What causes a collapse - and does it depend on frames of reference?

[wheelersbit]

I know there are many wavefunction collapse models - but with regards to the Copenhagen interpretation the idea is that a measurement will cause something to collapse into a particular state. What does the term "measurement" refer to? It makes one think of only something that a conscious being does. Are all wavefunctions that interact with a thing in a collapsed state, or since we have yet to measure them are they in a probabilistic state? Do we say that things we are unaware of, or mind-independent, interact with each other in a collapsed state? After all, what would it mean to say that probabilistic states in remote galaxies are interacting with each other?

I ask this because after reading Wheeler's "delayed choice" experiment it seems there's no definite series of events that happen, even in the past, until something is measured. My first thoughts in response were "What about all the things this photon interacted with?", "What if there was another observer in one of these galaxies"?

I apologize for the broad nature of this question - and the perhaps confusing elements I have thrown in but I find this all very exciting and am just seeking some clarification.

 

[bapowell]

A measurement involves an interaction with the system. How do you measure the position of an electron? One way is to hit it with a photon. That constitutes a measurement and has nothing to do with consciousness (of course, the larger sense in which we measure things in order to further knowledge is likely the result of consciousness, but the physical interaction giving rise to single measurements is not).

 

[wheelersbit]

A measurement involves an interaction with the system. How do you measure the position of an electron? One way is to hit it with a photon. That constitutes a measurement and has nothing to do with consciousness (of course, the larger sense in which we measure things in order to further knowledge is likely the result of consciousness, but the physical interaction giving rise to single measurements is not).

Thank you for your response. I'm having a hard time thinking of any event that doesn't in some sense perform a measurement by the definition you employed above. It seems like every event/interaction would be a measurement.

Even if I suppose a photon is traveling through empty space (virtual particles aside) - I would have to ask how it could have a definite "world line" or path in space while being purely probabilistic. Speaking of a definite trajectory for something probabilistic seems confused.

Also, just to clarify a thought experiment:
"Imagine two physicists performing a double split experiment, we'll call these the level 1 physicist
Now imagine 2 more physicists who are responsible for measuring the level 1 physicist's precise movements (which would reveal the result of the level 1 double slit experiment results). We'll call these the level 2 physicists. Would we say the electrons that were measured passing through the double slit are in a definite state to the level 2 physicists?"

I suppose the answered would be Yes

 

[atyy]

After all, what would it mean to say that probabilistic states in remote galaxies are interacting with each other?

My first thoughts in response were "What about all the things this photon interacted with?", "What if there was another observer in one of these galaxies"?

In Copenhagen, you divide the universe into classical and quantum realms. If there is another observer in one of those galaxies, then you and him are part of the classical realm. Your measurements do affect what he observes, but you cannot use that to transfer classical information to him faster than light. You only realize that your results are correlated after you come together and comapre observations. In this interpretation, quantum mechanics is nonlocal.

If you need to collapse a wave function, you can collapse it on any spacelike hypersurface that contains the measurement. Different "observers" will use different spacelike hypersurfaces, and so wave function collapse of one observer is not related by Lorentz transformation to the wave function collapse of another observer. However, all their results are related by Lorentz transformation, and their is no violation of special relativity.

 

[atyy]

It seems like every event/interaction would be a measurement.

A measurement is not any interaction. Quantum interactions are not measurements. A measurement is when a classical measuring apparatus probes a quantum system, and obtains information from it.

In the sense that we need common sense to say what a classical apparatus is, and what a quantum system is, then yes, an observer with some intelligence is needed to make an observation.

 

[atyy]

Also, just to clarify a thought experiment:
"Imagine two physicists performing a double split experiment, we'll call these the level 1 physicist
Now imagine 2 more physicists who are responsible for measuring the level 1 physicist's precise movements (which would reveal the result of the level 1 double slit experiment results). We'll call these the level 2 physicists. Would we say the electrons that were measured passing through the double slit are in a definite state to the level 2 physicists?"

For the level 1 physicist, when he makes a measurement he is classical, and the system is quantum, and he gets a definite result when he makes a measurement.

For the level 2 physicist, the level 2 physicist considers himself classical, and the level 1 physicist is considered quantum. The level 1 physicist is in a superposition of states until the level 2 physicist measures the level 1 physicist.

