Tag Archives: Bell’s theorem

The pleasures of reading Feynman on Physics – II

If you’re tired of hearing and thinking about COVID-19 24/7 even when you don’t want to, do what I did when I was a neurology resident 50+ years ago making clever diagnoses and then standing helplessly by while patients died.  Back then I read topology and the intense concentration required to absorb and digest the terms and relationships, took me miles and miles away.  The husband of one of my interns was a mathematician, and she said he would dream about mathematics.

Presumably some of the readership are chemists with graduate degrees, meaning that part of their acculturation as such was a course in quantum mechanics.  Back in the day it was pretty much required of chemistry grad students — homage a Prof. Marty Gouterman who taught the course to us 3 years out from his PhD in 1961.  Definitely a great teacher.  Here he is now, a continent away — http://faculty.washington.edu/goutermn/.

So for those happy souls I strongly recommend volume III of The Feynman Lectures on Physics.  Equally strongly do I recommend getting the Millennium Edition which has been purged of the 1,100 or so errors found in the 3 volumes over the years.

“Traditionally, all courses in quantum mechanics have begun in the same way, retracing the path followed in the historical development of the subject.  One first learns a great deal about classical mechanics so that he will be able to understand how to solve the Schrodinger equation.  Then he spends a long time working out various solutions.  Only after a detailed study of this equation does he get to the advanced subject of the electron’s spin.”

The first half of volume III is about spin

Feynman doesn’t even get to the Hamiltonian until p. 88.  I’m almost half through volume III and there has been no sighting of the Schrodinger equation so far.  But what you will find are clear explanations of Bosons and Fermions and why they are different, how masers and lasers operate (they are two state spin systems), how one electron holds two protons together, and a great explanation of covalent bonding.  Then there is great stuff beyond the ken of most chemists (at least this one) such as the Yukawa explanation of the strong nuclear force, and why neutrons and protons are really the same.  If you’ve read about Bell’s theorem proving that ‘spooky action at a distance must exist’, you’ll see where the numbers come from quantum mechanically that are simply impossible on a classical basis.  Zeilinger’s book “The Dance of the Photons” goes into this using .75 (which Feynman shows is just cos(30)^2.

Although Feynman doesn’t make much of a point about it, the essentiality of ‘imaginary’ numbers (complex numbers) to the entire project of quantum mechanics impressed me.  Without them,  wave interference is impossible.

I’m far from sure a neophyte could actually learn QM from Feynman, but having mucked about using and being exposed to QM and its extensions for 60 years, Feynman’s development of the subject is simply a joy to read.

So get the 3 volumes and plunge in.  You’ll forget all about the pandemic (for a while anyway)

 

Want to understand Quantum Computing — buy this book

As quantum mechanics enters its second century, quantum computing has been hot stuff for the last third of it, beginning with Feynman’s lectures on computation in 84 – 86.  Articles on quantum computing  appear all the time in Nature, Science and even the mainstream press.

Perhaps you tried to understand it 20 years ago by reading Nielsen and Chuang’s massive tome Quantum Computation and Quantum information.  I did, and gave up.  At 648 pages and nearly half a million words, it’s something only for people entering the field.  Yet quantum computers are impossible to ignore.

That’s where a new book “Quantum Computing for Everyone” by Chris Bernhardt comes in.  You need little more than high school trigonometry and determination to get through it.  It is blazingly clear.  No term is used before it is defined and there are plenty of diagrams.   Of course Bernhardt simplifies things a bit.  Amazingly, he’s able to avoid the complex number system. At 189 pages and under 100,000 words it is not impossible to get through.

Not being an expert, I can’t speak for its completeness, but all the stuff I’ve read about in Nature, Science is there — no cloning, entanglement, Ed Frenkin (and his gate), Grover’s algorithm,  Shor’s algorithm, the RSA algorithm.  As a bonus there is a clear explanation of Bell’s theorem.

You don’t need a course in quantum mechanics to get through it, but it would make things easier.  Most chemists (for whom this blog is basically written) have had one.  This plus a background in linear algebra would certainly make the first 70 or so pages a breeze.

Just as a book on language doesn’t get into the fonts it can be written in, the book doesn’t get into how such a computer can be physically instantiated.  What it does do is tell you how the basic guts of the quantum computer work. Amazingly, they are just matrices (explained in the book) which change one basis for representing qubits (explained) into another.  These are the quantum gates —  ‘just operations that can be described by orthogonal matrices” p. 117.  The computation comes in by sending qubits through the gates (operating on vectors by matrices).

Be prepared to work.  The concepts (although clearly explained) come thick and fast.

Linear algebra is basic to quantum mechanics.  Superposition of quantum states is nothing more than a linear combination of vectors.  When I audited a course on QM 10 years ago to see what had changed in 50 years, I was amazed at how little linear algebra was emphasized.  You could do worse that read a series of posts on my blog titled “Linear Algebra Survival Guide for Quantum Mechanics” — There are 9 — start here and follow the links — you may find it helpful — https://luysii.wordpress.com/2010/01/04/linear-algebra-survival-guide-for-quantum-mechanics-i/

From a mathematical point of view entanglement (discussed extensively in the book) is fairly simple -philosophically it’s anything but – and the following was described by a math prof as concise and clear– https://luysii.wordpress.com/2014/12/28/how-formal-tensor-mathematics-and-the-postulates-of-quantum-mechanics-give-rise-to-entanglement/

The book is a masterpiece — kudos to Bernhardt