Quantum Collapse: Unravelling the Mechanics

[hydrojet2005]

this is a question that has been bugging me from the beginning of my learning of quantum mechanics. why does the the wavefunction collapse when we do a measurement?
since we have no concrete idea about collapse, we use probability theory to understand quantum phenomenon. but at least from classical framework, we use probability when we don't know the full picture. in some sense we can call probability the 'mathematics of our ignorance'.
now bell has proved that no hidden variable theory of quantum mechanics is not possible. and because of that it seems that the it is impossible to understand the dynamics of collapse.
but why not? i may not be able to predict that at a particular measurement which eigenvalue shall i get, but can't i predict that given a specific type of measurement, that is understanding of all the parameters involved, we should be able to tell for which parameters which eigenvalue shall i get. i may not be able to control the parameters and hence we shall still need the framework of quantum mechanics, but is this proposition impossible?
in this respect i remember the famous comment of einstein - 'god doesn't play dice with the world'. but then even dice has some rules, some mechanics, some dynamics.

 

[alxm]

this is a question that has been bugging me from the beginning of my learning of quantum mechanics. why does the the wavefunction collapse when we do a measurement?

Well that's not quantum mechanics per se, it's the Copenhagen interpretation.

Personally, I regard it as a bit of a non-issue. The 'problem' or 'paradox' lies mostly in how the question is framed. (Zeno's paradox is another example). You're regarding the 'measuring' system and the 'measured' system as separate, when in reality, they are not, since they interact.

This all goes back to the early quantum physicists who were a bit confused, or rather, conservative. They were trying to stick with old 'classical' ideas, such as the idea that a system always has a definite value for its measurable properties, and that measurements, at least ideally, can be performed in a way that does not interfere.

If you drop all that and simply regard the wave function as the fundamental description of the system, rather than some mathematical device that could be used to get measurable values, then the metaphysics of it all becomes much simpler.

It's not an unusual thing. I recall reading something by Stephen Weinberg where he noted that it's not easy at all to follow the reasoning in Newton's "Principia", even to someone well-versed in Newtonian mechanics. Because, Newton wasn't really the first 'Newtonian' physicist. He was the last non-Newtonian physicist. I think the same type of confusion applies in this case.

 

[Pollock]

I think that the collapse of the wave function occurs only in the mind of the observer.In the old Schrödinger cat paradox,the cat (at least to my way of thinking) was never in a two state system.It was always in one state or the other,until a conscious mind knew which one.The whole measurement problem surely has to take account of the connection between consciousness and quantum phenomena.

 

[Bob_for_short]

The user alxm is right. The quantum events are the primary. The classical notions arise from quantum ones as the inclusive picture - all different events are piled up and considered as relating to one "free", for example, particle. Classical picture is a kind of cinematographic illusion. The primary are rare black points on each frame, the secondary or illusory is the "image" obtained with superimposing different frames.

Bob.

 

[hydrojet2005]

The primary are rare black points on each frame, the secondary or illusory is the "image" obtained with superimposing different frames.

Bob.

can you just explain to me what is meant by this statement?

 

[map19]

The idea that there is a collapse, or that an intelligence is required to collapse the waveform, or that conciousness affects quantum phenomena is rubbish.
If it were so you could, for example, record the result automatically and look at it a week later. What happens then ? does the waveform collapse a week after the event ?
Does a flea know if the cat is dead or alive ?

As I have said before on this forum the Cat was Schrödinger's parable showing the stupidity of the view prevelant at the time that nothing is there if no one is looking.

See the cartoon on Nearing Zero, where the attractive lab assistant is just a waveform when the Prof. is not looking at her.

Read about the deBroglie - Bohm version, beaten to death at the Solvay Conference in 1927. Read The Undivided Universe by Bohm.