 

[naima]

A measurement is not any interaction. Quantum interactions are not measurements. A measurement is when a classical measuring apparatus probes a quantum system, and obtains information from it.

In the sense that we need common sense to say what a classical apparatus is, and what a quantum system is, then yes, an observer with some intelligence is needed to make an observation.

I wrote in another thread:
"Can we say that an event is a measurement when it gives a "robust mark" which can be read?
The mark is robust when it contains many duplicate copies of the same information. "

Is this correct?

 

[wheelersbit]

A measurement is not any interaction. Quantum interactions are not measurements. A measurement is when a classical measuring apparatus probes a quantum system, and obtains information from it.

In the sense that we need common sense to say what a classical apparatus is, and what a quantum system is, then yes, an observer with some intelligence is needed to make an observation.

Perhaps this question is trivial - but is an electron microscope considered classical when an observer looks through it - but quantum when one doesn't? According to bapowell it would cause what's been measured to collapse - independent of a conscious observer.

 

[atyy]

I wrote in another thread:
"Can we say that an event is a measurement when it gives a "robust mark" which can be read?
The mark is robust when it contains many duplicate copies of the same information. "

Is this correct?

Yes, generally a measurement result is considered something which for the observer is a "classical" or "macroscopic" or "irreversible" mark. You can find "classical" in Landau and Lifshitz's text, while Asher Peres's textbook uses the latter two terms. There is a measurement problem in quantum mechanics, so this is a fundamental difficulty, but in practice it is ok, since we have enough common sense to know what a "macroscopic" measuring apparatus is, and what is "quantum".

There's an interesting discussion in Hay and Peres's "Quantum and classical descriptions of a measuring apparatus" http://arxiv.org/abs/quant-ph/9712044. The one part I don't entirely agree with in Peres's work is that he tends to avoid the notion of collapse, but I believe he has introduced it with his notion of blurring of the Wigner function, which converts the Wigner function to a classical probability distribution. But overall I like Peres's work very much.

 

[atyy]

Perhaps this question is trivial - but is an electron microscope considered classical when an observer looks through it - but quantum when one doesn't? According to bapowell it would cause what's been measured to collapse - independent of a conscious observer.

Basically, there's no end to these questions. In Copenhagen, the observer has already decided for himself what is classical and what is quantum, and quantum mechanics is just a way for him to calculate the probabilities of the results he gets when his classical apparatus probes the quantum system. To get a satisfactory answer, you have to turn to an interpretation without collapse such as de Broglie-Bohm theory for nonrelativistic quantum mechanics, or many-worlds. I'm not sure many-worlds works, but some versions of it are pretty convincing, eg. the Deutsch-Wallace version.

 

[WannabeNewton]

I would recommend getting "Lectures on Quantum Theory: Mathematical and Structural Foundations"-C.J. Isham (it's relatively cheap); with regards to your question in particular, read chapter 8-in particular section 8.5.

 

[Nugatory]

For the level 1 physicist, when he makes a measurement he is classical, and the system is quantum, and he gets a definite result when he makes a measurement.

For the level 2 physicist, the level 2 physicist considers himself classical, and the level 1 physicist is considered quantum. The level 1 physicist is in a superposition of states until the level 2 physicist measures the level 1 physicist.

Which is, of course, impossible (with thanks to Douglas Adams and a for all).

Substitute a cat for the level 1 physicist and you get Schrodinger's famous thought experiment. Of course Schrodinger was not trying to illustrate a point about cats or physicists in superposition; he was making a point about the problematic nature of the classical/quantum split in the Copenhagen interpretation.

 

[naima]

There's an interesting discussion in Hay and Peres's "Quantum and classical descriptions of a measuring apparatus" http://arxiv.org/abs/quant-ph/9712044. The one part I don't entirely agree with in Peres's work is that he tends to avoid the notion of collapse, but I believe he has introduced it with his notion of blurring of the Wigner function, which converts the Wigner function to a classical probability distribution. But overall I like Peres's work very much.

I did not find how do one blurs a wigner function.

 

[atyy]

I did not find how do one blurs a wigner function.

