Classical states and decoherence

[atyy]

QM works with Kolmogorov just fine.

The reason its Bayesian like is you often see subjective used with regard to state in Copenhagen eg:

1. A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)

Yes, that's Bayesian in spirit. but it's so vague I don't really count it as Bayesian. It could just mean one can shift the Heisenberg cut etc. To me a proper Bayesian account needs a prior (either objective or subjective, I prefer subjective). Personally, I like Copenhagen because of this subjective spirit, but technically it's vague, It's really more like, we don't know what the wave function is - it is the subjective knowledge of objective properties :) But we never say what the properties are, except that FAPP it's the wave function!

Anyway, this maybe brings up a difference between textbook-style Copenhagen and the more modern Quantum Bayesianism. In Copenhagen, since the wave function is not real, but represents FAPP the state of a single system or the ensemble prepared by a procedure, one can do tomography and say that tomography is finding out an "unknown quantum state". However, if the quantum state is truly subjective, it cannot be unknown (if it is my subjective belief, by definition it cannot be unknown to me). So I think Quantum Bayesianism properly speaking does not describe tomography as finding out an "unknown quantum state".

 

[lucas_]

bhobba and atyy.. thanks for the many assistance...

last question for this thread... when you are sitting down looking at the computer screen reading this message. How big is the extend of the decoherence branches or outcomes (that didn't manifest at least to this world).. how many meters away from the chair are the other branches/outcomes or does it include running downstair to get a drink or going to the bathroom.. or is it only in the different positions of your body like your left foot over your knees or hands over head or tilting your head to to left or right that differs in each branches/outcomes? I'd like to know how to estimate the extend of the other branches/outcomes that didn't manifest or in other many worlds... tnx..

 

[atyy]

last question for this thread... when you are sitting down looking at the computer screen reading this message. How big is the extend of the decoherence branches or outcomes (that didn't manifest at least to this world).. how many meters away from the chair are the other branches/outcomes or does it include running downstair to get a drink or going to the bathroom.. or is it only in the different positions of your body like your left foot over your knees or hands over head or tilting your head to to left or right that differs in each branches/outcomes? I'd like to know how to estimate the extend of the other branches/outcomes that didn't manifest or in other many worlds... tnx..

In the most naive form of Many-Worlds, branching occurs whenever one performs a measurement. The other worlds are simply the other terms in the superposition following perfect decoherence, so they differ according to the measurement outcomes. If one is doing a spin experiment, the difference could be spin up or spin down. If one is doing a Schroedinger cat experiment, the difference is dead versus alive cat.

However, there is almost never (or never?) perfect decoherence in finite time, so branching requires some coarse graining. I don't know how this really works (or if it works at all), but the difference between worlds would then presumably depend on the coarse graining.

 

[lucas_]

In the most naive form of Many-Worlds, branching occurs whenever one performs a measurement. The other worlds are simply the other terms in the superposition following perfect decoherence, so they differ according to the measurement outcomes. If one is doing a spin experiment, the difference could be spin up or spin down. If one is doing a Schroedinger cat experiment, the difference is dead versus alive cat.

However, there is almost never (or never?) perfect decoherence in finite time, so branching requires some coarse graining. I don't know how this really works (or if it works at all), but the difference between worlds would then presumably depend on the coarse graining.

You have not answered my specific question. Let's ignore Many worlds for now. When you are sitting down in chair in front of computer, what could you be doing in other branches in Copenhagen, the ones that didn't get manifested.. as you know Copenhagen has only one outcome.. but what are the range of other outcomes that didn't occur.. could you be playing computer games instead of just reading this message in other outcomes, how could you estimate what else you could be doing.. let's assume no splitting occurs. I know in many worlds, each possible eigenvalues of your atoms split own worlds. I'm just focusing solely on the decoherence global superposition which didn't include the atoms splitting, what are the extend of it with this specific example of you sitting in computer?

