QM

[109]

 
красивое объяснение, почему амплитуды обязаны быть комплексными, чтобы соответствовать физической реальности:

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Suppose we require that, for every linear transformation U that we can apply to a state, there must be another transformation V such that V² = U. This is basically a continuity assumption: we're saying that, if it makes sense to apply an operation for one second, then it ought to make sense to apply that same operation for only half a second.

Can we get that with only real amplitudes? Well, consider the following linear transformation:

This transformation is just a mirror reversal of the plane. That is, it takes a two-dimensional Flatland creature and flips it over like a pancake, sending its heart to the other side of its two-dimensional body. But how do you apply half of a mirror reversal without leaving the plane? You can't! If you want to flip a pancake by a continuous motion, then you need to go into ... dum dum dum ... THE THIRD DIMENSION.

More generally, if you want to flip over an N-dimensional object by a continuous motion, then you need to go into the (N+1)^st dimension.

But what if you want every linear transformation to have a square root in the same number of dimensions? Well, in that case, you have to allow complex numbers.

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http://www.scottaaronson.com/democritus/lec9.html

Comments

[ati.livejournal.com]

отличное объяснение.