Quantum Mechanics / measurement postulate

[JustinLevy]

I am really having trouble understanding some parts of quantum mechanics. Maybe I am thinking about it wrong, or maybe these issues are resolved in more advanced formulations... but I am learning non relativistic quantum mechanics, and the postulates seem contradictory to me.


I really dislike the measurement postulate of quantum mechanics for the following reasons:
- everything in quantum mechanics is deterministic except for that
- it is added ad hoc, and puts the measurement device outside of the quantum mechanics formulism
- it says the wavefunction collapses to an eigenvector of the operator corresponding to the observable being measured ... but does not describe HOW it collapses (does it collapse all at once / simultaneously, or the collapse starts at one point and \"ripples outward\", etc?)


So, can someone please help me understand this feature of quantum mechanics?

And, has anyone tried to formulate QM without this postulate (ie describe the measuring device quantum mechanically and show that somehow the equivalent to the measurement postulate happens as a natural consquence of the other postulates?). If so, I would be interested in reading up on this. Can anyone point me to some good textbooks (or publications) that show how the measurement postulate can be removed? The textbook we are using (Griffiths) is not helping me much here.

Thank you very much.

 

[dextercioby]

And, has anyone tried to formulate QM without this postulate (ie describe the measuring device quantum mechanically and show that somehow the equivalent to the measurement postulate happens as a natural consquence of the other postulates?)

Well, not really, it's one of QM's most debated aspect. However, this postulate due to von Neumann is valid, else it wouldn't be taught in schools all over the world.

Daniel.

P.S. It can't be removed, once one accepts the existence of entagled/mixed states. (also von Neumann is responsible for this thing)

 

[Hurkyl]

A quick summary of some alternatives are:

(1) Collapse is real. Deal with it.
(2) There's a secret field that is controlling what's happening.
(3) There is no collapse. You're just in a superposition of states, each of which looks like a collapse took place.
(4) There is no collapse. You just experience a particular basis state among the many that you could have.
(5) There are many aphysical degrees of freedom in the wavefunction picture. Collapse only affects things in an aphysical way.

 

[JustinLevy]

However, this postulate due to von Neumann is valid, else it wouldn\'t be taught in schools all over the world.

To make sure there is no confusion, I agree that the measurement postulate is valid: in that it is part of QM, and the predictions of QM agree with experiment.

But the measurement postulate requires us to treat measurement equipment classically (or at least not with Schrodinger\'s equations, etc). But what makes this collection of nuclei and electrons different? If the theory is correct and complete, we should be able to describe an entire closed system (measuring devices and all) using the same physics.

As you mentioned yourself, this is an often debated subject. I have asked around and many professors (and even a nobel laureate) feel similarly, but didn\'t feel comfortable telling me their specific point of view (I got the impression it was more that they still haven\'t settled on one and consider it a sticky issue).

P.S. It can\'t be removed, once one accepts the existence of entagled/mixed states. (also von Neumann is responsible for this thing)

Some people mentioned that decoherence due to interactions with the environment destroys entanglement. One even went so far as to suggest that the definition of \"macroscopic\" may be \"when an objects interaction with the environment prevents coherence\". And a measuring device, being macroscopic, that might just be how it works out.

I couldn\'t get any specifics, or publication lists.
Can anyone comment on whether this view is common? Where can I read up on it?

 

[JustinLevy]

Okay, if no one is going to answer that, hopefully someone can at least answer this:
When the wavefunction collapses due to a measurement, does it collapse simultaneously everywhere? And simultaneously according to who?

If not, how is the collapse \"propagated\" through the wavefunction?

The postulate does not specify the specifics of the collapse, so it is difficult to understand specifically how the wavefunction changes after a measurement.

 

[eep]

I would say the wavefunction collapses simultaneously. I don't know what you mean by "collapsing everywhere". Immidiately after a measurement, the wavefunction is such that it is 0 everywhere except at the point which corresponds to the observable which was measured, where it equals one. If one makes the same measurement *IMMEDIATELY* after the first measurement, you will get the same result. After a measurement, the wavefunction evolves according to Schrodinger's equation.