 

[StevieTNZ]

You have not answered my specific question. Let's ignore Many worlds for now. When you are sitting down in chair in front of computer, what could you be doing in other branches in Copenhagen, the ones that didn't get manifested.. as you know Copenhagen has only one outcome.. but what are the range of other outcomes that didn't occur.. could you be playing computer games instead of just reading this message in other outcomes, how could you estimate what else you could be doing.. let's assume no splitting occurs. I know in many worlds, each possible eigenvalues of your atoms split own worlds. I'm just focusing solely on the decoherence global superposition which didn't include the atoms splitting, what are the extend of it with this specific example of you sitting in computer?

It all depends on what the solution to the fundamental Schrodinger equation predicts as possible states. I don't think anyone has solved the equation for the initial conditions, and the time thereafter, you propose.

 

[bhobba]

When you are sitting down in chair in front of computer, what could you be doing in other branches in Copenhagen,

Copenhagen doesn't have other branches - there is one outcome and one outcome only. Like flipping a coin - you get heads or tails - not one 'branch' with heads and another with tails.

But within MW I don't think the question you asked is answerable - I certainly can't do it.

If someone else wants to make a stab I am all ears.

Thanks
Bill

 

[lucas_]

Copenhagen doesn't have other branches - there is one outcome and one outcome only. Like flipping a coin - you get heads or tails - not one 'branch' with heads and another with tails.

But within MW I don't think the question you asked is answerable - I certainly can't do it.

If someone else wants to make a stab I am all ears.

Thanks
Bill

I know Copenhagen doesn't have branches. I was asking what are the extend of the eigenvalues before the collapse to our single outcome eigenvalues. Is this the right language to use to ask what are the other Copenhagen outcomes that didn't occur. So in the example of sitting in front of a computer. Are the other position eigenvalues only goes say 1 meter around you such that in the other unmanifested outcomes.. you could be reclining your back or something. Let's not complicate with many worlds.. just the other eigenvalues that didn't occur prior to the collapse of this outcome (please rewords these and what are the proper words to use?)

 

[bhobba]

Is this the right language to use to ask what are the other Copenhagen outcomes that didn't occur

They didn't occur because the foundational axiom I mentioned before implies they didn't occur - you have one outcome that is mapped to the POVM that determines the probability of that one outcome. Its a nonsense question to ask without reference to a specific interpretation that modifies that implicit assumption. The interpretation that does that is MW.

And you are still locked in language like collapse - QM does not have collapse - only some interpretations do.

Thanks
Bill

 

[lucas_]

They didn't occur because the foundational axiom I mentioned before implies they didn't occur - you have one outcome that is mapped to the POVM that determines the probability of that one outcome. Its a nonsense question to ask without reference to a specific interpretation that modifies that implicit assumption. The interpretation that does that is MW.

Thanks
Bill

You don't get what I was asking. The outcome is probabilistic and the rest didn't occur.. but because it's random, instead of these eigenvalues of position we get now.. it could be others, and these made up the initial probability distribution, I was asking what are the other probability distribution that didn't occur. Could it made the position eigenstate of your body be slightly to the right such that you are say 1 foot to the right in those outcome that didn't occur but could have occur. Do you understand what I'm saying?

 

[atyy]

You have not answered my specific question. Let's ignore Many worlds for now. When you are sitting down in chair in front of computer, what could you be doing in other branches in Copenhagen, the ones that didn't get manifested.. as you know Copenhagen has only one outcome.. but what are the range of other outcomes that didn't occur.. could you be playing computer games instead of just reading this message in other outcomes, how could you estimate what else you could be doing.. let's assume no splitting occurs. I know in many worlds, each possible eigenvalues of your atoms split own worlds. I'm just focusing solely on the decoherence global superposition which didn't include the atoms splitting, what are the extend of it with this specific example of you sitting in computer?

The answer isn't any different from Many-Worlds, since it's just a matter of whether only one outcome is realized or all outcomes are realized.

