- Paperback: 384 pages
- Publisher: Penguin Press; 1 edition (27 May 2015)
- Language: English
- ISBN-10: 9780141977812
- ISBN-13: 978-0141977812
- ASIN: 0141977817
- Product Dimensions: 12.9 x 2.2 x 19.8 cm
- Boxed-product Weight: 281 g
- Average Customer Review: 1 customer review
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Quantum Mechanics: The Theoretical Minimum Paperback – 27 May 2015
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About the Author
Leonard Susskind (Author)
Leonard Susskind has been the Felix Bloch Professor in Theoretical Physics at Stanford University since 1978, and his online lectures are viewed all around the world. One of the fathers of string theory, he is the author of The Black Hole War and The Cosmic Landscape.
Art Friedman (Author)
Art Friedman is a life-long student of physics, and his career encompasses software engineering, teaching, and writing. When he's not busy puzzling over quantum entanglement, Art plays the fiddle.
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A little background about me: As an undergraduate, I took Modern Physics and received an A; I also took Quantum Mechanics at the graduate level and received an A. Then, in my Ph.D. program, I took Nuclear Physics and received an A. That was several years ago, so I decided to dive back into the topic to refresh my understanding. So while I'm no expert, there certainly was a time in the not-too-distant past in which many university professors would say that I had at least some basic understanding of QM. That said...
I seriously struggled through this book. I read it very slowly to the end, did the problems, re-read it, and still failed to learn anything new from it. In contrast, I also used several other resources to learn QM (including a free online MIT course on QM, lectures and a book by Feynman, and even a few "philosophy" books on QM by Tim Maudlin and Peter Lewis) and found them incredibly helpful.
As it turns out, there are several things in Susskind's book that I did understand, but they were things that I learned from other sources. In other words, I learned literally nothing new from his book.
The book contains very few (if any) fundamental explanations of anything -- the book is mostly equations riddled with text written in a language that you'd only understand if you were already intimately familiar with QM. For example, he never explains why complex numbers are required in QM (although he promises to on p. 21!). Turns out it's a pretty important reason, not to mention very interesting, relating to how probabilities combine. He never explains why it matters that an operator acting on an eigenvector simply multiplies the vector by a number (eigenvalue). He never explains what a Hermitian operator fundamentally is, or why this all takes place in Hilbert space (or what that is). He never explains the relationship between discrete QM (which utilizes matrices) and continuous QM (which utilizes integrals), or why that would matter (representing spin versus position, for example).
He never -- and this is KEY -- NEVER explains where the heck QM came from. QM came, in part, from the realization that the probability distributions we would expect from a particular experiment did not fit classical predictions. The normal means of combining probabilities by AND and OR rules didn't work in certain cases: for example, by adding a second possible path for a particle to pass, it became possible to REDUCE the number of particles that landed in certain places (an effect called "interference"). However, if instead possible events were designated by characteristic numbers (we call them "complex amplitudes"), such that individually their probabilities were just the square of the amplitude's magnitude, then we CAN make the right experimental predictions if we combine the amplitudes according to the rules of probability. Anyway, this is a long way of saying that QM was a huge GUESS, and it has turned out, after uncountably many experiments, to be confirmed. But Susskind never discusses this. Same for the Uncertainty Principle. He "derives" the uncertainty equation without ever mentioning that Heisenberg's formulation was based on a thought experiment regarding measurement, and that the Uncertainty Principle wasn't empirically confirmed until decades after it was assumed to be true. The mathematical "proof" that Susskind puts forth depends on the assumption that a particle has a wavelength and that the Fourier transform of a particle's position yields its momentum. But that's circular, since if you've already assumed that the particle's position function contains information about its momentum, then obviously the more information you have about one, the less you have about the other. That doesn't mean the proof or assumptions are wrong, but without knowing them, the curious and skeptical reader will simply be frustrated by Susskind's failure to offer any kind of context.
If you are a neophyte, this book is not for you. If you are educated and have already taken several courses in QM and want a refresher, this book is not for you. I'm not sure who it's for -- someone who's already an expert?
I can't recommend this book with any less enthusiasm.
“A young man was sent by his own village to a neighboring town to hear a great Rabbi. He was to bring back a report in which all could share. When he returned he told his eagerly awaiting fellow citizens: “The Rabbi spoke three times. The first was brilliant; clear and simple. I understood every word. The second was even better, deep and subtle. I didn’t understand much, but the Rabbi understood it all. The third was by far the finest; a great and unforgettable experience. I understood nothing and the Rabbi himself didn’t understand much either.”
Professor Susskind (1) of Stanford University is far ahead of Bohr’s Rabbi – he understands it all. To Susskind “Everything is easy in Quantum mechanics” (2). So easy that he always “destroys his lecture notes to prevent his lectures being the same next time” (3).
“Given enough time, with no distractions, you could use [his book (4)] to eventually master Quantum Mechanics” (5). An attractive challenge as the book is only 350 pages.
