Why does wave-function collapse occur?

questionpost

As I understand it, the term "collapse" is a little over-exaggerated, but why is it that we measure things as points and not waves even though particles exist as waves?

bhobba

First, as Feynman points out, only particles exist, no detector has detected waves - what always appears is particles.

Secondly the issue of wave function collapse is interpretation dependent. It only exists if you think a quantum state has an external existence like say an electric field. You can simply view it as a device to calculate probabilities. You will find a discussion of this in Chapter 9 of Ballentine - Quantum Mechanics. Bottom line here is the assumption it has that kind of existence leads to all sorts of issues so its best not to interpret it that way. What is thought of as waves is simply that states sometimes have wave like solutions - but if you think of a state as a calculational device only then the so called wave-particle duality is rather moot.

Look at it this way. Suppose you have a possibly biased dice then you would describe it by 6 positive numbers that add up to one - that would be its state. It doesn't have an existence 'out there' - it simply is a way of describing the likely occurrence of a certain face of the dice lying up. The same with a quantum state. When you observe the outcome of throwing the dice the state does not collapse - you simply make an observation. Looked at this way Shrodenger Cat, and other contrivances, is rather trivial - it has no more a mystery than tossing a dice.

For my personal view of QM check out:
http://arxiv.org/pdf/quant-ph/0101012v4.pdf

Basically in a stochastic theory you have two choices - a theory where you have continuous transformations of so called pure states - and ones where that is not allowed. The former (basically) leads to QM - the latter standard probability theory.

This is not to say QM does not have deep mysteries (eg non local behavior and what properties it has between observations), but by viewing the theory this way they can be kept under control without being bogged down with foundational issues.

Thanks
Bill

juanrga

Sometimes the motion of particles resembles that of a wave. However, particles do not exist as waves, but as... particles.

Essentially you are asking why particles behave as particles.

salvestrom

Ugh. There seems to be no consensus on this subject.

questionpost

If particles actually existed as particles and did not oscillate like waves, shouldn't they lose all their energy by traveling real distance over time and accelerating?

bhobba

Come again - can't follow that one. In QM you can actually derive the dynamics from Galilean invariance - you can see the details in Chapter 3 of Ballentine that I gave before. In the classical limit they behave exactly like Newtonian mechanics says they should and do not accelerate by themselves.

As far as interpretation goes - those that posted there is no consensus are correct - the view I gave is basically the shut up and calculate view - but other interpretations have a different take.

Thanks
Bill

questionpost

So in otherwords, your saying that because we measure or calculate particles as particles and not waves, that they exist only as particles and now waves?

bhobba

I am saying they are only ever detected as particles - never as waves so the most reasonable thing to do is model them as particles. But they obey the rules of QM which is described by a quantum state that has, in some circumstances, wave-like solutions. However whether a state has a real existence is open to question - I view it purely as a device for calculating probabilities.

Thanks
Bill

questionpost

And I assume you already know about the double-slit experiment (just to be sure)? Because I do not know how electrons could me measured in those locations they are at in that experiment without the electrons themselves following discrete wave mechanics.
Unless by "solutions" to you mean somehow working backwards from results?
Because I don't think this is just a basic pop-science mis-understanding, but at the same time, we don't actually see particles themselves as waves even though they seem to have to travel as waves to end up in the locations they do.

bhobba

The problem here is you are ascribing a classical view to a quantum experiment. The state has wavelike properties and that is why the particles display an interference effect typical of waves when measured by the screen in the double slit experiment - which only ever shows particles. What the particle does when it is not measured is anyone's guess. Feynman describes it as in some sense particles go through both slits. My view is you can't say anything other than the state, which may or may not have an external existence, displays an interference effect typical of waves.

Thanks
Bill

StevieTNZ

It has wave-like properties. The quantum system is probably neither a particle or wave, thought of in the classical sense.

bhobba

It is most certainly agreed what atomic sized particles are - they are quantum objects. What can't be agreed on is how to interpret QM.

Your second statement is correct - it is not a wave nor classical particle - but a quantum particle which is something entirely different and definitely weird - although with some acquaintance you get used to it and get an idea of why it must be like that - check out:
http://arxiv.org/pdf/quant-ph/0111068v1.pdf

'The usual formulation of quantum theory is very obscure employing complex Hilbert spaces, Hermitean operators and so on. While many of us, as professional quantum theorists, have become very familiar with the theory, we should not mistake this familiarity for a sense that the formulation is physically reasonable. Quantum theory, when stripped of all its incidental structure, is simply a new type of probability theory. Its predecessor, classical probability theory, is very intuitive. It can be developed almost by pure thought alone employing only some very basic intuitions about the nature of the physical world. This prompts the question of whether quantum theory could have been developed in a similar way. Put another way, could a nineteenth century physicist have developed quantum theory without any particular reference to experimental data? In a recent paper I have shown that the basic structure of quantum theory and countably infinite dimensional Hilbert spaces follows from a set of five reasonable axioms. Four of these axioms are obviously consistent with both classical probability theory and with quantum theory. The remaining axiom states that there exists a continuous reversible transformation between any two pure states. This axiom rules out classical probability theory and gives us quantum theory. The key word in this axiom is the word “continuous”. If it is dropped then we get classical probability theory instead.'

Basically QM is necessary in a stochastic theory if you want to model continuous transformations - for the exact meaning of that see the link above.

Thanks
Bill

rodsika

Remember a molecule composing of 430 atoms called buckyball can still interfere with itself in the double slit. These buckyballs obviously stay as particles in between (as it's hard to imagine the 430 atoms with their protons and neutrons just dissolving into waves in between). But what propel them into certain regions to form inteference patterns using your reasoning above?

salvestrom

@bhobba: I'd very much like to hear how you feel about multiverse concepts. Your descriptions here are very straightforward, "down to earth". I'd also like to see if I have a grip on your view by restating it:

From the ground up. There is field. Fluctuations occur in the field. Excitations are particles. When unviewed particles are doing something they are treated as waves - the wave function being the probability spread (is that misleading of me?) It may be possible they are actually moving like waves. When a particle/wave is interacted with (including measurement/observation) it has a definite particle form.

One more thing: what is the field? I understand the mathematical concept of scalar and vector fields - numbers assigned to points in spacetime - but what does the field record in this situation? Energy fluctuations? Or is this not the idea?

questionpost

Wow I didn't know they called it a Bucky-Ball outside of Wisconsin

jambaugh

One way to understand it is to rephrase the loaded terminology: Wave functions don't collapse, they get updated. That corresponds to CI where the wave function is understood as a symbolic representation of possible quantum behavior and not as a direct representation of the physical reality of the quantum.

In that understanding updating the wave function given a change of knowledge is the same as updating say the probability distribution of where to find a lost sailboat given an observation that it was not in sector X.

The update is qualitatively the same as with a classical probability distribution though the way of representing probabilities of observations is distinct.

salvestrom

It is named after an inventor called Buckminster Fuller, from Massachusets, for its resembelance to a geodesic dome he invented. The ball part comes from its similarity to the association football ball. So says wikipedia, bless them.