Thursday, June 11, 2015

Is quantum suicide allowed?

So here is my dilemma. I'm still reading "The Hollow Man" by Dan Simmons to Clare. The story starts with hero Jeremy losing his beloved wife Gail to the agonies of cancer. The hero and his wife are telepathic. (We are prepared thus far to suspend disbelief).

In one thread of the story, Jeremy falls apart in grief and descends into a hobo-existence (this is set in America) - there is a purposeful analogy to Dante. In the other thread, we get flashbacks to Jeremy's research as a mathematician, full of gobbledegook about personality/consciousness as hologram, the Schrödinger equation and populist quantum theory. It's the data dump from hell, riddled with spurious guff. This I don't read to Clare.

In the end, you sort of know that Jeremy and Gail are going to get reunited, but how can this be? The answer is a variant of quantum suicide. My question: do I dare read this to Clare; does it pass the suspension of disbelief test?

I can get away with the idea of a quantum superposition. Most people know that, for example, a particle's position can't be definitely localised - we say its wave function is spread out. This is equivalent to saying that it's in a superposition of location states. It's basic quantum mechanics, experimentally observed and not the least bit speculative.

We can also have discrete rather than continuous superpositions: the best known is Schrödinger's famous cat. This is also legitimate science though the fine details remain unresolved.

Now to quantum suicide (Wikipedia article). It's like you replace the cat and the radiation-triggered cyanide is replaced by a gun. You decide to shoot yourself. Now, there is some probability that the gun will misfire due to some unlikely outcome of events down at the quantum level. So the time-evolution of you with the gun evolves into a superposition like this:

|You and gun not fired>  =>  a|you-alive and gun-misfired> + b|you-dead and gun-fired>

a and b are coefficients expressing the relative amplitudes of these two states, with |b| expected to be enormously larger than |a| for a reasonably reliable gun.

In the standard interpretation of quantum mechanics, this simply means that you'll most likely end up dead: end of story. The superposition quantum state 'collapses' to the
 |you-dead and gun-fired>
state with probability |b|2 (or maybe you got lucky with probability |a|2) once somebody notices (these days we invoke decoherence).

But in the many-worlds interpretation there are no collapses. All states of a superposition are realised in separate versions of the universe. Since you have no consciousness when you're dead, your continuing sense of self will continue to exist in the universe with this state:
|you-alive and gun-misfired>

Quite a lot of physicists believe in the many-worlds interpretation: it seems the only way to make objective sense of quantum mechanics and to remove the subjective role of a 'collapse-inducing' observer. But would Clare, my proxy for 'the person in the street', believe it for the purposes of a plot denouement?

I don't think so. And that's why Dan Simmons novel just doesn't work and I continue with the challenging work of real-time editing!