King's Cross - the Heisenstation

I've been working on a little theory. Non-British readers might be interested in this as a piece of cultural information, particularly if they're planning to be in London for the 2012 Olympics. Be warned - there will be math! You don't need to understand it to get my drift, though. Skip any bits that look too tough, it won't matter.

Regular rail travellers between East Anglia and London will have noticed that at King's Cross station, platform assignments for the outbound trains can be a little...random. Not only that, the assignments are often made with only about five minutes to go before the scheduled departure time.

Now, it's easy to put this down to simple incompetence. After all, on the European continent, timetables routinely show both the time and - crucially - platform of each departure. And these aren't just terminals, most are through stations dealing with a massive volume of traffic, and they can be handling trains from neighbouring countries too. Compared to that, dealing with a much smaller number of arrivals at a single-country^*1 terminus ought to be easy, yes?

Well, it probably is. So why can't King's Cross get it right? I believe the answer lies not in hopelessly inept staff and incompetent rail networks but in quantum physics.

In brief: King's Cross is an Heisenstation. Or Heisenbahnhof. Or both.

If you have any familiarity at all with popular quantum physics, you'll have heard of Shrödinger's Cat. If you haven't there's a slightly silly explanation here. It's a(n almost) practical illustration of Werner Heisenberg's^*2 Copenhagen Interpretation of quantum indeterminacy. (Let's leave it as a thought experiment. It might get you in trouble with the animal rights activists if you tried it out for yourself.)

In our Heisenbergian imaginings, King's Cross exists in a superposition of states for any given train planned to depart, each state corresponding to a possible platform. If all platforms were available, the state equation would be:

|ψ> = _p=0∑¹¹ |θ_p>

Keen readers will note that this appears to start from platform 0, not platform 1. Yes, that's right. King's Cross (KGX) acquired a "platform zero" a few years ago, to the delight of mathematicians and programmers everywhere.

However, King's Cross is a working station, and moreover it's English, so you can almost guarantee that some platforms will be unavailable. Let's define the vector of excluded states (platforms) as:

|χ> = _p=0∑¹¹ (|θ_p> if unavailable(p))

So our final superposition is:

|ψ> = (_p=0∑¹¹ |θ_p>) - |χ>

(Bonus assignment: do this using state probabilities instead.)

So much for the math. Now some more concrete stuff. (There's too much concrete around KGX already, but we'll let that aside.)

Normally, humans are considered to be quantum observers, whose observation during the progress of an experiment collapses the probability wave function and settles it to a final value. In other words, the presence of people waiting for the platform indicator to show the assigned platform for a given train ought to settle the platform assignment immediately. This leads us to a startling assertion:

Passengers do not count in, and have no relevance to, the operation of King's Cross

A little contemplation, combined with bitter experience, will quickly confirm this prediction by practical demonstration.

Which leads us to the question: how does that wave function collapse? How do we ever achieve a platform assigment?

It is my contention that the qualified observer must in fact be a person outside the system, someone for whom the platform assignment is a matter of no direct consequence, someone who, in effect, doesn't care.

That would be the station staff.

Extra credit assignment

For extra credit, prove or disprove the statement: at King's Cross, it is possible to know with absolute certainty, at any given instant prior to departure, either a train's platform number, or its actual departure time, but not both.

Next week

In next week's tutorial, we attempt to calculate the overall directed Brownian motion effect on the disabled, slow or elderly of the "platform rush", as more agile and able-bodied commuters jostle past them, competing to secure their seats on the train following the last-minute platform announcement.

We will also explore the likelihood that any given member of those less-able passengers will manage to find a seat once the fast-moving passengers have been seated, taking into account the probability of the late-scheduled train having already departed before they could get to it.

^(*1) The United Kingdom is a country, damn it! I know because every bloody web form in the world says so.
^(*2) Yes, I know, there were others too. Let's not get Borhing about it.

The East London Tech City: what will happen after the 2012 Olympics?

There was some interesting editorial on the "East London Tech City" on page 50 of Tuesday 9th November's London Evening Standard. (You can read it at standard.co.uk for up to 28 days: select e-Edition; free registration required.)

There appears to be an expectation that, despite the apparent technology bias suggested by the name, the majority of businesses resident there will be focused upon solutions for the financial sector, rather than pure technology per se.

It's going to be a fascinating thing to watch. Normally, I'd suppose that that would have to be the overwhelming business sector, since the costs of renting relatively central London property for a company would be way beyond the pockets of any but the firms most benefiting from rich City clients. However, I can imagine a certain amount of desperation on behalf of the land owners to get units occupied however they can, as soon as the athletes move out. It may change the rules of the game, at least for a while.

Could East London be the next M4 Corridor? It's not impossible. But the difficulty of commuting into the area from affordable suburbs might just restrict its potential. In the end, it might just be the haunt for City-related businesses anyway - after all, even in a property slump, few others' employees can afford Docklands warehouse-conversion flats.