Paul P. Mealing

Check out my book, ELVENE. Available as e-book and as paperback (print on demand, POD). 2 Reviews: here. Also this promotional Q&A on-line.

Friday, 30 December 2011

The Quantum Universe by Brian Cox and Jeff Forshaw

I’ve recently read this tome, subtitled Everything that can happen does happen, which is a phrase they reiterate throughout the book. Cox is best known as a TV science presenter for BBC. His series on the universe can be highly recommended. His youthful and conversational delivery, combined with an erudite knowledge of physics, makes him ideal for television. The same style comes across in the book despite the inherent difficulty of the topic.

In the last chapter, an epilogue, he mentions writing in September 2011, so this book really is hot off the press. Whilst the book is meant to cater for people with a non-scientific background, I’m unsure if it succeeds at that level and I’m not in a position to judge it on that basis. I’m fairly well read in this area, and I mainly bought it to see if they could add anything new to my knowledge and to compare their approach to other physics writers I’ve read.

They reference Richard Feynman (along with many other contributors to quantum theory) quite a lot, and, in particular, they borrow the same method of exposition that Feynman used in his book, QED. In fact, I’d recommend that this book be read in conjunction with Feynman’s book even though they overlap. Feynman introduced the notion of a one handed clock to represent the phase, amplitude and frequency of the wave function that lies at the heart of quantum mechanics (refer my post on Schrodinger’s equation, May 2011).

Cox and Forshaw use this same analogous method very effectively throughout the book, but they never tell the reader specifically that the clock represents the wave function as I assume it does. In fact, in one part of the book they refer to clocks and wave functions independently in the same passage, which could lead the reader to believe they are different things. If they are different things then I’ve misconstrued their meaning.

Early in their description of clocks they mention that the number of turns is dependent on the particle’s mass, thus energy. This is a direct consequence of Planck’s equation that relates energy to frequency, yet they don’t explain this. Later in the book, when they introduce Planck’s equation, they write it in terms of wavelength, not frequency, as it is normally expressed. These are minor quibbles, some might say petty, yet I believe they would help to relate the use of Feynman’s clocks to what the reader might already know of the subject.

One of the significant facts I learnt from their book was how Feynman exploited the ‘least action principle’ in quantum mechanics. (For a brief exposition of the least action principle refer my post on The Laws of Nature, Mar. 2008). Feynman also describes its significance in gravity in Six-Not-So-Easy Pieces: the principle dictates the path of a body in a gravitational field. In effect, the ‘least action’ is the difference between the kinetic and potential energy of the body. Nature contrives that it will always be a minimum, hence the description, ‘principle of least action’.

Now, I already knew that Feynman had applied it to quantum mechanics, but Cox and Forshaw provide us with the story behind it. Dirac had written a paper in 1933 entitled ‘The Lagrangian in Quantum Mechanics’ (the Lagrangian is the mathematical formulation of least action). In 1941, Herbet Jehle, a European physicist visiting Princeton, told Feynman about Dirac’s paper. The next day, Feynman found the paper in the Princeton library, and with Jehle looking on, derived Schrodinger’s equation in one afternoon using the least action principle. Feynman later told Dirac about his discovery, and was surprised to learn that Dirac had not made the connection himself.

But the other interesting point is that the units for ‘action’ in physics are mx2/t which are the same units as Planck’s constant, h. In other words, the fundamental unit of quantum mechanics is an ‘action’ unit. Now, units are important concepts in physics because only entities with the same type of units can be added and subtracted in an equation. Physicists talk about dimensions, because units must have the same dimensions to be able to be combined or deducted. The dimensions for ‘action’, for instance, are 1 of mass, 2 of length and -1 of time. To give a more common example, the dimensions for velocity are 0 of mass, 1 of length and -1 of time. You can add and subtract areas, for example, (2 dimensions of length) but you can’t add a length to an area or deduct an area from a volume (3 dimensions of length). Obviously, multiplication and calculus allow one to transform dimensions.

One of the concepts that Cox and Forshaw emphasise throughout the book is the universality of quantum mechanics and how literally everything is interconnected. They point out that no 2 electrons can have exactly the same energy, not only in the same atom but in the same universe (the Pauli Exclusion Principle). Also individual photons can never be tracked. In fact, they point out a little-known fact that Planck’s law is incompatible with the notion of tracking individual photons; a discovery made by Ladislas Natanson as far back as 1911. No, I’d never heard of him either, or his remarkable insight.

Cox and Forshaw do a brilliant job of explaining Wolfgang Pauli’s famous principle that makes individual atoms, and therefore matter, stable. They also expound on Freeman Dyson’s and Andrew Leonard’s 1967 paper demonstrating that it’s the Pauli Exclusion Principle that stops you from falling through the floor. Dyson described ‘the proof as extraordinarily complicated, difficult and opaque’, which may help to explain why it took so long for someone to derive it.