I was thinking more of his book http://books.google.com/books?id=IjCNzbJYONIC&printsec=frontcover#v=onepage&q&f=false (p316 and p376).

But in his paper, he talks about it a bit "(If we had chosen another state, whose Wigner function had negative regions, it would have been necessary to smooth the oscillations of W(q, p), so as to make it everywhere positive [13].)" http://arxiv.org/abs/quant-ph/9712044 (just before Eq 42). Also, in the discussion, he writes "In general, if Wigner’s function is explicitly needed, it has to be non-negative for a semi-classical treatment to proceed. Fortunately, this condition is likely to be fulfilled for any macroscopic apparatus which is not in a pure state, but rather in a mixed state with
$Δq
Δp ≫\hbar$ (this inequality is the hallmark of being “macroscopic”) [15]. All the negative parts of W are then washed away by the coarseness of the apparatus."

The Wigner function is conceptually the quantum counterpart of the distribution in phase space which we evolve by Liouville's equation classically. But the Wigner function has negative bits, so it isn't a probability distribution.

 

[StevieTNZ]

Where collapse of the wave function occurs has yet to be determined. However we know if we take QM formalism, it cannot be at the macroscopic apparatus as that would lead to inconsistent QM predictions. (See Ghirardi's thought experiment in "Sneaking a Look at God's Cards", and David Albert's "Quantum Mechanics and Experience").

 

[DennisN]

Where collapse of the wave function occurs has yet to be determined.

...and if collapse of the wave function occurs at all.
Interpretations_of_quantum_mechanics#Comparison_of_interpretations

 

[bhobba]

Thank you for your response. I'm having a hard time thinking of any event that doesn't in some sense perform a measurement by the definition you employed above. It seems like every event/interaction would be a measurement.

That's where this thing called decoherence comes in:
http://www.ipod.org.uk/reality/reality_decoherence.asp

Only some interactions can decohere an object, and these days it is generally thought an observation has occurred once decoherence happens.

Thanks
Bill

 

[bhobba]

Is this correct?

No - but the issue is subtle and one can be excused for thinking things like that.

In modern times it's when decoherence has occurred.

For example a few stray protons is enough to decohere a dust particle and give it an apparent definite position. The word apparent here has to do with decoherence only causing apparent collapse. The following explains the detail of exactly what that means:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

But without the technical detail it simply means for all practical purposes a collapse has occurred.

This is one of the issues with explaining stuff in forums like this. I say QM is a theory about marks left here in the classical world - and it is. But there are subtleties to it such that in modern times its usually associated with dechoerence - and how these days the emergence of a classical world is explained. But, strictly speaking, in Copenhagen its about marks left here in the macro world - which leads to issues and why, strictly speaking Copenhagen is wrong. However its more along the lines of fixing a minor problem, rather than totally disproving it:
http://motls.blogspot.com.au/2011/05/copenhagen-interpretation-of-quantum.html

'Is that true? Is that a sign of a problem of the Copenhagen interpretation?

It is surely true. It's how the world works. However, one may also say that this was a point in which the Copenhagen interpretation was incomplete. They didn't quite understand decoherence - or at least, Bohr who probably "morally" understood what was going on failed in his attempts to comprehensibly and quantitatively describe what he "knew".

However, once we understand decoherence, we should view it as an explicit proof of this fifth principle of the Copenhagen interpretation. Decoherence shows that the states of macroscopic (or otherwise classical-like) objects whose probabilities are well-defined are exactly those that we could identify with the "classical states" - they're eigenstates of the density matrix. The corresponding eigenvalues - diagonal entries of the density matrix in the right basis - are the predicted probabilities.'

It's like when I say a few stray photons is enough to decohere a dust particle and give it a definite position. That's really only an APPARENT definite position, but constantly giving caveats etc etc would really make posts too long so you tend to just gloss over the fine points.

Thanks
Bill

 

[bhobba]

...and if collapse of the wave function occurs at all.

You beat me to it.

And even if it does occur, in many interpretations such as most variants of Copenhagen, it's simply something that occurs in theorists calculations and doesn't exist in any real sense - like the probability of a dice being 1/6th for each side but when you throw it is changes to a 1 for one side and zero for the rest. Big deal.

