Friday, July 11, 2008

Quantum Mechanics for Beginners












(image as posted in Wikipedia)


This is a response to a query a fellow made on BackReaction which I’ve taken the liberty to address here rather then clog up the space as it is in regards to an unrelated matter to the mentioned post. However, in as my interest in the question supersedes what I perceive as the true motivation for the query I offer the following.

Dany asks:

“Please suggest sequence of three books (time ordered) best suitable for the beginner to grasp QM (independent or tutored learning)”

For basic (non relativistic) QM, disregarding the math prerequisites, I would say perhaps the following:

  • (1) The Feynman Lectures on Physics-Volume III (Feynman-Leighton-Sands)
  • (2) Quantum Mechanics and Experience (David Z. Albert)
  • (3) The Undivided Universe (David Bohm and Basil Hiley)

If on the other hand one only wants the whole thing as just the facts and nothing but the facts, you can simply read Bohm’s initial primer on the whole subject - Quantum Theory. However, since just after writing this book Bohm was prompted to come up with a clearer explanation I view this book more from of a historical perspective rather than an explanative one.

22 comments:

Anonymous said...

Hi Phil,

“Again, I perceive this as some sort of a leading question rather then something that has relevance to this post. However, I must admit I do find your query interesting for I’ve had similar thoughts.”

Bee:” A main topics in today's issue of the Frankfurter Rundschau (one of the major German newspapers) is dedicated to the quality of teaching at universities… Maybe I was particularly unlucky with my lecturers, but the classes I had to take were in the best case useless, in the worst case demotivating, if not debilitating…I do well learning from books, so to me it wasn't a huge problem.”

Phil Warnell:”This is simply a reaction to just another of the frustrating aspects of anonymity for if not the case I would respond to Dany directly.”

If you assume that I understand your comment, that not a case. The topic entitled “Research and Teaching” and mainly devoted to the quality of teaching. Therefore I for example also don’t understand what that has to do with money, grants, travels, conferences, socialization and anonymity. However, IMO it has to do with the excessive noise produced by publication of low quality and obscure books written by writers with no natural teaching skills and no contributions in physics.

You should read my comments and questions always literally. QM is under intensive development more than 100 years and it is general consensus that it is not achieved the consistent formulation yet. To teach such material is particularly very difficult. Therefore, I asked the above question.

Your answer surprise me and therefore interesting. You suggest starting with Feynman Lectures. I consider that the suicide attempt. Notice, that there is no relation between your answer and the photo of participants of the 5-th Solvay. Some of them wrote books on QM but you ignore that. Why?

Regards, Dany.

P.S. I appreciate that you always find my query interesting, albeit always irrelevant.

Anonymous said...

P.P.S. I guess that you didn’t mean that the above photo present the beginners in QM albeit it is the empirical fact.

Regards, Dany.

Arjen Dijksman said...

The Feynman lectures III is indeed one of the best books for a beginner to grasp QM. Or perhaps it's the least worst. Trying to grasp QM *is* suicide attempt with any textbook;-) I would recommend a beginner, before starting with the Feynman lectures, to read (or look at) the QED lectures (QED, the Strange Theory of Light and Matter, also by Feynman). Bohm's Undivided Universe is also fine. Some of Bell's Speakable and Unspeakable texts are also an option.

Phil Warnell said...

Hi Dany,

“they call the certain community of “researchers” – “край непуганных идиотов”.

“However, in our case I would say: запуганных.”

Well Dany I wouldn’t call Bee a resident of your ‘land of fearless idiots’ yet most of us that drop by from time to time could be counted as such. As for being ‘fearful’ instead Bee has never had me feel that way even though she is the professional and I only the interested novice. I however cannot speak for your credentials or experience yet you do come off as being connected with it all somehow. I think however it only fitting then that when I comment I stick to the topic discussed. This research and teaching topic had to do with whom, when and how people should become researchers or teachers or when both are more appropriate. It had nothing to do with the nuts and bolts of either in practice.