 

[Pollock]

You say "the idea that there is a collapse--------is rubbish.Do you think then that the two forms of the wavefunction continue to exist independently? ;do you really mean that!?.If so,how do you explain why we only see one outcome when we make a measurement ?. I agree with your view about "the stupidity of the view----that nothing is there if no one is looking",and I would say that even when no one is looking,a quantum system will have come down on one side or the other of the quantum fence.

 

[Monitor16807]

When someone has a car accident an observer going to help the person inside thinks: He might be dead or alive(Wave function), when that person finally sees the driver (Measurement) one of the 2 possibility is not possible anymore (Collapse of the Wave function).

Is this a good example?

 

[QuantumBend]

When someone has a car accident an observer going to help the person inside thinks: He might be dead or alive(Wave function), when that person finally sees the driver (Measurement) one of the 2 possibility is not possible anymore (Collapse of the Wave function).

Is this a good example?

Yes, and it is reading then start again. Not COLLAPSE all, only CHANGE. What we want knowing happening when two wavfunction strike together do know they it?

 

[ZapperZ]

When someone has a car accident an observer going to help the person inside thinks: He might be dead or alive(Wave function), when that person finally sees the driver (Measurement) one of the 2 possibility is not possible anymore (Collapse of the Wave function).

Is this a good example?

No, it is not a good example.

There have been so many threads on this here on PF that I feel silly repeating all of this again, but here goes.

There is a difference between classical and quantum system. This is no big surprise. Let's say you toss a coin and it falls into a box before you can see how it lands. So you don't know if it is head or tail. Same situation as the accident. Does this mean that the coin system is now in a superposition of states of "head" and "tail"? No, it doesn't! The coin is a classical system. It doesn't work that way. We detect no superposition effects of |head> + |tail> wavefunction.

What you have is that the coin is already in a definite state. It is just that you do not know what it is. So you say that there is a 50% probability that the coin produces head, and 50% probability that it is tail. It is either OR.

This classical statistics is clearly different than the superposition of a bipartite quantum system. A quantum system, before it is measured, is really in a superposition of ALL the possible states that it can have. It means that there is no definite out YET before it is measured, and before you take a peak at it. This is clearly different than the classical (coin) system, where in that situation, the coin already has a definite state, and it is just our ignorance that is forcing us to consider all the possibilities.

Now, how can one tell the difference between the two if, upon measurement, all we see is just ONE value? This is where knowing what is meant by "non-commuting" and "non-contextual" observablein quantum mechanics is crucial. One can make a measurement, say, or a non-commuting observable value, which will preserve the superposition of the the other non-commuting observable. For example, say [A,B] != 0, where A and B are observables. If I measure B, the wavefuction collapses for B, but NOT for A! If I can find some way of making such a measurement on the identical system repeatedly, I may be able to detect that A is in a superposition of states even though I'm only measuring B.

This is naively what is done when we detect bonding-antibonding states in chemistry, the coherence gap in the SQUID experiments out of Delft/Stony Brook, etc.. etc. These phenomena cannot occur if the systems are already in a definite state. This is why we invoke the superposition principle as vital in QM, because it fits into numerous experimental observations, and why it is VERY different than classical systems.

Edit: I've posted references in this post:

https://www.physicsforums.com/showpost.php?p=2103739&postcount=201

Zz.

 

[map19]

The Bohm - DeBroglie view of quantum processes is much better in my view. Bohm notes that although the treatment of statistical processes is satisfactory in the Copenhagen view, the individual quantum processes use unsatisfactory assumptions - like the collapse of the wave function. The mysterious wave-particle duality. The inability to give a clear notion of what the reality (ontological interpretation) of a quantum system should be.
Then there's nonlocality.
(I've somewhat paraphrased Bohm)
Read: - The Undivided Universe by Bohm.

From Cambridge University Cavendish Lab. http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html

 

[cesiumfrog]

it's not easy at all to follow the reasoning in Newton's "Principia", even to someone well-versed in Newtonian mechanics. Because, Newton wasn't really the first 'Newtonian' physicist. He was the last non-Newtonian physicist.

