Bridging the Gap

[employee2-4601]

Hi folks,

Not sure if this is in the right place, so apologies if it's not.

I recently bought The Quantum Universe by Brian Cox and Jeff Forshaw and, despite reviews stating that it was the best introduction to quantum mechanics going, I got stuck almost immediately owing to the high maths content. I'd really like to teach myself the necessary mathematical subjects related to QM, but have no idea where to start. The last time I studied maths was at GCSE level nearly fifteen years ago. Can anyone suggest/recommend any good books to 1) help me brush up on GCSE maths which, I'll be honest, is probably worse than rusty, and 2) give me an introduction to the more advanced subjects needed for astrophysics and quantum mechanics?

[cloudsweeper]

QM is about uncertainty, quantisation, and wave-particle duality in the atomic and sub-atomic world. A good intro book is 50 Quantum Physics Ideas by J. Baker. 

Doug.

[johnfosteruk]

Volume 3 of the Feynman lectures covers QM concepts well.

[employee2-4601]

Cheers guys, I'll check 'em out

[Macavity]

15 hours ago, employee2-4601 said:

I recently bought The Quantum Universe by Brian Cox and Jeff Forshaw and, despite reviews stating that it was the best introduction to quantum mechanics going, I got stuck almost immediately owing to the high maths content...

There are sufficient numbers of (erudite) sceptics re. unconventional of "clocks" in this work?

I remember (along with a few others) being sufficiently perturbed by his new ideas re. the Pauli
Exclusion principle. Back then, I was on TWITTER and queried this: "Buy my Book", he said!

I am unconvinced that trying out "revolutionary" ideas in beginner (non-expert) texts work? 
(Though, like many satisfied customers, I might make an exception with Richard Feynman...)

[Colinlp]

15 hours ago, employee2-4601 said:

Hi folks,

Not sure if this is in the right place, so apologies if it's not.

I recently bought The Quantum Universe by Brian Cox and Jeff Forshaw and, despite reviews stating that it was the best introduction to quantum mechanics going, I got stuck almost immediately owing to the high maths content. I'd really like to teach myself the necessary mathematical subjects related to QM, but have no idea where to start. The last time I studied maths was at GCSE level nearly fifteen years ago. Can anyone suggest/recommend any good books to 1) help me brush up on GCSE maths which, I'll be honest, is probably worse than rusty, and 2) give me an introduction to the more advanced subjects needed for astrophysics and quantum mechanics?

I sympathise, I went to study Physics at Liverpool as a mature student who was hopeless at maths some 25 years earlier at school. Liverpool uni were kind enough to give us a dummies guide to difficult maths and it basically followed this excellent textbook

http://www.ebay.co.uk/itm/Engineering-Mathematics-K-A-Stroud-/152055390783?hash=item236735223f:g:2h8AAOSwJMhXEL9y

If you really want to get your head stuck into some QM then work your way through the relevant sections of that book and you'll be well on the way. Maths is however a skill where practice, practice and more practice is needed just to keep pace. Personally I think life is too short and unless you really have a deep rooted interest then there are more fun things to do in life

[andrew s]

This is by no means easy. I studied physics and maths at degree level and did a PhD in physics. However, I did not major in QM but have always tried to keep abreast with developments.

I have on and off studied the maths needed to understand QM (Hilbert spaces, Linear Operators etc.) only to find the that was all out of date and QED /QCD was where it is at. If you couple this with the fact that most popular accounts of QM are wrong or at best misleading including those by famous physicists (Feynman's book on QED is a fine exception) it is a tough call.

I don't really know what to advise other than to be clear what you want to understand. My main motivation was to understand how the classical world we all experience emerges from the QM world accepting that was how it was at the basic level. This seems to have been answered by the development of the theory of dechoherence.

Many discussion are about the interpretation of QM rather than its predictions which all valid interpretation agree on. So if interpretation is your interest you don't need the maths just an opinion.

Regards Andrew

[employee2-4601]

I did look at buying QED by Feynman (still my favourite physicist of all time). Methinks another trip to the book shop is in order!

[George Jones]

I, too, like QED by Feynman. The clocks (mentioned above by Macavity) used to illustrate phase by Cox and Forshaw also are used by Feynman. The other book by Feynman on quantum theory, The Feynman Lectiures Volume III, is quite nice, but it much heavier on the maths than is Forshaw and Cox.

