What really is a Wave Function?

[Varon]

I think all the confusion and arguments of what is measurement in quantum mechanics can be boiled down to what really is a wave function. My head is spinning for a week thinking all about it and the following organize my thought about it. Correct me if I'm wrong and where I'm wrong in the categorization of the differences between the meaning of wave function.

1. Does the wave function represent the properties of the system? (Copenhagen)
2. Is a wave function only a tool to calculate probabilities and nothing more? (Statistical Interp)
3. Does wave function represent the system itself? (Objective Collapse)
4. Is a wave function a reservoir of the system/objects itself (Many Worlds Interpretation)
5. Is a wave function only an informational configuation space with a new force pushing the real object? (Bohmian Mechanics)
6. what else? (pls. add more)

Is the above categorization accurate? Pls. correct it if any part wrong. I want to understand the distinctions of the differences.

Instead asking people here whether position properties exist in principle before measurements, I think it is more accurate to ask them which of the above they believe.

For now the most popular is Copenhagen and Statistical Interpretation as it comprise orthodox QM. So let's focus on it. Can't experiments be done to distinguish whether the wave function is only a tool to calculate probabilities or whether wave function represent the properties of the object (here position property doesn't exist before measurement)?

Bohr, Heisenberg, Born, Wheeler believe that the wave function represent the properties of the system itself and measurement involve observers to collapse it.

While Einstein, Schroedinger believe it is just tool to calculate probabilities.

In this forum, Neumaeir is of the latter group. While I think Fra is of the former. Tom.stoer is agnostic or doesn't know.

Now I guess DrChinese who believes the object exists between measurement believes the wave function is just a tool to calculate probabilities and nothing more? But if he believes the wave function represent the properties of the system, then between measurement, it is just a ray in Hilbert Space, it has not yet collapsed to any Eigenvectors. So how can position properties even exist while the ray is not yet collapsed? (DrChinese?? Pls. elaborate).

How about you, what do you think is a wave function?

Very important. Is it correct to assume that if the wave function really represent the properties of the system. Properties like position, momentum don't exist in principle between measurements because the system is a ray in Hilbert space and not yet collapsed?

Speaking of Hilbert Space. For those who believe the wave function is just a calculation tool, then the Hilbert space is nothing more than information table. But for those who believe the wave function represent the properties of the object, then the Hilbert Space is more than probability space, the ray is the object itself! (right?)

In this message. I'm not looking for answers of what is the right interpretation. Because I know we don't know. I just want to understand the distinctions amonst them and whether I understand it right the different ideas of different people of the wave function and the distinctions. Specifically I want to know whether in the interpretation where the wave function represent the properties of the object (Bohr Copenhagen). Property like position doesn't exist in between measurement because it is just a ray in Hilbert space and not yet collapsed. Right?

 

[Varon]

I wrote this because I read the following in Quantum Enigma:

"Even students completing a course in quantum mechanics, when asked what the wavefunction tells, often incorrectly respond that it gives the probability of where the object is. The text we teach from emphasizes the correct point by quoting Pascual Jordan, one of the founders of quantum theory: "Observations not only disturb what is to be measured, they produce it."

I think if your professor is like Neumaier who holds a hybrid point of Copenhagen + Statistical interpretation. He would not tell you that observations produce the position as well in addition to just show where the object it, isn't it.

Anyway. I wonder if there is a wave function interpretation where the particle intrinsic properties like mass, charge is part of the wave function. Here the wave function directly represent the entire object, I wonder if Many Worlds is like this. (?)

 

[Varon]

Isn't it that Mass and charge is always present and definite. Don't we have experiments where mass detectors were in the double slit. Then we can know the location of the mass hence the position of the particle!

Also any experiment has weight the double slit setup? If before measurement, the box weight less, then we know even mass vanish along with position in between measurements. Well?

 

[Fra]

I know observer is very important in your model. In fact, I think you are a follower of the Existential Interpretation by Zurek isn't it where observing is like information transfer?

Zureks said something nice that I like: "what the observer KNOWS, is indistinguishabel from what hte observer IS"

So some of what I said relate to Zurek, but not the same.

where observing is like information transfer?