As for the QM books and all I agree that even though it has been more then eighty year since its establishment it’s difficult to come up with good teaching material such like can be found for so called classical aspects of physics. As for not recommending text book written by the founders, I would say that between the confusion in the early years and the fact that all were brilliant researcher not many were good teachers and their books reflect that. Therefore I would only recommend them for the advanced student.

As for the books I selected I have a reason and that when you start with Feynman he describes the basic issues pretty well, beginning with the two slit experiment and works through to a method of calculating results (outcomes) using his path integral or sum over histories approach. From the pragmatic shut up and calculate side it does well for what’s at first required with Feynman himself admitting he doesn’t understand it or why it is this way and proclaims no one does.

This then sets the student up for the second book by David Albert who really points out and goes deep into the quantum logic and formalism and how it’s normally dealt with. Then he proceeds to show some of the weakness with the measurement problem, superposition and non local question in a clear and concise manner pointing out the strengths and weakness of competing interpretations. If you haven’t read it I would boast that even you may learn something.

The last book by Bohm serves as the counter example to the claim that you can’t have a quantum theory that is consistent with QM that has hidden variables which Bohm proved otherwise with the only required stipulation being that the theory is intrinsically non local. So in my opinion between these three books the student has a good basis for being able begin to think for themself in regards to the subject.

Best,

Phil

P.S. By the way the title “Quantum Mechanics for Beginners” was meant to have the tie in you suggest as they were the beginners. It should also be noted that still today we await the final word on the subject and such it was only the beginning.

Phil Warnell said...

Hi Arjen ,

Before I say anything I would like have it known that I had a quick look at your site and from what I quickly gathered it looks interesting and as such I will have to return when I have more time to really give it the once over.

I see that you agree with some of my suggestions and if you read my reply to Dany I’ve expanded as to what my reasons are. Also, as for reading Bell that would have been my fourth choice had Dany’s stipulation allowed for that many. None the less this is a must read even the paper on how to teach SR as it also relates firmly with the issues at hand as they form to be today.

I’d also be interested to know which way the wind blows for you as far as Quantum Theory is concerned. As for me if you have read any of my other blatherings in this blog you will discover I’m principally a Bohmian and not the Goldstein or Durr type, yet rather the Bohm and Hiley variety where one takes Bohm’s quantum potential seriously.

Best,

Phil

Phil Warnell said...

Hi agian Arjen ,

Oh yes, I forgot to ask why one would introduce QED to a novice since it being a relativistic extension of QM with Dirac being its founder with his famous antimatter prediction? In the serious sense this is where all the games and slight of hand begins with renormalization and such which in truth still plagues the route to what are the so called subquantum theories. For me that’s the last place I’d start a beginner.

Best,

Phil

Anonymous said...

Hi Phil,

“Well Dany I wouldn’t call Bee a resident of your ‘land of fearless idiots’ yet most of us that drop by from time to time could be counted as such.”

I wonder sometimes from the twists of your logic:
1) Bee/Stefan is managers/owners of their blog; it is only natural let to others to express their opinions. Follow the same logic I also resident of the same land since I didn’t present my list yet.
2) Bee pushes certain, well defined agenda. I have no reason not to respect that, insult her or something like that. Moreover, in spite that Bee let others to present the opinions which contradict her views and contradict her agenda. I think that it deserves appreciation and I expressed that clearly in different occasions.
3) My question was addressed only to those involved in the teaching and active research.

“By the way the title “Quantum Mechanics for Beginners” was meant to have the tie in you suggest as they were the beginners. It should also be noted that still today we await the final word on the subject and such it was only the beginning.”

I am also wondering I am forced to teach you read and write English: I didn’t suggest that and the above photo presents the FOUNDERS of QM far remote from being beginners; almost every one of them knew and understood QM better than the modern “experts” – travelers and chatterers – altogether. Also the majority of today researchers don’t await the “final word”, they try to find it.