They also do an excellent job of explaining how quantum mechanics allows transistors to work, which is arguably the most significant invention of the 20th Century. In fact, it’s probably the best exposition I’ve come across outside a text book.

But what comes across throughout their book, is that the quantum world obeys specific ‘rules’ and once you understand those rules, no matter how bizarre they may seem to our common sense view of the world, you can make accurate and consistent predictions. The catch is that probability plays a key role and deterministic interpretations are not compatible with the quantum universe. In fact, Cox and Forshaw point out that quantum mechanics exhibits true ‘randomness’ unlike the ‘chaotic’ randomness that is dependent on ultra-sensitive initial conditions. In a recent issue of New Scientist, I came across someone discussing free will or the lack of it (in a book review on the topic) and espousing the view that everything is deterministic from the Big Bang onwards. Personally, I find it very difficult to hold such a philosophical position when the bedrock of the entire physical universe insists on chance.

Cox and Forshaw don’t have much to say about the philosophical implications of quantum mechanics except in one brief passage where they reveal a preference for the 'many worlds' interpretation because it does away with the so-called ‘collapse’ or ‘decoherence’ of the wave function. In fact, they make no reference to ‘collapse’ or ‘decoherence’ at all. They prefer the idea that there is an uninterrupted history of the quantum wave function, even if it implies that its future lies in another universe or a multitude of universes. But they also give tacit acknowledgement to Feynman’s dictum: ‘…the position taken by the “shut up and calculate” school of physics, which deftly dismisses any attempt to talk about the reality of things.’

In the epilogue, Cox and Forshaw get into some serious physics where they explain how quantum mechanics gives us the famous Chandrasekhar limit, developed by Subrahmanyan Chandresekhar in 1930, which determines how big a star can be before it becomes a neutron star or a black hole. The answer is 1.4 solar masses (1.4 times the mass of our sun). Mind you, it has to go through a whole series of phases in between and that’s what Cox and Forshaw explain, using some fundamental algebra along with some generous assumptions to make the exposition digestible for laypeople. But the purpose of the exercise is to demonstrate that quantum phenomena can determine limits on a stellar scale that have been verified by observation. It also gives a good demonstration of the scientific method in practice, as they point out.

This is a good book for introducing people to the mysteries of quantum mechanics with no attempt to side-step the inherent weirdness and no attempt to provide simplistic answers. They do their best to follow the Feynman tradition of telling it exactly as it is and eschew the magic that mysteries tend to induce. Nature doesn’t provide loop holes for specious reasoning. Quantum mechanics is the latest in a long line of nature’s secret workings, mathematically cogent and reliable, but deeply counter-intuitive.

8 comments:

pk said...

Well, you effectively succeeded in stimulating e-book covetousness in at least this one prospective reader, and I felt certain (in a naturally non-Heisenbergian sort of way) I'd be able to find a copy in Amözinger's Cat-alog for the Kindle, but alas, when I opened the app, the Forshaw wave function collapsed, and the fox (theretofore presumably both alive and dead) turned out actually to nave been necrotic the whole time, wherefore did it stink (but only in this universe, and only by dint of being dead). I feel confident that in some parallel universe, I'm actually reading it, rather than going flagrantly nuts with insomnia and quantum agita, contemplating my recent divorce. Was it pre-released in Australia? I was thinking maybe I could get it from amazon.antipodeanparallel universe.com, but if I already have, then I'd only confuse myself.

Paul P. Mealing said...

Hi PK,

The link from your email gives a subtly different format to my blog. You've got rid of the stuff on the right so the post fills the whole page.

When you mentioned kindle, I thought you must have acquired ELVENE on kindle, but, of course, you've already read it (in paperback).

I got my copy of The Quantum Universe through Amazon UK, which is where I get most, but not all, of my non-fiction books.

Australia is usually the last place on the planet to get a copy of anything, though, of course, we are inundated with everything from both US and UK for movies, music and books, which is why local artists (in all these fields) go overseas to get recognition. New Zealand and Canada suffer the same fate.

Regards, Paul.

Paul P. Mealing said...

Actually, I just looked up Amazon UK and I saw that the kindle version is available to UK customers only.

Regards, Paul.

pk said...

Hi Paul,

Unless you're being non-literal in a subtly humorous way that eludes me (not hard to do: an oncoming bus could elude me these days), I'm perplexed by your allusion to "the link from [my] email," since I haven't sent you one (not in aeons), and the only links I can think of are the silly one ("dontopenthebox.collapsedwave.com") I provided in lieu of a link to my blog (which has likewise gone unrevised for aeons -- at least, by me) -- and possibly a link from that blog to yours, which ought not to have changed, unless someone's been meddling. Howsoever, if you did receive an email from someone purporting to be me, I'm concerned it may have been a hack or a prank. I've been hors de combat for so long, I'm not even sure which email account it was from which last I wrote you (probably in 2009), but if it began with the letters "pb," that one would probably long ago have been relegated to the inactive list. I'll check its status, though, to see whether there's been unauthorized use, and otherwise to resurrect it. Please do let me know, however (brief note here would probably be least problematical), if you actually did receive an email from a pk-spoofer, though it's hard to imagine why anyone (even in this universe) would bother: I'm far closer to collapse than the cat, but it was nice to touch bases again. I hope all is much better with you.

