After the 'Theoretical minimum' series, what is essential to know about QM?

[entropy1]

@entropy1 - Actually you can find find intuitive models of entanglement that you can visualize in your mind like you visualize a rock falling to the ground, just don't take them too seriously and don't push them too far. For example:

Two entangled particle are really "one thing," not two things. So picture 3D space as a 2D plane. Picture a circle in an orthogonal plane, with the center in the first plane. The two entangled particles are the intersections of the circle (one thing) and the plane. Now color half of the circle white and the other half black. Rotate the circle in its plane around its center (as a model of "what really happens"). The two intersections (particles) will always be correlated, if one is white the other is black.

Yes, however, doesn't that impose non-locality as a fact?

 

[Demystifier]

Yes, however, doesn't that impose non-locality as a fact?

So?

 

[Giulio Prisco]

Yes, however, doesn't that impose non-locality as a fact?

Yes it does.

 

[entropy1]

Yes it does.

Well, then it's easy.

 

[ogg]

A couple of random points.
In his video lectures, Susskind 'explains' entanglement by asking students something along the following (sorry, its been a few years): If I have two coins: a penny and a dime and place one in my pocket and the other in a friend's. If she then travels 10 light-years from me and at an agreed upon time looks into her pocket, how long will it take her to determine what coin is in my pocket? (Assuming no change of clothes, etc.) If your answer is anything LESS than 10 years, then you seemingly have a violation of locality, since any signal I send (at agreed upon time) will take >= 10 yrs to reach her.
Second point: QFT and more specifically the Standard Model (of Particle Physics) is not the same as QM, but QM is used as an umbrella term describing both QM and QFT. It is QFT which is the more "fundamental" basis for our understanding of the physical world.
Third: While QM/QFT involves relatively "simple" math, Yang-Mills Theory (QFT) has yet to be proved to be mathematically consistent (see Wikipedia entries, especially Constructive quantum field theory; as well as Millennium Prize Problems; Yang-Mills Theory; QFT; etc.)
Fourth: Relativistic QFT involves (surprize, surprize!) relativistic physics. General Relativity is NOT simple math. (although the need to go much beyond the much simpler Special Relativity is moot).
Fifth: As a starting "rule of thumb" you need to practice something for ~10,000 hours to become "skilled". This is the type of time commitment you should plan on IF your goal is to "understand" QFT or QM. People like me who have NOT put in the sweat and time might be able to follow along in the solution of a non-trivial problem, but can't claim that given a random physical system (real world) that we could correctly predict the outcome of a specified experiment a priori. I am satisfied with understanding QM in very broad strokes and in only the smallest most simplified systems. Your mileage may vary.

 

[Demystifier]

Well, then it's easy.

All conceptual puzzles in physics are easy when you think of them in the right way.

 

[RockyMarciano]

There is no dependence of one theory on the other, neither regarding the math nor regarding measurement issues.

(Sorry for the late reply, I couldn't answer earlier.)
The dependence I referred above is just paraphrasing the words of the great physicist Lev Landau in the first pages(2-3) of his Quantum mechanics(nonrelativistic) volume in theoretical physics. He wrote:"...we first examine the special nature of the interrelation between quantum mechanics and classical mechanics. A more general theory can usually be formulated in a logically complete manner, independently of a less general theory which forms a limiting case of it.[...] It is in principle impossible, however, to formulate the basic concepts of quantum mechanics without using classical mechanics [...] Hence it is clear that, for a system composed only of quantum objects, it would be entirely impossible to construct any logically independent mechanics.[...] Thus quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case, yet at the same time it requires this limiting case for its own formulation."

 

[A. Neumaier]

It is in principle impossible, however, to formulate the basic concepts of quantum mechanics without using classical mechanics

This was considered true when Landau wrote his book, but it is no longer true since we know better how macroscopic (i.e., classical) properties derive from microscopic (i.e., quantum) ones.

 

[entropy1]

I was wondering if Ballentine would be a nice follow up for Susskind's TM?

 

[Truecrimson]

How well can you handle Griffiths right now? (Not that one has to get past Griffiths first but Ballentine will be harder than that.)

 

[entropy1]

How well can you handle Griffiths right now? (Not that one has to get past Griffiths first but Ballentine will be harder than that.)

I haven't started on Griffiths yet. What would you recommend to me at this point: Ballentine or Griffiths?

 

[Truecrimson]

Since you said that Griffiths was too advanced for you a month ago, I suspect that you will have to slog pretty hard to get through Ballentine.

I don't like Griffiths that much because it's weak on postulates and anything that involves matrices. For examples, I think Griffiths never talks about unitary operators in quantum mechanics or the Lüders rule for degenerate eigenvalues. (He definitely doesn't talk about density operators.) And his treatment of spins is just bad.

But if it's the right level for you, then by all means go for it! You will learn almost everything an undergrad needs to know about quantum mechanics.

 

[entropy1]

Since you said that Griffiths was too advanced for you a month ago, I suspect that you will have to slog pretty hard to get through Ballentine.

