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

[LarryS]

The adagium of most quantumphysics-afficionado's is: "Shut up and calculate" - 'learn the formalism'. So I started with Leonard Susskind's 'Theoretical minimum' textbooks.

So now I know a little (very little) about the formalism, I started to wonder to which extent I have to go to educate myself in order to understand what I need to know. Is what you learn ever enough? And if not, why start with quantummechanics at all? Is it at all satisfying to study QM? Or is it that you learn more precisely what you don't know?

So my question is: after the 'Theoretical minumum' series, what is essential to know about QM? I have planned "Mathematical Methods in the Physical Sciences" by Mary Boas, follow by "An Introduction to Quantummechanics" by David Griffiths. This is quite a lifelong planning for me it seems to me. So, do I know anything more than I did when I've read all this? Is it worth it to read all this?

Can anyone elaborate on this? Much appreciated.

Susskind has done a TON of physics video courses in conjunction with Stanford University. If you have watched those only listed under theoreticalminimum.com you have probably not watched them all. There maybe additional courses under cosmolearning.com and also just under youtube.com. I have found all these courses extremely helpful in understanding modern physics. Also, IMHO, you will need to watch the series on Classical Field Theory if you want to understand QFT.

 

[entropy1]

I would also like to throw in a piece of advice: If you are new on the subject of QM, it might pay to start re-reading "The Theoretical Minimum: QM" when you've reached chapter 8. If you go back to the beginning, much of what is said there makes even more sense with the knowledge gained from the first read. My two cents.

 

[Giulio Prisco]

Is there a level at which one could say you know 'enough' to 'understand' QM? And if not, does that mean I will never understand it?

No and no. The fact that scientists are still arguing over interpretations of QM means that there are still gaps in our understanding of QM. In this sense, nobody knows enough to understand QM. But you can leave interpretations aside and come to "understand" QM well enough to use it for practical specific applications (they say "shut up and calculate"). Also, there is always the possibility of new theoretical developments in quantum interpretations (never say never).

 

[A. Neumaier]

One more question: what do we actually learn from studying QM except for the formalism? Does the formalism give any more insight in nature, and if so, which?

It gives a nearly endless number of insights when studied in enough breadth and depth.
It shows that all our concepts are uncertain when applied to Nature. It explains the meaning of chemical reactions and why some chemical elements bond much more than others. It explains the periodic system of elements. It allows to predict the possible results of chemical experiments and allows one to design new chemical substances. It explains the color of metals, gold, and other substances. It explains why the sun is burning for millions of years without changing much. It explains why a chair is hard enough to sit on although it consists of a myriad of pointlike particles that together make up less than 1% of the space occupied. It explains why water freezes at zero degree Celsius and boils at 100 degrees. It explains things like superconductivity or superfluidity. It allows you to understand why transistors work and how to design their properties. It predicts the results of high energy collision experiments that make headlines in newspapers. It allows to take part (a bit) in the thoughts of numerous Nobel prize winners in physics and chemistry. It allows you to read the Scientific American with a deeper understanding.

Does the 'grasp' one gets on the math give any satisfaction, and if so, why?

For many it does. For many others it is boring like math was for all their life. Why? Because it is interesting for the first group, and the interests of the second group lie elsewhere. You need to find out for yourself to which group you belong.

 

[entropy1]

For many it does. For many others it is boring like math was for all their life. Why? because it is interesting for the first group, and the interests of the second group lie elsewhere. You need to find out for yourself to which group you belong.

I have to say I am not a big hero at math; to the contrary: I'm really not good at it, so that is frustrating to me at times when studying QM. But I have to say that what I've studied from The Theoretical Minumum (it's really the basics, I know ) gives me a lot greater understanding of for instance entanglement. I had an idea in my head, and then, "puff!", it suddenly makes a lot of sense! (Or at least I think it does... )

 

[Giulio Prisco]

entropy1 - Think of math (at least of the thin math used by Susskind in the TM books) as very precise words. Math is really formalized common sense. The core concepts of QM can be explained with rather simple math. In comparison, fluid dynamics is a nightmare.

 

[Giulio Prisco]

By the way, the TM course has only two books so far but many excellent video lectures covering most of modern physics, including advanced quantum mechanics.

 

[entropy1]

So I guess I am not going to find out how it is possible that two entangled particles exhibit a (measurement-)correlation except for the fact that the formalism describes how the pure quantumstate of the pair leads to the correlation?

 

[Giulio Prisco]

So I guess I am not going to find out how it is possible that two entangled particles exhibit a (measurement-)correlation except for the fact that the formalism describes how the pure quantumstate of the pair leads to the correlation?

But you just explained it! ;-)

OK, you want to find an intuitive model of entanglement that you can visualize in your mind like you visualize a rock falling to the ground. I'm afraid that no, you aren't going to find it. Evolution has programmed us to throw rocks, not entangled particles.

 

[Giulio Prisco]

@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.

 

[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.