One option is to take Roger Penrose's to the extreme, i.e., to read Cox and Forshaw, but to pass over all the maths. Penrose, a very good mathematician indeed, writes about what he does when there is a mathematical equation that he does not understand in some mathematical physics that he is reading "I recommend a procedure that I normally adopt myself when such an offending line presents itself. The procedure is, more or less, to ignore that line completely and to skip over to the next actual line of text!"

Another option is to post here some questions that you have about Cox and Forshaw.

[ollypenrice]

13 hours ago, George Jones said:

I, too, like QED by Feynman. The clocks (mentioned above by Macavity) used to illustrate phase by Cox and Forshaw also are used by Feynman. The other book by Feynman on quantum theory, The Feynman Lectiures Volume III, is quite nice, but it much heavier on the maths than is Forshaw and Cox.

One option is to take Roger Penrose's to the extreme, i.e., to read Cox and Forshaw, but to pass over all the maths. Penrose, a very good mathematician indeed, writes about what he does when there is a mathematical equation that he does not understand in some mathematical physics that he is reading "I recommend a procedure that I normally adopt myself when such an offending line presents itself. The procedure is, more or less, to ignore that line completely and to skip over to the next actual line of text!"

Another option is to post here some questions that you have about Cox and Forshaw.

Penrose's trick is fine when the jumps are infrequent. When you have to jump directly from the foreword to the index the uncertainty principle becomes overwhelming...

lly

[Macavity]

I think one should never get TOO downhearted about lack of mathematical abilities?
Mine were never THAT good (Old style Grade "C" at A-level!) but I still found a niche
within Particle Physics. A Ph.D. job building experiments/electronics/programming. 
(A minor GRIPE is the tendency for SOME to think of you as a "technician", but...)

There is certainly a GAP though! Back in the day (late 70s) there were NO (obvious)
textbooks that bridged the gap between "standard" (A-level, B.Sc. even Ph.D level?)
courses, and that particular knowledge / ability that allowed *original* thinking.  

I did work with one guy of *significant* ability in Maths/Theoretical Physics. OTOH,
he was always willing to "muck in" with the hardware guys! One time he asked me
if I'd too mind too much if we BOTH went to a seminar Quantum Chromodynamics.

After a couple of blackboards full of Langrangian Gauge Theories, I interrupted the
apparent "reverie" of my friend: "Do you understand any of this, Bill"? I whispered.
"Of course not! But Bl**dy Good Stuff, Eh?" I was happy to take his word for it!

It is certainly NICE to completely understand things (Frankly, and mostly, I don't)
I think there can be a certain "rhythm" and aesthetic beauty to a page of maths?
Even if it's fairly incomprehensible and (dare I say) perhaps not necessarily true.

[employee2-4601]

I agree. I've read several books about physics as well as watching any Feynman video I can get my YouTube hands on. A lot of it goes over my head, but what I do understand is fascinating. I would, however, like to learn a little bit of the language. Up to now it's been like watching a foreign film with subtitles. You get a translation, but a large part of what they're saying is lost.

[George Jones]

Then the book that Colinlp referenced above seems to be good. More about the author and the book:

https://en.wikipedia.org/wiki/Ken_Stroud

https://www.timeshighereducation.com/news/method-is-more-than-the-sum-of-its-parts/150737.article

[Tiki]

4 hours ago, employee2-4601 said:

I agree. I've read several books about physics as well as watching any Feynman video I can get my YouTube hands on. A lot of it goes over my head, but what I do understand is fascinating. I would, however, like to learn a little bit of the language. Up to now it's been like watching a foreign film with subtitles. You get a translation, but a large part of what they're saying is lost.

There is quite a gap between 'rusty GCSE maths' and the excellent Stroud book mentioned above.

You could perhaps try something like Vol.I of the Feynman Lectures on Physics with a view to filling in any gaps of your mathematical knowledge along the way.  The book is quite wordy with much wisdom and a lot of original analogies along the way. Feynman excelled not only as a scientist. Mathematics is a dry subject to some and well motivated physical arguments leading to equations might be both interesting and helpful.

QED for a fiver s/h delivered to the door has to be pretty good value too.

