Thursday, June 25, 2015

Polish Guy Singing "Crazy"

Jacek (that's YAH-tsek, but you can call him Jack) is a friend of mine who takes part in a Thursday evening rehearsal session downtown that I lead at a program called ArtBeat. I think this is a phenomenal version of Crazy, the Patsy Cline signature song. (Not everyone knows that Willie Nelson wrote it.) I helped a little with the arrangement on this, but despite our best efforts the two patch changes on the instrumental solo were kind of surprising to us (as you might be able to tell from Jacek's facial expression.)

If you like this video, pass it on to your friends.

Saturday, April 4, 2015

I. L. Peretz 100th Yohrzeit

Today is the 100th anniversary of the death of Yiddish writer I. L. Peretz. They say that a hundred thousand people thronged the streets of Warsaw for his funeral.

Peretz was, in his best moments, a genius without parallel in the Yiddish world. I've had a personal role in trying to keep Peretz's work alive. It's brilliant work and it's actually important if you care at all about who you are and where you came from. Of course, not everyone sees it that way. In fact, my work hasn't been much appreciated in the Jewish world. But at least I've done something.

My biggest project was my musical setting of Peretz's epic poem "The Ballad of Monsich". You can see it on Youtube here:

This was taken from the Winnipeg Fringe Festival in 2005, and there's actually eleven videos. This is the first one, but if you want the whole playlist, it should link from here.

 But I almost forgot one other project I did, which was an incredibly chilling poem about power and hypocrisy called Solomon's Throne, which still rings true today. It was never published anywhere, and so I thought it would be fitting on this, the 100th anniversary of Peretz's death, to post it on the internet. You can link to the PDF here: it includes the transcribed Yiddish (using German spelling) side-by-side with the English translation.  I'm going to say without modesty that my translation is pretty f#%$ing brilliant.

Tuesday, February 3, 2015

Penetrating the Barrier: Some Calculations

Yesterday I calculated the difference between the two ground states of the double well (the infinte well with a finite barrier in the middle.) The two states were of course the symmetric and the antisymmetric cases, with the antisymmetric having a slightly higher energy:

I picked a wavelength of 44 angstroms (7 angstroms = 1 radian) for the sine wave, and a decay length of 2 angstroms for the exponential region, so the ration of the two parameters was 7:2. And then I picked the dimensions of the box so that the waves would just fit inside. And that's pretty much all you need to do the calculation. The Wikipedia formula asks you to calculate the transmission coefficient in terms of E and V, the energies in the two zones respectively, but the formula they give is a bit can re-express it just in terms of the ratio (7:2 in this case) of the two characteristic lengths:
You can see I've got r = 7/2, and ka = 4, so plugging in the numbers, we get a transmission coefficient of 1/2483, or close to 0.04%.   Is this the same as I got using the steady state solutions?

Yesterday I calculated that the wavelengths of the symmetric and antisymmetric modes were different by 0.4% (about one part in 250). But in quantum mechanics wavelength is momentum, and energy is frequency (momentum squared). So the frequencies are different by one part in 125.

Here is where it gets interesting. You start out with the electron all on one side of the barrier. How do you do that? By having the symmetric and antisymmetric modes in phase so they re-inforce on the left and cancel on the right. After 125 cycles, they will be back in phase again. But after 62.5 cycles, the relative phases will be all the wave function will be on the right hand side.

Is this the same result as we got from the Wikipedia formula? It's hard to say, because the Wikipedia formula is expressed in terms of the Copenhagen interpretation as the "probability" of a particle getting through the barrier. Where is my "particle" in terms of standing waves?

Well, one way to interpret it would be to imagine the particle bouncing back and forth in the potential well. If it bounces once on each cycle, that means after hitting the wall 62 times, it gets completely through to the other side. That's like a 1.5% penetration on each cycle...more like 3% or 4%, actually, because there's the competing probability of it returning from whence it came. That's a lot more than the Wikipedia calculation. Have we done something wrong?

It's actually not quite that bad. Remember in quantum mechanics there's a discrepancy between the phase velocity and the group velocity. For electrons, the group velocity is twice the phase velocity. We've been treating the electron as though it travels with the phase velocity of the wave's actually twice that, so where we thought it was hitting the wall 62.5 times, it was actually 125 times. So our nominal penetration ration goes down by half, to below one percent. That's a little better, but still a long way off. What gives?

There is a fascinating answer to this question, and it gives us a very deep insight into the whole subject of quantum resonance. We said that each time an electron strikes the barrier, it has a 1/2500 chance of getting through. But what does this mean in terms of the wave function? It means the amplitude of the transmitted function is one fiftieth. The power goes as the amplitude squared.

