Having trouble understanding the wave function collapse.

[elfmotat]

What about the act of observation actually causes a particle to break the superpostion and "decide" what its state is? What property does the observer posses that changes the the way particles behaves?

 

[Dmitry67]

wavefunction collapse is a part of Copenhagen Interpretation.
There are many other interpretations where there is no such weird thing.

 

[elfmotat]

Thank you, i'll look into them. I just don't see how there could be some intrinsic property of a conscious observer that would cause particles to act differently - obviously because consciousness isn't some magical force, it's just the interaction of neurons which are made of the same matter as the stuff in question.

 

[Bob_for_short]

What about the act of observation actually causes a particle to break the superposition and "decide" what its state is? What property does the observer posses that changes the the way particles behaves?

An act of observation is always an interaction with a device. In QM world there are probabilities of this or that observation. The notion of probability implies (belongs to) many-many events. There is no wave function collapse as there is no probability collapse.

In other words, each particular measurement does not give a complete information about a quantum state but a series of measurements does. The wave function describes these sets, not a particular event.

 

[Pio2001]

What property does the observer posses that changes the the way particles behaves?

There is none. This is just an interpretation. A formalism that have been chosen to describe what happens.
What really happens, no one knows. We know some things about what happens, but the core of the process remains completely mysterious.

We know that the process seems to obey a "fundamental randomness". More precisely, any law that would govern that process would break special relativity (Bell's theorem applied to Aspect's experiment). Since nothing deterministic have been observed so far, the conclusion remains open : maybe there is no law, or maybe something happens that escapes special relativity.

 

[Dmitry67]

1 core of the process remains completely mysterious.

2 We know that the process seems to obey a "fundamental randomness".

1 no, check Quantum Decoherence
2 no, it is interpretation-dependent

 

[tickle_monste]

1 no, check Quantum Decoherence
2 no, it is interpretation-dependent

Intriguing. How do you mean that the fundamental randomness is interpretation-dependent?

 

[Fredrik]

I'll just quote myself again:

I still think of a measurement as an interaction that, through the process of decoherence, entangles the eigenstates of some operator with macroscopically distinguishable states of a system that for practical purposes can be considered classical. So we're not getting rid of decoherence either. I don't think decoherence has solved the "measurement problem", but it has given us the best definition we have of what a measurement is.

Isham had some very interesting comments about wavefunction collapse in his book. Suppose a silver atom prepared in the spin state |s>=|+>+|-> is sent through a Stern-Gerlach apparatus without any kind of detector to tell us where the atom has ended up. The interaction with the apparatus entangles the spin states with position eigenstates, so that the time evolution of the |position>|spin> state is

|center>|s> → |left>|+>+|right>|->

What Isham pointed out is that if we now put a measuring device (e.g. another Stern-Gerlach apparatus with a different orientation, and with particle detectors at the positions of its outgoing beams) in the position where the right "beam" comes out, we're going to have to take the state before the measurement to be |right>|->. We still haven't measured anything, but we have "collapsed" the wavefunction simply by putting the measuring device on the right. This illustrates the importance of distinguishing between state preparation and measurement, and that the "collapse" isn't a physical process at all (in this "interpretation"). It's just a selection of what to measure.

The book I'm talking about is "Lectures on quantum theory: mathematical and structural foundations" by Chris Isham. Also recommended is "Quantum mechanics: a modern development" by Leslie Ballentine.

 

[Dmitry67]

Check this: http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics#Comparison

As you see, there are several DETERMINISTIC interpretations.
So neither "randomness" nor "collapse" are the intristic properties of QM.

 

[Fredrik]

Dmitry, don't you think QM is hard enough even without confusing students with lots of different interpretations? Especially when many of those interpretations aren't even well-defined.

 

[kote]

Good point Fredrik. I'll take my shot...

What about the act of observation actually causes a particle to break the superpostion and "decide" what its state is? What property does the observer posses that changes the the way particles behaves?