“If you haven’t read it I would boast that even you may learn something.”

There is no computer on my desk. Instead, usually there are about 20books opened which surround my working place. I learn and relearn something each day. I didn’t read either D.Albert or D.Bohm books. I was not convinced that I should do that.

Hi Arjen,

“Trying to grasp QM *is* suicide attempt with any textbook”.

I certainly don’t agree with that. In that case it is better not to begin.

Regards, Dany.

Phil Warnell said...

Hi Dany,

“am also wondering I am forced to teach you read and write English: I didn’t suggest that and the above photo presents the FOUNDERS of QM far remote from being beginners;”

Well Dany you wonder why you have problems on Bee’s and Stefan’s blog and in your response to me lay the answer. That is you come across as both arrogant and antagonistic at almost every turn. I’m not convinced any of what you say is in the spirit of learning, sharing opinion or knowledge, yet rather to serve as an ego boost that you seem to require for reasons unknown. I suggest if you are simply looking for a good fight to visit your local Таверна and call the first person you meet a идиот.

“I didn’t read either D.Albert or D.Bohm books. I was not convinced that I should do that.”

It has become evident even with the little experience I have in regards to your thinking that this response turns out to be also not much of a surprise. I would ask first how would one form an opinion other then only after reading them. If it relates to what others have said in terms of recommendation or assessment you have never presented yourself as one that places much stock in anyone’s opinion. I also notice you didn’t leave your three choices for selected texts, is that because you feel you shouldn’t waste your time or is it resultant of you not having written them yet? :-)

Regards,

Phil

Arjen Dijksman said...

Hello Phil,

Concerning Quantum Theory I describe myself as an idea gatherer, trying to mix the best of all ideas. Physics is not my profession but I have active interest in the foundation of QT.

I like the pilote-wave view on QM because it allows to develop realistic insights on the most elementary (=simple) phenomena of nature. Both particle and wave picture make sense in that view. I very much like Feynman and his way to give ordinary insight in some abstract concepts of QM.

I find that the manner how Feynman introduces the physics of photons and electrons in his QED popular lectures is very visual: arrows that rotate as they travel through space. That may easily be used in a de Broglie wave-particle interpretation and helps to give physical meaning to mathematical arduous stuff.

I don't know of D. Albert's book but I sure will take a look.

R2K said...

That is a great picture : )

nige said...

"Oh yes, I forgot to ask why one would introduce QED to a novice since it being a relativistic extension of QM with Dirac being its founder with his famous antimatter prediction? In the serious sense this is where all the games and slight of hand begins with renormalization and such which in truth still plagues the route to what are the so called subquantum theories. For me that’s the last place I’d start a beginner."

- Phil

Hi Phil,

Feynman's own response to this attack on his work is that path integrals are the only known accurate way to do quantum mechanics, since the non-relativistic Heisenberg/Schroedinger methods are physically false (quantizing particle position/momentum instead of quantizing the field which they treat classically!).

Nobel laureate Richard P. Feynman, has debunked the mainstream first-quantization uncertainty principle of quantum mechanics. The indeterminate electron motion in the atom is simply caused by second-quantization: the field quanta randomly interacting and deflecting the electron.

"... Bohr ... said: ‘... one could not talk about the trajectory of an electron in the atom, because it was something not observable.’ ... Bohr thought that I didn’t know the uncertainty principle ... it didn’t make me angry, it just made me realize that ... [ they ] ... didn’t know what I was talking about, and it was hopeless to try to explain it further. I gave up, I simply gave up ...”

- Richard P. Feynman, quoted in Jagdish Mehra’s biography of Feynman, The Beat of a Different Drum, Oxford University Press, 1994, pp. 245-248. (Fortunately, Dyson didn’t give up!)