In the coupled well system, the transmitted wave is in phase each time it re-strikes. So the amplitude on the transmitted side goes as one fiftieth, two fiftieths, three fiftieths, etc. After only fifty strikes, it is 100 percent through!

Not exactly....because once the amplitude starts building up on the right hand side, there is the probability that it will come back through the other way. But early in the game, that probability is negligible. So while the amplitude is growing as 1/50, 2/50, 3/50....   the probability is growing as 1/2500, 4/2500, 9/2500... in other words, it is growing parabolically.

How close does this parabola fit to the sine wave which represents the oscillating probability? Pretty close, as it turns out. I'm not going to do it in detail, but if you look at the Taylor Expansion for the cosine function, the x-squared term projects to -1 at when x = 1.41 radians (the square root of two. On our sine wave, where 125 strikes (the electron striking the wall) makes is a half-cycle, that comes to 56 strikes.

It's pretty close.

Quantum Tunneling: A Different KInd of Calculation

I did some interesting physics yesterday so I thought I should write it up. The question was about quantum tunneling. It came from my friend's 3rd year Physical Electronics course in Electrical Engineering. You had a MosFET with a silicon dioxide insulating layer between the gate and the channel. They gave you the the barrier potential in the insulator, and told you to assume an electron with a certain energy (less than the barrier potential) in the gate. What was the "probability" or rate of tunneling?

This is a pretty standard problem which you can look up on Wikipedia. You calculate the form of the free-electron solutions in all three regions and match up the boundary condition. It's a little messy but it works.

I thought I could do better. The problem is messy because the conditions are different on the left and right hand sides. So I came up with the idea of working with symmetries. Instead of taking a freely propagating wave from the left and following it through the barrier, I put the whole thing inside a bigger potential well and considered the steady state solutions. Of course there are two minimum-energy solutions: the symmetric and the anti-symmetric, separated by a very tiny energy difference.

I don't like to carry too many letter symbols so I picked numbers that would come out nicely. From the terms of the problem, it's easy to calculate the free-propagation constants in both regions. So I allowed myself to tweak the problem parameters so the propagation constants come out to nice integers. Assuming pi = 22/7, here is the problem as I set it up:

You see I gave the well a width of 20 (you can call it 20 Angstroms if you like or 20 millimeters, it won't matter in the's all about the geometry.) Can you see why this fits the sine wave perfectly? It's because the wave penetrates into the barrier. I've assumed that the penetration length is 2, so 20+2=22 and everything fits. The anti-symmetric solution is the same basic idea:

You can see I set it up so that there is a wavelength of 44, which fits perfectly into the box. But actually that's a bit of a cheat. If I were matching up a sine wave to an exponential at the boundary, then I would indeed get a wavelength of exactly 44, because of the well-known property of an exponential whereby the projection of the slope intersects the x-axis at exactly the decay length (I'm also assuming the sine wave is in the small-angle regime where sin(x)=x):

I don't really care about the constant in front of the sine wave, but I just threw it in here to show that it's easy. I used the property of sine waves that the projection of the tangent from the zero-crossing reaches the altitude of the sine wave after one radian. The point is that if I'm matching my sine wave (period = 44) to an exponential (decay length = 2) then this is how they line up. Everything fits.

Except I'm not exactly matching the sine wave to an exponential. I'm matching it to cosh (in the symmetric case) and sinh (in the antisymmetric case. Cosh is just a little higher and a little less it matches the sine wave at a slightly different position. Actually...the only way to match it up is to make the sine wave just a little bit longer. Instead of a half-length of 22 angstroms, the sine wave stretches to around 22.04....close to 0.2%, if you like. Similarly, in the anti-symmetric solution, the sine wave has to be shortened by the same amount. So the anti-symmetric solution has a slightly higher frequency than the symmetric solution.

We'll see what the implications of this are when we come back. did I calculate the 0.04 angstroms? That's the beauty of this's pure geometry, just looking at the ration of the function with its derivative on both sides of the boundary, and using the small-angle approximation tan(x) = x. It falls right out.

Thursday, December 4, 2014

Wave Function Collapse Explained by Quantum Siphoning

It's almost five years since I posted my original article on Quantum Siphoning and I think it's time for a second look. The idea is to explain the collapse of the wave function by means of normal time evolution. Specifically, how does the very weak "wave function" of the light from a distant star induce the reduction of silver bromide ("collapse of the wavefunction") on a photographic plate?

