Understanding the Wavefunction: Interpreting its Role in Quantum Mechanics

[madness]

Do you think the wavefunction is something which represents our knowledge of a system, or is it something physical? In the former case, could the same system be given a different wavefunction for different observers, depending on their knowledge of the system? From what I have learned of QM, it seems to me that the whole theory is based around what information we have about a system. However, if the wavefunction can be different for different observers, then Wigner's friend type paradoxes could occur which I find confusing.

 

[Fra]

You'll get different opinons, here is my highly personal view of your interpretational question.

Do you think the wavefunction is something which represents our knowledge of a system, or is it something physical?

I'd say both. I don't see the contradiction - I think of it as "physical information", as opposed to information existing only in some mathematical universe or external context.

IMO information/knowledge needs a physical basis, ie. a physical observer to encode it. (If "observers" disturbs you, or gives you creepy associations, instead just think of a "matter system" encoding the information - which an observer after all is, this has nothing to do with the human brain IMO)

In the former case, could the same system be given a different wavefunction for different observers, depending on their knowledge of the system?

Yes, but to even make sense of the important point is that a communication between the two observers must be defined so that their different information can be communicated, otherwise the notion of "different wavefunctions for different observers" is not something that makes a difference. I think generally a disagreement implies that a physical interactions/forces may exists between the observers. Classification of interactions, might thus amount to classification of disagreements. The strenght of the interactions might be rated as degrees of disagreement as per some yet to find information divergence measure.

A simple example is different relativistic(special or general) observers, that do see different things. However in standard formalism their is a relation between what they see, defined by the transformations that transforms one observers into the other.

Thus one may find an observer invariant form of the information, that is invariant with respect to the transformations that generates all possible observers, and thus observer independent.

But the real problem is to infer *information about those transformations* also by means of interactions. This introduces a complex self-reference. OR you could just settle with defining these things as part of a fixed background context - this is the standard procedure.

/Fredrik

 

[madness]

In that case would the wavefunction collapse for one observer when the other tells him the result of the measurement? Seems strange to me. And since the collapse causes irreversible changes to the system, it seems that there should be paradoxes associated with this point of view.

 

[Dmitry67]

madness,
check other interpretations
and especially this table:
http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics#Comparison

 

[Fra]

In that case would the wavefunction collapse for one observer when the other tells him the result of the measurement? Seems strange to me. And since the collapse causes irreversible changes to the system, it seems that there should be paradoxes associated with this point of view.

Apparent paradoxes I'd say probably for many cases. Sure this is my interpretation and part of a personal reconstruction of the formalism but to throw out a generalisation I think a lot of the paradoxes you might have in mind, would in my view be interpreted as forces, serving to rectify and annihilate the inconsistency - because the context will allow you to infere the "contraductions" are IMO not fixed. Instead the apparent contradictions implies a selective pressure to destruct the inconsistent context.

But that's a different discussion, you might see the other twisted threads in BTSM where I tried to convey the general idea.

But this view of mine is sure not one of the more common interpretations to beware.

Of course there is no replacement for making your own judgement.

/Fredrik

 

[alexepascual]

Do you think the wavefunction is something which represents our knowledge of a system, or is it something physical? .

The answer to this depends on the particular "interpretation of quantum mechanics"
But with respect to knowledge of the system, there are two types of "lack of knowledge" one has to do with a system that is in a particular state but you just don't know it (mixed state) and the other implies that the system is in a superposition of the different possibilities (pure state). This distinction is shown mathematically by different forms of the "density matrix".
It is disputed if the wave function is real or not. But when you make a quantum measurement and collapse the wave function, you are choosing (randonly) between a set of possible outcomes and converting one into "reality". I would say that even though there is debate on wether the wave function is a element of reality or not, the outcome of a measurement is considered real.

In the former case, could the same system be given a different wavefunction for different observers, depending on their knowledge of the system?.

Once the first observer makes a measurement, the wave function that the second observer studies will have changed. His knowledge is the same, but his lack of knowledge includes some ignorance that is not due to the inherent uncertaintly of the system but just to not having looked. Observers don't need to be human beings. They can be macroscopic detectors that record the results of measurement. The environment that surrounds the quantum system under consideration also serves as a measurement device because it serves to keep a record of the particular outcomes of wavefunction collapse. When observers compare notes, these always agree. (We know this form day-to-day experience in the macroscopic world and we need the theory to reflect that fact).

From what I have learned of QM, it seems to me that the whole theory is based around what information we have about a system. However, if the wavefunction can be different for different observers, then Wigner's friend type paradoxes could occur which I find confusing.

I think I partially answered to this question above. Observer's don't need to be human beings, although some people will dispute this. Still there are paradoxes. Paradoxes are made sense of differently by different interpretations of quantum mechanics.
Oh! by the way, paradoxes are supposed to be confussing. That's the fun part!
I also think it is a good idea to take a look at the table Dmitry suggested.