Nice observation.

 

[Pollock]

Yes, and it is reading then start again. Not COLLAPSE all, only CHANGE. What we want knowing happening when two wavfunction strike together do know they it?

This sentence doesn't make grammatical sense.What do you really mean?

 

[DeShark]

Now, how can one tell the difference between the two if, upon measurement, all we see is just ONE value? This is where knowing what is meant by "non-commuting" and "non-contextual" observable in quantum mechanics is crucial. One can make a measurement, say, on a non-commuting observable value, which will preserve the superposition of the the other non-commuting observable. For example, say [A,B] != 0, where A and B are observables. If I measure B, the wavefuction collapses for B, but NOT for A! If I can find some way of making such a measurement on the identical system repeatedly, I may be able to detect that A is in a superposition of states even though I'm only measuring B.

But what if the observable here commutes with every other physical observable? That is to say, measuring whether the coin is heads or tails won't change any other physical observable? Is that right? So, I could look at the date of the coin and then look whether it's heads or tails and the observation of the date won't affect or interfere with the heads or tails state of the coin. This seems reasonable to me. All these macroscopic measurements seem to commute to me and I'm just back to good old classical probability. But that's not to say that the quantum theory should fail to describe this system and I fail to see any reason that quantum mechanics doesn't work for large systems as well as small. It's just that if there is any non-commutation, the effects are generally minuscule.

I have a feeling I must be wrong here, because you've emphasised an enormous difference between this macroscopic (not classical) case and the microscopic case generally treated with quantum mechanics.

Edit: If there is a genuine difference between macroscopic and microscopic systems, what use is schroedinger's cat, the atypical macroscopic system described as a superposition of two base states, |dead> and |alive>

 

[ZapperZ]

But what if the observable here commutes with every other physical observable? That is to say, measuring whether the coin is heads or tails won't change any other physical observable? Is that right? So, I could look at the date of the coin and then look whether it's heads or tails and the observation of the date won't affect or interfere with the heads or tails state of the coin. This seems reasonable to me. All these macroscopic measurements seem to commute to me and I'm just back to good old classical probability. But that's not to say that the quantum theory should fail to describe this system and I fail to see any reason that quantum mechanics doesn't work for large systems as well as small. It's just that if there is any non-commutation, the effects are generally minuscule.

I have a feeling I must be wrong here, because you've emphasised an enormous difference between this macroscopic (not classical) case and the microscopic case generally treated with quantum mechanics.

Edit: If there is a genuine difference between macroscopic and microscopic systems, what use is schroedinger's cat, the atypical macroscopic system described as a superposition of two base states, |dead> and |alive>

I don't know exactly what you are asking here.

If A and B commutes, then for a non-degenerate case, measurement of A will also give you B. For example, H and p commutes for a free particle. If you know momentum, then the energy is also determined. There's no mystery here.

What is invoked in the Schrödinger Cat-type experiment is the non-commuting/non-contextual observables. These DO exist!

Furthermore, the "size", as in microscopic versus microscopic isn't the issue. It is how well and to what extent can you maintain coherence of the system. In the Delft/Stony Brook experiments, they showed a superposition in a system as large at 10^11 particles! This is because superconductivity can show coherence at the "macroscopic" scale! There's nothing that say that we can't have it larger. The big problem is how to isolate the system from coupling to the environment that will destroy the coherence.

Zz.

 

[DeShark]

The big problem is how to isolate the system from coupling to the environment that will destroy the coherence.

Zz.

I don't really understand this line. Coherence of what?

Yes, it looks like I completely forgot what commuting means. Swap every time I said "commuting" to "non-commuting". I might even have meant anti-commuting, but I'm not sure. Obviously measuring the heads or tails state of the coin won't tell you what date the coin is. Although, looking at the coin, you could see both the state of the coin and its date (assuming the date is printed on both sides, which it isn't).

