Heisenberg’s Dilemma, or the Principle of Quantum Equivalent Exchange

Posted: March 28, 2012 in Histories & Auguries

For theory’s sake, suppose that a hard-to-trace group of free-state electrons (that is, valence electrons not in a bound state in an atom) have been posited to lurk about a given sample of a semiconductor crystal. You, as the experimenter, want to find out the general location of this elusive group of electrons, but have difficulty doing so. This last part is no coincidence, and owes its occurrence to a redoubtable theory called Heisenberg’s Uncertainty Principle. In order to “see” an object as tiny as an electron, we have to shoot a photon at it; however, the photon’s kinetic energy, upon striking the electron, could disrupt either its position or momentum (in so few words – I won’t get into the details here). As a consequence, the information about the electron will never be complete.

Suppose, now, that the only way to lure out these shy creatures is with a bait of some sort. We knowing that electrons are negatively charged, and respond to one of two things: repulsion from other electrons, or attraction to a positively-charged particle, either a proton or a positron. A proton is ridiculously massive next to an electron, but a well-placed sample of positrons would cause enough of a stir. The electrons can be spotted as they leave their trail, approaching their antiparticle brethren. So, success! You’ve accounted for your missing electrons.

Why it's tough for Quantum Mechanics to find love.

There is, however, a downside: In your haste to find your free electrons, you seemed to have overlooked a possible electron-positron collision that could result in an ugly explosion. The low-end energy is about 511 keV, enough to get you shocked by a Taser, according to my flimsy research. Oops. There go the positrons. But, hey! You’ve found your electrons, nonetheless. Was it worth the cost of losing the positrons?

To most of us in the larger world, this overly-simplistic experiment has little relevance. But let’s put this in metaphor in perspective: Suppose now, instead of an experimentalist in Caltech or Stanford, you are a cryptanalyst in Bletchley Park at the height of World War II, working feverishly to crack the enemy’s encrypting code or “crib.” There is a flotilla of Allied merchant ships steaming through the Atlantic, and on its way to provide badly-needed resources to the British Isles. Sketchy intelligence have reported that a pack of hostile German U-Boats cruise the waters, with the sole intent of destroying these supply ships. They are a wily, disciplined bunch, never breaking radio silence except when reporting weather, or at the onset of an attack. The Allied convoy is spread out at sea, with no air support, and little communication; the naval liaison officer on your team knows that they’ll be ripe for the picking, sitting ducks for the wolf packs. However, in order to know where they are exactly, you’ll need to find out where either party is, when they start transmitting. Unsecured transmissions can be traced via Directional Finding (DF) techniques. If you get enough radio transmissions, then a squadron of fighter planes could be rushed in to the location to fend off the enemy and save whatever is left of the convoy.

"Did we hit a positron... or a proton?"

There’s a bigger dilemma, and one on which the general outcome of the war effort depends. Knowing that the enemy uses an encryption device and methods to secure its transmissions, you realize that this may be a one-in-a-million opportunity to crack the enemy’s “crib” and enable you to to listen in on his plans, well in advance. Doing so would allow your troops and allies to eavesdrop on him, in future naval campaigns — nay, any given battle or theatre of operation — and give enough time to plan.  As a codebreaker, such things as the “greater good” and lives saved or lost are abstractions that you do not have the luxury of pondering. You have to ignore the death toll and remain focused on the mission at hand: Obtain enough data to glean a common pattern in the code, that would reveal itself over time. But to do so, a ship or an entire convoy, would have to be sacrificed in the process.

This is the dilemma presented  in the spy thriller Enigma. Upon learning about the presence of a hostile force of German U-Boats, ace cryptoanalyst Tom Jericho deduces that adequate data about their code won’t be possible, until a U-Boat breaks radio silence, upon sighting the convoy. At that point, the wolf pack would be busy in radio chatter, passing on short-line transmissions about weather, sea conditions, armaments, battle formation and the like. By Tom Jericho’s estimate, it would take 25 transmissions within a space of day, before his team can piece together an operational code mimicking that of the enemy’s. However in gathering enough data to break the code, they would have to risk sacrificing the convoy.


--------"Are you sure you've lost your electrons?" ------"I'm positive!"

The movie further explores the concept of “the greater good,” when it delves into the infamous Katyn Forest Massacre, and the efforts of the British secret service to cover up the potentially-explosive deal-breaker from their American allies. As agent Wigram muses, “It’s what Hitler would give his last ball for!” Ultimately, we know that even American leaders looked the other way as their Russian allies committed unspeakable atrocities. All for the cause of “The Greater Good.” It could be said that many a conflict has been defined, not so much as what was at stake, but at the price of obtaining that prize. People often think of World War II as “The Good War,” when the Evil Axis Powers were soundly defeated by the Allied Forces of Good. I sometimes think of it as a conflict when innovative, often terrible and brutal methods of warfare were developed, all at the cost of untold millions in human life. There is no better example than the inception of the first wartime atomic bomb.

Much is said about Equivalent Exchange in the anime series Fullmetal Alchemist. This Principle dictates that one might obtain something in exchange for something offered, which is of equivalent or greater value. While the series mostly focuses on the human element of reciprocity, it also shows the darker side of Equivalent Exchange, in the form of human transmutation and the Philosopher’s Stone. Unfortunately, we have gone well beyond the benign, quid-pro-quo society that has shaped our early civilization.  Why trade hard work and sacrifice, when you can leverage the odds and play the numbers to your favor? It’s essentially how modern success has been shaped. Purveyors of consumerism would have you believe that such success can be dumbed-down and duplicated, with minimal effort. Of course, many who have been burned by the Financial Crisis of 2008 now know better. Perhaps we ultimately did see Equivalent Exchange at work, albeit in a subtle form. In our mad rush to achieve prosperity, we managed to lose our heads and sell our souls. Hopefully, it’s not permanent. But a little humble pie is in order. After all, as the man said, “When one with experience meets one with money, the one with experience gets the money — and the one with the money gets the experience.”

So how’s that for Equivalent Exchange?

Copyright Anabasius 2012


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