Thanks
Bill

 

[bhobba]

Substitute a cat for the level 1 physicist and you get Schrodinger's famous thought experiment. Of course Schrodinger was not trying to illustrate a point about cats or physicists in superposition; he was making a point about the problematic nature of the classical/quantum split in the Copenhagen interpretation.

Indeed.

But some get really confused about it.

The solution is utterly trivial in Copenhagen. The detector either detected a particle or not - that's where the essential mystery resides. Everything is commonsense classical from that point on - the cat is either alive or dead - not in some weird superposition.

What it showed is we need a fully quantum theory of measurement.

Much progress has been made on that - but some issues still remain.

Thanks
Bill

 

[bhobba]

Where collapse of the wave function occurs has yet to be determined. However we know if we take QM formalism, it cannot be at the macroscopic apparatus as that would lead to inconsistent QM predictions. (See Ghirardi's thought experiment in "Sneaking a Look at God's Cards", and David Albert's "Quantum Mechanics and Experience").

That's simply plain wrong. For example if you place a screen in front of an emitted photon it is the interaction of the photon and screen that leaves a mark, flash or whatever at a definite position.

The screen has decohered the photon into an improper mixed state.

What the interaction doesn't necessarily explain, because it's very interpretation dependent, is why we get an outcome. The improper mixed state says with a certain probability it will give a certain position - but why we get any outcome at all it leaves up in the air. However the issue is a doodle for many worlds and Bohmian Mechanics.

Added Later:
I think I am not the only one that has issues with this 'thought experiment'
https://www.physicsforums.com/showthread.php?t=571798

Thanks
Bill

 

[StevieTNZ]

That's simply plain wrong. For example if you place a screen in front of an emitted photon it is the interaction of the photon and screen that leaves a mark, flash or whatever at a definite position.

The screen has decohered the photon into an improper mixed state.

What the interaction doesn't necessarily explain, because it's very interpretation dependent, is why we get an outcome. The improper mixed state says with a certain probability it will give a certain position - but why we get any outcome at all it leaves up in the air. However the issue is a doodle for many worlds and Bohmian Mechanics.

Added Later:
I think I am not the only one that has issues with this 'thought experiment'
https://www.physicsforums.com/showthread.php?t=571798

Thanks
Bill

Have you even read the references I cite? Because what you say doesn't apply to those references.

 

[bhobba]

Have you even read the references I cite? Because what you say doesn't apply to those references.

Well actually I do have a copy of Sneaking a Look at God's Cards and could go to it and try and sort this issue out.

What I said applied to your claim 'However we know if we take QM formalism, it cannot be at the macroscopic apparatus as that would lead to inconsistent QM predictions' - which is so obviously wrong I think the onus is on you to explain and justify it rather than me try and sort it out.

Just one reason its wrong is Von Neumann showed the cut could be placed anywhere - including at the measuring apparatus. It would also make a mockery of decoherence interpretations which, often, places it precisely there.

Start a thread on it if you like - but for a claim like this you need to justify it clearly and carefully.

Thanks
Bill

 

[Maui]

Well actually I do have a copy of Sneaking a Look at God's Cards and could go to it and try and sort this issue out.

What I said applied to your claim 'However we know if we take QM formalism, it cannot be at the macroscopic apparatus as that would lead to inconsistent QM predictions' - which is so obviously wrong I think the onus is on you to explain and justify it rather than me try and sort it out.

Just one reason its wrong is Von Neumann showed the cut could be placed anywhere - including at the measuring apparatus. It would also make a mockery of decoherence interpretations which, often, places it precisely there.

Start a thread on it if you like - but for a claim like this you need to justify it clearly and carefully.

Thanks
Bill

Shouldn't the, hmmmm..., macroscopic apparatus(whatever that means quantum mechanically) be governed by the same qm rules as quantum particles? With that in mind, it's kind of weird to posit a special, privileged role to certain multi-body qm systems.

 

[bhobba]

Shouldn't the, hmmmm..., macroscopic apparatus(whatever that means quantum mechanically) be governed by the same qm rules as quantum particles? With that in mind, it's kind of weird to posit a special, privileged role to certain multi-body qm systems.

Why is it weird?

