Tuesday, 20 December 2011

The Problem with a Theory of Everything

There is a quest in physics to produce a theory of everything, a theory that unifies quantum mechanics and general relativity. Put another way, this is a search for a theory that unifies quantum and classical physics. It is possible that there is a flaw in the current approach taken by those endeavouring to find this theory.

I've got it into my head that it would be beautiful and devilishly simple if the quantum world produced the classical world through a process of emergence. This may seem to be almost inconsequentially obvious, but let us take this thought a little further.

The state, at some given point in the future, of a system produced through emergent behaviour can be exceedingly hard to predict. With enough components some systems simply become impossible to predict. Often the only way to obtain the state at the required point in time is to compute each step of the system until the desired point in time is reached.

So let's assume that it is true that quantum behaviour produces classical behaviour through a process of emergence. Given that this system is exceedingly complex, it may be impossible to predict the state of a classical system when provided complete information about the quantum start state. It's worse than this though, we know from Heisenberg's uncertainty principle that we cannot have complete information about the state of a quantum system. Without complete knowledge of the start state, it must therefore surely be impossible to predict any future state with 100% accuracy. Let us assume that it is indeed impossible. This implies that it would also be impossible to take the stochastic principles of quantum mechanics to form a coherent theory that can provide us with the classical determinism that is emerges from the quantum level. In other words, it would be impossible to unify quantum physics with classical physics to produce a theory of everything.

It seems to me that if our two assumptions really do hold true, a theory of everything really is impossible. Indeed we find that despite the attempts of many great minds, such a theory has not yet emerged. The problem could be sheer difficulty, but perhaps the problem with a theory of everything is that there isn't one.

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