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So, when wavefunction collapses, there is a spike occuring. Does this mean that there are parts with the continuous probability of 0? (For example, x position from -9 to -3 has probability of 0, while from -3 to 3, the probability of 100% (1) and so on)

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"collapse" is a bad term for probabilities, imo. There is a 2% probability that there will be an earthquake larger than 3 richer where I live. After an earthquake happens the probability it happened is 1. It does not mean during the quiet times that the place is rocked by any fraction of the probability. –  anna v Sep 15 '12 at 14:36
    
@annav I get this, but why is the wavefunction said to be peaked after the collapse? Is this like an electron occupying the size of an electron that we know of? –  Do Go Sep 15 '12 at 15:08
    
As far as I am concerned it is bad terminology. After the event happens the probability that it happened is 1. That is what the "collapse" says. In any case after the measurement the potentials are different the correlations are different and the wavefunction for the system, "particle and measurement" is a new solution of the equation of the system, in potential problem quantum mechanics, or a different Feynman diagram, in quantum field theoretical formalism, which last is the more correct view. If you find an ionisation trace at x+dx it says that the probability the particle passed is 1. –  anna v Sep 15 '12 at 15:53
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"Collapse" is a bad term for probabilities, imo.

An analogy: There is a 2% probability that there will be an earthquake larger than 4 richter per year where I live. After an earthquake happens the probability it happened is 1. It could be a spike in time t. It does not mean that during the quiet times the place is rocked by any fraction of the probability. After the event the probability "spikes" at 1. Note that this is a different probability distribution than the one before the event, which had a flat 2% all through.

In quantum mechanical probabilities, before a measurement is done, or an interaction that changes the system, happens, there exists a function called wave function which describes the probability of finding the particle at (x,y,z,t). This function is a solution of the specific boundary conditions and potentials of the situation.

After the event happens the probability that it happened is 1.This is a classical description of the system. That is what the "collapse" says. In any case after the measurement the potentials are different, the correlations are different and the wavefunction for the system, "particle and measurement" is a new solution of the equation of the system, which is also different, in potential problem quantum mechanics. Different Feynman diagrams will be involved to give the probabilities of finding the particle at (x,y,z,t), in quantum field theoretical formalism, which last is the more correct view.

The "spike" 1 in probabilities comes after the fact of the interaction, it is not predictive. The position in spacetime measured for the particle, (x,y,z,t) will of course obey the Heisenberg uncertainty principle. Thus if you measure the momentum px the space position has a dx.

In this picture, an antiproton, annihilates on a proton (which we cannot see because it is at rest):

antiproton annihilation

This is an event that had a probability to happen depending on the crossection of antiproton annihilation which obeys solutions of a quantum mechanical equation, i.e the system proton-antiproton has a wavefunction that gives the probability of the event happening. After it happens that wavefunction is no longer valid ( the "collapse" term) because as you see a number of new players with their variables enter the quantum mechanical problem and certainly a completely new solution is imperative to describe the system after the time of interaction. The "spike" with probability 1 does not correspond to a quantum mechanical state, i.e. a wavefunction ( a solution of a QM equation) but is an after the fact classical description of the system.

The quantum field theoretical framework allows us to calculate this (i.e. the probability for antiproton proton to annihilate into 8 pions), which would be impossible in a simple potential model, as a many body problem.

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