Only some type of interactions decohere, and they usually involve a lot of separate interactions to 'scramble' phase:
http://www.ipod.org.uk/reality/reality_decoherence.asp
'The off-diagonal (imaginary) terms have a completely unknown relative phase factor which must be averaged over during any calculation since it is different for each separate measurement (each particle in the ensemble). As the phase of these terms is not correlated (not coherent) the sums cancel out to zero. The matrix becomes diagonalised (all off-diagonal terms become zero). Interference effects vanish. The quantum state of the ensemble system is then apparently "forced" into one of the diagonal eigenstates with the probability of a particular eigenstate selection predicted by the value of the corresponding diagonal element of the density matrix.'

Usually it's the system being measured, environment, and measurement apparatus that's involved in decoherence - but not always - as per the example I gave.

Thanks
Bill

 

[Maui]

Why is it weird?

Only some type of interactions decohere, and they usually involve a lot of separate interactions to 'scramble' phase:
http://www.ipod.org.uk/reality/reality_decoherence.asp
'The off-diagonal (imaginary) terms have a completely unknown relative phase factor which must be averaged over during any calculation since it is different for each separate measurement (each particle in the ensemble). As the phase of these terms is not correlated (not coherent) the sums cancel out to zero. The matrix becomes diagonalised (all off-diagonal terms become zero). Interference effects vanish. The quantum state of the ensemble system is then apparently "forced" into one of the diagonal eigenstates with the probability of a particular eigenstate selection predicted by the value of the corresponding diagonal element of the density matrix.'

Usually it's the system being measured, environment, and measurement apparatus that's involved in decoherence - but not always - as per the example I gave.

Thanks
Bill

Because there is no justification why certain systems should be considered "macroscopic apparatus" where the collapse occurs. All you can do is imagine that it it can, compare the results and conclude that observationally and FAPP it can(it is far from obvious that collapse happens at the apparatus). Actually, certain experiments, as StevieTNZ rightly countered, contradict this explanation - e.g. the quantum eraser.

 

[bhobba]

Because there is no justification why certain systems should be considered "macroscopic apparatus" where the collapse occurs. All you can do is imagine that it it can, compare the results and conclude that observationally and FAPP it can(it is far from obvious that collapse happens at the apparatus). Actually, certain experiments, as StevieTNZ rightly countered, contradict this explanation - e.g. the quantum eraser.

As Von neumann proved the collapse can be put anywhere so there in no justification for saying it can't occur in an apparatus.

But that is not my point. My point was there is a problem with the usual Copenhagen interpretation that the introduction of decoherence removed. Nowadays an observation is generally considered to be when decoherence has occurred so these issues do not arise.

I have zero idea how the quantum eraser disproves decoherence. If it did that would be BIG news because at least two common interpretations, MWI and Decoherent Histories would go down the gurgler - not to mention the Ignorance Ensemble interpretation.

Thanks
Bill

 

[Maui]

I have zero idea how the quantum eraser disproves decoherence. If it did that would be BIG news because at least two common interpretations, MWI and Decoherent Histories would go down the gurgler - not to mention the Ignorance Ensemble interpretation.

Thanks
Bill

It doesn't. Decoherence alone does not solve the measurement problem without additional assumptions and I would say that the QE disproves the assumption that decoherence(and obtaining sinlge outcomes) happens when a quantum system interacts with a classical measurement apparatus. As you like to say - 'it's more subtle than that'.

 

[bhobba]

It doesn't. Decoherence alone does not solve the measurement problem without additional assumptions

I have zero idea why you bring this up.

I have specifically stated it doesn't.

The claim is it resolves a problem with Copenhagen as to exactly when an observation has occurred. Its usual to say its when a mark or something like that is left here in the macro world. But pinning that down exactly is an issue, so instead of that these days modern versions associate it with decoherence which is much easier to define and is not dependent on the existence of a classical world.

The link I gave to Lubos's explanation of Copenhagen, the issue it has, and how decoherence fixed it explains it pretty clearly.

All this is purely in relation to the query about what count as a mark.

Its very obvious what it is in any particular situation, but it is better to not base it on things that, while obvious in practice, can't be pinned down precisely.

Thanks
Bill