Your question implies that there is such a thing as (separable) objective reality. It's important to remember that this assumption is being made, since the influential Copenhagen Interpretation, at least, disagrees. Having said that, given your assumption of realism, the wave function represents our best knowledge of reality, but nothing described by it is actually real on a basic level. Particles, as you think of them, are at best a macroscopic approximation of reality, and as such you should not expect descriptions in terms of particles to always be accurate. All that happens with the act of observation is we uncover more about the real situation that we are modeling, imperfectly, with the wave function.

Changing assumptions can drastically change the description of what happens, and the story I told is only conditionally true. For an alternate story using the Copenhagen Interpretation see https://www.physicsforums.com/showpost.php?p=2314204&postcount=2

 

[Dmitry67]

Dmitry, don't you think QM is hard enough even without confusing students with lots of different interpretations? Especially when many of those interpretations aren't even well-defined.

Good question.
I don't know if it is better for the students
But I don't like that CI is used in most of the popular books.

 

[Phrak]

Some--not all--interpretational baggage associated with quantum mechanics dignifies an observer with the role of 'collapsing a wave function'. The bare bones mathematical structure of quantum mechanics says nothing what-so-ever about cause and effect. Unfortunately only these probability amplitudes make contact with experiment, prompting no end of confusion over what parts of this mathematical structure should be associated with what we would desire to call physical reality.

This entire quantum mechanical business was a very bad idea from the beginning. We can only hope that sometime in the future this discord may vansih giving way to something more harmonious with our cognitive demands.

 

[Pio2001]

1 no, check Quantum Decoherence

Quantum decoherence does not address randomness. It explains why interferences between the different possible outcomes disappear, but it does not provide the slightest clue about why one outcome is observed when we perform an experiment. Strictly speaking, it predicts that all outcomes exist.

2 no, it is interpretation-dependent

That's why I said "seems". Quantum mechanics introduce a new concept : absolute randomness.
So far, we know that among these three concepts, absolute randomness, anti-realism, and non-locality, at least one is needed to account for what we observe.

 

[Dmitry67]

1 yes, that is why after Quantum Decoherence had been discovered (replacing old mysterious 'collapse') MWI appears the most natural solution. So I agree with you that Decoherence itself does not explain everything without MWI. But do you agree that MWI is deterministic, so there is no randomness?

2 Yes, I agree, it introduce it as an option. We need to make a sacrifice: we can chose to sacrifice realism, determinism, locality or introduce hidden variables. But at least 3 interpretations in a list I provided are deterministic, so it is not inevitable.

 

[Hurkyl]

but it does not provide the slightest clue about why one outcome is observed when we perform an experiment. Strictly speaking, it predicts that all outcomes exist.

Whether or not all outcomes happen has essentially nothing to do with whether one outcome is observed when we perform an experiment.

 

[Zarqon]

Hmm, what exactly is the main problem of the universe containing intrinsically random elements?

A quantum state in a superposition |0> + |1>, obviously gives a perfectly deterministic answer when measured in the (|0> + |1>), (|0> - |1>) basis. Only when measured in a "wrong" basis, like e.g. (|0>, |1>) does it give a random result. It doesn't feel so strange to me that asking the wrong question yields a weird answer. It's like asking a green spot whether it's black or white; you're bound to receive a random answer. (yes, this is very simplified, don't take it too far :P ).

My point is rather that randomness could simply be viewed as natures own built in safety-answer, for everyone asking the wrong questions. A deterministic universe on the other hand seem to suggest everything is predetermined, doesn't it? I'm trying to understand why exactly people find determinism more comforting than randomness?

 

[kote]

Hmm, what exactly is the main problem of the universe containing intrinsically random elements?

A quantum state in a superposition |0> + |1>, obviously gives a perfectly deterministic answer when measured in the (|0> + |1>), (|0> - |1>) basis. Only when measured in a "wrong" basis, like e.g. (|0>, |1>) does it give a random result. It doesn't feel so strange to me that asking the wrong question yields a weird answer. It's like asking a green spot whether it's black or white; you're bound to receive a random answer. (yes, this is very simplified, don't take it too far :P ).

