives the remaining equations using the Lagrangian and Euler-Lagrange equations. And he does so in a brilliant way, with every step being easy to follow and perceptible. I had also learned some special relativity in engineering school, though from a simplified point of view. The sections on special relativity were excellent and they compose the three initial chapters, but my favourite lectures from this Volume were actually the ones related to classical field theory, even if they were much more demanding mathematically.
In one of the best sections of the whole book, Susskind points out the four fundamental principles underlying all of physics. These are the action principle, locality, Lorentz invariance and gauge invariance. He then explains the ideas, before using them mathematically to produce results. Another highlight was that many of the different concepts we previously learned, such as the action principle, Lagrangian, Euler-Lagrange equations, Hamiltonian and Noether’s theorem, among others, play a major role in classical field theory. It all comes together in the end.
This is my favourite book in the series. It is better edited and I also believe the authors have learned with the previous Volumes and improved upon their work. The explanations are even better this time around and there are many reviewing sections reminding the readers of concepts which were introduced earlier in the book. Leonard Susskind and Art Friedman deserve all the praise, as they have written a brilliant book.
Note: I would also like to mention the opening sections in each lecture, which feature Art and Lenny (both authors) having a relaxed conversation. These were just great fun and I’ve come to enjoy them each time more as the series goes on. As Groucho himself might have said: “Humor is reason gone mad”.
May 3, 2019
This is the third book of the author's famous series “The Theoretical Minimum” - and probably, in my personal opinion, the finest of the three in terms of conceptual lucidity, clarity, approachability, and conciseness.
Reading it has been a thoroughly pleasant experience.
The main subjects of this book are special relativity and classical field theory, and this book is very successful in treating both subjects at a good level of detail, requiring, as a pre-requisite, only undergraduate knowledge (if you are familiar with multivariate calculus and linear algebra, and you have knowledge of the principle of stationary action, you should be OK): I must point out though that, whilst there are many books on special relativity (in some cases exploring the subject at a deeper level), the biggest section of the book, dedicated to classical field theory (with a focus on EM and relativistic fields) is where the author has been most successful, and the part which I greatly enjoyed.
As the author correctly stated, classical field theory is a fundamental part of physics, as it ties together electromagnetism, classical mechanics and special relativity. It also provides a framework for studying any fields (such as hydrodynamics, for example), and most importantly it is a crucial prerequisite for the study of quantum field theory in particular, but also does help with the approach to general relativity. I wished I had a better confidence in this field before I embarked on the detailed study of quantum field theory and general relativity – it would have definitely streamlined the process and reduced the gradient of my learning curve.
Coming back to this book, I particularly enjoyed how the author manages to tie together and cross-reference, in a coherent whole, all the elements treated in his book.
I particularly enjoyed the absolutely brilliant derivation of Maxwell's inhomogeneous equations from a stationary action principle, and the equally brilliant treatment of the Maxwell equations in tensorial form.
Concepts such as gauge invariance, the procedure for the construction of the appropriate Lagrangian for relativistic fields, the various continuity equations, and the Poynting vector, are all explained with precision, clarity and conciseness.
The only (minor) issues are in relation to the occasional slightly cavalier attitude of the author in relation to mathematical precision (which, to be fair, is a more general issue with a few physicists, whose abuse of mathematical accuracy and notation can occasionally reach irksome levels): for example, the Dirac Delta is NOT a function, but a distribution – you may define it as a functional or, if you wish, as the result of a limiting process of a specific sequence of functions. But, again, it is not a function (to be fair, while the author keeps calling it a function, he does say in one place that "it is not an ordinary function"). There are also a couple of minor instances where the author gets slightly confused with the interplay of co-variant and contra-variant indices, a couple of minor typos, and a couple of instances where there is a bit too much hand-waving, but nothing serious at all. Also, the author definition of tensors is good, and more than adequate for the subjects treated, but not the best I have ever found, to be perfectly honest.
Overall, it is a brilliant book, extremely easy to read, very informative, and highly recommended to all readers interested in a reasonably detailed but highly accessible introduction to SR, but especially to classical field theory and electromagnetism. The author has successfully positioned his teaching and publications in the poorly covered area between the more specialist publications for practitioners, and the typical popular science books; he definitely deserves praise for this, even when his efforts might not have consistently been, in the past, as fruitful as in this instance. Science and rational thinking have recently come under under sustained attack, especially in Trump's America, and anything that can enable (or at least facilitate) the diffusion of the scientific culture and perspective is greatly needed.
4.5 stars, rounded up to 5.
PS: there is also a series of lectures freely available online (https://theoreticalminimum.com/course...) that covers a substantial part of the items developed in the book. However, the latter is of better quality and it does cover more ground. I am really happy that I purchased it.
Reading it has been a thoroughly pleasant experience.
The main subjects of this book are special relativity and classical field theory, and this book is very successful in treating both subjects at a good level of detail, requiring, as a pre-requisite, only undergraduate knowledge (if you are familiar with multivariate calculus and linear algebra, and you have knowledge of the principle of stationary action, you should be OK): I must point out though that, whilst there are many books on special relativity (in some cases exploring the subject at a deeper level), the biggest section of the book, dedicated to classical field theory (with a focus on EM and relativistic fields) is where the author has been most successful, and the part which I greatly enjoyed.
As the author correctly stated, classical field theory is a fundamental part of physics, as it ties together electromagnetism, classical mechanics and special relativity. It also provides a framework for studying any fields (such as hydrodynamics, for example), and most importantly it is a crucial prerequisite for the study of quantum field theory in particular, but also does help with the approach to general relativity. I wished I had a better confidence in this field before I embarked on the detailed study of quantum field theory and general relativity – it would have definitely streamlined the process and reduced the gradient of my learning curve.
Coming back to this book, I particularly enjoyed how the author manages to tie together and cross-reference, in a coherent whole, all the elements treated in his book.
I particularly enjoyed the absolutely brilliant derivation of Maxwell's inhomogeneous equations from a stationary action principle, and the equally brilliant treatment of the Maxwell equations in tensorial form.
Concepts such as gauge invariance, the procedure for the construction of the appropriate Lagrangian for relativistic fields, the various continuity equations, and the Poynting vector, are all explained with precision, clarity and conciseness.