‘I would like to put the uncertainty principle in its historical place: When the revolutionary ideas of quantum physics were first coming out, people still tried to understand them in terms of old-fashioned ideas ... But at a certain point the old-fashioned ideas would begin to fail, so a warning was developed that said, in effect, “Your old-fashioned ideas are no damn good when ...” If you get rid of all the old-fashioned ideas and instead use the ideas that I’m explaining in these lectures – adding arrows [path amplitudes] for all the ways an event can happen – there is no need for an uncertainty principle!’

- Richard P. Feynman, QED, Penguin Books, London, 1990, pp. 55-56.

‘... when the space through which a photon moves becomes too small ... we discover that light doesn’t have to go in straight [narrow] lines, there are interferences created by the two holes, and so on. The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, such as inside an atom, the space is so small that there is no main path, no “orbit”; there are all sorts of ways the electron could go, each with an amplitude. The phenomenon of interference becomes very important, and we have to sum the arrows to predict where an electron is likely to be.’

- Richard P. Feynman, QED, Penguin Books, London, 1990, Chapter 3, pp. 84-5.

However, the physically false, non-relativistic Heisenberg/Schroedinger approach is easier to apply to bound states like atoms, so it is falsely taught as QM, just as the Bohr atom is falsely taught in high schools.

nige said...

Phil: if you will just permit me to make add another comment to provide more justification for Feynman's second quantization, here is a solid example of the failure of first quantization mathematics:

“The quantum collapse [in the mainstream interpretation of first quantization quantum mechanics, where a wavefunction collapse occurs whenever a measurement of a particle is made] occurs when we model the wave moving according to Schroedinger (time-dependent) and then, suddenly at the time of interaction we require it to be in an eigenstate and hence to also be a solution of Schroedinger (time-independent). The collapse of the wave function is due to a discontinuity in the equations used to model the physics, it is not inherent in the physics.”

– Dr Thomas S. Love, Departments of Mathematics and Physics, California State University.

“In some key Bell experiments, including two of the well-known ones by Alain Aspect, 1981-2, it is only after the subtraction of ‘accidentals’ from the coincidence counts that we get violations of Bell tests. The data adjustment, producing increases of up to 60% in the test statistics, has never been adequately justified. Few published experiments give sufficient information for the reader to make a fair assessment.”

– http://arxiv.org/PS_cache/quant-ph/pdf/9903/9903066v2.pdf

Phil Warnell said...

Hi Nige,

To be honest I’m more than a bit of a Feynman fan myself, as like deBroglie and Bohm he attempted to ground the world of the quanta within the confines of the physically conceivable. His diagrams were part of his attempt to do this.

However, his sum over histories approach still boils down to having QM to be totally indeterminist in the strictest sense, as although it acknowledges the effect of interference of the wave, it gives it no physical embodiment to it beyond it being a symptom of the theory, rather than a agent.

That is to say that the summing he is referring to is given no space in time to occur within the physical world and forms not to be any more of a physical explanation of path then that of Lagrange. For me a true theory will be totally extendable from the physical to the mathematical, rather than the other way around.

Best,

Phil

Arjen Dijksman said...

Hello Phil,

I agree. Truly extendable theories from the physical to the mathematical world may be developed if one models Feynmans particles and de Broglie/Bohm pilot-waves with physical objects that fit experimental results and obey the mathematical quantum rules. I developed this idea in an essay for the current FQXi contest.

Regards,
Arjen

Phil Warnell said...

Hi Arjen,

I developed this idea in an essay for the current FQXi contest.

That sounds intriguing and I would admit also to having similar ideas, but ashamedly lack the mathematical prowess to develop them. I would ask if you could send me a copy of what you submit to the FQX! Contest or point me to it on their Web site after it’s submitted.

Just so you be aware in my toy model which I call the Bow Wave approach the particles have a unigue architecture and serve to create the wave in their wake. It works pretty well for a photon, yet I’ve never extended it much beyond . Also in my model the substance of the wave has the particle to be taken almost as an intruder (for lack of a better term), which in turn has both a compressive result upon this substance centering around the particle(s) and a dispersive one. Not something I would ever detail in a web blog for as I said I can lend it no rigorous mathematical footing and simply a fanciful idea I’ve had for a while.

