Double slit experiment and Interaction

[atyy]

I googled:
"an improper mixture is a proper" mixture
I got 1 result. It is in this forum!

The reduced density matrix obtained after a partial trace over entangled subsystems is what is being referred to as an "improper mixture". So here are some examples of similar discussions, even though they don't use the term "improper mixture".

http://arxiv.org/abs/quant-ph/0312059 p9 "However, note that the formal identification of the reduced density matrix with a mixed-state density matrix is easily misinterpreted as implying that the state of the system can be viewed as mixed too (see also the discussion by d’Espagnat, 1988)."

Similar language is used in the very interesting discussion of http://arxiv.org/abs/quant-ph/9706027 p3 "This argument is often summarized as the statement “the partial trace does not derive state reduction.”

Also discussed in https://www.amazon.com/dp/0198509146/?tag=pfamazon01-20 p82. This one is not free, unfortunately.

 

[Rajkovic]

atyy, do you really believe in MWI? lol .. I Don't even know why you brought that **** metaphysical nonsense here
Bill took all my doubts, all this woo woo is BS, period.

Bill, and about the pilot wave theory ? To me, It's the best theory, and makes sense!

 

[bhobba]

I googled: "an improper mixture is a proper" mixtureI got 1 result. It is in this forum!

Its been discussed many more times than once on this forum often in relation to the following paper:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Thanks
Bill

 

[bhobba]

atyy, do you really believe in MWI? lol .. I Don't even know why you brought that **** metaphysical nonsense here

Atty believes in Copenhagen which is actually very similar to mine - ignorance ensemble - the difference basically being the view of probability:
http://en.wikipedia.org/wiki/Ensemble_interpretation

You have to understand however mathematically MWI is extremely elegant - when you look at it carefully its not non-sense - but still too weird for me.

Bill took all my doubts, all this woo woo is BS, period.

Glad to be of help.

Bill, and about the pilot wave theory ? To me, It's the best theory, and makes sense!

That's fine - its a valid interpretation. But you may find your view changing as you learn more.

Thanks
Bill

 

[lucas_]

The reduced density matrix obtained after a partial trace over entangled subsystems is what is being referred to as an "improper mixture". So here are some examples of similar discussions, even though they don't use the term "improper mixture".

I have been reading on this continuously in any available references and figured out that if you don't perform the trace over the other degrees of freedom or over other entangled subsystems you have to measure each subsystem and have many mixed states.. here can one consider many proper mixed states (instead of just one improper mixed state in one subsystem) in different subsystem of the entangled system measured? What is the implication or consequence. What topic does this fall under so I'll just read about the details in the references (so I won't have to ask each detail which I know can piss people). Thank you.

http://arxiv.org/abs/quant-ph/0312059 p9 "However, note that the formal identification of the reduced density matrix with a mixed-state density matrix is easily misinterpreted as implying that the state of the system can be viewed as mixed too (see also the discussion by d’Espagnat, 1988)."

Similar language is used in the very interesting discussion of http://arxiv.org/abs/quant-ph/9706027 p3 "This argument is often summarized as the statement “the partial trace does not derive state reduction.”

Also discussed in https://www.amazon.com/dp/0198509146/?tag=pfamazon01-20 p82. This one is not free, unfortunately.

 

[lucas_]

I have been reading on this continuously in any available references and figured out that if you don't perform the trace over the other degrees of freedom or over other entangled subsystems you have to measure each subsystem and have many mixed states.. here can one consider many proper mixed states (instead of just one improper mixed state in one subsystem) in different subsystem of the entangled system measured? What is the implication or consequence. What topic does this fall under so I'll just read about the details in the references (so I won't have to ask each detail which I know can piss people). Thank you.

By the way. The following is the exact details of the problems I have. I know already the math of proper mixed state and my most deep impression of it is Bill calling it "sweet in quantum land" (see below). So I figure if you can separately measure each subensemble of entangled system, then you have many separate proper mixed states (because you don't trace out other subsystem bec you measure each too). So would this avoid improper mixed state (where you trace out other subsystem/subensemble) and just treat it as many proper mixed states (by measuring each subsystem) which would make everything also "sweet in quantumland" and there prior to observation. This is my only question and I'd have no further questions for the sake of the OP. Bhobba wrote:

"If you observe a system whose state is already in one those possible outcomes then nothing happens, no collapse - nothing - QM is easy. One way to physically get a mixed state is to randomly present pure states to be observed, the pi representing the probability that state has been selected for observation. Suppose the |bi><bi| are the outcomes of your observation. For such a situation measurement problem solved - the state you observe is what's there prior to observation, nothing collapses or changes, and everything is sweet in quantum land. Such states are called proper mixed states."

 

[lucas_]

By the way. The following is the exact details of the problems I have. I know already the math of proper mixed state and my most deep impression of it is Bill calling it "sweet in quantum land" (see below). So I figure if you can separately measure each subensemble of entangled system, then you have many separate proper mixed states (because you don't trace out other subsystem bec you measure each too). So would this avoid improper mixed state (where you trace out other subsystem/subensemble) and just treat it as many proper mixed states (by measuring each subsystem) which would make everything also "sweet in quantumland" and there prior to observation. This is my only question and I'd have no further questions for the sake of the OP. Bhobba wrote:

"If you observe a system whose state is already in one those possible outcomes then nothing happens, no collapse - nothing - QM is easy. One way to physically get a mixed state is to randomly present pure states to be observed, the pi representing the probability that state has been selected for observation. Suppose the |bi><bi| are the outcomes of your observation. For such a situation measurement problem solved - the state you observe is what's there prior to observation, nothing collapses or changes, and everything is sweet in quantum land. Such states are called proper mixed states."