The only (minor) issues are in relation to the occasional slightly cavalier attitude of the author in relation to mathematical precision (which, to be fair, is a more general issue with a few physicists, whose abuse of mathematical accuracy and notation can occasionally reach irksome levels): for example, the Dirac Delta is NOT a function, but a distribution – you may define it as a functional or, if you wish, as the result of a limiting process of a specific sequence of functions. But, again, it is not a function (to be fair, while the author keeps calling it a function, he does say in one place that "it is not an ordinary function"). There are also a couple of minor instances where the author gets slightly confused with the interplay of co-variant and contra-variant indices, a couple of minor typos, and a couple of instances where there is a bit too much hand-waving, but nothing serious at all. Also, the author definition of tensors is good, and more than adequate for the subjects treated, but not the best I have ever found, to be perfectly honest.
Overall, it is a brilliant book, extremely easy to read, very informative, and highly recommended to all readers interested in a reasonably detailed but highly accessible introduction to SR, but especially to classical field theory and electromagnetism. The author has successfully positioned his teaching and publications in the poorly covered area between the more specialist publications for practitioners, and the typical popular science books; he definitely deserves praise for this, even when his efforts might not have consistently been, in the past, as fruitful as in this instance. Science and rational thinking have recently come under under sustained attack, especially in Trump's America, and anything that can enable (or at least facilitate) the diffusion of the scientific culture and perspective is greatly needed.
4.5 stars, rounded up to 5.
PS: there is also a series of lectures freely available online (https://theoreticalminimum.com/course...) that covers a substantial part of the items developed in the book. However, the latter is of better quality and it does cover more ground. I am really happy that I purchased it.
April 13, 2018
I ate this up like candy. Which probably isn't the best way to approach it! What I mean is, I really enjoyed reading this. And I felt like I understood almost every step along the way. But I didn't stop and do the exercises. For real understanding, one simply must do the math. It is like the difference between watching a gymnast and becoming a gymnast. I'm no gymnast.
The fact that the authors can make me even feel like I understood almost everything is a great achievement. They delivered on their promise to make the material "as simple as possible, but no simpler". The second part of that phrase is important: "but no simpler". Math is required, and fairly advanced math at that. You must read and understand the equations as well as the text. They hold your hands to some extent, by including most of the intermediate steps in any derivation, and repeating key equations and diagrams multiple times. But you need to be comfortable with algebra and calculus with multiple variables. The linear algebra and tensor notation that you need is explained as the book goes along, as well as reminders of "div", "grad", "curl". But if this is the first time you are seeing those things, you will struggle to keep up. The symbols become more and more abstract as you go, which is why very powerful statements can be made in very few symbols.
Sometimes it felt so simple that "a five year old could understand it." But I'm sure that a few months from now I'll need to find that five year old to explain it to me again! (Apologies to Groucho.)
If equations are not your thing, try Very Special Relativity: An Illustrated Guide which does a very good job of explaining special relativity using only Minkowski diagrams and no equations. Better yet, consult the diagrams in that book as you read this one. Those diagrams are sometimes easier to follow because they use color to differentiate reference frames. Both books suffer from the same problem of failing to put proper scale markings on the axes of the moving reference frame, which leads these authors to make hand-waving arguments about why the hypotenuse of certain triangles should be considered shorter than the other two sides. Really, that phrase which sounds like non-sense can make simple sense if you just draw-in the scale markings on both sets of axes. Even the Wikipedia page about Minkowski diagrams gets that right.
This is book 3 in a series, yet I read 3 first, then 2, then 1. That worked for me, but I don't recommend it. You could certainly skip book 2 on Quantum Mechanics, because there is none of that in here. But you should at least read book 1 because it derives regular Newtonian mechanics from a Lagrangian function and the principle of least action. That isn't the way Newtonian mechanics is usually taught, but it is a more fundamental way of understanding it, and that technique is heavily used to develop field theory here and to derive Maxwell's equations from first principles (which again, is not the way it is usually taught).
Except for their attempts at humor -- of which the less said, the better -- I'm quite impressed. I will go back and read the preceding books, and will probably try my hand at the upcoming one on general relativity, though I can't see how they could possibly make that math simple enough for me.
Update: I have now read books 3, 2 and 1 (yes, in that order!) and still enjoyed this one the most. In 3, we just start with using Hamiltonians and Lagrangians without much intro. Book 1 contains that intro and it involves a bunch of derivations. Boring! (But necessary.) Book 1 seems to have more typos, and really lousy typesetting for the equations. Book 2 was the easiest of them all for me, but that is because all the math work in that book is stuff I did many times in grad school. I didn't bother to do the math again while reading it, so it was a great for giving me the "forest not the trees" view. My experience in grad school was "all trees no forest".
The fact that the authors can make me even feel like I understood almost everything is a great achievement. They delivered on their promise to make the material "as simple as possible, but no simpler". The second part of that phrase is important: "but no simpler". Math is required, and fairly advanced math at that. You must read and understand the equations as well as the text. They hold your hands to some extent, by including most of the intermediate steps in any derivation, and repeating key equations and diagrams multiple times. But you need to be comfortable with algebra and calculus with multiple variables. The linear algebra and tensor notation that you need is explained as the book goes along, as well as reminders of "div", "grad", "curl". But if this is the first time you are seeing those things, you will struggle to keep up. The symbols become more and more abstract as you go, which is why very powerful statements can be made in very few symbols.
Sometimes it felt so simple that "a five year old could understand it." But I'm sure that a few months from now I'll need to find that five year old to explain it to me again! (Apologies to Groucho.)
If equations are not your thing, try Very Special Relativity: An Illustrated Guide which does a very good job of explaining special relativity using only Minkowski diagrams and no equations. Better yet, consult the diagrams in that book as you read this one. Those diagrams are sometimes easier to follow because they use color to differentiate reference frames. Both books suffer from the same problem of failing to put proper scale markings on the axes of the moving reference frame, which leads these authors to make hand-waving arguments about why the hypotenuse of certain triangles should be considered shorter than the other two sides. Really, that phrase which sounds like non-sense can make simple sense if you just draw-in the scale markings on both sets of axes. Even the Wikipedia page about Minkowski diagrams gets that right.
This is book 3 in a series, yet I read 3 first, then 2, then 1. That worked for me, but I don't recommend it. You could certainly skip book 2 on Quantum Mechanics, because there is none of that in here. But you should at least read book 1 because it derives regular Newtonian mechanics from a Lagrangian function and the principle of least action. That isn't the way Newtonian mechanics is usually taught, but it is a more fundamental way of understanding it, and that technique is heavily used to develop field theory here and to derive Maxwell's equations from first principles (which again, is not the way it is usually taught).
