The standard model is a tyrant

#3
Its rules for calculating seemed infallible, and while they could quickly become intractable, I believed that with infinite computing one could, in theory, compute the probability of any event, including whether I’d have eggs for breakfast next Tuesday.
The interesting thing, is that most of this is incredibly disconnected from ordinary physics and chemistry.

The world of ordinary physics and chemistry underwent its own moment of tyranny with the Schrodinger equation. I am sure that this equation is a vast simplification of the corresponding equation in the standard model, and yet it too runs out of steam because of computational limits. It is interesting to see how this happens. A system of one particle can be represented by a wave function of three space coordinates and one time coordinate - ψ(x,y,z,t) - already a fairly daunting mathematical object. However, a system of two particles requires a function of seven coordinates - ψ(x1,y1,z1,x2,y2,z2,t)!

Solving the Schrodinger equation consists of solving a second order partial differential equation with derivatives with respect to all those arguments.

Thus each extra particle extends the complexity of the wave function enormously. A very few systems can be solved exactly - notably the hydrogen atom (not molecule), and something as 'complicated' as an isolated hydrogen molecule (H2) can only be solved approximately. The approximations get rapidly worse as the system gets bigger, so that although a human could be represented by a Schrodinger equation, that could never even be written down, never mind solved!. Indeed solving the equation for a large molecule, or a single bacterium is also utterly out of reach.

So even with the vast simplification from standard model to Schrodinger's equation, predicting what someone will choose to do, is utterly impossible in practice.

The sense in which a human (say) is determined by his or her own Schrodinger equation is entirely theoretical, but one has to ask if it is real at all - are we an evolving solution of a very complicated equation? I used to assume we are - which made me a materialist - but now I don't.

David
 
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