Science Feature: Lost In Hilbert Space

Posted Monday, January 9th, 2012 10:00 am GMT -4 by

In an SF story I was once writing I needed to get the hero out of his closed prison cell. In the old physics, he could simply have blown a hole in the wall with some explosives – but of course, the guards never let him have any.

In physics terms, the scientist is trapped by inter-molecular forces in the cell walls. An explosion simply dumps energy which disrupts these bonds – the fragments (and our hero) burst free.

But how to make things work with the new physics?

My first thought was new fields. So I started to look at the inflation field of the early universe , or some of the new stuff in supersymmetry. This is still something I continue to research but I’ve come to believe they don’t really help. The coupling between new fields and the potential barrier would still be via energy transfer so it’s just another explosion – I’ve no idea what a controlled local inflation field would do but it doesn’t seem very survivable.

A more promising approach is via the many-world interpretation of quantum mechanics. For example, in chapter 15 of his book The Labyrinth of Time, Michael Lockwood describes a variant quantum theory model involving an actuality dimension, i.e. space-time-actuality, although this is probably just a fancy interpretation of Hilbert Space. So we have to imagine that alongside our hapless scientist there are an infinite number of his copies adjacent in actuality. ‘Farther away’ there are worlds where the prison was never built and it’s just prairie, or whatever, (the metric in actuality is related to probability).

What the story needs is a spherical volume enclosing our scientist, to put him in a quantum superposition across all the variants of actuality, and then adjust the amplitudes to zero for those worlds where the hero is presently incarcerated. Then his only copies will be free ones, and he can walk away across the prairie. His next step will be to reverse the process and dial his probabilities back to his original world: reminds me of the Infinite Improbability Drive.

How can we do such ‘amplitude engineering’? Well, in a sense we do it already whenever we set up situations where quantum interference can occur (like the two slit experiment), but on this scale we really need some new science. I think the answer lies in paradox. If we set up a paradoxical situation, then we will find the quantum amplitude (and therefore probability) of that outcome is zero. The best source of paradoxes is time travel so what we need is a ‘world-line mirror’ which the prisoner can set up to reflect his world-line into the past.

Since this would cause paradoxes, what would actually happen is that his world-line will diffract into alternative worlds in actuality where the mirror doesn’t exist. And a world-line mirror – a kind of time machine – requires space-time engineering: in other words quantum gravity. So maybe this is a fancy way for him to do some of that really difficult macroscopic quantum tunneling – with non-vanishing probability for a change.

So now we have it. Our scientist makes a discovery in grand unified theory, and his colleagues on the outside build him a controllable world-line mirror hidden in a smuggled MP3 player. Twiddle some knobs, walk a few hundred meters, twiddle some more and he’s free! Of course, it’s possible that time-reflection will actually work, he’ll simply turn into antimatter and then annihilate with himself!