 

[bhobba]

You don't get what I was asking. The outcome is probabilistic and the rest didn't occur.. but because it's random, instead of these eigenvalues of position we get now.. it could be others, and these made up the initial probability distribution, I was asking what are the other probability distribution that didn't occur. Could it made the position eigenstate of your body be slightly to the right such that you are say 1 foot to the right in those outcome that didn't occur but could have occur. Do you understand what I'm saying?

In probability there is no probability that didn't occur. You don't know something with certainty so you assign a probability. When that something happens we know with a dead cert what the outcome is.

Look at it another way. Copenhagen is in fact compatible with quite a few different interpretations eg BM and MW. In BM everything is deterministic - probabilities are introduced due to lack of knowledge of initial conditions and in QM you can't know them exactly so you can only speak of probabilities - but everything is objective - there is no different possible outcome. In MW its the opposite - you don't actually get an outcome - we experience simply some aspect of this universal wave-function. Your query doesn't make sense in BM, only MW. Copenhagen is agnostic to it.

Thanks
Bill

 

[lucas_]

In probability there is no probability that didn't occur. You don't know something with certainty so you assign a probability. When that something happens we know with a dead cert what the outcome is.

Look at it another way. Copenhagen is in fact compatible with quite a few different interpretations eg BM and MW. In BM everything is deterministic - probabilities are introduced due to lack of knowledge of initial conditions and in QM you can't know them exactly so you can only speak of probabilities - but everything is objective - there is no different possible outcome. In MW its the opposite - you don't actually get an outcome - we experience simply some aspect of this universal wave-function. Your query doesn't make sense in BM, only MW. Copenhagen is agnostic to it.

Thanks
Bill

Let's take the case of double slit experiment. Copenhagen says it can pass any slits and be in any position, so we have the corresponding eigenstate and eigenvalues of positions in the detectors. But we only have one outcome, only one detector detects the emitted photon. The other unrealized eigenvalues are the other *possible* positions of the photons in the detector and which path. In the case of decoherence, there are quadtrillions and more of the interferences, but they still have eigenvalues. So how do you estimate the other unrealized eigenstates/eigenvalues similar to the double slit experiment where other detector positions have unrealized outcome? So if the range of the undetected photons in double slit is in the other side of the detectors at far left of the slit (instead of the realized outcome right side), what is the equivalent in terms of your sitting in computer, what is the unrealized position eigenstates in analogy to the double slit unrealized detections?

 

[lucas_]

The answer isn't any different from Many-Worlds, since it's just a matter of whether only one outcome is realized or all outcomes are realized.

There is a difference between Copenhagen and Many worlds, in Many Worlds, the Schroedinger Cat can be dead and alive in different branches (it can spawn worlds or split macroscopic branches). But in Copenhagen, this is not possible.. macroscopic branches or macrostate can't be spawned... unless you can show that dead cat and alive at are outcomes that can be realized in Copenhagen?

 

[bhobba]

Let's take the case of double slit experiment. Copenhagen says it can pass any slits and be in any position, so we have the corresponding eigenstate and eigenvalues of positions in the detectors.

It doesn't say that. It speaks only of observations - not going through slits or being in any position.

Here is the a correct quantum account of the double slit:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

If you want to discuss that can you reference that account please.

Thanks
Bill

 

[bhobba]

There is a difference between Copenhagen and Many worlds,

Copenhagen is a minimalist interpretation compatible with a number of others such as MW and BM. That's why your question makes no sense in Copenhagen - only in somthing like MW.

Thanks
Bill

 

[lucas_]

Copenhagen is a minimalist interpretation compatible with a number of others such as MW and BM. That's why your question makes no sense in Copenhagen - only in somthing like MW.

