Assuming we're going by Schrodinger's equation and the standard wave function of psi and delta x.
What would happen if a wave function collapsed?
Hi Soheibben,
This article seems to be quite good, check it out: http://en.wikipedia.org/wiki/Wave_function_collapse
Best,
Alex
There's obviously something seriously wrong with the widespead idea that "measurement" is what causes the collapse of the wavefunction. A measurement process must be only a very special case of collapse, because in most of the universe there is nobody measuring anything!
I can imagine a wave function/state vector evolving in time according to the Schrödinger equation. This is like classical physics - the uncertainties of QM must come from elsewhere. So I imagine that, now and then, at various random times, the wave function is changed in a random way, re-adjusting the spectra of probabilities of the various "observables" that the wave function is carrying. That is the 'collapse'. The deterministic evolution given by the Schrödinger equation then continues until another random re-adjustment takes place.
Please tell me if you can see anything wrong with this interpretation.
It seems to me that this scenario is consistent with what we know about quantum mechanics. I can imagine a computer simulation, in which we have an algorithm for solving the Schrödinger equation from initial conditions, linked to a random number generator for deciding when a 'collapse' happens, and for deciding the new initial conditions.
The problem now is that I can further imagine that the random number generator is actually a pseudo-random number generator (which is what computers actually use when randomness is needed). A pseudo-random number generator is an algorithm. It is a deterministic system. Could it be, then, that the uncertainty - the inherent probabilistic nature of reality - that QM has revealed - is only an illusion because the mechanism underlying wave-function collapse is inaccessible to observation?
(I'm not necessarily advocating this. I'm asking if anyone can see a flaw...)
Ah... yes, I see. So, I was wrong to let the collapse happen at random times - though in some circumstances (decay of a radioactive atom for example) that does seem to be what is happening. In other situations, collapse happens because, as you reminded me, the system (the wave function) interacts with something external to itself - as when an observable is measured, or in the double slit experiment when the radiation encounters the screen and is converted to a "particle". Nevertheless, between collapses, it is accepted that the Schrödinger equation determines the evolution, as in a classical theory - the wave function doesn't "stay collapsed". I'm still left with an intuitive feeling that my "thought experiment" could be refined and elaborated to eliminate its faults. And that disturbs me because it looks dangerously close the "hidden variables" idea, which, so far as I know, has been debunked.
"Your suggestion might have something to do with "martingales". If you figure out what they are and if it is so, tell me, please!"
ok (-: (Can't promise anything, though...)
So: the wavefunction "collapses" by interacting with something outside the system. But then don't the system and the "something outside itself" (eg an electron and a "measuring apparatus") form a single system? (That's a rhetorical question.)
Is a camera an "observer", or does the "collapse" only happen when a "person" looks at the image? (That's another rhetorical question...)
" I think I can safely say that nobody understands quantum mechanics." - Feynman
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