Regards,
PK

P.S. Congrats on the Kindle-adoption of Elvene. I liked the reviews, there and on goodreads.

pk said...

P.P.S. Occurs to me belatedly (not really sentient, today) that, by "email," you may just have meant the posted comment, itself, which blogger was for some reason displaying in a hinky fashion. If that's the explanation (rather than my more characteristically paranoid first take), then it may only have been that I'd composed the thing on my smartphone, which is what I use for virtually all my web activity these days (easiest from bed) and the browser may have introduced some hidden, epenthetic null or other occult characters. (Le navigateur a ses raisons que la raison ne connaît point.) Really do regret that I can't get that book, but I've recently (within living memory) ploughed through Greene's The Hidden Reality and Gribbin's In Search of the Multiverse, so perhaps it would have been overkill. No cat-aclysm. :)

Paul P. Mealing said...

Hi PK,

Yes, the second missive is closer to the truth. Comments on my blog are automatically sent to my email account with a link to the post, including ones I write myself, like this one.

I have a condition called polly myalgia rheumatica since May this year (it's still 2011, though only just in Oz; a little over 12 hrs left as I write). It put me in hospital for a week whence I wrote my post on Schrodinger's equation, and I'm now on steroids.

I just helped celebrate my mother's 90th birthday, still going strong and independent. She does puzzles by the bookfull and she can beat me at scrabble, and I call myself an author. A woman of remarkable resilience and intelligence with bugger all formal education. Her father was even more remarkable as he taught himself to make violins while living in the Australian bush. They don't make them like they used to.

Regards, Paul.

pk said...

Hi Paul,

I think for you to "call [yourself] an author" is more than a Cartesian truth, but one amply grounded in the perceptions of others (your humble interlocutor, included), disinclined as I am to entertain epistemological visions of the universe as consisting of seven billion disparate, non-intersecting solipsistic bubbles, so that I do bow to that consensually-validated proposition (that you're a damned good one, too). That said, I am profoundly sorry to hear about your polymyalgia rheumatica, and especially that its severity was such as to require your hospitalization, but I think possibly part of your implicit intent in sharing your own recent medical ordeal (part of the effect of your so doing, irrespective of intent) was not just to commiserate, but to remind me that suffering and affliction we have always to confront, and we need to try to be like your parents, the ones they don't make any more. As you may have inferred (from my comments and my generally demented divagations, if nothing else), I'm coping with some neurological problems of my own, among others, and since my spouse bailed, have been doing so with less admirable stoicism and persistence than you, yourself, have exhibited, disquisiting lucidly on matters quantum mechanical while having to accommodate to steroids and nosocomial discomforts. I understand that steroids are usually really effective, at least in treating the symptoms of PMR, so I hope you're getting some relief. The reminder, anyway, to persevere didn't come amiss. One place I think you showed almost unimaginable stoicism, incidentally, was in enduring the indefatigably snotty ad hominem condescension of Rutten, in aid of his conviction that no one but he can understand the truly illuminating benefits of fatuous, esoteric logical convolutions that are all in Vogue (I think they should have been consigned to the magazine) in this season's counterintuitive, logic-of-the-month club. I think there is no possible world in which the fellow is not interspersing his arguments with exhortations to his justifiably consternated detractors to go back to kindergarten. I'm a logician (retired and disabled , but withal, still someone academically credentialled), and his dismissive, supercilious comments conjoined with his nonsensical attempt to conjure spirits from the vasty deep by invoking magical words (to which, by the way, I think Patrick did altogether too much honor; the man is a saint) made me apoplectic. I can only stand in awe of your measured and modest responses. I spent six months sleeping in my car and in hotels, and none of it made me so angry as his treatment of you and others in that agonizingly protracted exercise in possible worlds epistemological silliness.

Please take good care of your health.

Regards,

PK

Paul P. Mealing said...

Hi PK,

Thanks for your kind words. Yes, I'm coping quite well, thanks to the wonders of medication; I'm even attempting to maintain some level of fitness.

To be honest, your situation is much more difficult than mine. The only advice I can give is to look to friends. There is a tendency to withdraw under these circumstances when good company is the best medicine. I speak from experience.

It's just over an hour to 2012 here, so I can only wish you all the best for the New Year.

Best regards, Paul.