Except for their attempts at humor -- of which the less said, the better -- I'm quite impressed. I will go back and read the preceding books, and will probably try my hand at the upcoming one on general relativity, though I can't see how they could possibly make that math simple enough for me.
Update: I have now read books 3, 2 and 1 (yes, in that order!) and still enjoyed this one the most. In 3, we just start with using Hamiltonians and Lagrangians without much intro. Book 1 contains that intro and it involves a bunch of derivations. Boring! (But necessary.) Book 1 seems to have more typos, and really lousy typesetting for the equations. Book 2 was the easiest of them all for me, but that is because all the math work in that book is stuff I did many times in grad school. I didn't bother to do the math again while reading it, so it was a great for giving me the "forest not the trees" view. My experience in grad school was "all trees no forest".
August 5, 2018
I like the idea of the theoretical minimum books; they are something more than popularizations, something less than textbooks, and promise to teach the math necessary for a real understanding of the science as it is needed. This is the third book; it follows directly on what was presented in the first book on classical physics, and I'm not sure why Susskind (the principal author) decided to separate the two by the book on quantum theory, which is based on different ideas and different math. Unfortunately, I read the first book more than a year ago, and the wait for this to come out and be purchased at the library meant that my memory was somewhat vague on what I had learned in that, especially since my physics courses in college were not only long ago but didn't even mention Lagrangians and least action which are the basis of Susskind's approach. I would suggest that the reader who, like me, has never learned this material in school or had courses in vector and tensor calculus should read volumes one and three right after one another and then go back to volume two (or perhaps wait for volume four on general relativity which probably also follows on one and three rather than on the second volume).
The present book is in two parts. The first part, on special relativity, seemed rather simple, perhaps because the ideas were familiar to me from many more popular accounts. The second part, on classical field theory (centering on Maxwell's equations) was much more difficult; this is where the Lagrangians and vector calculus kicked in. Some of the difficulty undoubtedly was due to the shortcomings of my mathematical background, although I did minor in math in college back in the dark ages, but some I would have to put on the authors, who made it more confusing than necessary. The most annoying feature of the book was that literally almost every chapter introduced a new system of notation -- not for new concepts, but for the same equations. The authors use at least six different ways of writing the same vectors, and at least four different notations for partial derivatives. It was very frustrating to have to learn the substance of the equations simultaneously with new formal ways of writing them, and especially to spend ten minutes puzzling over what an unfamiliar-looking equation was actually saying only to realize that it was the same equation that was explained in a previous chapter using a different notation. I think just from a paedagogical standpoint it would have made more sense if the authors had chosen one (fairly expansive) notation and stuck with it, explaining the more condensed notations at the end in an appendix after I had learned what the equations actually meant. I know pencils are expensive when you're saving up for a new supercollider, but still. . .
Despite this, I was surprised at how much of the book I understood; essentially almost everything except the last chapter, which (as in most math books based on courses or lectures) sped up to squeeze in everything the authors wanted to cover before the class ended. This was what happened with my college calculus course, which covered Gauss's theorem and Stokes theorem on the last day -- perhaps the best thing I got out of this book was finally understanding what those two theorems were about. I'm not sure that the book would really be totally understandable to someone with just a high school calculus background, as the authors suggest, but it certainly comes closer than say Penrose's Road to Reality which made the same claim and in fact assumed a knowledge of complex analysis. This series may not be the absolute beginner's choice, but it comes as close as any I've found so far.
The present book is in two parts. The first part, on special relativity, seemed rather simple, perhaps because the ideas were familiar to me from many more popular accounts. The second part, on classical field theory (centering on Maxwell's equations) was much more difficult; this is where the Lagrangians and vector calculus kicked in. Some of the difficulty undoubtedly was due to the shortcomings of my mathematical background, although I did minor in math in college back in the dark ages, but some I would have to put on the authors, who made it more confusing than necessary. The most annoying feature of the book was that literally almost every chapter introduced a new system of notation -- not for new concepts, but for the same equations. The authors use at least six different ways of writing the same vectors, and at least four different notations for partial derivatives. It was very frustrating to have to learn the substance of the equations simultaneously with new formal ways of writing them, and especially to spend ten minutes puzzling over what an unfamiliar-looking equation was actually saying only to realize that it was the same equation that was explained in a previous chapter using a different notation. I think just from a paedagogical standpoint it would have made more sense if the authors had chosen one (fairly expansive) notation and stuck with it, explaining the more condensed notations at the end in an appendix after I had learned what the equations actually meant. I know pencils are expensive when you're saving up for a new supercollider, but still. . .
Despite this, I was surprised at how much of the book I understood; essentially almost everything except the last chapter, which (as in most math books based on courses or lectures) sped up to squeeze in everything the authors wanted to cover before the class ended. This was what happened with my college calculus course, which covered Gauss's theorem and Stokes theorem on the last day -- perhaps the best thing I got out of this book was finally understanding what those two theorems were about. I'm not sure that the book would really be totally understandable to someone with just a high school calculus background, as the authors suggest, but it certainly comes closer than say Penrose's Road to Reality which made the same claim and in fact assumed a knowledge of complex analysis. This series may not be the absolute beginner's choice, but it comes as close as any I've found so far.
November 2, 2017
This is the third book in a series explaining physics to people who are not afraid of a few equations. The first, The Theoretical Minimum, covered so-called classical physics, and was absolutely brilliant. It deservedly became a best seller. The second, on quantum mechanics, was nowhere near as successful at getting the concepts across, in no small measure because those concepts are much harder to grasp than the concepts involved in the kind of physics Newton dealt with. This book lies somewhere between the two, but much closer to The Theoretical Minimum. The special relativity part of the book is as good as the first book, and gets Einsteinian concepts across clearly and simply, but does include equations. Great stuff if you are up to A level maths, and you can read around the equations if you are not. But that only covers 113 of the 425 pages. Most of the rest, apart from a couple of pretty technical appendices, deals with classical (that is, not quantum) field theory. This is much heavier going, but explains things like the electromagnetic field and leads you up to the equations, discovered by James Clerk Maxwell, that explain electromagnetism. Curiously, it was those equations that actually gave Einstein the inspiration for his special theory!
Five stars for the first part and three for the second. It will be interesting to see how these authors deal with the general theory of relativity, which I guess must be their next project.
Five stars for the first part and three for the second. It will be interesting to see how these authors deal with the general theory of relativity, which I guess must be their next project.