 

[johnfosteruk]

6 hours ago, employee2-4601 said:

I agree. I've read several books about physics as well as watching any Feynman video I can get my YouTube hands on. A lot of it goes over my head, but what I do understand is fascinating. I would, however, like to learn a little bit of the language. Up to now it's been like watching a foreign film with subtitles. You get a translation, but a large part of what they're saying is lost.

I think that you just have to accept some things as a given, especially with the crazy world of QED/QM. If you're trying to understand it because you're Feynman and you're looking to explain everything then that won't do but if it's 'recreational' it pays off. Accept it and understand what you can. 

As the great man said in 'Fun to Imagine' - "You have to know what it is that you’re permitted to understand and allow to be understood and known, and what it is you’re not........... But I really can’t do a good job, any job, of explaining magnetic force in terms of something else you’re more familiar with, because I don’t understand it in terms of anything else that you’re more familiar with."

[George Jones]

5 hours ago, Tiki said:

There is quite a gap between 'rusty GCSE maths' and the excellent Stroud book mentioned above.

This  is what I though when I saw the title, but then I used the "look inside" at Amazon to look at a detailed table of contents for the seventh edition. I admit to being unfamiliar with CGSE maths, but much of the first 360 pages might be covered before the final year of high school in Canada. For example, the first 70 pages is on arithmetic, with about 10 pages (including revision) on arithmetic fractions. This is followed by 40 pages on algebraic expressions.

[Macavity]

Part of the problem is that people who are very familiar with the terminology and
the notation of mathematics omit some VITAL (to them obvious) information?

As a random (hopefully not too off-putting!) "QM" example: The Dirac Equation: 

https://en.wikipedia.org/wiki/Dirac_equation  

UK A-Level Maths had provided me with modest abilities re. "Calculus" - I knew
about differentials  being the "gradient of graphs" and integrals  being the "area
under the graph" etc. etc. Maybe I had some notion of Matrix Algebra, but... 

THE REAL problem with the above was that no one told me (I hadn't realised!)
that a lot of the above was Matrix Algebra and notation - Not just x² + y² etc.
Once appreciated I could make modest "progress" with the above. And, for me
it was about reducing the FEAR FACTOR rather than detailed understanding.

I DO THINK there is good reason why a young chap (chapess!) *should* learn
the basics... Calculus, Matrix Algebra are just two aspects? Also to understand
Summation... subscript / superscript notions would help? BUT MOSTLY just to
get an overview of "What's going on" in a typical page Higher Mathematics? 

Ultimately to realise that so much of this is actually "pretty hard" stuff. [IMO]

</wibble>

P.S. If you want a good (and entertaining) BOOK for your bookshelf
(Or a great door-stop!) try "The Road to Reality" by Roger Penrose:

https://www.amazon.co.uk/Road-Reality-Complete-Guide-Universe/dp/0099440687/ref=sr_1_1?ie=UTF8&qid=1461337792&sr=8-1&keywords=the+road+to+reality

Not sure it is "the solution" for novice or intermediate, but good fun! 

[Tiki]

      On ‎4‎/‎21‎/‎2016 at 22:19, Tiki said:

There is quite a gap between 'rusty GCSE maths' and the excellent Stroud book mentioned above.

 

On ‎4‎/‎22‎/‎2016 at 04:22, George Jones said:

This  is what I though when I saw the title, but then I used the "look inside" at Amazon to look at a detailed table of contents for the seventh edition. I admit to being unfamiliar with CGSE maths, but much of the first 360 pages might be covered before the final year of high school in Canada. For example, the first 70 pages is on arithmetic, with about 10 pages (including revision) on arithmetic fractions. This is followed by 40 pages on algebraic expressions.

Ahh, I was unwittingly referring to 'Advanced Engineering Mathematics' by KAStroud and not the book mentioned by Colinlp above. George's description of the book indicate that it would be useful to someone with rusty GCSE maths.

 

[Physicist13]

I'd say try and do an OU course or some online course but one where you can interact with people and ask questions. FOr QM you def need the maths and learn the ability to interpret the maths in the physical world..bizarre though the results are. Books are great but it def needs human interaction too....

Dont be scared!! I got O level B in maths and C in A level!..... enthusiasm is the key!!

P