Sunday, 22 July 2012

Practical Physics And The Robbins-Henry Feline Transport System

Henry, Official Blog Cat, just walked out of his enclosed litter tray and into the living room.  This took The Julia somewhat by surprise, mainly because she'd locked him outside five minutes before.

Is this, perhaps, because cats are sneaky little blighters and can worm in through windows and sneak into their litter trays when you're not looking?

Or is it because I've invented a cat teleporter?  It's quite simple.  You know the whole Schrödinger's Cat thing?

The idea is that the cat can be both alive and dead at the same time.  Well that's not quite the whole story.  The cat's medical status is a bit vague anyway.  Schrödinger was no vet*, you see, he never really specified what he meant by dead.  Lack of mew?  Cardiovascular failure?  Brain death? Advanced decomposition?

What he actually meant was the chain of events that leads to a dead cat.   Or a live one for that matter.  He was objecting to the idea of an atom being in two places by trying a bit of reductio ad absurdum.  If an atom can be in two places at once, he said, that means that there's two different universes that flow out of it.

Imagine, he said, that there's a particularly important atom, one that we're going to look at.  We know that if we look at the atom in one minute's time then there's a 50% chance the atom will have decayed while we waited:

Once we start the clock running we have two possible results:  in one future chain of events the atom doesn't decay and nothing happens.  In the other future chain of events the atom decays, the Geiger counter goes "click", the relay opens, the hammer falls, the bottle smashes, the poison spills and the cat dies.

Schrödinger's argument was that between the clock starting and us looking to see if the cat was alive or dead, both chains of events were valid according to the maths, that there was nothing in quantum theory which prevented two different realities, or chains of events, from both being perfectly possible as far as we know.  He believed the universe had to follow a single chain of events, and one only, and the maths should show this.

He was wrong, as most of the pioneers of quantum theory were at some point, in fact there's still a good possibility that they all got together at what's called the Solvay Conference and decided to be wrong together.  They all met in Denmark, Schrödinger and Planck and Einstein, Eddington and Bohr and Born, and put together the "real world" description of what's going on in the maths of quantum theory.  It's called the Copenhagen Interpretation, and there's still a fair chance it's wrong.

They decided that particles exist as wave functions, wibbly-wobbly "stuff", to steal a phrase.  When any of these wave functions interacted with anything else, they "collapsed" and became  a single, measurable particle.

So where does Henry come in with his litter tray and teleportation ability?

Well go back to the chains of events which led to Schrödinger's cat being alive or dead - it doesn't have to involve boxes and poison and hammers.  Just because you have a Nobel Prize in physics it doesn't give you a monopoly on inventing strange cat-based scenarios, any of us are allowed to do it.

So the Robbins-Henry Theorem suggests that there are two, equally likely chains of events which lead to  Henry (Official Blog Cat) either being in his litter tray and being outside.  All you have to do to transport the cat from outside the house to inside the litter tray is to have one single, perfectly random interaction with a single atom go the other way.  OK, you might need to go tweak the universe in precisely the right time and place to set off a realistic chain of events, but it's possible in theory.  And if you don't observe the cat from the moment you prod that particular atom to the moment you look at the litter tray (or outside) and find the cat, the Copenhagen Interpretation suggests it could be, and therefore is, in both states.  There is a single wave function which is called Henry, and until I look outside or at the litter tray the Henry Wave Function is in both.  When I look it collapses instantly into one of the two Henrys, and either way he's bloody pleased with himself, what with mastering teleportation and all.

But this is the argument from the point of view of Schrödinger's beliefs and the Copenhagen Interpretation.  There's another way of looking at it.

Hugh Everett III suggested that the wibbly-wobbly stuff of a particle was, in fact, an ever expanding cloud of every possible particle, essentially lots of "might be" particles all superimposed on each other.  Many particles, which when we look at the wibbly-wobbly cloud, becomes a single particle.  What happened to all the others?  Everett's suggestion is that they're still around somewhere.  Not here, obviously, that would make the entire universe one blazing ball of energy appearing from nowhere**, but somewhere else.  And given that every particle in the universe appears to behave like this, it's going on a lot, with every tick of time.

The only explanation that springs to mind is the idea of a multiverse.  Many universes, all existing at once, with every possible chain of events played out.

So we open Everett's box and have a look at Everett's cat, and what do we see?  Either a dead cat, or a live cat, big deal.  The only extra information we've received is which particular universe we're in a minute after we started the experiment.  The explanation from Everett's point of view is obvious to the point of being mundane.  It's not some wacky feline paradox that will be mentioned 77 years later on The Big Bang Theory, it's just kind of obvious.

Personally, I reckon there's a hint there.

So how did Henry's (OBC) teleportation display work according to Everett?  Well, it's entirely possible that when you don't have enough information to decide which universe you're in (cat inside or out) that you can legitimately be said to be in both.  Until something happens which makes you change your mind, both possibilities are true.  You're in one of two universes, the cat is in one of two universes, and until you meet neither of you know where either of you are.

This brings about a particularly mind-blowing suggestion from the edge of physics:

You're in many universes at once, which are all exactly the same except for the location of the cat.  In all of them identical copies of you are wondering exactly the same thing, "where's the bloody cat?".  These different versions, which are identical in every way until they find the cat, exist in the same state an atom does, they're all part of a big wibbly-wobbly "You".

So, with that in mind, let me pose a question.  When you wonder where the cat is, and imagine he may be outside, or in his litter tray, or under the couch, or hiding behind the curtains, then what is more likely?  Is your brain creating multiple simulations of reality, in seconds, which all conform to likely cat-locations, or are the various different versions which make up the wibbly-wobbly-you simply comparing notes?

I've no idea why it's always cats with physics by the way, and I'm sorry.  I'm a dog person, but the behavioural  psychologists wouldn't have me.

* He should have taken lessons from Richard Feynman, who once decided to keep his brain ticking over outside physics by learning biology.  He went down to the University library and asked for a map of a cat.

** That does sound spookily familiar though...