Two households, both alike in dignity, in fair Germany, where we lay our scene. The star-crossed lovers in this version of the story are Erwin Schrödinger and Werner Heisenberg, who independently develop two versions of quantum mechanics. However, in contrast to the many times in science where two people make the same discovery, Schrödinger's and Heisenberg's theories look completely different. Schrödinger based his theory on a partial differential equation; Heisenberg based his on matrix algebra. The quantum virtuoso Paul Dirac would later prove the two approaches were equivalent, but for a few turbulent years in the early 1920s Schrödinger and Heisenberg battled for the hearts and minds of the physics community, each expecting to be greeted as liberator.
Predictably, what with differential equations being complicated and hard and matrix algebra being straightforward and easy, physics embraced Schrödinger's approach and threw Heisenberg to the wolves.
Seriously.
The Standard History of quantum mechanics is that Schrödinger won because he used familiar mathematics (a version of the wave equation) whereas Heisenberg fell by the wayside because matrices were considered esoteric and impenetrable.
See, that dog there just don't hunt. I've known a few physicists in my day, and while they're some of the most arrogant bastards on the planet, one thing they're not is dumb. Matrix algebra is not beyond their ken, neither today nor in 1920. Something else is afoot.
What the physics history books can't bring themselves to say is Heisenberg's approach fell by the wayside because it's so -- I don't know how else to put this -- because it's so goddamn weird. It's not weird like saying 2 + 2 = 5, it's weird like saying 2 + 2 = put pants on your head, spin around three times, and moo. And while there is nothing particularly complicated about putting pants on your head spinning around three times and mooing, as soon as I tell you it's how all of physics works, the only rational response is for your brain to shut down. It's a defense mechanism, superego collapsing the mental bridge at Khazad Dum lest the Balrog burn the sanity from your noggin. Heisenberg is to physics what David Lynch is to cinema.
I don't doubt physics majors eat PDEs for breakfast and so physics welcomed Schrödinger into their home like the vampire Lestat. However, I recall bumping into the wave equation many times back in engineering school and the take home message was always the same: In these two or three highly contrived and artificial situations it has a solution but dare step outside that comfort zone and you'll get curb stomped like Urkel at Derek Vinyard's house. So excuse me if I don't accept Schrödinger as being the "easy" version of quantum mechanics. Which is a problem because it's the version every physics textbook on the planet insists on presenting.
I don't need to understand quantum mechanics. It does not intersect my private or professional life. But I'd like to, at least a little. I want to experience its heady thrill, I really do. But I have stared at the wave equation, and stared at it (and stared at it) and it just will not speak to me. I suppose you could say I just can't be Schrödinger's cat.
Hence, we should applaud Thomas Jordan and his slow deliberate resurrection of Heisenberg's quantum mechanics one crazy flying buttress at a time in Quantum Mechanics in Simple Matrix Form. He really really wants the reader to become a convert, or if not convert than at least give fair hearing to the psychotic beauty of his master's creation, even though should you realize for a moment the thing makes no sense you will be gunned down like a redshirt on the planet of the OK Corral, when Spock had to mind meld everyone so they knew the bullets weren't real.
Applaud I do. That being said, it cannot be denied Jordan shoots himself in the foot about as often as not. If you know even a little his presentation can seem shady. Exhibit A: Jordan hammers home the equation QP – PQ = ih/2π (as he should -- it's Heisenberg's Rosetta stone). Here, P and Q are matrices, and if you know anything about anything, you know that QP – PQ = ih/2π is nonsense. It's unpossible. This has nothing to do with quantum mechanics; as written, the LHS is a matrix and the RHS is a scalar. That's a show stopper. Eventually (and by "eventually" I mean SEVENTEEN CHAPTERS later), Jordan finally presents a correct version of the equation by including the identity matrix on the RHS: QP – PQ = ih/2π I. Why the subterfuge? This sort of plot tension may work in fiction, but in a textbook it gives your reader the heebie jeebies.
One gets the feeling Jordan is constantly hiding something, as if a lifetime of disapproving glances and whispered invectives of the physics establishment has left him defensive on the one hand and terrified the crazy train is one bad burp away from going off the rails on the other. Each chapter a lick and a promise that real soon now something is about to happen. Forever meandering about the suburbs instead of just hitting the town. Forever smoothing imagined ruffled feathers. Someone from Dover should have sat poor Thomas down with a stenographer and a bottle of Schnapps. You are among friends now; go ahead and tell your side of the story.
As a result of the text's meanderings, I've only made it through the first half. Yet, the first half is capped by Heisenberg's correction of the Rayleigh-Jeans equation, which is the bedrock of modern QM. So Jordan has done me a solid. Whereas Schrödinger's equation is forever beyond my comprehension (something something upside down triangle, squishy d, capital psi, something) even I can remember OP – PQ = ih (NB: the "h" should have a little line through it). And with Jordan's help, I've used it to do real actual quantum mechanics!
After some R&R I may even return to the second half, ready to tussle with Pauli spin matrices and the Bohr atom and Bell's inequalities and more vague innuendo and historical asides. For now, however, I am satisfied.
Let Jordan slay your quantum demons on Amazon
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