When I first encountered Douglas Adams’ great work, ‘The Hitchhiker’s Guide to the Galaxy’, I was particularly impressed by the Heart of Gold’s engine, the ‘Infinite Improbability Drive’, which exploited Heisenberg’s Uncertainty Principle. According to the Guide, the drive “passes through every conceivable point in every conceivable universe almost simultaneously,” meaning the traveler is “never sure where they’ll end up or even what species they’ll be when they get there,” and therefore it’s important to dress accordingly.
What a great idea! Why is NASA spending billions on underpowered chemical rockets when quantum theory offers us the stars? What on earth is stopping us?
Put the Heart of Gold starship to one side for a moment and consider a humble electron, stationary in deep space. Let’s suppose its position can be localized to a precision of one millimeter. How uncertain would its position be after, say, an hour?
You’re probably thinking of that electron as a tiny, lonely, charged point hanging out there in space, all by itself between the stars: but that isn’t what the math says. According to quantum theory that tiny electron is a highly localized wave, like that spike of water which shoots up after you drop a ball-bearing into a pond. What that spike is going to do is to spread out – after an hour, our electron-wave is a sphere one kilometer in diameter which would take you ten minutes to walk across.
The electron hasn’t become an enormous blob in space. The math is telling you that if you now check its location, the electron will be found somewhere within that one kilometer bubble (at a definite location of course). Note that this has nothing to do with it drifting on account of some initial velocity – the electron started out classically stationary; it’s a purely quantum phenomenon.
A kilometer in an hour doesn’t sound much: that isn’t going to take us to the stars. But perhaps the Heart of Gold can do better? As a starship, it’s obviously a bit heavier than an electron: let’s suppose it weighs in at 100 tons. And we could certainly fix its position better than a millimeter… Given the thermal vibration of its constituent particles, let’s suppose it could be localized to within the diameter of a hydrogen atom, one Angstrom Unit. (Heisenberg tells us that the tighter we fix the position, the faster the wave spreads out).
So how far could the Heart of Gold’s wave-function spread in, say, a year? We put the numbers in and the answer is… less than 1.6 x 10-22 meters, one ten-millionth of the diameter of a proton.
The final nail in the coffin of the Infinite Improbability Drive is a phenomenon known as decoherence, the bane of quantum computing. Due to interactions with the environment such as the Cosmic Microwave Background, the spherical wave for the Heart of Gold would collapse in 10-19 seconds. Forget about even that whole year for wave-spreading: our ‘starship’ is going absolutely nowhere.
I guess that’s why NASA are staying with their rockets.