Thanks
Bill

Well. Maybe the following is how I imagine or assume it when I think of these things.. Many Worlds occur for a few seconds, then Copenhagen Collapse occur to them with only one World chosen whose outcome or selection is guided by Bohmian Pilot wave. This is what I imagine all these years. Is it not possible, is there no papers that mentioned it? and what is the flaw of the Unified Interpretations where you combine them together?

 

[bhobba]

Well. Maybe the following is how I imagine or assume it when I think of these things.. Many Worlds occur for a few seconds, then Copenhagen Collapse occur to them with only one World chosen whose outcome or selection is guided by Bohmian Pilot wave. This is what I imagine all these years. Is it not possible, is there no papers that mentioned it? and what is the flaw of the Unified Interpretations where you combine them together?

Why would you imagine such a weird world where interpretations change?

But that doesn't change anything. The question you asked only makes sense in MW or some similar interpretation.

Thanks
Bill

 

[lucas_]

Why would you imagine such a weird world where interpretations change?

But that doesn't change anything. The question you asked only makes sense in MW or some similar interpretation.

Thanks
Bill

So if Copenhagen/Ensemble are minimalist that need extra other, then we can say people who subscribe to Copenhagen/Ensemble are those who want to avoid the issues or hide them under the rug? Since you re one.. you admit you are a positivists who only focus on what you can measure? But since Many worlds and Bohmians don't seem likely. Then what are we left of?

Have you read Tegmark the Mathematical Universe? Here he says we are just simulations using the Copenhagen logarithm.. if true, then Tegmark Interpretation would complete Copenhagen as it would finally explain it all?

 

[bhobba]

So if Copenhagen/Ensemble are minimalist that need extra other,

Why you jump to the conclusion they need them I don't quite understand.

It goes back to the third part of the measurement problem mentioned previously - the problem of outcomes. Copenhagen, ensemble, etc makes no hypotheses why we get outcomes - they just accept it. Others like MW and BM do and they are compatible with those that don't specfy why.

The question you asked is only meaningful in interpretations similar to MW.

Thanks
Bill

 

[lucas_]

Why you jump to the conclusion they need them I don't quite understand.

It goes back to the third part of the measurement problem mentioned previously - the problem of outcomes. Copenhagen, ensemble, etc makes no hypotheses why we get outcomes - they just accept it. Others like MW and BM do and they are compatible with those that don't specfy why.

The question you asked is only meaningful in interpretations similar to MW.

Thanks
Bill

I mentioned "they need them" because I read it in the popular Maximilian decoherence paper where he stated

"3. The concept of classicality in the Copenhagen interpretation

...Based on the progress already achieved by the decoherence program, it is reasonable to anticipate that decoherence embedded in some additional interpretive structure could lead to a complete and consistent derivation of the classical world from quantum mechanical principles."

So what do you think are the possible "interpretive structure"? is he referring to Many Worlds or Bohmian?

 

[atyy]

There is a difference between Copenhagen and Many worlds, in Many Worlds, the Schroedinger Cat can be dead and alive in different branches (it can spawn worlds or split macroscopic branches). But in Copenhagen, this is not possible.. macroscopic branches or macrostate can't be spawned... unless you can show that dead cat and alive at are outcomes that can be realized in Copenhagen?

In Copenhagen, if there is uncontrolled decoherence, then the outcomes will be dead or alive.

 

[bhobba]

So what do you think are the possible "interpretive structure"? is he referring to Many Worlds or Bohmian?

I don't know from that how you get they need them. He is taking about it in the context of the three parts of the measurement problem and having an explanation for the so called problem of outcomes. But as I mentioned previously you can simply accept it and move on.

There are many possible candidates - even Quantum Darwinism you started out with may bear fruit and give a fully quantum explanation. Until there is a way to distinguish them experimentally your guess is as good as mine.

Thanks
Bill

 

[StevieTNZ]

I see my post hasn't been commented on, and in fact *I think* answers the question being posed.

 

[atyy]

I see my post hasn't been commented on, and in fact *I think* answers the question being posed.

