# Interpretation of a wave function collapse

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1. Jun 13, 2015

### Happiness

Suppose the system is in a state of superposition of two determinate states (of an observable) and has equal probability of getting each determinate state, when observed. An observation forces the collapse of the wave function to either one of the determinate state (say, states A and B).

Since the observation is the cause of the collapse, can I say that if I know all the information about the observation/measurement, then I will be able to deduce which state (A or B) the wave function will collapse to?

For example, if I toss a fair coin, I will get heads half the time and tails half the time. If I know all the information (the forces on every particle in the system, their mass, temperature, etc. ) in a particular toss, then will I be able to deduce the result of the toss with certainty?

2. Jun 14, 2015

### bhobba

First it is an axiom of QM that all it predicts is probabilities - it called the Born Rule. Interestingly it can be derived from other assumptions via the important Gleason's Theorem (see post 137):

That's just by the by out of interest - don't get too worried if its a bit over your head.

Another issue is the formalism doest actually have wave-function collapse - it's part of interpretations - some have it, some don't.

Some interpretations are deterministic (meaning if you knew all the information you can predict the outcome) others are not.

The thing is QM adds a twist to this - it turns out, in interpretations that are deterministic, its not possible to know, in principle, the initial conditions so you cant predict the future. In those interpretations probabilities arise due to an inherent lack of knowledge.

Classically, in practice you cant predict the outcome of flipping a coin because, in practice, you cant know the initial conditions with enough accuracy to do it. It principle you can and could predict it - its just a matter of practicalities.

That's the key difference between classical and quantum - al least as far as determinism goes.

Of course we have interpretations that are not deterministic - but there is no way to tell the difference from interpretations that are, at least no-one has figured out how to. Choosing an interpretation is to a large extent a matter of taste. In fact its mostly a discussion about the nature of probability:
http://math.ucr.edu/home/baez/bayes.html

Those who favour a deterministic interpretation of QM believe probabilities are not fundamental - but that's their view - all sorts of others exist.

Thanks
Bill