What I meant to ask was "why is there any difference between the case of a coin and the case of a quantum system, with regards to the mathematical description?". I see that there is a difference in interpretation and in that regard I'm agreed that in one case we do not know, although the state is defined and in the other case, we do not know until we make the measurement. It seems like you're assuming the Copenhagen interpretation implicitly.

 

[Count Iblis]

No, it is not a good example.

There have been so many threads on this here on PF that I feel silly repeating all of this again, but here goes.

There is a difference between classical and quantum system. This is no big surprise. Let's say you toss a coin and it falls into a box before you can see how it lands. So you don't know if it is head or tail. Same situation as the accident. Does this mean that the coin system is now in a superposition of states of "head" and "tail"? No, it doesn't! The coin is a classical system. It doesn't work that way. We detect no superposition effects of |head> + |tail> wavefunction.

What you have is that the coin is already in a definite state. It is just that you do not know what it is. So you say that there is a 50% probability that the coin produces head, and 50% probability that it is tail. It is either OR.

This classical statistics is clearly different than the superposition of a bipartite quantum system. A quantum system, before it is measured, is really in a superposition of ALL the possible states that it can have. It means that there is no definite out YET before it is measured, and before you take a peak at it. This is clearly different than the classical (coin) system, where in that situation, the coin already has a definite state, and it is just our ignorance that is forcing us to consider all the possibilities.

Now, how can one tell the difference between the two if, upon measurement, all we see is just ONE value? This is where knowing what is meant by "non-commuting" and "non-contextual" observablein quantum mechanics is crucial. One can make a measurement, say, or a non-commuting observable value, which will preserve the superposition of the the other non-commuting observable. For example, say [A,B] != 0, where A and B are observables. If I measure B, the wavefuction collapses for B, but NOT for A! If I can find some way of making such a measurement on the identical system repeatedly, I may be able to detect that A is in a superposition of states even though I'm only measuring B.

This is naively what is done when we detect bonding-antibonding states in chemistry, the coherence gap in the SQUID experiments out of Delft/Stony Brook, etc.. etc. These phenomena cannot occur if the systems are already in a definite state. This is why we invoke the superposition principle as vital in QM, because it fits into numerous experimental observations, and why it is VERY different than classical systems.

Edit: I've posted references in this post:

https://www.physicsforums.com/showpost.php?p=2103739&postcount=201

Zz.

The fact that we don't detect superpositions like |head> + |tail> is simply because due to very fast decoherence the rest of the universe becomes entangled with the state of the coin. So, in general, we have a superposition like:

|head>|universe_1> + |tail>|universe_2>

There is then no way to do interference experiments to demonstrate the difference between a classical state in which the coin has either tail up or head up. But the formalism of quantum mechanics still demands that, generically, you end up in a superposition of two very different states.

The only way to get rid of the superposition is to assume new physics in which non-unitary effects lead to a real collapse of the wavefunction. But there isn't a shred of evidence for such non-unitary effects.

 

[ZapperZ]

The fact that we don't detect superpositions like |head> + |tail> is simply because due to very fast decoherence the rest of the universe becomes entangled with the state of the coin. So, in general, we have a superposition like:

|head>|universe_1> + |tail>|universe_2>

There is then no way to do interference experiments to demonstrate the difference between a classical state in which the coin has either tail up or head up. But the formalism of quantum mechanics still demands that, generically, you end up in a superposition of two very different states.

The only way to get rid of the superposition is to assume new physics in which non-unitary effects lead to a real collapse of the wavefunction. But there isn't a shred of evidence for such non-unitary effects.

Then how do you explain all those observations that I've cited? Obviously, the presence of the coherence gap in the SQUID measurement is a result of such superposition, and it was measured! No analogous effect can be demonstrated for the classical state.

Zz.

 

[ZapperZ]

I don't really understand this line. Coherence of what?