May 3, 2022
Last term, I took an Introduction to Theoretical Physics course whose syllabus ranged from classical mechanics to classical field theory, relativity and cosmology. The part that frustrated me the most was classical field theory because it was completely foreign to me, and its new notations didn't help either. Perhaps my confusion arised because of the limited time that the lecturer had, so after finishing the course, I tried to find more materials on this particular topic to read. I found Theoretical Minimum series by professor Susskind of YouTube, and eventually I found this 3-book series. I was really impressed by how the authors explained this topic which had eluded me for months. I was smiling throughout his derivation of Maxwell's equations from the lagrangian and the principles of least action because it was so beautifully done.
I hope to read his next book in the series soon. And by the way, he asked us to mention Groucho no matter how subtle it is so that he could be sure that we actually read the book, but I don't know who he was. Will google that now.
I hope to read his next book in the series soon. And by the way, he asked us to mention Groucho no matter how subtle it is so that he could be sure that we actually read the book, but I don't know who he was. Will google that now.
August 31, 2024
Stokes and Gaus Theorem could have been explained better.
Loved seeing different concepts tied together. The book gives a needed big picture that is often lost in classes at university.
-Groucho, I'll be seeing you in general relativity
Loved seeing different concepts tied together. The book gives a needed big picture that is often lost in classes at university.
-Groucho, I'll be seeing you in general relativity
August 21, 2024
This book saved my ass <333
June 27, 2019
Most texts on electromagnetism start out historically, i.e., teaching you the experimentally derived Coulomb's law, Ampere-Maxwell law, Gauss' law etc. Then they proceed to the Maxwell equations, and then they talk about how to solve the equations in different (manually solvable) situations. Then they talk about special relativity, Lorentz invariance, and stuff like that. This, I think, is a good way to learn this subject - for beginners.
However, this book takes a sort of unorthodox approach. It starts out with special relativity (SR), then uses the principle of least action coupled with Lorentz invariance, to derive Maxwell's equations completely theoretically. I loved this approach very much, since this shows the sheer beauty and elegance of symmetries and the principle of least action. I probably wouldn't recommend it to a beginner because of the book's higher mathematical sophistication compared to introductory EM books. But I also think that a beginner (with, of course, a course of Lagrangian and Hamiltonian mechanics under his/her belt) should be able to study this book without major problems. The explanations are clear enough, so, yeah.
Maybe to the disappointment of some, the star of this book is NOT Maxwell's equations. You won't get much of the applications of the equations here. They're just byproducts of studying classical fields. I don't think that's a problem, since the title of the book doesn't contain anything about electromagnetism. The protagonist here is classical field theory. Something which you need to study if you want to study the cornerstones of modern physics - General Relativity (GR), and Quantum Field Theory (QFT). If you're interested to tackle GR and/or QFT, you should give this one a read before jumping in.
Oh, and one last thing. All hail Groucho!
However, this book takes a sort of unorthodox approach. It starts out with special relativity (SR), then uses the principle of least action coupled with Lorentz invariance, to derive Maxwell's equations completely theoretically. I loved this approach very much, since this shows the sheer beauty and elegance of symmetries and the principle of least action. I probably wouldn't recommend it to a beginner because of the book's higher mathematical sophistication compared to introductory EM books. But I also think that a beginner (with, of course, a course of Lagrangian and Hamiltonian mechanics under his/her belt) should be able to study this book without major problems. The explanations are clear enough, so, yeah.
Maybe to the disappointment of some, the star of this book is NOT Maxwell's equations. You won't get much of the applications of the equations here. They're just byproducts of studying classical fields. I don't think that's a problem, since the title of the book doesn't contain anything about electromagnetism. The protagonist here is classical field theory. Something which you need to study if you want to study the cornerstones of modern physics - General Relativity (GR), and Quantum Field Theory (QFT). If you're interested to tackle GR and/or QFT, you should give this one a read before jumping in.
Oh, and one last thing. All hail Groucho!
May 6, 2018
With the third installment of The Theoretical Minimum, it seems that Leonard Susskind and Art Friedman have found their respective stride. This book covers Special Relativity and Classical Field Theory as the title suggests, and as the context of the series suggests it covers the subjects in an engaging manner meant for the common man. Of course, Susskind does suggest that you should have a small backing in Calculus and Linear Algebra to make it go more smoothly but the book is still entertaining nonetheless.
Since this is the third book in the series, Susskind suggests that you go and take a peek at the section on Hamiltonians and Lagrangians from the first book and brush up on that. Once you have done that, Professor Susskind explains the idea of relativistic motion in a way that most should be able to understand. For example, if you go into space and apply a constant amount of force to your body, you should be able to accelerate to a velocity faster than that of light! To that incredibly wrong statement, Professor Susskind has an answer. Generally, if you accelerate to a velocity that is an appreciable fraction of c, you will also accumulate mass and be forced to use more force.
In any case, the book contains 11 chapters which are called Lectures in this case. We get to build Lagrangians and apply them to fields and do all sorts of interesting things with advanced mathematics. The book is also funny in the opening portions of the chapters. So with all that, I give this book a 5 out of 5.
PS, I also liked the Groucho reference.
Since this is the third book in the series, Susskind suggests that you go and take a peek at the section on Hamiltonians and Lagrangians from the first book and brush up on that. Once you have done that, Professor Susskind explains the idea of relativistic motion in a way that most should be able to understand. For example, if you go into space and apply a constant amount of force to your body, you should be able to accelerate to a velocity faster than that of light! To that incredibly wrong statement, Professor Susskind has an answer. Generally, if you accelerate to a velocity that is an appreciable fraction of c, you will also accumulate mass and be forced to use more force.
In any case, the book contains 11 chapters which are called Lectures in this case. We get to build Lagrangians and apply them to fields and do all sorts of interesting things with advanced mathematics. The book is also funny in the opening portions of the chapters. So with all that, I give this book a 5 out of 5.
PS, I also liked the Groucho reference.
December 5, 2018
Where do I even begin reviewing this absolutely marvelous treasure of a series? These books are what I have been looking for for the past couple of decades, and they just keep on “hitting the spot” with each new installment; just as I was getting antsy about not understanding what a tensor is, making vague plans about finding a good tutorial or book of some kind, along comes Susskind and explains it in nine pages. And then, just as I was thinking “wow, that was hardcore”, he covers gauge symmetry, a notoriously slippery concept to explain, in another nine.