Best,

Phil

Arjen Dijksman said...

Phil,

I submitted my FQXi essay yesterday so you may find it at http://fqxi.org/community/forum/topic/545.

Your Bow Wave idea sounds interesting. Does the particle have a periodical motion?

Cheers,
Arjen

Phil Warnell said...
This comment has been removed by the author.
Phil Warnell said...

Hi Arjen,

I truly like your essay as it gathers upon similar thoughts and opinions that I’ve held also for a while. I definitely would agree that more can be understood about QM if there is a synthesis formed between the revelations of deBroglie- Bohm and those of Dirac and Feynman. I hope your essay wins or at the very least draws some attention. Also, from what I gather it appears you have returned to university to continue your studies, which I find as to be good news.

As for my own toy model, yes the photon ( particle part) is needle like as you envision and is enveloped in the compressive substance of the wave. As it travels it forms a shock wave in front having the rear of needle spin around and impacting the sides of the envelope in a pivoting motion. With the forward motion limited to C any increase in energy only acts to further stretch the envelope to diminish the width at the sides, which in turn increases the revolution speed (pivoting) of the particle, thereby increasing the frequency of the wave. Anyway if you have a email address I’ll send you a pdf containing a verbal/pictorial brief of the concept. Just don’t laugh to loudly after seeing it:-)

Best,

Phil

Arjen Dijksman said...

That's pretty close to the needle model I develop in my essay. You tried to handle photon acceleration as an increase in internal energy? By the way, my email is materion at gmail.com. I'm looking forward to visualize your model.

With respect to the essay at FQXi, mentioning pilot waves doesn't help to draw some attention. I think I'll have to focus on persuasion. Maybe I should have called them otherwise.

Cheers,
Arjen

Phil Warnell said...

HI Arjen,

Thanks for letting me know where to send along my ramblings:-) Once again I must say I truly like how you are approaching all of this and I wish more would try to gather what stands as being uniquely relevant from all the models, rather than focusing on simply one. I thus have always founnd it somewhat ironic that the more a physicist takes QM seriously, the less seriously what they say is considered by their peers. I’m also intrigued by the recent particle/wave macro experiments you draw note of in your essay, as I’ve always imagined the actions of nature being in many respects the same regardless of scale. Perhaps one day such invariance may in itself be considered as a postulate of physics, as being also a conserved quality.

Best,

Phil

Peeter Joot said...

I can provide my 2c about two of the authors, for self teaching QM.

Feynman's book has a lot of interesting commentary, but I find it hard to learn from due to the lack of problems. I'd be curious if anybody is able to use that to study from as a primary reference without first learning the subject elsewhere.

I've not looked at the Bohm book you mentioned, but his older QT book is excellent. It is old fashioned but very thorough, and as a Dover book the price is right. You can read this book quite readily, with not much more prerequisties than understanding Fourier Transforms. For me, "readily" also included skipping some of the early intro content, where the E&M and thermodynamics content actually makes it some of the hardest parts of the book (for me at least).

A book that I'd suggest avoiding for a beginner is Liboff's. Absolutely no motivation is provided, with only black magic to get to the details. Once you know some of the subject from other sources. Once you know some QM Liboff's book is actually not so bad, but I pity anybody who tries to (or has to) use it as an original primary reference.

Phil Warnell said...

Hi Peter ,

Yes I would agree that Bohm’s Book “Quantum Theory” as being an excellent one, yet the books I mentioned where to first give the reader what is and what remains still unanswered strictly in respect to QM’s formalism. Feynman and Bohm I chose as a contrast as to how the central matters are approached, while David Albert’s book exposes what issues that need attention and how successful each of the current approaches serve in being able to do this. In the end if I were restricted to only be able torecommend one as the first to begin it would be Albert’s book as I would have it as necessary reading for all physics students.

Best,

Phil