Do you not understand the usage of "coherence" in what I posted, or do you not understand "coherence" as used in QM, i.e. the onset of classical phase with decoherence?

Yes, it looks like I completely forgot what commuting means. Swap every time I said "commuting" to "non-commuting". I might even have meant anti-commuting, but I'm not sure. Obviously measuring the heads or tails state of the coin won't tell you what date the coin is. Although, looking at the coin, you could see both the state of the coin and its date (assuming the date is printed on both sides, which it isn't).

What I meant to ask was "why is there any difference between the case of a coin and the case of a quantum system, with regards to the mathematical description?". I see that there is a difference in interpretation and in that regard I'm agreed that in one case we do not know, although the state is defined and in the other case, we do not know until we make the measurement. It seems like you're assuming the Copenhagen interpretation implicitly.

In the classical case, the description is never a "superposition" of the actual state, but rather in the state of YOUR knowledge of the system. This is why the absence of "realism" in QM, i.e. the absence of an already-established state that hasn't been measured, is such a major issue with QM. I think I've highlighted a paper in the "Noteworthy papers" sticky that showed that even when one invokes non-locality, one still cannot save realism. It means that these states in QM are not yet determined until they are measured. This is clearly different than the classical case where "either or" cases occurs. You will get either head, or tail, but not a mixture/superposition of both, even before you toss the coin or take a look after the coin lands. Not only that, you cannot perform ANY experiment (there's none so far) equivalent to the experiments that I've mentioned.

Zz.

 

[Count Iblis]

Then how do you explain all those observations that I've cited? Obviously, the presence of the coherence gap in the SQUID measurement is a result of such superposition, and it was measured! No analogous effect can be demonstrated for the classical state.

Zz.

The observations are consistent with quantum mechanics. Even the measured decoherence time is consistent with theoretical predictions.

After the system has decohered you cannot experimentally demonstrate a difference between the following two possibilities:

a) The system undergoes a "real collapse" in the non-unitary sense (requires new physics)

b) The system does not undergo any non-unitary evolution, rather it has become completely entangled with the environment.

The reduced density matrix for a) and b) are the same and there is no way to distinguish between the two alternatives.

 

[ZapperZ]

The observations are consistent with quantum mechanics. Even the measured decoherence time is consistent with theoretical predictions.

After the system has decohered you cannot experimentally demonstrate a difference between the following two possibilities:

a) The system undergoes a "real collapse" in the non-unitary sense (requires new physics)

b) The system does not undergo any non-unitary evolution, rather it has become completely entangled with the environment.

The reduced density matrix for a) and b) are the same and there is no way to distinguish between the two alternatives.

What "measured decoherence time"?

We're not talking about decoherence here, because if that is truly the cause of the morph from quantum to classical world, then we're talking about classical physics, which isn't what this thread is about. We're talking about the superposition of states being measurable.

Zz.

 

[Count Iblis]

What "measured decoherence time"?

We're not talking about decoherence here, because if that is truly the cause of the morph from quantum to classical world, then we're talking about classical physics, which isn't what this thread is about. We're talking about the superposition of states being measurable.

Zz.

Ok, but after about 10^(-7) s or so, no superpositions are measured, which is perfectly consistent with the assumption that due to interactions with the environment you go from a superposition of the form:

|environment> [|state_1> + |state_2>]

to

|environment_1> |state_1> + |environment_2>|state_2>]

Then, this means that the classical world should always be described as decoherent superpositions of the latter form. This means that superpositions are relevant (albeit undetectable) whenever your (incomplete) knowledge about the system doesn't constrain you to be located in only one of the sectors |environment_j>.

 

[ZapperZ]

Ok, but after about 10^(-7) s or so, no superpositions are measured, which is perfectly consistent with the assumption that due to interactions with the environment you go from a superposition of the form:

|environment> [|state_1> + |state_2>]

to

|environment_1> |state_1> + |environment_2>|state_2>]

Then, this means that the classical world should always be described as decoherent superpositions of the latter form. This means that superpositions are relevant (albeit undetectable) whenever your (incomplete) knowledge about the system doesn't constrain you to be located in only one of the sectors |environment_j>.