Well, nine pages of heavy lifting, based on hundreds of preceding pages, but he bloody goes and does it to the point where my understanding of high-level physics concepts blossoms further with each new chapter. Yes, occasionally these books are really heavy lifting, often in unexpected areas (who would have thought that of the two topics in the title the innocuous-sounding “classical field theory” would be the real mind-bender), but coupled with the video lectures they are precisely the mind-opening magic medicine that allows me to understand actual real “equations and all” higher level physics (something I am more or less decent at) without necessarily requiring me to do any actual physics or math (something I seriously suck at).
The only problem now is the impending long wait for the next book about (fingers crossed) the general theory of relativity.
Well, nine pages of heavy lifting, based on hundreds of preceding pages, but he bloody goes and does it to the point where my understanding of high-level physics concepts blossoms further with each new chapter. Yes, occasionally these books are really heavy lifting, often in unexpected areas (who would have thought that of the two topics in the title the innocuous-sounding “classical field theory” would be the real mind-bender), but coupled with the video lectures they are precisely the mind-opening magic medicine that allows me to understand actual real “equations and all” higher level physics (something I am more or less decent at) without necessarily requiring me to do any actual physics or math (something I seriously suck at).
The only problem now is the impending long wait for the next book about (fingers crossed) the general theory of relativity.
January 10, 2019
Truly man's best friend outside of a dog
December 30, 2024
The overarching project here can be identified as : How to write a Lorentz invariant Lagrangian for a classical (i.e. non quantum) particle-field system that preserves locality and gauge invariance; subsequently using it to derive the equations of motion using Euler-Lagrange.
Each of these concepts takes up entire chapters, but it has been done remarkably well for a book that expects no more background than its predecessor (https://www.goodreads.com/book/show/1...), hand holding the reader through the conceptual developments from the simple to the complex. e.g. Analysis for a particle/field in isolation before considering the combined system.
Special Relativity is presented from first principles to establish the idea of frame independent laws that respect Lorentz transformations, followed by field theory and the idea of "particle affects field affects particle", a short introduction to tensor notation, and finally the derivation of Maxwell's equations from a purely theoretical basis rather than the actual historical development that abstracted from experimental discoveries of Oersted, Ampere, Coulomb, Faraday.
Humor and witticisms abound, making physicists look less of foreboding maniacs pondering over inscrutable symbols and more like curious children with an urge to peek into the mind of God, despite being admonished against the futility of the ambition.
Each of these concepts takes up entire chapters, but it has been done remarkably well for a book that expects no more background than its predecessor (https://www.goodreads.com/book/show/1...), hand holding the reader through the conceptual developments from the simple to the complex. e.g. Analysis for a particle/field in isolation before considering the combined system.
Special Relativity is presented from first principles to establish the idea of frame independent laws that respect Lorentz transformations, followed by field theory and the idea of "particle affects field affects particle", a short introduction to tensor notation, and finally the derivation of Maxwell's equations from a purely theoretical basis rather than the actual historical development that abstracted from experimental discoveries of Oersted, Ampere, Coulomb, Faraday.
Humor and witticisms abound, making physicists look less of foreboding maniacs pondering over inscrutable symbols and more like curious children with an urge to peek into the mind of God, despite being admonished against the futility of the ambition.
December 3, 2018
Love this series! Personally, I found the topic of this book a bit less interesting than the previous two (classical mechanics and quantum) but it does a splendid job linking time, space, energy and light! Looking forward to the next one!
May 13, 2025
per fi l’he acabat 😭😭😭
està molt ben escrit i explicat. sens dubte m’ha fet plantrjar-me llegir-me més llibres acadèmics (si pot ser de coses que m’interessin més però súper guai ).
jsjsjsjs si estàs estudiant física o quelcom similar, tel recomano 😌😌.
està molt ben escrit i explicat. sens dubte m’ha fet plantrjar-me llegir-me més llibres acadèmics (si pot ser de coses que m’interessin més però súper guai ).
jsjsjsjs si estàs estudiant física o quelcom similar, tel recomano 😌😌.
July 13, 2018
Hugely educational and interesting as usual, within and without the boundary of the dog.
June 28, 2019
I got this book because I really loved the first two of the series, but also because I am really intrigued about the topic of relativity. And Lenny and Art did not let me down! This is an amazing journey to the land of relativity and to field theory.
Initially I thought that the field theory part will be minor, but it really covers almost two thirds of the book. When I first realised, I was a bit disappointed, but now I realise that the authors added one more topic in my interest list!
This is my review. If you don't like it, I can write another one :)
Initially I thought that the field theory part will be minor, but it really covers almost two thirds of the book. When I first realised, I was a bit disappointed, but now I realise that the authors added one more topic in my interest list!
This is my review. If you don't like it, I can write another one :)
February 12, 2018
Special Relativity and Classical Field Theory: The Theoretical Minimum.
By Leonard Susskind and Art Friedman.
Reviewed by Galen Weitkamp.
I’m becoming a big fan of The Theoretical Minimum Series. Last year I read (and thoroughly enjoyed) the first two volumes. What You Need To Know... and Quantum Mechanics. I just now finished Special Relativity and Classical Field Theory. It’s a blast. Lenny and Art are carrying the wit, humor and the seriousness of George Gamow’s legacy (I’m thinking One Two Three...Infinity) into the future.
There are lots of books for the lay public which attempt to explain the principles of science, convey something of the excitement of discovery and a personal awe of the cosmos; but very few actually empower the reader. Very few bridge the gap between reading about science and actually understanding it. Lenny and Art have constructed three such bridges.
Special Relativity and Classical Field Theory is their most recent contribution. Should you decide to read it (and I think you should outside of a dog) you will need a little bit of algebra and calculus, a willingness to exert a little bit of effort and perhaps a copy of the first volume in this series (What You Need To Know To Start Doing Physics) by your side.
The book begins with a discussion of inertial reference frames: connecting how things look to an observer in one frame to how they look to another person using a different frame of reference. Time dilation, space contraction, the twin-paradox, the speeding limo in the garage problem and Minkowski’s geometrical ‘visualization’ of the principles of relativity are very nicely laid out in simple form.
By chapter three we’re examining the role of the action principle in special relativity. This is especially important in the later chapters on classical field theory. A traditional textbook would derive Maxwell’s equations for the electromagnetic field from the hard won laws that Faraday and other experimentalists wrested from nature in the laboratory. Lenny and Art instead derive Maxwell’s theory from an action principle, and then show how the equations capture the laws discovered by the experimentalists. They show how special relativity and electromagnetic theory is all one piece.
