## Thursday, January 26, 2012

### Guide to the Perplexed Part III

It had been five months since my last post when I returned to blogging with an article on the collapse of the wave function. One of the most famous examples of wave function collapse is the appearance of flecks of metallic silver on a photgraphic plate exposed to the light of a distant star. Any reasonable calculation of the energy density of an electromagnetic wave shows that it is impossible to gather enough energy to drive the chemical transition AgBr => Ag + 1/2Br2, and this circumstance is taken as proof that the energy of the light must be concentrated into particles called photons. In this article, I outline the thermodynamic argument which shows that when we treat the whole silver bromide crystal as a solid solution, the reaction actually becomes spontaneous at very low concentrations. In other words, the energy necessary to detect the light is already present in the crystal, and you don't need to invent a "photon" to supply it.

I don't know if it was before or after I wrote that article that I discovered something that would change my life: Google Blogger tracks your statistics! I discovered that people were actually reading my articles, and suddenly everything was different. I don't know if you'd call it an awful lot of hits, but I was getting two or three hundred clicks a month. This changed everything.

The first thing I posted was an old article about the Mid-East conflict that I had first circulated by email back in 2006. Then I got right back to physics. My next article was about something that I figured out over twenty years ago. I had been trying to calculate how much power you could absorb from an AM radio station with a well-designed crystal radio, and I discovered that the theoretical power was independent of the length of your antenna. This seems like an absurd result, but there is a formula for it in the books, and it's true. The catch is that you can't easily build a perfect antenna because of imperfections in real materials, mostly due to the resistivity of copper. But in theory the result is true and it is mathematically derived. What is different in my approach is that I show how you can understand the result pictorially, and working from simple pictures you can get a pretty good ballpark of the exact theoretical result.

What the whole world seems to have missed about this calculation is its enormous implications for quantum mechanics. In Schroedinger's picture, a hydrogen atom is nothing more or less than a tiny crystal radio antenna, and everything that a hydrogen atom does, in terms of its interaction with the electromagnetic field, can be understand in terms of its properties as a classical antenna. In particular, this new perspective makes a mockery of those old textbook calculations where you evaluate the photo-electric effect by looking at the cross-sectional area of an atom. The effective electrical cross-section of an antenna has nothing to do with its physical cross-section, and this is a purely classical effect that you don't need to explain with "photons".

Meanwhile, now that I was posting again my hit count had taken a sudden upswing. Google doesn't just give you the hits, it tells you the country of origin and the search engine keywords; so I was pretty excited one day to notice my first visitor from the Palestinian Territories, so I couldn't resist giving a friendly shout-out to whoever he was. It was only aftertwards I realized that he might have just as easily been an Israeli "settler"; but either way, I'm glad to see him.

Another surprise from the Blogger statistics was the number hits I got from people who googled "perturbation theory" and "ladder operators". So I wrote a follow-up to my earlier musings on the subject. It's a more mathematical topic than I normally ought to bite off, but I still think my pictorial perspective adds something to the big picture.

In my many internet discussions over the years about the photo-electric effect, I had often heard of the semi-classical school of Jaynes and Scully. I had always assumed that my approach was more or less in line with theirs, and when people ridiculed me for my ideas, I would sometimes invoke Jaynes for moral support. I was pretty shocked only last year to learn that I was wrong: Jaynes and Scully take a classical field and apply it to the quantum atom, but then instead of allowing the atom to evolve through time evolution from the excited state to the ground state (which is what I do), they still calculate the quantum leap transition probabilities.  In other words, if my approach is "semi-classical", then Jaynes and Scully should actually be considered hemi-semi-classical. Or whatever. You know what I mean. I explain it all in the linked blogpost.

Coming up with a semi-classical ("no-photon") explanation for the photo-electric effect was a defining moment in my life, and for ten years I would go on the internet and try to argue it. The most common way people would shoot me down was to say "maybe you can explain the photo-electric effect, but you can't explain the Compton effect." And they were right: I couldn't. Until one day I did. This was a paradigm breaker! I thought for sure I would win the Nobel Prize for this. Sadly, it was not to be. It turns out my explanation was identical to the explanation that Schroedinger had already published in 1927. It's true that in 1919 Compton had "proved" that you couldn't explain the effect according to the wave theory, but that was because he treated the electron as a little charged ping-pong ball. The wave theory explanation is a totally natural outcome of the Schroedinger equation of 1926, but by then the photon paradigm had been so firmly established that even Schroedinger was ignored and marginalized when he argued against it.

In the meantime I had gotten into a discussion on StackExchange.com about transmission line impedances, and so to get myself back in the game, I re-did some old calculations about a parallel-plate waveguide. You get some very interesting results if you just assume that for a freely propagating wave between two plates, there must be no net attraction or repulsion between the plates. This discussion led to some very cool calculations of transmission-line impedances, which I calculate as usual with very pictorial methods. Next I take a pretty big leap and apply these methods to calculate the radiation resistance of a half-wave dipole. Everybody knows this is supposed to come out to 73 ohms, but for most people that number is pretty mysterious. I don't get it exactly right, but I definitely justify it to within a reasonable accuracy, and all by very graphic methods.

In my next post, I find myself again dragged back to the Middle-East conflict. Here I resurrect an old proposal of mine to adopt the usage of Arabic Script to write Hebrew. It's a fantastic idea on all kinds of levels, and it would do huge things to bring Arabs and Jews together, but nobody in Israel is listening to me. I'll keep trying.

As I mentioned, Google Blogger gives me statistics on country of origin, and naturally the U.S. and Canada lead the list, followed by Germany, Russia, and the United Kingdom. Surprisingly, the next spot on the list is up for grabs, and is hotly contended by such countries as India, the Netherlands, South Korea, and...tiny Slovenia, which for a brief moment edged out the other contenders for sole possession of sixth place. I acknowledge them in this post.

My next series of articles was motivated by a question from my nephew, who asks "why is energy e=mc^2, and not m-c-cubed  or whatever? Although this question can be easily answered with dimensional analysis, the actual reason is harder to justify than you might think, and I was led pretty far into uncharted territory (for me anyway) when I tried to justify it via relativity.

My next series of articles deals with perhaps the most baffling and certainly the most talked-about paradox in all of quantum mechanics:  the question of entanglement, with Alice and Bob and the crossed polarizers and all that stuff. It gets pretty involved and I think we'll continue with this topic when I return.