My point is rather that randomness could simply be viewed as natures own built in safety-answer, for everyone asking the wrong questions. A deterministic universe on the other hand seem to suggest everything is predetermined, doesn't it? I'm trying to understand why exactly people find determinism more comforting than randomness?

It's only the wrong question if reality isn't located in relativistic space-time. Space-time implies that these questions can be asked. Also, determinism is causation. There's a cause for everything. There's a reason for everything. Randomness flies in the face of the laws of logic that we use to make sense of, well, anything.

 

[SergioPL]

Space-time is a deterministic mathematical frame, but this does not means that every interaction must be deterministic.

The quantum model makes the world very difficult to understand since every particle becomes a complicated wave function that it's only capable of giving undetermined results from reality but it's the only model that has been proved usefull to explain the world at very small sizes.

 

[Pio2001]

Whether or not all outcomes happen has essentially nothing to do with whether one outcome is observed when we perform an experiment.

That's right. The tricky thing is why we observe a given result instead of the others. No theory or interpretation yet deals with this experimental prediciton.

But do you agree that MWI is deterministic, so there is no randomness?

Not in its usual form. The above event, observable by a given observer, remains random in MWI.

But MWI may be extended with hidden variables in order to get a local determinist and realist version of QM. JesseM gives some hints about it in his message about the EPR experiment : https://www.physicsforums.com/showthread.php?t=206291#11

I found a paper that goes a bit further (Mark Rubin, 2001) : http://arxiv.org/abs/quant-ph/0103079
It was then published in Foundations of Physics Letters Vol. 14, No. 4, pp. 301-322, 2001.

Rubin finds that in order for MWI to be deterministic and local, we need "labels" and a kind of additional "initial-condition information" (last paragraph of page 14 in the Arxiv pdf). I came to the exact same conclusion as him, but reasonning in the Schrödinger representation of operators, instead of Heisenberg's. Then the labels and the initial condition information (which I find to be the wave vector that caused the world to split) are associated with the "worlds", which does not introduce any more "proliferation", as Rubin says, than the world proliferation itself. That solves the holistic problem of any particle having to carry forever the information about every past interaction it went through.
These additional data are exactly what ColorSpace was asking for in the discussion with JesseM : they are the information needed to properly match the copies of both observer.

I'm currently writing a paper about it. Since I'm no physicist, I'll submit it is the independent research section of the forum.

 

[Dmitry67]

Not in its usual form. The above event, observable by a given observer, remains random in MWI

I am afraid you're a victim of a very common misconception about MWI. People ask: ok, there are 2 outcomes, cat alive and cat dead, but why *I* see only dead one (or alive one)? For *me* it is random, right?

This is wrong. In MWI an observer is not a line, it is a tree. It 'splits' when being decoherenced with an outcome. So MWI predicts that in one branch one observer is asking "but why cat is dead?" and in another one "but why cat is alive?"

So you see, in MWI the situation is symmetric and deterministic. No randomness. Just an illusion of it.

 

[kote]

I am afraid you're a victim of a very common misconception about MWI. People ask: ok, there are 2 outcomes, cat alive and cat dead, but why *I* see only dead one (or alive one)? For *me* it is random, right?

Let's let P represent "The cat is dead." You're saying that I'm not allowed to ask, "is P true or false?"

Let's let x qualify the branch that I have an illusion of following. You're saying that I'm not allowed to ask, "is P(x) true or false?"

So, there's no such thing as truth?

 

[Dmitry67]

P is not a function of an event x. It is also a function of a branch.
P(x,b)
In branch 0 P(x,0)=0
In branch 1 p(x,1)=1
It is deterministic.

I can give you another example. begin from an empty string.
''
Then add 0 and 1 to each row in a list. You get '0' and '1'
Repeat this step. You get '00', '01', '10', '11'
After a while you get a list of 2**N bit strings.
You look at any of them: '10101000111010110111101100101' and it appears random.
And yet the whole generation procedure (which is an analog of the physical law in that toy universe) is deterministic!