You can read about the grandeur of the universe, be awed by comparisons of size and distance and mystified by many worlds and other entanglements. But the best way to develop real respect for the universe, its laws and truth is to engage it in its own language and with honest effort and curiosity. As Groucho Marx once said, “Those are my principles, and if you don’t like them...well, I have others.”
By Leonard Susskind and Art Friedman.
Reviewed by Galen Weitkamp.
I’m becoming a big fan of The Theoretical Minimum Series. Last year I read (and thoroughly enjoyed) the first two volumes. What You Need To Know... and Quantum Mechanics. I just now finished Special Relativity and Classical Field Theory. It’s a blast. Lenny and Art are carrying the wit, humor and the seriousness of George Gamow’s legacy (I’m thinking One Two Three...Infinity) into the future.
There are lots of books for the lay public which attempt to explain the principles of science, convey something of the excitement of discovery and a personal awe of the cosmos; but very few actually empower the reader. Very few bridge the gap between reading about science and actually understanding it. Lenny and Art have constructed three such bridges.
Special Relativity and Classical Field Theory is their most recent contribution. Should you decide to read it (and I think you should outside of a dog) you will need a little bit of algebra and calculus, a willingness to exert a little bit of effort and perhaps a copy of the first volume in this series (What You Need To Know To Start Doing Physics) by your side.
The book begins with a discussion of inertial reference frames: connecting how things look to an observer in one frame to how they look to another person using a different frame of reference. Time dilation, space contraction, the twin-paradox, the speeding limo in the garage problem and Minkowski’s geometrical ‘visualization’ of the principles of relativity are very nicely laid out in simple form.
By chapter three we’re examining the role of the action principle in special relativity. This is especially important in the later chapters on classical field theory. A traditional textbook would derive Maxwell’s equations for the electromagnetic field from the hard won laws that Faraday and other experimentalists wrested from nature in the laboratory. Lenny and Art instead derive Maxwell’s theory from an action principle, and then show how the equations capture the laws discovered by the experimentalists. They show how special relativity and electromagnetic theory is all one piece.
You can read about the grandeur of the universe, be awed by comparisons of size and distance and mystified by many worlds and other entanglements. But the best way to develop real respect for the universe, its laws and truth is to engage it in its own language and with honest effort and curiosity. As Groucho Marx once said, “Those are my principles, and if you don’t like them...well, I have others.”
January 27, 2018
Inspired
This is the three book in the series I have read. The first book set up a lot of the mathematical machinery used here, namely the Lagrangian and the Hamiltonian along with conservation laws and symmetries.
I struggled a bit with the second book on quantum mechanics - have to go back and have another crack at that one.
But this one was REALLY good. The setup of the book was so logical and the mathematical development was so well paced that I could feel much greater mathematical sophistication that helped me to anticipate many of the subsequent developments. Now, I will not say that I could erase all the equations and mathematical reasoning segments from the book, and as an exercise, recreate them from memory, calculation, and my own reasoning, but I will say that if you go over the material at a comfortable pace and are willing to look back a chapter or two or three to remind yourself of some key detail, you will be very well rewarded with a view into special relativity, electrodynamics, and classical field theory.
Now back to Quantum.
I cannot wait for General Relativity to come out. Chapter 11 seemed like almost like a cliffhanger to change gears into gravitational field theory.
In your reference frame, take the time to read this book. As for general relativity, when it comes out, You Bet Your Life I will read that one.
This is the three book in the series I have read. The first book set up a lot of the mathematical machinery used here, namely the Lagrangian and the Hamiltonian along with conservation laws and symmetries.
I struggled a bit with the second book on quantum mechanics - have to go back and have another crack at that one.
But this one was REALLY good. The setup of the book was so logical and the mathematical development was so well paced that I could feel much greater mathematical sophistication that helped me to anticipate many of the subsequent developments. Now, I will not say that I could erase all the equations and mathematical reasoning segments from the book, and as an exercise, recreate them from memory, calculation, and my own reasoning, but I will say that if you go over the material at a comfortable pace and are willing to look back a chapter or two or three to remind yourself of some key detail, you will be very well rewarded with a view into special relativity, electrodynamics, and classical field theory.
Now back to Quantum.
I cannot wait for General Relativity to come out. Chapter 11 seemed like almost like a cliffhanger to change gears into gravitational field theory.
In your reference frame, take the time to read this book. As for general relativity, when it comes out, You Bet Your Life I will read that one.
January 17, 2018
Tough book but good. Derives E&M's, Maxwell's, equations from the field tensor and lagrangians. The Metric tensor (Eta mu nu), the Field tensor (F mu nu), the Energy momentum tensor (T mu nu), yea good times and non-trivial concepts. Loooking forward to the next book on General Relativity. The fact that this book is accompanied by Youtube videos of Susskind's lectures brings to mind the quote: "I find television very educating. Every time somebody turns on the set, I go into the other room and read a book."
October 7, 2018
Perhaps the most challenging book of the theoretical minimum series so far. The exposition of special relativity is the most lucide I've read so far tho. But I had to drudge through the classical field theory. Though I understand it piece by piece, it's a bit difficult to pull all the pieces together, especially because I can't remember the load of information that it's offering. Well, can't say it's the book's fault since I'm the one who's cramming.
November 11, 2018
This is one of the best physics books I have read these recent years.
I have studied these subjects at grad school but the way in which the different subjects were introduced here is much better.
Also, it was very easy to follow despite the many years without practicing and the technical details weren't all over the place (that doesn't mean there aren't any).
I highly recommend it. Waiting for the GR one to come. ;)
I have studied these subjects at grad school but the way in which the different subjects were introduced here is much better.
Also, it was very easy to follow despite the many years without practicing and the technical details weren't all over the place (that doesn't mean there aren't any).
I highly recommend it. Waiting for the GR one to come. ;)
November 25, 2018
Not as good as the second book, but still a very nice book for those who want to learn some physics for fun without giving up on the math. Some sections on classical field theory got a bit boring; it felt like the same repeated derivations based on Euler-Lagrange equations for a bunch of slightly-varied Lagrangians. I think those parts could have used a bit more of an overview with motivation of where it is all going/why we care about deriving all these variants.
April 25, 2018
This is a really great book. This series is a great introduction to modern physics and this book did not let me down. I highly suggest anyone that is going to try to read Jackson they should take the time to read this first. I personally think the section on tensors is one of the best explanations of the subjects I have seen.
