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Alright peoples, introductory quantum mechanics question. Our book states that a measurement of position is loosely defined as something which collapses the wave function to a delta function, something that (at least, for the informal mathematical manipulation) preserves the state of immediate successive measurements; if you measure the position of the *same* particle two times very, very close to each other, you should get near-similar results.

Our professor claims that this is simply not a good view; he says that it's better to view a measurement as a distinct action that does not so much alter the wave function, per se, as alters our view of probability from that point on.

Does anyone have a different (or reconciliatory) view, or is able to explain why this distinction would be important?

It's hard to reconcile the mathematics with the physical reality of QM.

Mathematically speaking, you observe a quantum system, you 'operate' on it and it spits out a measurement and jumps/collapses to a state so that if anyone else comes along and performs the same operation, they'll get the same value spat out at them.

If you 'operate' on the system using a momentum operator/observe the momentum of the system, the system spits out a momentum value and jumps to an eigenstate. You know the momentum and so does anyone else who performs the 'momentum operation'. But if someone comes along and 'operates' on the eigenstate using a position operator, it will spit out a position value but will jump to another state so you're no longure sure about what the momentum is.



What really makes it head scratching though is, because the wave collapses to an eigenstate, everyone else who comes along and makes the same measurement shortly afterwards will get the same result. The probability function is not an individual perspective of the wavefunction. The only way you could have any hope of reconciling the maths with a physical analogue is by defining an observation as an interaction that can be described by Thermodynamics. But even that's not perfect.

Or if you're a sci-fi nut you could believe in the many world interpretation which has the handy feature of never collapsing the wavefunction.

Or you could get involved with Quantum electrodynamics and forget the whole thing.

The problem is (as you probably well know) what constitutes a measurement?

QED has it's own interpretation problems. Feynamn path integrals, for example, don't seem to have any physical analogue that sits well.

Personally, I think the interpretations are best left for pub arguments and that we should just crack out our observables and run with it from there.

Ha. It's got more to do with the instrumentalist position I take. There's no pressing reason to suggest that our current mathematical description if anything more than an useful model; thus, why bother with all the ontology? Strictly speaking, I see no reason why we ought to believe that things like fermion fields actually exist in the universe as physical objects, why we cannot simply treat them as concepts which aid in our ability to make accurate predictions about the universe.

What about in quantum computing? I haven't done real research into this, but according to Penrose they've taken up the question of interpretation because it's actually affecting their attempts at qbit computers.

But in either case, the definition of a measurement comes into play. For an instrumentalist, it allows for more subtle nuances in technique that might not have otherwise been seen as possible (or, in this case, likely to turn up any result); beyond that, it becomes part of a more cohesive and complete theory.

I guess what I'm saying is that some of the questions that can be deemed more "philosophical" - such as this one - are of real importance to both theorists and experimentalists. In my view, at least, they should have the same definitions for what things *are*, with different interpretations of what they *mean*. I think that accurately defining a measurement would be important to both areas.