It does, that's why I retreated to Schroedinger's cat.

 

[lucas_]

Yes, the window analogy is more or less accurate. Let's go with the simplistic version of collapse just for the idea. A measurement P collapses the wave function randomly into an eigenstate of P. Then if a different measurement Q is made the wave function will randomly collapse into an eigenstate of Q. So for example if I measure position, the wave function will collapse into a narrow peak. Now if I measure momentum, the wave function will collapse into a spread out wave. If I alternate between position and momentum measurements, the wave function will keep jumping between being peaked and spread out. So in Zurek's analogy, each tourist is making a different measurement and so collapsing into an eigenstate of the respective measurements, so reality will be all jumpy.

In addition to Zurek's approach, other lines to explaining the conditions under which repeated or continuous measurements give classical results are:
http://arxiv.org/abs/1305.2517
http://arxiv.org/abs/1407.8090

I think in those papers, one does get a stochastic differential equation describing a jumpy reality. But as long as the jumps are "small", one will have recovered classical trajectories.

Atyy. Something I want to ask for clarifications. It is stated in the Maximillian book page 86 that:

"By contrast, measurements on a closed quantum system will in general alter the state of the system.

It is therefore impossible to regard quantum states of a closed system as existing in the way that classical states do. This raises the question of how classical reality emerges from within the quantum substrate, i.e, how obserables are "objectified" in the above sense. The environment-induced superselection of preferred states discussed in the previous Section 2.8 has certainly made a significant contribution toward answering this question by explaining why only a certain subset of the possible states in the Hilbert space of the system are actually observable. Nonetheless, the problem sketched in the previous paragraph remains, as any direction measurement performed on the system would, in general, still alter the state of the system."

Then he mentioned quantum Darwinism where multiple observers can determine the state of the system from the environment fragments without directly perturbing the system. I'd like to clarify the following:

1. In the quantum substrate of system + environment, is our system a closed quantum system? If not, why does he worry that any direct measurement on the system would still alter the state of the system? In an open system, decoherence with environment can make the system unperturbable by any observer so why propose quantum Darwinism when even without this, the system can't be altered by any measurements of the observer?

2. In case you would say the quantum substrate and especially the system is a closed quantum system and perturbable by observer (is this what you believe?), then what experiments can you do that would directly perturb the system by maybe shining multiple lasers on them (here you can't say you are determining the state of the system by intercepting fragments in environment) such that you want to change the Hamiltonian from position to energy eigenstates such that the laser can make the object vanish in position and becoming pure energy eigenstates. Why is this not possible and how do you make it possible in the window for example?

3. Is quantum Darwinism still valid in Copenhagen, or only in the new Existential Interpretation?

Thank you.

 

[bhobba]

By contrast, measurements on a closed quantum system will in general alter the state of the system.

If what you are observing in the closed system is in a mixed state from entanglement where its 'components' are the eigenvalues of what's observing it there is no way to tell if it altered anything or not. This is one of the key points about decoherence explaining apparent collapse.

The point he is making relates to his issue three of the measurement problem - you don't know if it did or not ie you can only say it didn't change it if it was a proper mixed state - otherwise you can't say that - there is no way of telling - but you can't say it didn't alter the state of the system.

Schlosshauer's book contains very little detail on Quantum Darwinian. You really need to read Zureks paper:
http://arxiv.org/pdf/0903.5082v1.pdf

It focusses on the fact different observers don't observe exactly the same thing - they see different fragments - he shows they still 'see' the same thing.

Its a tacit assumption of the decoherence program all observer's will see the same outcome - he shows it must be the case. Ignorance ensemble takes the earliest point decoherence occurs and places the cut right there so the issue doesn't arise.

Thanks
Bill

 

[lucas_]

If what you are observing in the closed system is in a mixed state from entanglement where its 'components' are the eigenvalues of what's observing it there is no way to tell if it altered anything or not. This is one of the key points about decoherence explaining apparent collapse.