January 27, 2019
Great book to dive into the Special Relativity theory from the beginner-mathematician perspective!
But you will need to do all the of exercises to grasp everything.
As for an advanced math student, this book has a lot of words - I wanted sometimes more math and formulas - a more formal way, you know :) But nevertheless - this book was made to popularize science and it is doing it the right way!
But you will need to do all the of exercises to grasp everything.
As for an advanced math student, this book has a lot of words - I wanted sometimes more math and formulas - a more formal way, you know :) But nevertheless - this book was made to popularize science and it is doing it the right way!
January 4, 2022
I try to read one serious science book every year over the Christmas break. Leonard Susskind's Theoretical Minimum books have been a great source of holiday reading for me - hard enough to be challenging but easy enough that I can understand most of them, if I just read slowly and carefully and reread the steps that don't instantly make sense to me. In the earlier Theoretical Minimum books, this got me up to about a 90% comprehension rate. This one was a little harder for me. It clocked in at around 80%.
I was already generally familiar with special relativity, four dimensional spacetime and Lorentz transformations, so that part of the book was mostly review for me. I also had some basic knowledge of classical field theory, but when the book got into applying the least action principle, Lagrangians and Hamiltonians in the context of field theory, the going got tougher. I was still able to understand concepts and the derivations, but without feeling that I had developed an intuitive grasp of the material. Guage Symmetry is still a mystery to me, though I thought that the explanation of it in this book was better than I have gotten elsewhere, so I feel like I am now finally on the road to understanding it. But when the book got into electrodynamics and began using tensors and the operations of vector analysis - divergence, gradient and curl, my head began to spin. These are concepts that are taught at one level of math above what I completed in college, and though I understand what they are, I have no facility in applying them so I found myself constantly referring back to the appendix where these things are explained. As a result, my level of understanding suffered.
Still my overall experience of this book was very positive. If it was easy, it wouldn't be fun. I learned some new things and deepened my understanding of some of the most important theories of physics. I do think that you have to be rigorous and understand the math to have a full appreciation of the beauty of this material. I look forward to my next Theoretical Minimum book.
And just to prove I got to the end - The secret word of the day is "Lagrangian."
I was already generally familiar with special relativity, four dimensional spacetime and Lorentz transformations, so that part of the book was mostly review for me. I also had some basic knowledge of classical field theory, but when the book got into applying the least action principle, Lagrangians and Hamiltonians in the context of field theory, the going got tougher. I was still able to understand concepts and the derivations, but without feeling that I had developed an intuitive grasp of the material. Guage Symmetry is still a mystery to me, though I thought that the explanation of it in this book was better than I have gotten elsewhere, so I feel like I am now finally on the road to understanding it. But when the book got into electrodynamics and began using tensors and the operations of vector analysis - divergence, gradient and curl, my head began to spin. These are concepts that are taught at one level of math above what I completed in college, and though I understand what they are, I have no facility in applying them so I found myself constantly referring back to the appendix where these things are explained. As a result, my level of understanding suffered.
Still my overall experience of this book was very positive. If it was easy, it wouldn't be fun. I learned some new things and deepened my understanding of some of the most important theories of physics. I do think that you have to be rigorous and understand the math to have a full appreciation of the beauty of this material. I look forward to my next Theoretical Minimum book.
And just to prove I got to the end - The secret word of the day is "Lagrangian."
December 11, 2024
Susskind (and Friedman) write this series of books with a mission. Traditional explore each problem acording to some level of difficulty (math foundations -> review basic equations -> easy case -> harder case... so on). They do not: they have a target, and this target gives them a directed narrative.
The target is to show how a unified Lagrangian description can give you, basically, everything. In order to reach that Lagrangian, they introduce special relativity, which finally produces the key ingredients, such as 4-vectors, proper time, kinetic energy and momentum.... (ok, they do indulge in classic relativity topics, otherwise the book would be too lean and too dry).
Then, they construct a proper theory of electromagnetism, both for fields and particles. I something pops up, such as the wave equation, they discuss it. But only if, and when, it appears.
This effort is outstanding. This topic is not easily explained at all! Similarly to their book on quantum mechanics, they have lowered the level of this field to a point that is basically impossible to improve. Only Penrose's The Road to Reality approaches this idea (but, in my opinion, fails).
Other than a few minor details are perhaps improvable. For example, the book seems completely independent from their previous one on quantum mechanics, while e.g. the wave equation clearly shows parallelisms with the Schrödinger equation. There are also some connections that can be established with their first book on classical mechanics. Also, Quantum Mechanics was full of interesting exercises, and here there are few of them. But, these are quite minor points overall, for a book that is now sitting on top of my list of favorite "accessible" physics books, up there with Feynman
The target is to show how a unified Lagrangian description can give you, basically, everything. In order to reach that Lagrangian, they introduce special relativity, which finally produces the key ingredients, such as 4-vectors, proper time, kinetic energy and momentum.... (ok, they do indulge in classic relativity topics, otherwise the book would be too lean and too dry).
Then, they construct a proper theory of electromagnetism, both for fields and particles. I something pops up, such as the wave equation, they discuss it. But only if, and when, it appears.
This effort is outstanding. This topic is not easily explained at all! Similarly to their book on quantum mechanics, they have lowered the level of this field to a point that is basically impossible to improve. Only Penrose's The Road to Reality approaches this idea (but, in my opinion, fails).
Other than a few minor details are perhaps improvable. For example, the book seems completely independent from their previous one on quantum mechanics, while e.g. the wave equation clearly shows parallelisms with the Schrödinger equation. There are also some connections that can be established with their first book on classical mechanics. Also, Quantum Mechanics was full of interesting exercises, and here there are few of them. But, these are quite minor points overall, for a book that is now sitting on top of my list of favorite "accessible" physics books, up there with Feynman
March 28, 2024
I did it! I actually finished this one!
With the previous book, I made a mistake - I started Quantum Mechanics between the jobs. When I got back to work, I put the book away for a while and then couldn't pick it up. The math part was too hard to follow after a break. So this time I kept reading a few pages almost every day, so I could remember the logic and math notations and it really helped.
The beginning was truly fascinating. You simply start moving a reference frame and everything drastically changes. The book gets to E=mc[2] very quickly and really shows how Newton's physics is just a special case of Einstein's one and then... things get complicated (and kind of boring). There is a lot of math - there are the same equations that get derived in different ways from each other and since I was lazy and wasn't doing any math exercises in the book, they all started to look kind of the same. 3-vector, 4-vector, tensor, change from relativistic values to normal and then let's do it all over again. The part about Maxwell's equations was all like that.