Again, what "decoherence time"?

A superconductor stays superconducting for as long as you keep it cold. There's no "decoherence" time, it stays coherent due to the nature of a "quantum protectorate"! That's why we it to measure many quantum effects.

How did we get into decoherence time? And why is it relevant here, because once I could show the effect of superposition, I've already demonstrated how that is different from classical physics. And NH3 molecule has no "decoherence time" either!

Zz.

 

[Count Iblis]

I don't disagree here. My point is simply that what we call the classical world is simply the quantum world in disguise. The disguise being that any superpositions are always entangled with the environment so that it looks like if you don't have any superposition at all.

But if we assume that at the classical level we really do not have superpositions, then one has to assume a non-unitary collapse of the wave function, for which there is no evidence at all.

 

[ZapperZ]

I don't disagree here. My point is simply that what we call the classical world is simply the quantum world in disguise. The disguise being that any superpositions are always entangled with the environment so that it looks like if you don't have any superposition at all.

But being "entangled" with the environment can destroy such quantum property! It has been shown that the interaction with just ONE other particle is sufficient to destroy the single-particle coherence and start to produce classical property. So your claim that "superpositions are always entangled with the environment" is unverified and contrary to such experimental observation. It also doesn't make sense in light of such an experiment and the claim of a quantum protectorate.

The whole point of decoherence is coupling to the environment. You turned this around by arguing that such coupling actually is built in even when the system maintain coherence. Can you please provide references that actually use such an argument?

Zz.

 

[cesiumfrog]

But being "entangled" with the environment can destroy such quantum property! It has been shown that the interaction with just ONE other particle is sufficient to destroy the single-particle coherence and start to produce classical property.

..right, and it's also been shown that measurement of the other particle can restore the quantum property. Uh, what are you two arguing over?

Zz is stating the fact that a quantum superposition is distinguishable from a classical probability distribution (addressing the OP's disbelief of the hidden variable disproof).

Count Ibis is stating the fact that MWI is not distinguishable from Copenhagen. (And thereby is pointing out that Zz's statement can still be made even without evoking any arbitrary distinction between classical and quantum systems. This is relevant because the OP also asked about the mysterious processes of "measurement" and "collapse".)

 

[ZapperZ]

..right, and it's also been shown that measurement of the other particle can restore the quantum property.

So where is the "measurement of the other particle" in D. Akoury et al., (Science v.318, p.949 (2007)) that resorted the quantum property of the single particle? Do you also have an example of coupling to the environment that also restored such quantum property?

Zz.

 

[cesiumfrog]

So where is the "measurement of the other particle" in D. Akoury et al., (Science v.318, p.949 (2007)) that resorted the quantum property of the single particle?

In Fig.2B, your "classical property" has been induced by interaction with another particle, but in Fig.3 the quantum coherence is restored by measuring that other particle. (This is a "textbook" example for MWI, by the way.. I still don't see why you think people are disagreeing with you.)

 

[ZapperZ]

In Fig.2B, your "classical property" has been induced by interaction with another particle, but in Fig.3 the quantum coherence is restored by measuring that other particle. (This is a "textbook" example for MWI, by the way.. I still don't see why you think people are disagreeing with you.)

But that "restoration" is the 2-particle state, not the single-particle state! The coherence of the single-particle state is gone forever! The 2-particle state are now the analogous state that one get out of the standard bipartite Bell-type entanglement. It is not the original state. There's no restoration.

Zz.

 

[Count Iblis]

The CNOT gate has been demonstrated in experiments. So, starting from:

[|0> + |1>]|0>

we get the entangled state:


|0>|0> + |1>|1>

Apply the CNOT operator again, and we get the original state back.