The point he is making relates to his issue three of the measurement problem - you don't know if it did or not ie you can only say it didn't change it if it was a proper mixed state - otherwise you can't say that - there is no way of telling - but you can't say it didn't alter the state of the system.

Schlosshauer's book contains very little detail on Quantum Darwinian. You really need to read Zureks paper:
http://arxiv.org/pdf/0903.5082v1.pdf

It focusses on the fact different observers don't observe exactly the same thing - they see different fragments - he shows they still 'see' the same thing.

Its a tacit assumption of the decoherence program all observer's will see the same outcome - he shows it must be the case. Ignorance ensemble takes the earliest point decoherence occurs and places the cut right there so the issue doesn't arise.

Thanks
Bill

But that passage in page 86 is about quantum Darwinism under the topic "2.9 Redundant Encoding of Information in the Environment and "Quantum Darwinism". Anyway. Can you give an example of what you are saying in "If what you are observing in the closed system is in a mixed state from entanglement where its 'components' are the eigenvalues of what's observing it there is no way to tell if it altered anything or not.". For example, let's take the case of an entangled electron with spin up and spin down. Say the spin up and spin down are components of the eigenvalues. What is the sense there is no way to tell if it's altered or not during observation? Please use this example of entangled electron pair, thanks.

 

[bhobba]

What is the sense there is no way to tell if it's altered or not during observation? Please use this example of entangled electron pair, thanks.

The system here is not the entangled electrons - its the entangled electrons AND the observational apparatus - that's where the decoherence occurs. It is the interaction with the observational apparatus that transforms the superposition of the up/down spin to a mixed state and breaks the entanglement with the other electron.

Note what I said:

If what you are observing in the closed system is in a mixed state from entanglement where its 'components' are the eigenvalues of what's observing it there is no way to tell if it altered anything or not. This is one of the key points about decoherence explaining apparent collapse.

It's not in a mixed state until decohered by the spin observational apparatus.

Actually in answering another query about this I noticed you can find the full gory detail in Chapter 7 of Susskind:
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

It results from the fact if you observe one part of an entangled system it looks like a mixed state to what's observing it - the math is in the above.

Thanks
Bill

 

[lucas_]

The system here is not the entangled electrons - its the entangled electrons AND the observational apparatus - that's where the decoherence occurs. It is the interaction with the observational apparatus that transforms the superposition of the up/down spin to a mixed state and breaks the entanglement with the other electron.

Note what I said:It's not in a mixed state until decohered by the spin observational apparatus.

Actually in answering another query about this I noticed you can find the full gory detail in Chapter 7 of Susskind:
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

It results from the fact if you observe one part of an entangled system it looks like a mixed state to what's observing it - the math is in the above.

Thanks
Bill

Ok. I will read it (but need to prioritize buying stuff). I just want to know what you mean you can't know if you alter them. Supposed you use apparatus that can measure spin up or down.. if it shows spin up.. and other observers apparatus show spin down.. you know they are altered, by the different results of different observers, do you agree with this?

 

[bhobba]

Ok. I will read it (but need to prioritize buying stuff). I just want to know what you mean you can't know if you alter them. Supposed you use apparatus that can measure spin up or down.. if it shows spin up.. and other observers apparatus show spin down.. you know they are altered, by the different results of different observers, do you agree with this?

Its simple. It's got to do with the difference between a proper and an improper mixed state. The mixed state is pu |u><u| + pd |d><d|. If you observe that with the up-down observable you will get |u><u| with probability pu and |d><d| with probability pd. Now is that because it was in state |u><u| with probability pd and similarly for |d><d|? If so the observation did nothing - no change. In interpretations like BM or GRW that actually is the case and is how they resolve the measurement problem. But they may not be true - the observation may have changed the mixed state to a pure one - there is no way of telling. Remember this is a mixed state - not a superposition - interference terms have been suppressed.

Thanks
Bill