There were some really cool things in that part - how Maxwell almost accidentally discovered that the product of two small mysterious constants is actually 1/c[2], for example. And the interplay between fields and particles was really nicely explained ("charges tell fields how to vary"). But honestly, I'd like something in-between this one and what Hawkins used to write. A bit less math and a bit more concepts.
But I am still planning to read the next book in the series, about General Relativity. Understanding gravity from this point of view sounds too exciting.
With the previous book, I made a mistake - I started Quantum Mechanics between the jobs. When I got back to work, I put the book away for a while and then couldn't pick it up. The math part was too hard to follow after a break. So this time I kept reading a few pages almost every day, so I could remember the logic and math notations and it really helped.
The beginning was truly fascinating. You simply start moving a reference frame and everything drastically changes. The book gets to E=mc[2] very quickly and really shows how Newton's physics is just a special case of Einstein's one and then... things get complicated (and kind of boring). There is a lot of math - there are the same equations that get derived in different ways from each other and since I was lazy and wasn't doing any math exercises in the book, they all started to look kind of the same. 3-vector, 4-vector, tensor, change from relativistic values to normal and then let's do it all over again. The part about Maxwell's equations was all like that.
There were some really cool things in that part - how Maxwell almost accidentally discovered that the product of two small mysterious constants is actually 1/c[2], for example. And the interplay between fields and particles was really nicely explained ("charges tell fields how to vary"). But honestly, I'd like something in-between this one and what Hawkins used to write. A bit less math and a bit more concepts.
But I am still planning to read the next book in the series, about General Relativity. Understanding gravity from this point of view sounds too exciting.
May 31, 2021
An excellent review of 19th and 20th century classical field theory. The book is written for a reader with a technical background who's not afraid of a bit of calculus, but it is mathematically self-contained. I have a rusty recollection of undergraduate physics, and this book made for enjoyable light reading.
A note: this book is the 3rd in Susskind's series on "The Theoretical Minimum" needed to understand physics, but you could start here if you're comfortable with integrals and vector calculus. Otherwise, you could start with the first book in the series, which covers math used in physics. The second book, about quantum mechanics, is not necessary to get the most out of this book.
In this book, Susskind guides the reader through the technical details of special relativity and the theory of electromagnetism, inserting personal insights and giving a clear picture of his idea of beauty in physics. He makes a compelling case for the elegance of Maxwell's equations and the principles of Lorentz invariance and gauge invariance.
Along the way, Susskind notes connections to general relativity and quantum field theory. His New York sense of humor makes for light-hearted reading. I would recommend this book to anyone who, like me, has textbook-phobia but still wants to learn more about theoretical physics.
5/5
A note: this book is the 3rd in Susskind's series on "The Theoretical Minimum" needed to understand physics, but you could start here if you're comfortable with integrals and vector calculus. Otherwise, you could start with the first book in the series, which covers math used in physics. The second book, about quantum mechanics, is not necessary to get the most out of this book.
In this book, Susskind guides the reader through the technical details of special relativity and the theory of electromagnetism, inserting personal insights and giving a clear picture of his idea of beauty in physics. He makes a compelling case for the elegance of Maxwell's equations and the principles of Lorentz invariance and gauge invariance.
Along the way, Susskind notes connections to general relativity and quantum field theory. His New York sense of humor makes for light-hearted reading. I would recommend this book to anyone who, like me, has textbook-phobia but still wants to learn more about theoretical physics.
5/5
July 22, 2022
This is the third book in Leonard Susskind's excellent series "The Theoretical Minimum". Like the previous books in the series, this volume too is probably not suited for readers who know nothing about the topics it covers - which are special relativity, electromagnetism and more generally, classical field theory. Instead, it's the perfect book for a reader who already has at least a vague understanding of what these things are - and want to learn them in a rigorous way, and understand them much better, and also think about them like real physicists think.
And the book really delivers on the "understand them much better" promise. Its structure is amazing, in way I haven't seen before. It isn't organized historically - with electric fields first, then electromagnetism and finally special relativity. No, it goes the other way around: It begins with special relativity, then using the Lagrangian "stationary action" principle (from book 1) it derives the relativistic motion equations, and then it introduces the concept of "a field" and how a field effects a particle and vice versa - and how this effect must be due to the action principle. The first example is of a scalar field (which was an eye-opening approximate parallel to how the Higgs scalar field gives mass to particles), but then it moves on to vector fields. It then develops the equations for the electromagnetic field - including the famous Maxwell's equation - without making almost any assumptions. It turns out that the electromagnetic field isn't just an arbitrary field - it is in fact the simplest field which is Lorentz-invariant (as required by relativity) and gauge-invariant. Along the way we learn what gauge invariance is, and also valuable mathematical tools that are needed to understand what physicists write, such as tensors, covariant and contravariant indexes, and a lot of notation that physicists developed to shorten the equations they write.
If you want to understand physics the way physicists do, but don't have the time or energy to read a textbook, this series is highly recommended. Even Graucho recommends it (if you don't know why I wrote that, read the entire book).
And the book really delivers on the "understand them much better" promise. Its structure is amazing, in way I haven't seen before. It isn't organized historically - with electric fields first, then electromagnetism and finally special relativity. No, it goes the other way around: It begins with special relativity, then using the Lagrangian "stationary action" principle (from book 1) it derives the relativistic motion equations, and then it introduces the concept of "a field" and how a field effects a particle and vice versa - and how this effect must be due to the action principle. The first example is of a scalar field (which was an eye-opening approximate parallel to how the Higgs scalar field gives mass to particles), but then it moves on to vector fields. It then develops the equations for the electromagnetic field - including the famous Maxwell's equation - without making almost any assumptions. It turns out that the electromagnetic field isn't just an arbitrary field - it is in fact the simplest field which is Lorentz-invariant (as required by relativity) and gauge-invariant. Along the way we learn what gauge invariance is, and also valuable mathematical tools that are needed to understand what physicists write, such as tensors, covariant and contravariant indexes, and a lot of notation that physicists developed to shorten the equations they write.
If you want to understand physics the way physicists do, but don't have the time or energy to read a textbook, this series is highly recommended. Even Graucho recommends it (if you don't know why I wrote that, read the entire book).
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