 

[JustinLevy]

I would say the wavefunction collapses simultaneously.

Simultaneously according to who?
Your definition makes wavefunction collapse not lorentz invarient. So I do not believe that is the correct answer.

Can you think of another answer?
Or does anyone else know?

 

[eep]

I think it is the correct answer because it's one of the postulates of quantum mechanics.

 

[JustinLevy]

I think it is the correct answer because it is one of the postulates of quantum mechanics.

Do you understand why that can not be the answer?

According to special relativity, global simultaneity is not agreed on between frames. Your definition therefore violates special relativity, unless you specify which frame the collapse is simultaneous in and specify what makes this frame unique.

Or are you saying: yes, quantum mechanics can not be formulated relativistically?

I do not believe that is the answer.

 

[eep]

Isn't that one of the biggest problems in physics today? That quantum mechanics and relativity are not compatible? I've only studied non-relativistic quantum mechanics so I'm unsure as to what, if any, changes there are in terms of the collapse of the wavefunction. However, how can you perform a measurement on something if you're not in the same frame? The wavefunction obviously collapses in the frame of the measuring device, and that collapse is instantaneous. My knowledge of relativity is rather limited, however. Maybe someone else can better answer.

 

[octol]

Yes while quantum mechanics can be formulated in a relativistic way (QFT), the mechanics behind the wave function collapse, the so called "measurement problem" IS a major unsolved problem in theoretical physics. This is of course closely connected to the problem of how to interpret QM.

Niels Bohr brainwashed a whole generation of physicists into believing that the problem (of the interpretation of quantum theory) had been solved fifty years ago. (Murray Gell-Mann, Noble Prize acceptance speech, 1976)

Two candidates for a solution to this problem that I like; the idea of nonlinear evolution causing a state vector collapse, or the suggestion of Penrose that the curvature of spacetime (gravity) is responsible.

A solid explanation with experimental evidence to back it up would really be a huge breakthrough.

 

[eep]

Can you give some more explanation of these two ideas?

 

[George Jones]

Can you give some more explanation of these two ideas?

I wrote a bit about Penrose's ideas in https://www.physicsforums.com/showpost.php?p=910951&postcount=4".

Regards,
George

 

[JustinLevy]

A solid explanation with experimental evidence to back it up would really be a huge breakthrough.

Aww.. oh well. I was hoping this was already solved and I just needed to read up.

Can you expand a bit on the non-linear evolution idea?
Are you saying that there are no stationary states?


Also, have you heard much about the decoherence \'solution\' that some students have told me about? (a few posts back I mention the rough ideas they told me)


This has gotten quite a bit off of coursework now. Maybe it should be moved to the Quantum mechanics forums (hopefully many there could offer more references to literature).

 

[octol]

A good place to start is

http://plato.stanford.edu/entries/qm-collapse/

and an interesting article is

http://arxiv.org/pdf/quant-ph/0003083

I'm no expert in the field, but the way I understand it is that there are small nonlinearities present, either hidden or added explicitly to the theory, such that at small masses and without external influences the system still behaves in the standard linear way. But when we have large masses or external influences (such as measuring equipment), the system becomes unstable causing a state vector collapse. One nice thing about this is that might be testable, since a nonzero collapse time is predicted. Also nonlinear evolution might be able to explain nonlocal phenomena as well since this is a characteristic trait of nonlinear systems.

 

[JustinLevy]

Thank you very much!
I have not read through them yet. I will do so right now :)

Also nonlinear evolution might be able to explain nonlocal phenomena as well since this is a characteristic trait of nonlinear systems.

I am not sure what you are referring to here, as the only thing I know of that is non-local in quantum mechanics is the measurement postulate. And also, nonlinear evolution does not mean there is nonlocality. If the authors are presenting this as an alternative to the measurement postulate, they are doing so to remove nonlocality from quantum mechanics.

I am probably just misunderstanding what you meant here. Sorry if there is any confusion.