The traditional explanation is that this phenomenon proves the existence of photons, because the energy of the wave has to be concentrated in a point in order to provide:

a) the positive energy needed to account for the energy difference between silver bromide and metallic silver; and,

b) the additional energy needed to overcome the "bump" of promoting an electron into the conduction band.

The traditional picture looks like this:

 And they say you can't explain this with classical electromagnetism because the classical wave is far to weak to concentrate enough energy in that one little silver atom. Hence the photon.

I don't buy it. The first problem with this argument is that the thermodynamics is flawed. The photographic plate is not a device which captures energy and converts it to chemical form. The energy is already present in the plate in chemical form. Yes, it's true that the standard enthalpy of metallic silver is greater than that of silver bromide. But to calculate the spontaneity of the reaction you need to take into account the concentrations. The silver concentrations in an exposed photographic plate are parts per trillion. At those concentrations, the free energy of the reactions actually tilts the other way! I've done the calculation here. You don't need the energy of the "photon" to drive the reaction. The energy is already available in the chemistry of the plate.

But what about the "activation energy"...the bump of energy needed to get the electron into the conduction band, the intermediate stage of the process? That's where Quantum Siphoning comes in. The energy released when the target silver atom gets reduced is pumped back into the crystal to break up the silver bromide bonds. But how can it do that?

I couldn't figure this out for the longest time because I was trapped in the paradigm of a single electron getting transferred from one site in the crystal to another. But that's not what electrons are. They aren't particles with their own distinct identities. They are a collective wave function with multiple excitations. Anyone who knows about quantum field theory knows this is true.You simply can't describe an atom with two electrons by saying "this electron is here and that one is there". They are both excitations of a single wave function.

And the funny thing is, the same is true on some level for the x-trillion silver atoms which are part of a single silver bromide crystal. You can't say that a photon comes along and knocks an electron out of a single silver atom. What you can say is that a wave passes through the crystal and disturbs the wave function of the whole crystal so it is driven, ever so slightly, into a superposition of states where there is some amplitude that "an electron" is in the conduction band.

This is where people have trouble understanding where I'm going next. And the reason they have trouble is the way quantum mechanics is taught, from a strictly Copenhagen perspective of particles and quantum leaps. Nobody tells them about the equally-valid Schroedinger picture of wave functions and time evolution, which gives exactly the same results for all kinds of ordinary things, including the black body spectrum, the photo-electric effect, and even the Compton effect. I explain the connection between the two pictures in a series of blogposts starting here.

What people don't understand is that everything an atom does in its interactions with ordinary thermal light can be understood by looking at the superpositions of states calculated by the Schroedinger equation, and applying the charge density interpretation to the resulting wave functions, instead of Copenhagen's "probability density". People don't know this!

But it's much worse than that. They certainly don't know the full implications of the wave function picture, as I've listed two paragraphs back. That is not so surprising. What is horrifying to me is that they don't even know the basic and obvious fact that is you take the superposition of the s and p states of a hydrogen atom, you get an oscillating charge other words, and antenna.

They don't know this...and when I tell them, they don't believe it. Even though its an obvious consequence of the well-known solutions of the Schroedinger equation.

And if they don't believe that the Schroedinger equations gives you a hydrogen atom with an oscillating charge distribution, then how are they going to believe that the very same tiny oscillating charge behaves exactly like a classical antenna? That's the calculation I did in those articles I pointed out above, comparing the Copenhagen picture to the Schroedinger interpretation.

And yet there is nothing that should be terribly controversial about anything I have said so far in this article. It's certainly unfashionable to talk about charge densities instead of probabilities, but there is nothing objectively wrong with it. What is appalling to me is that it is so very unfashionable that educated physicists scoff at the very notion that applying Maxwell's equations to the charge density picture gives you correct quantum-mechanical results. But it most certainly does.

So how does all this apply to the photographic plate? It's really very simple. The trillion-or-so silver atoms in the silver bromide crystal are little receiving antennas. The presence of a very week electromagnetic wave drives them ever so slightly into the excited state. What state is that? It's a state where the conduction band is ever-so-slightly excited.

Now there is one particular silver atom which is the target site, the site which we hope to convert to metallic silver. The presence of charge density in the conduction band will naturally couple to this target atom. And this coupling turns that special site antenna. Just like the trillion little silver bromide antennas...but with a difference. Those silver bromide sites were receiving antennas. This target silver atom is...a transmitting antenna. Just as an atom being driven from a lower energy state to a higher energy state functions as a receiving antenna, so does an atom capturing an electron from a higher energy state into a lower energy state function as a transmitting antenna. I explain how these things work in this blogpost about the Crystal Radio.

