Friday, 24 April 2015

Schrodinger's cat in literature

Schrödinger wrote: A cat is penned up in a steel chamber, along with the following device ...: in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

I suspect that allusions in literature to Schrödinger's cat aren't always understood correctly. Why is that situation any different to these?

  • A soccer referee tosses a coin before a match, covers it, asks a captain to call heads or tails. Until the coin's revealed, nobody knows what it is.
  • A prisoner's locked in a dungeon and the key thrown away. Sooner or later they'll die, but we won't know when.

At the sub-atomic level, strange things happen. We can predict probabilities of where a particle is likely to be with great accuracy, but we don't know where it actually is until we look. So far, this sounds like the coin situation - 50% chance of heads, 50% chance of tails. The difference is that whereas in the coin situation the coin's state is fixed before it's revealed, in the subatomic case the possible states simultaneously exist until the moment of observation, at which point the particle suddenly decides where it will be.

This may sound odd, but we're prepared to accept it for sub-atomic particles because experiments support it. Time for some terminology

  • "superposition" - the simultaneous multiple states
  • "interference" - the effect of the states on each other (i.e. proof that the states exist). "an individual particle, such as a photon (light particles) can cross its own trajectory and interfere with the direction of its path" (from http://whatis.techtarget.com/definition/quantum-interference)
  • "collapsing the probability function" - decision time
  • "The Copenhagen interpretation" - the idea that a system stops being a superposition of states and becomes a specific state when an observation takes place.

Suppose that instead of one particle there are several - a human-sized bundle of them in a room. Suppose that this bundle has the same indeterminacy as a single particle. We might be able to calculate probabilities of the person's position (50% likely to be in bed, say, and 50% looking out of the window). To us outside the room the person IS 50% in bed AND 50% at the window, but now that we have a sentient, self-conscious being instead of a sub-atomic particle we have difficulty putting ourselves in the situation of the person, who must surely be in only one place. However, being in one place would break one of the most successful theories ever.

Schrödinger's paradox has 2 extra features added to the scenario that I've sketched -

  • The stakes are raised. The indeterminacy concerns not position but life
  • Rather than saying that the cat behaves like a particle, its life depends directly on the behaviour of a particle. A machine translates probability from one scale to another.

Life and self-awareness are emergent qualities - ones that are hard to deduce, calculate or describe using the underlying concepts. The characters in these thought experiments may be self-consciousness, but what does that mean? At what precise moment is the cat dead? Maybe it could be revived?

The worldview of the people outside the box is hard to sustain (how can the cat in the box be both alive and dead?), but trying to imagine the worldview of the cat (or better still, a person) inside the box is harder still. One theoretical way out is multiverses - the idea that the universe splits into 2 with one copy having a live being and the other copy a dead one. But when does it split? Whenever an observation is made?

Translate the scenario from involving particles to involving thoughts, and the paradoxes disappear. Suppose someone's asked "Will you marry me?" They might have anticipated the question, knowing how they'd reply. That corresponds to the coin tossing situation. Alternatively, they may be uncertain, hoping they won't be asked. But the questioner insists on an immediate answer (they've just been offered a job abroad, maybe). Somehow, from the mess of conflicting thoughts, a single answer must be given. That corresponds more to the cat situation - the question forces a collapse of the probability function.

The idea's been used by several SF writers and some less illustrious poets, often for comic effect. The idea of large-scale superposition is I think the key feature of the concept. Examples used by writers may include

  • Replacing Death Row by cells like the cat's
  • Having more than one entity in the cell - perhaps all existing self-conscious entities except one - God.

Frayn's "Copenhagen" is considered a worthy artistic treatment of such issues.

The title of Heidi Williamson's poem "Schrodinger's pregnancy test" promises more superposition than the poem explicitly delivers. It begins with "For her, theoretical physics/ is a bird soaring next to a plane" ending with "All it takes/ is a broad mauve line in a window// for it to land, bang/ on her heart". Interestingly, a search online for "Schrodinger's pregnancy test" comes up with entries like that of naming the time between where the author describes what it's like to await the test results - "What makes this experience unique, compared to situations of waiting in unknown like waiting for results of a job application, is that the box of indeterminancy is located within your own body. That box that contains one truth and the experience of living with two, that is placed in the intimate space of your self.".

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