Wave function is a combination of eigenfunction?

[wasi-uz-zaman]

hi, i read in quantum mechanics wave function is a combination of eigenfunctions and according to Orthodox interpretation measurement causes the wave function to collapse into one of the eigenfunction of the quantity being measured. Is this explanation still valid?

 

[tom.stoer]

This interpretation as "orthodox interpretation" is still valid. But there are other, competing interpretations like "many-worlds". No interpretation is right or wrong. They are all in agreement with physics (that's why these are competing intpretations, not competing theories)

 

[vanhees71]

The collapse is by no means unproblematic. In my opinion it's not a necessary assumption for the use of quantum theory to real physical situations and thus one should avoid it. It's also for sure not even true. Often the measured object, like a photon, is even destroyed in the measuring process.Then for sure after such a measurement the state of the system is not in an eigenstate of the measured observable's representing operator.

 

[tom.stoer]

Often the measured object, like a photon, is even destroyed in the measuring process.Then for sure after such a measurement the state of the system is not in an eigenstate of the measured observable's representing operator.

Where's the problem? When the photon is destroyed the state is in the zero-photon subspace.

The problem with your argument is the following: you can construct interpretations of the state vector which are in conflict with some other interpretations or philosophical considerations regarding "reality" etc.; but afaik you cannot prove or falsify (mathematically or experimentally) that the collapse interpretation is physically wrong.

Therefore I agree with

The collapse is by no means unproblematic. In my opinion it's not a necessary assumption for the use of quantum theory to real physical situations and thus one should avoid it.

but I do not agree with

It's also for sure not even true.

 

[vanhees71]

But what about the good old EPR paradoxon? The socalled "realistic" interpretations of the state, i.e., of the wave function or the state vector, representing a pure state, (or perhaps even the general case of a statistical opertor?) as a physical entity leads to the trouble with Einstein causality as detailed in EPR's famous paper.

So I think it's more save to follow the minimal statistical interpretation (or ensemble interpretation), according to which the state describes the probabilistic features of physically real systems (say an electron, just to avoid the additional quibbles with massless particles like photons), which can only be assessed by preparing ensembles of systems in the state to be investigated.

Formally, then not the abstract entities of the theory (vectors/statistical operators in Hilbert space representing the states and self-adjoint operators representing the observables) but equivalence classes of definite preparation procedures represent the "real system".

 

[tom.stoer]

But what about the good old EPR paradoxon? The socalled "realistic" interpretations of the state, i.e., of the wave function or the state vector, representing a pure state, (or perhaps even the general case of a statistical opertor?) as a physical entity leads to the trouble with Einstein causality as detailed in EPR's famous paper.

So I think it's more save to follow the minimal statistical interpretation (or ensemble interpretation), according to which the state describes the probabilistic features of physically real systems (say an electron, just to avoid the additional quibbles with massless particles like photons), which can only be assessed by preparing ensembles of systems in the state to be investigated.

Formally, then not the abstract entities of the theory (vectors/statistical operators in Hilbert space representing the states and self-adjoint operators representing the observables) but equivalence classes of definite preparation procedures represent the "real system".

I could agree to everything what you are saying regarding interpretations, reality, their problems etc., but that's not the point. I think I was clear in my last post: you can neither disprove (mathematicall) nor falsify (experimentally) the collapse interpretation. Therefore I do not agree with

It's also for sure not even true.

 

[vanhees71]

But, when I measure, e.g., a photon's polarization by the observation that it is absorbed by a polarization foil, I do not have a photon in the corresponding polarization. This is a very simple example for the fact that not all measurements lead to a projection into the corresponding eigenstate.

There are some measurement procedures, known as ideal von Neumann measurements, that allow the filtering into a given eigenstate of the measured quantity, e.g., the Stern-Gerlach experiment, where you split an unpolarized beam of (neutral) particles in spatially well separated angular-momentum eigenstates (through entanglement of position and angular momentum!). Filtering out one beam then leads to a pure angular-momentum eigenstate. In this sense, sometimes you have a kind of collapse. Such procedures I'd rather call a preparation than a measurement.

 

[tom.stoer]

if the photon is absorbed then there is no photon anymore and therefore it makes no sense to say that it has some polarization; it collapsed to a "no photon eigenstate"

but if the photon passes the polarization filter it has exactly its polarization - which does not mean that you have prepared it, as you say; but later you can check the polarization n times applying n filters - and the photon will pass all n filters; therefore it is safe to say that the photon collapsed into a corresponding "polarization eigenstate"

 

[vanhees71]

Why don't you call that a preparation?

 

[tom.stoer]

It doesn't matter how I call it; I don't see the conflict between the "collaps interpretation" and any experiment; I think nobody does

Some claim that "Copenhagen" is out, has problems, ballast, is unphysical, or that MWI means "taking QM literally", that MWI has less ontological ballast (others claim that MWI has more ontological ballast), ...

But I do not see any experiment that proves "Copenhagen" or "collaps" to be wrong; therefore I do not agree to your sentence that "It's also for sure not even true." If by "it" you mean the interpretation than these are only words. But if you mean physics than you are not right, otherwise you would have to show us an experiment which falsifies "Copenhagen"