I spent my QM time reading Susskind's TM!

So is Ballentine the better choice?

 

[Truecrimson]

So is Ballentine the better choice?

Yes, if you can read it.

Roughly speaking, Susskind is for motivated laypeople. Griffiths is for undergrads. Ballentine is for grad students.

 

[atyy]

Ballentine is for grad students.

I would say Ballentine is for grad students because one must be advanced enough not to be misled by Ballentine's severe errors.

 

[entropy1]

What is the best plan for my background?

 

[entropy1]

Is there any book that (more or less) covers the "Advanced QM" course of the TM by Susskind? I prefer a book over video's...

 

[Truecrimson]

Is there any book that (more or less) covers the "Advanced QM" course of the TM by Susskind?

You mean this course?
http://theoreticalminimum.com/courses/advanced-quantum-mechanics/2013/fall
Any good QM textbooks will cover the QM part. To tackle QFT textbooks requires at least undergrad QM and some more maths.

Depending on your taste, any of these books could be fine as a first introduction to QM beyond Susskind:
Townsend
https://www.amazon.com/dp/1891389785/?tag=pfamazon01-20
Schumacher and Westmoreland
https://www.amazon.com/dp/052187534X/?tag=pfamazon01-20
Zettili
https://www.amazon.com/dp/0470026790/?tag=pfamazon01-20
Shankar
https://www.amazon.com/dp/0306447908/?tag=pfamazon01-20
Sakurai
https://www.amazon.com/dp/0805382917/?tag=pfamazon01-20

They are all more advanced (and more complete) than Griffiths and I believe easier than Ballentine. There are, of course, many more books in the market, but these are the ones that I'm most familiar with. I highly recommend Schumacher and Westmoreland for concepts and Zettili for tons of solved problems.

 

[entropy1]

You mean this course?
http://theoreticalminimum.com/courses/advanced-quantum-mechanics/2013/fall

Yes.

Any good QM textbooks will cover the QM part. To tackle QFT textbooks requires at least undergrad QM and some more maths.

Perhaps I should stress I only read the beginners course of Susskind. The 'Advanced' course on the internet I didn't follow. So I need a book on the latter level.

 

[Truecrimson]

Perhaps I should stress I only read the beginners course of Susskind. The 'Advanced' course on the internet I didn't follow. So I need a book on the latter level.

Yeah. Most QM textbooks including the ones I listed will cover both Susskind's "QM" and the first half of his "advanced QM" course. I haven't learned QFT properly so I don't want to recommend something that I don't read. You can search bhobba's posts and others in this forum for QFT books for beginners.

Note that any actual textbook will be more in-depth than Susskind. It'll be hard to find a book that cover just as much coverage and as little details as Susskind. (I didn't know one for QM before Susskind himself wrote it.) So ultimately how far you should go will depend on what you want out of this.

 

[MichPod]

You might need to find some introductory level QM book. Definitely more broad and deep than "Theoretical Minimum" of Susskind, but still more adapted for a beginner than most of undergraduate level books.

Learning QM may bring some or even much disappointment - this is a big and hard subject. You'll definitely know (much of) something before you finish one good undergraduate level book, but this "something" may or may be not exactly what you wanted to know, it may or may not answer your possible questions about what QM is and why QM is really this way, and what the world really is and your knowledge will probably not have any application in your life. I have also heard of people who realized they learned just nothing after finishing a QM course - it may depend on the book you learn and on the course/teacher.

Just as a personal example, with learning basics of QM, I got much fun of gaining ability to read and understand some scientific articles and from just being slightly exposed to how crazily complex the contemporary theories are. People who invented QM are real heroes and that I could not understand without learning QM. Understanding these things is part of knowing the culture and the top achievements of humanity. I had also some original interest in QM foundations, which brought me to QM learning, and even though this interest was not much satisfied until now, learning basics of QM gave me some hope I may one day go deeper into this field.

 

[MichPod]

This was considered true when Landau wrote his book, but it is no longer true since we know better how macroscopic (i.e., classical) properties derive from microscopic (i.e., quantum) ones.

Do you mean decoherence theory or anything else/additional specific which changed the situation from Landau's time? Do you have any reference on book/article where QM is introduced/discussed satisfactory without using classical mechanics?

 

[A. Neumaier]

Do you mean decoherence theory or anything else/additional specific which changed the situation from Landau's time? Do you have any reference on book/article where QM is introduced/discussed satisfactory without using classical mechanics?

Decoherence goes part of the way; other statistical mechanics does the remainder. For references see https://www.physicsforums.com/posts/5396296/ and http://physicsoverflow.org/35537.

The only book I know of where quantum mechanics is introduced without classical mechanics is my online book,

• Arnold Neumaier and Dennis Westra,
  Classical and Quantum Mechanics via Lie algebras,
  2008, 2011.

Well, both are introduced side by side to show the close similarities. But nowhere is it assumed that a classical world exists outside of the quantum models.