Sunday, June 24, 2012

A Mechanic Does The South

A mechanic does Borges' The South (Translated from my Spanish, so take your chances with the English.)

I apologize to readers who come by car, I'm a mechanic not of cars but of the quanta.

The influence of quantum mechanics in The South, by Jorge Luis Borges

Read the text before reading the essay.
The South in English

The work of writer Jorge Luis Borges has been analyzed from various points, including the mathematical. His magical-realist tale The South is a very frequently assigned text for students of literature in Spanish. Borges wrote the story before the year 1944, by the time modern physics (Einstein's relativity and quantum mechanics of Schrödinger, Heisenberg, Bohr, Einstein, Dirac and others) and was in full flower and its ideas (especially those of the relativity of time and probabilistic evolution) had come to form part of the minds of artists and common people. (Of course Foucault may view this as causality violation.)

What is it that comes to mind when you mention quantum mechanics? Emotionally, fascination and fear, and then thoughts about the Schrödinger cat in a box, the separation between the observer and the observed, the effect of interaction between them (an "experiment"), the probabilities and the uncertainty principle of Heisenberg. You see these themes in the text.

The cat in the cafe in the train station, "the magical animal." Its presence in the text serves to underline the unreality of the situation of Dahlmann, that he is no longer part of the world ("this contact was illusory") and as a subtle reminder of Schrödinger's cat.

A quantum system can be a combination of states that are distinguishable: for example the system of a radioactive atom can be in a mixed state of pure intact and pure decayed,
for example: | atom> = (0.87) | intact> + (0.71 + i 0.71) (0.5) | decayed>
with complex amplitudes whose magnitudes are the probabilities of finding the atom intact or decayed atom when we do an experiment. (In the above case when we make the experiment on an identical set of atoms on the average 75% will intact and 25% will have decayed.)
However, an animal, a macroscopic system, can only be alive or dead, we are disturbed about the state of cat as a complex combination of live and dead states, for example, what would our representation of the cat state as:
 | Cat> = (0.87) | alive> + (0.71 + i 0.71) (0.5) | dead> mean?
Normally we do not have to take issue with this since we can not put a cat in such a mixed state.

The trick is to couple the macroscopic state of the cat with the quantum state of a system. In the Schrödinger gedankenexperiment, we put a cat inside a closed box with a fissible atom and a radioactivity detector which opens a bottle of poison gas when it detects the splitting of the atom, which yields the coupling of corresponding states of the atom and the cat.
When we start the experiment the atom is in a pure state of not having fissioned. Based on the dynamics of the nucleus, it immediately begins to evolve into a mixed state of pure intact and pure decayed over time, and the amplitude of the decayed state increases to 1 with an exponential decay. The cat begins alive and in a live state. After a while, both the atom and the cat will be in states similar to those above.

Analogously, after being injected in the hospital, to us Dahlmann is a mixed state of living or dead / dreaming feverishly. Our doubts about Dahlmann's state evolve towards certainty of his death. But at an intermediate point, is he alive or dead?

The separation between observer and observed: Dahlmann feels "like they were separated by glass." If there are two beings, either can be the observer and the other the observed. The cat may be there to test the state of Dahlmann. As meta-observers, we do not know if the cat has felt the caresses of Dahlmann, and we continue with questions about the state of Dahlmann.

The effect of experiment: In classical mechanics, if we know the dynamics of a system, the observations after an experiment to measure, for example, the position and velocity of a thrown ball, allow us to know both the past and the future state of the system. In quantum mechanics, to the comtrary, unless we know the previous state the experiment only allows us to know the future state and generally only probabilistically predict the outcome of a future experiment. (Using Bayesian analysis on an ensemble one may deduce something of the previous state.) In contrast, in The South, in the hospital, "a masked man stuck him with a needle." We knew the prior state Dahlmann - wounded and sick. But for readers, the injection causes the start of the uncertainties, the bifurcation of the state between dead and alive. Furthermore, the dynamics of the story cause more and more separation between the two directions and more uncertainty.

Uncertainty: There is uncertainty about the state of Dahlmann until the end of the story, but I don't see that is shaped according to the Heisenberg principle.

Probabilities: We can argue, and the students did so very much, the chances of this dead or alive Dahlmann during the second part of the story. But what distinguishes quantum mechanics is not classical stochasticity and the probability distribution of the state - such as the classical mechanics we have in the statistics - rather the quantum state is a distribution of complex amplitudes, whose absolute value is the probability distribution, and interference between the amplitudes leads to the more dramatic effects of quantum mechanics (eg Young's experiment with ultra-low intensities of light).

I remind you also that Borges, like physicists, is very fond of symmetries. Borges and reality like slight anachronisms, and Borges anticipates that the issue of possible violation of causality in quantum mechanics: the Einstein-Podolsky-Rosen paradox and corresponding gedankenexperiment were described only in the 1950s.

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