Question about collapsing wave functions

[VoidChimera]

So, from my understanding, some particles like electrons exist as a particle and a wave/probability field. What I was wondering, was that when the wave function collapses, is its location determined on the actual location of the particle, which we just can't measure and so represent it as a 'probability field', or does the particle actually exist as a wave/field which 'outputs' a particle at a semi-random location within the field when it collapses?

If it's the latter, is there anything capable of influencing the particles location, or is it completely random and isolated?

(P.S. My only formal education in this field is Honors Chem last year and was rather cursory, the rest has been from other possibly unreliable sources, as such what I'm saying could be absolutely wrong and senseless. If it is feel free to let me know and i'll delete this thread or take other appropriate action)

 

[bhobba]

So, from my understanding, some particles like electrons exist as a particle and a wave/probability field.

Although often espoused in beginning texts the wave particle duality is basically a crock of the proverbial. It part of the semi historical view many textbooks take, but since 1927 when Dirac came up with his transformation theory it was consigned to the dustbin.

See the FAQ section:
https://www.physicsforums.com/showthread.php?t=511178

Its exactly the same for electrons.

Here is the real essence of QM from lectures given at MIT:
http://www.scottaaronson.com/democritus/lec9.html

What I was wondering, was that when the wave function collapses, is its location determined on the actual location of the particle, which we just can't measure and so represent it as a 'probability field', or does the particle actually exist as a wave/field which 'outputs' a particle at a semi-random location within the field when it collapses?

First there is nothing in the formalism of QM about collapse. Again its another semi truth beginning texts espouse but it's not really true. Some interpretations have collapse, some don't. And in most observations the thing being observed is destroyed so even in interpretations that have collapse its the exception rather that the rule only applying to so called filtering observations.

QM is a theory about the statistical outcomes of observations - what its doing, being, existing etc etc when not observed the theory is silent about. The thing called the state is simply a mathematical aid in calculating those statistics.

If you are REALLY interested in QM check out the following video's:
http://theoreticalminimum.com/

These is also an associated textbook:
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

However it will involve some calculus, which, hopefully you have at least a smattering of.

Without at least that background its hard to delve too deeply into this stuff - otherwise its basically a lot of hand-waving.

At the handwaving level I rather like the following:
https://www.amazon.com/dp/0473179768/?tag=pfamazon01-20

It's not actually about QM, but of a deeper theory called Quantum Field theory that QM is an approximation to. Strangely, this deeper theory at the beginner level, seems to avoid many of the pitfalls of other approaches such as wave particle duality, collapse etc.

Thanks
Bill

 

[atyy]

So, from my understanding, some particles like electrons exist as a particle and a wave/probability field. What I was wondering, was that when the wave function collapses, is its location determined on the actual location of the particle, which we just can't measure and so represent it as a 'probability field', or does the particle actually exist as a wave/field which 'outputs' a particle at a semi-random location within the field when it collapses?

In the Copenhagen interpretation, a collection of particles does "exist" as a wave before the measurement. This wave does not exist in the 3D space we see, but rather in a higher dimensional abstract space. The dimension of the abstract space is determined by the number of particles in the collection. This wave determines the probability distribution of the results of measurements that one makes. For example, if one measures the position of a particular particle, the resulting position values that one observes are distributed according to the wave in the abstract space. One can be agnostic about whether the particle really has a position before the measurement is made. It is ok to think that the wave only outputs positions when one makes a measurement. So the wave is not necessarily anything real, but just a method to correctly predict the probabilities of experimental results.

However, there is an interpretation called the de Broglie-Bohm interpretation in which each particle has a definite position before the measurement is made. The probabilistic outcomes are due to our inability to prepare the system in a particular configuration.

So the answer to your question (at least for position measurements) is that you can take your pick. The Copenhagen interpretation is more minimal and practical for calculating, but it raises some philosophical questions because the Copenhagen interpretation divides the universe into two: a macroscopic reality in which we live and make measurements, and a quantum part which is described by the wave in abstract space. In contrast, the de Broglie-Bohm interpretation solves that philosophical problem, but introduces additional variables, so is less practical to calclulate with.