The very weak electromagnetic wave is gone. It disturbed the silver bromide crystal to a very tiny extent, leaving a small amount of energy distributed among the ground state (silver bromide) and the two other states...the conduction band and the reduced silver site. And the combination of those two states creates a tiny classical antenna...a transmitting antenna buried in the middle of that micro-crystal. And now Quantum Siphoning takes over.

I always knew that the target silver atom would re-transmit energy at the optical frequency. I just never knew how the silver bromide "molecule" could re-capture that energy, which was going out in all directions. Until I realized it's not a single silver-bromide site which is's the whole silver-bromide crystal. Each silver-bromide site within that crystal is a receiving antenna, and those receiving antennas surround the target silver atom, which is transmitting. It's a perfect classical siphon. As the electron amplitude flows into the target silver atom, the conduction band is being depleted. But the energy released at the target site, in the form of re-radiated e-m waves, is captured by the surrounding silver-bromide sites...thereby replenishing the conduction band.

There is no photon. There is no collapse of the wave function. There is nothing but the ordinary, natural time-evolution of the Schroedinger function, working together with Maxwell's equations.

It's a perfect classical siphon.

Friday, November 28, 2014

What's wrong with the education system

When I was a grad student twenty-some years ago, my profs knew me as a guy who liked to come up with his own way of analyzing things. My thesis advisor was in Electrical Power, and everything there is done by "modelling". You have a motor or a transformer, and there is a "model" which represents its internal parameters like "core losses" or "magnetizing inductance". You do some external measurements from which you calculate those parameters, and then you analyze the machine as a simple circuit using the parameters you just calculated.

I never did this. I always worked from physical logic and analyzed things from the ground up. Once my advisor asked me, "Marty, why don't you like models?" (He was Rob Menzies, actually a very capable engineer and a pretty good prof.) I told him I didn't like them because they encouraged you to work by numbers without actually understanding what you were doing. I don't know if he got my point, but the other day I had a flashback to that moment.

I was working with some Engineering students the other day and one of them asked me a question from his Power Systems course. It was about transformers. You do some measurements on the transformer and calculate its equivalent circuit parameters. I asked him to show me the question, and he did. It started off something like this:

"You have a single-phase transformer rated 20 kVA, 2200V primary and 220 secondary. You do an open circuit test and measure 220V, 2.5 A and 100 Watts. Then you do the short circuit test and measure 150V, 4.5A and 250 Watts. Determine the equivalent circuit parameters."
 I asked him to show me how those measurements were done. So he started to draw out the circuit model, which looks something like this:

Okay, I said, where do you measure the 220 volts? He started to point to one of the components, I don't remember which one, it might have been Xm, and I said: "No, you can't measure the internal parameters, those are only theoretical constructs. You can only measure the actual transformer".

He didn't exactly get it. So I drew this picture:

"THIS is what a transformer looks like", I told him. "There are only four wires. You have a voltmeter, an ammeter, and a wattmeter. Where do you hook them up?"

He was stumped. He had to admit that he had no idea.  They never talked about that in class. The prof told them that there was something called an "open circuit test" and something called a "short circuit test", that you get these measurements, and then you put them into these formulas, and the result is the equivalent circuit parameters (the ones you see all over the transformer model in the first diagram). No one ever talked about what it actually means.

And that's why I don't like models. Because they fool you into thinking that you know what you're doing, when you really don't. Actually, this particular student was pretty smart. He recognized right away that he'd been strung along, but he'd gone along with it because he had no choice. You follow directions or you fail. There's no time to second-guess the system and question what you're learning. And that makes him an exception.

The problem with education system is that by the time they've gotten this far, most students are no longer capable of recognizing what's wrong with the whole scenario. If I'd have confronted the typical engineering student with the fact that he was doing the calculation blindly even though he didn't even know where the voltmeter was supposed to be hooked up, he would have simply replied that it didn't matter, that you didn't need  to know that stuff because the right way to do it was just to follow the steps that the professor had laid out. And he would get the right answer on the test.

But that's not the biggest problem. The real tragedy of the education system is that it is doing exactly what society demands of it: churning out obedient workers for the government/industrial bureaucracy who will do what they are told without questioning or even trying to understand the reason behind it.

Friday, October 31, 2014

Why I Hate YIVO

We had an interesting discussion going about Galois Theory over the last little while, so I'm a bit loath to change direction in mid-stream, but I'm still working on getting all my Jewish Post articles up on the internet. So here's another one, this time about Yiddish spelling.