Only 350 pages perhaps, but it assumes you are versed in Classical Mechanics (which you aren’t). Realistically, you need Susskind’s first book (6) plus a preliminary YouTube series of 9 x 1.5 hour lectures on Quantum Entanglement (7). Plus you will need assistance from 10 x 1.5 hour YouTube lectures (8) in parallel with the book. Still a realistic challenge given the results (9).
According to Susskind, Quantum Mechanics is much more fundamental that classical physics. “As far as we know quantum mechanics provides an exact description of every physical system” (10). Moreover, “the logic of classical mechanics of Newton is incorrect, the underlying structure is inadequate” (11). Not only should we logically learn quantum mechanics first, it is technically much easier than classical mechanics (12).
Susskind lives in a Quantum Mechanical world, the real world, deploring our choice of units that makes Avogadro’s Number (13) and the speed of light (14) ridiculously large and Planck’s Constant (15) ridiculously small. He blames historical chemists who measured things by comparison to the size of their hands. Choosing units appropriate to the sub-atomic scale, such as making Planck’s constant = 1, would make his world feel normal.
For those who enjoyed science and mathematics to a reasonable level (16) but who had to follow a career to survive in the world, this is more an opportunity than a challenge. Not that it is not a challenge! It is a mind tingling challenge. A way of familiarizing with the real subject with the actual equations - not a popularization.
The fascinating history of Archimedes, Johannes Kepler and Isaac Newton fitting an ellipse to the Mars orbit and concluding with the Law of Gravity is only the half of it. Understand how the mathematics of vectors and matrices are fitted to the real world being Quantum Mechanics. Like Archimedes the French mathematicians Joseph-Louis Lagrange, Siméon Poisson, and the Irish mathematician William Rowan Hamilton were nice enough to magically or inadvertently provide the mathematics a long time prior to make it possible. Why this mathematical physics works no one knows, neither Susskind nor the Rabbi.
One moment you feel like like Niels Bohr’s student in his third lecture then you are stunned when Professor Susskind commences a short summing-up by saying, in a matter-of-fact way, that an equation derived in the lecture is called Schrödinger’s equation (17)! Or that the postulates he has been talking about are Dirac’s postulates of Quantum Mechanics formulated in the 1930’s which have never needed to be replaced (18). Or, early on, describes a vector and says that it is Dirac’s notation (19).
Finally, Susskind is to be applauded. If this can be done with Quantum Mechanics, it can be done in any subject of Physics or Mathematics or any other area of study. There must be a value in doing this (other than ex-auto workers retraining themselves for jobs at CERN) as the work will inevitably not continue to be publically funded unless tax-payers have some idea what it is.
PS: The advantage of a career outside Physics is to know “you always write the minutes before the meeting”. Bohr’s student may finally have understood so little that he was not game to return to his village. As a precaution I have written this travelogue well before completing the trip.
(1) Leonard Susskind is the Professor of Theoretical Physics at Stanford University, and director of the Stanford Institute for Theoretical Physics. His Wikipedia entry is a good read in itself.
(2) Lecture 9, Quantum Entanglements
(3) Lecture 9, Quantum Entanglements
(4) Quantum Mechanics – The Theoretical Minimum by Leonard Susskind & Art Friedman. The “minimum” means just what you need to know to proceed to the next level.
(5) Science News: quote from back cover of Susskind’s book.
(6) The Theoretical Minimum – What you Need to Know to start doing Physics Leonard Susskind and George Hrabovsky.
(7) Quantum Entanglements, Susskind, Stanford University, YouTube. It seems that the old unadorned lecture format has stood the test of time with only the whiteboard and marker (when it works) replacing the blackboard and chalk.
(8) Modern Physics, Quantum Mechanics, Susskind, Stanford University, YouTube.
(9) Well, you did not expect to read 350 pages straight cover to cover and then know Quantum Mechanics, did you? This is a 6 to12 month project – reading, watching YouTube lectures, frantic note taking hoping you might understand it later (the iPad pause button being a luxury unavailable in university lectures), revision, pushing forward, retreating, then finally with your newfound knowledge applying for a job at CERN.
(10) Page xix.
(11) Lecture 1, Quantum Mechanics
(12) Page xx.
(13) Avogadro's number, number of units in one mole of any substance (being its molecular weight in grams) ≈ 6×1023.
(14) Speed of Light: c ≈ 3×108 m/s.
(15) Planck’s Constant: The energy contained in a photon, the smallest possible ‘packet’ of energy in an electromagnetic wave ≈ 6.6x10-34 joule-seconds.
(16) Realistically, for those who think they know classical Newtonian Physics and remember studying vectors and matrices, exponentials such as eiθ = cosθ + isinθ and who once knew the expansion of sin(θ + Φ).
(17) Lecture 9, Quantum Entanglements
(18) Lecture 4, Quantum Mechanics
(19) Page 11, Quantum Mechanics – The Theoretical Minimum
8 May 2016
* Not loosing the reader in the math
* Not dropping so much math, that it all becomes abstract bullsh*t
Great introduction, or review if you've had quantum.
Also, if you are learning quantum for the first time, it's highly recommended, since it emphasizes the CONCEPTS and CONSEQUENCES, rather than getting you lost in lengthly (and not terribly useful) derivations.