 

[kote]

P is not a function of an event x. It is also a function of a branch.

Didn't you just say that we aren't allowed to specify the branch - we aren't allowed to refer to the "for me" branch?

Edit: I don't know of anyone who argues that the past isn't deterministic (in your sense of having probabilities of 0 or 1) within a branch, whether we assume one branch or many. What we're interested in is the future. So what's the probability, P(x,1), of the cat showing up alive vs dead? Doesn't allowing us to specify a branch require that we be able to ask that question?

 

[Hurkyl]

Let's let P represent "The cat is dead." You're saying that I'm not allowed to ask, "is P true or false?"

That's correct. Asking if the cat is dead in MWI is exactly as nonsensical as asking if some object is at rest in SR. On their own, those questions do not make sense physically -- they require some extra scaffolding before they can be meaningful.

 

[kote]

That's correct. Asking if the cat is dead in MWI is exactly as nonsensical as asking if some object is at rest in SR. On their own, those questions do not make sense physically -- they require some extra scaffolding before they can be meaningful.

Correct me if I'm wrong, but it seems to me that MWI denies meaning to all synthetic propositions (if understood in a form that is not reducible to standard QM through branch specification). What metaphysical benefit do we get from doing this? What good is denying randomness in reality if statements about reality are meaningless anyways?

 

[Pio2001]

So MWI predicts that in one branch one observer is asking "but why cat is dead?" and in another one "but why cat is alive?"

So you see, in MWI the situation is symmetric and deterministic. No randomness. Just an illusion of it.

I see what you mean. That seems to be a correct way of dealing with Schrödinger's cat, I must admit.

But non-locality in EPR experiments still needs to be dealt with. Ok, Bell's theorem doesn't apply in MWI, but MWI turns the wave function into an ontology. This is a major problem in EPR experiments because no objective wave function can describe the system and the observers between the instant of the measurements and the instant where their future light-cone meet. Some more data needs to be introduced in the MWI in order to completely modelize the experiment.

 

[Hurkyl]

Correct me if I'm wrong, but it seems to me that MWI denies meaning to all synthetic propositions (if understood in a form that is not reducible to standard QM through branch specification).

I'm not sure what precisely you mean here. The main point as I understand it is that it is not physically meaningful to ask unconditional questions.

Suppose we open the box and peek inside. It is not meaningful to ask "Is the cat alive?" -- it is only meaningful to ask "Given what I've observed, is the cat alive?"

This is true, incidentally, no matter what physical theory and interpretation we use. It's just that when we use interpretations that have the "definite outcomes" feature, then absolute questions like "Is the cat alive?" and conditional questions "Given what I've observed, is the cat alive?" have the same answers -- and therefore we can safely forget that all questions are conditional.

 

[kote]

I'm not sure what precisely you mean here. The main point as I understand it is that it is not physically meaningful to ask unconditional questions.

Suppose we open the box and peek inside. It is not meaningful to ask "Is the cat alive?" -- it is only meaningful to ask "Given what I've observed, is the cat alive?"

This is true, incidentally, no matter what physical theory and interpretation we use. It's just that when we use interpretations that have the "definite outcomes" feature, then absolute questions like "Is the cat alive?" and conditional questions "Given what I've observed, is the cat alive?" have the same answers -- and therefore we can safely forget that all questions are conditional.

I would argue that CI (well, Bohr anyways) requires the "given what I've observed" condition. The whole purpose of making reality explicitly subjective is so you can have actual entity realism without that qualification.

My question is, how can any synthetic proposition, even when qualified, have a truth value (meaning) without definite outcomes?

 

[Hurkyl]

My question is, how can any synthetic proposition, even when qualified, have a truth value (meaning) without definite outcomes?

Let me answer your question with a question. How can distances be physically meaningful in Galilean relativity, despite the fact position has no physical meaning?