My regular readers will have noticed that sometimes I include a short passage of transcribed Yiddish in my articles. Last week I quoted the memoirs of Yekhezkel Kotik, where he desccribes the jealousy of the poor Orthodox village priest at the luxurious lifestyle of his Polish Catholic counterpart, with his lavish mansion and his four beautiful “sisters” living together with him:

“Nur der orimer Rusisher galakh, velkher flegt platsn far kine fun dem raykhn lukses-lebn fun dem katoylishn galakh, hot far zayne poyerim, di poreytsishe layb-knekht geshvoyren, az di sheyne fraylayns zaynen gor nisht zayne shvester, zey zaynen im vild-fremde, kokhankes zaynen zey im…”

Except that’s not exactly the way it appeared last week. (The original is shown at the bottom of this article.) What you see above is the official transcription system mandated back in the 1920’s by the Vilna-based Jewish Scientific Institute, the  Jüdische Wissenschaftlicher Institute, or YIVO (the acronym being derived from their own phonetic spelling: Yidishe Visenshaftlikhe Institut). It was kind of like our own version of the French Academy, except for Yiddish.

Just as the French Academy sees one of its main goals as the safeguarding of the purity of the language from foreign (especially English) pollution, so was YIVO’s greatest concern in those days the incursion of Germanisms, which were known as daytshmerisms. (That word is a bit of a puzzle, by the way, for which I have never found a wholly satisfactory explantion. My best theory is that the ending comes from Mähren, the German name for Moravia, hence Deutsch-Mährisch.)

Expecially offensive to YIVO was the suggestion that Yiddish was not a real language, but merely a zhargon, a corrupt version of German. Thus motivated, we can see why YIVO would have sought to impose a stricty phonetic spelling system where, for example, “chutzpah” is spelled khutspe and “schmaltz” is spelled shmalts. In effect, YIVO proclaims to all the world that whatever Germanic or other origins a word may have is simply…irrelevant. I remember a conversation I once had with a Yiddish academic as to the origin of a word, I think it was golen, meaning “to shave”. Was it a German word or a Hebrew word, I asked? The Professor was unperturbed. “It is a Yiddish word”, he answered with finality, as though that were all that needed be said.

If there’s anything I’ve learned about Yiddish, it’s that the origins of a word were anything but “irrelevant”. We are taught in school that some English words come from Latin, and some come from Greek; but when we speak English, those origins are completely invisible to us. They’re all just words. Yiddish was totally different. Every Yiddish speaker, no matter how uneducated, knew instinctively if a word came from German, Hebrew, or Russian. The nuance carried by a word or phrase was often strongly influenced by its origins. The YIVO academics could fume that it was demeaning for writers to substitute loftier-sounding German expressions for everyday Hebrew terms (like gesicht instead of ponim, as Yehoash did in his translation of the first verse of Genesis); but like it or not, that kind of “code-switching” was deeply ingrained in the language and the culture. Often it was used for humorous effect. Either way, the mixed heritage of Yiddish was a defining aspect of its character, and not something to be ashamed of.      

But more than that, I think we’re cutting off our nose to spite our face if we ignore the German yikhus of our language. If we care at all about preserving Yiddish, then its relationship to German is for my money the biggest asset we have. We have a huge body of literature, historical writing, and music which we, in North America, have all but abandoned. We send our children to Hebrew School, and then to University where they can fritter away years taking courses in History of Film or Feminist Psychology or whatever, and I’m saying maybe they should take a course in Intro German. Because with a smattering of Hebrew and German under your belt, you’d be surprised how accessible that enormous body of Yiddish becomes, and what a window it opens into our past.

So my solution is that we transcribe Yiddish in a way that reflects as much as possible the two great languages from it is descended. There are some suttleties here and there involving vowel shifts which I think I’ve dealt with rather well with a cunning system õf döts ând squiggles. Maybe I’ll talk about it in more detail another time. But for now, here is the passage I started out with, re-written using my Germanized system. I think compared with the YIVO phonetics (at the top of this article) it looks pretty cool my way:

“Nur der ârimer Russischer galakh, welcher flegt platzen far kinah (envy) vun dem reichen luxus-leben vun dem Kathòlischen galakh, hât var seine pauerim, die poretzische leib-knecht (the squire’s serfs) geschwòren, as die schöene Fräuleins seinen gâr nischt seine schwester, séi seinen ihm wild-fremde (total strangers), kokhankes seinen séi ihm…”