There is an important distinction. It's sort of like that, but there is no external (observer independent) DESCRIPTION of this information transfer.

The transfer only looks like an interaction, seen from a second observer.

This is also RELATED initialy to Rovelli's thinking.
Se "relational quantum mechanics"
http://arxiv.org/abs/quant-ph/9609002

At least the beginning(!) is good reading!

But IMHO, Rovelli doesn't finish what he started, as he tries to be both radical and conservative at the same time (ie he doesn't wnat to change QM; just interpret it).

/Fredrik

 

[Fra]

1. Does the wave function represent the properties of the system?

I think the wave function of S represents the state of the observing system O encoding expectations of S.

So the wavefunction is not intrinsic to the system, it's more intrinsic to the observers description of the system (an it's current state as emergent from a history of interactions with S).

Unitary evolution (in between measurements) is IMO the self-evolution of the observers information of the system. Ie, information about states and motions, implies an expected evolution. When in equilibrium with the environment, this expectation "mirrors" the actualy evolution of the system.

Observations just "correct" the expectations, and wavefunction. What is an sort of quasi-objective description of the the SYSTEM would rather be the equivalence class of all possible wave functions of all fellow observers in it's environment. But this would be non-local.

/Fredrik

 

[Varon]

Zureks said something nice that I like: "what the observer KNOWS, is indistinguishabel from what hte observer IS"

So some of what I said relate to Zurek, but not the same.


There is an important distinction. It's sort of like that, but there is no external (observer independent) DESCRIPTION of this information transfer.

The transfer only looks like an interaction, seen from a second observer.

This is also RELATED initialy to Rovelli's thinking.
Se "relational quantum mechanics"
http://arxiv.org/abs/quant-ph/9609002

At least the beginning(!) is good reading!

But IMHO, Rovelli doesn't finish what he started, as he tries to be both radical and conservative at the same time (ie he doesn't wnat to change QM; just interpret it).

/Fredrik

How does your view differ to Zurek? Pls. mention the differences. That way I can understand Zurek's more clearly because even after weeks of studying it. I'm not sure of what he is saying. Anyway. Let's analyze a part:

http://arxiv.org/ftp/quant-ph/papers/0306/0306072.pdf

"The overarching open question of the interpretation of quantum physics—the “meaning of the wave function”—appears to be in part answered by these recent developments. Two alternatives are usually listed as the only conceivable answers. The possibility that the state vector is purely epistemological (that is, solely a record of the observer’s knowledge)
is often associated with the Copenhagen Interpretation (Bohr 1928). The trouble with this view is that there is no unified description of the Universe as a whole: The classical domain of the Universe is a necessary prerequisite, so both classical and quantum theory are necessary and
the border between them is, at best, ill-defined. The alternative is to regard the state vector
as an ontological entity—as a solid description of the state of the Universe akin to the classical states. But in this case (favored by the supporters of Everett’s Many Worlds interpretation), everything consistent with the universal state vector needs to be regarded as
equally “real.”

The view that seems to be emerging from the theory of decoherence is in some sense somewhere in between these two extremes. Quantum state vectors can be real, but only when the superposition principle—a cornerstone of quantum behavior— is “turned off” by einselection. Yet einselection is caused by the transfer information about selected observables.
Hence, the ontological features of the state vectors—objective existence of the einselected states—is acquired through the epistemological “information transfer.”

~~~~~~~~~~~~~~~~~~~~~~~``

Fra. Do you agree everything with Zurek about Einselection and the details above? Pls. comment on it. I'm sure you understood the concept of Einselection. If not, try to read the pdf above and others. He has views very similar to yours and I want to know the differences between your view and him, or whether you got the original views from him and improve/alter on it. Also pls. tell me where you got all your ideas so I can research directly the original references. Zurek and company just continue where Bohr left off in the measurement problem that is put under the rug by standard quantum mechanic or QM instrumentalists who just obey "Shut Up and Calculate".

When Zurek mentions about information transfer. Is he talking of literal transfer of information from the quantum state to the observer. But he said it's epistemological. What kind of information medium is he talking about that is epistemological and not even has ontology? Radio wave has ontological reality. What kind of information transfer is epistemological?