Is the answer you can't attribute any mixed state to the subsystem independently because it is one entangled system and only a single or isolated subsystem can be measured via the concept of improper mixed state? If yes. Then it answers my question and entangled system is not sweet in quantum land as Bill expressed proper mixture is. Please someone confirm if this is completely true so I can move on. Thank you!

 

[naima]

Also discussed in https://www.amazon.com/dp/0198509146/?tag=pfamazon01-20 p82. This one is not free, unfortunately.

Thank you Atyy
I am reading this book for some time!
Could you please look at my question (without answer in atomic physics
It is also about mixture and pure state.

 

[lucas_]

Is the answer you can't attribute any mixed state to the subsystem independently because it is one entangled system and only a single or isolated subsystem can be measured via the concept of improper mixed state? If yes. Then it answers my question and entangled system is not sweet in quantum land as Bill expressed proper mixture is. Please someone confirm if this is completely true so I can move on. Thank you!

After reading 50% of bhobba and atyy old messages. I think I got it. Proper mixed state is classical ignorance. But in the improper (and even proper mixed state if you consider the entire pure state of the system), why is the transition from the entangled pure state to mixed state.. why this outcome. Herein lies the mystery. While you can choose between MWI or bohmians. I think the Tegmark mathematical universe interpretation makes more sense in such we are living inside a system programmed by math. Nuff said. I will finally move on. Thanks bhobba, atyy and others for our weeks of exchanges on the math aspect of it all. Now you can continue focus on the OP questions so he learns more.

 

[Rajkovic]

Can someone tell me if this interpretation of MWI is correct?MWI: "Every time you make a choice or imagine anything you create at least two POTENTIAL universes. Once there's outcome all the other POTENTIAL universes cease to exist"

give me a light... in this "theory" , Where are these "universes" (Or hypotheses, whatever) that were created? in Universe's imagination? lol, I can't understand it. MWI would be almost equal to the Multiverse?

I just want to learn it, even tho, I know this isn't correct. at all.

 

[kith]

Copenhagen has a flavour in which naive, common sense realism is privileged, a view completely consistent with BM and MWI. But in another thread, kith brought up that maybe all physical theories need a cut. As I understand it, since a cut means the observer cannot be included in the theory, if we believe that the observer is also governed by laws of physics, then we are challenged to construct a more complete theory.

The interesting thing is that we have candidates for more complete theories in two different directions. dBB deals with what you write above and doesn't introduce new physics while beyond the Standard Model theories like String theory don't deal with what you write above and do introduce new physics. So my suggestion was that maybe the cut is here to stay in future theories involving new physics and we shouldn't picture the old theories as cut-free just because we can.

(However on second sight, things aren't so clear. dBB may be a different and more correct theory then QM, String theory has a hard time of predicting observable new physics, and maybe the two different directions aren't so different and progress on the measurement problem will lead to progress on quantum gravity. I just don't see it coming.)

 

[kith]

MWI: "Every time you make a choice or imagine anything you create at least two POTENTIAL universes. Once there's outcome all the other POTENTIAL universes cease to exist"

No, all outcomes are realized in some universe. So after a spin experiment, there is one universe where the spin has been measured as up and one where it has been measured as down.

 

[rootone]

No, all outcomes are realized in some universe. So after a spin experiment, there is one universe where the spin has been measured as up and one where it has been measured as down.

Are they not just possible outcomes though?, and only one of them actually IS realized?
Or do we have to conclude that the other possible outcomes must have a physical reality - that there actually does exist another universe, (or a part of the same universe), where the experimenter is in every respect the same person but the experiment gave a different result?

 

[bhobba]

MWI: "Every time you make a choice or imagine anything you create at least two POTENTIAL universes. Once there's outcome all the other POTENTIAL universes cease to exist"

No. Its a load of new age gibberish.

MWI is actually a devastatingly simple, beautiful, and elegant interpretation. Its simply this. After decoherence, in the improper mixed state, each 'component' of the mixed state is interpreted as a world. No collapse or anything. You simply have everything evolving according to the Schrodinger equation.

give me a light... in this "theory" , Where are these "universes" (Or hypotheses, whatever) that were created? in Universe's imagination? lol, I can't understand it. MWI would be almost equal to the Multiverse?

They are in a sense not 'created' - they were there all the time - everything is deterministic. They don't reside anywhere. You just can't consider them separate worlds until after decoherence. It's like in classical mechanics the position and momentum at time 0 fully determines when particles will bang into each other, but you can't consider them to have done so until it happens.

I just want to learn it, even tho, I know this isn't correct. at all.

Check out this guy and his book:
http://users.ox.ac.uk/~mert0130/

Thanks
Bill

 

[bhobba]

Are they not just possible outcomes though?, and only one of them actually IS realized?

No. The interpretation is after decoherence each, what would usually be considered a possible outcome, is realized. They are called separate worlds.

Technically the state after decoherence has the form ∑pi |bi><bi|. The interpretation interprets each |bi><bi| as a world.

Or do we have to conclude that the other possible outcomes must have a physical reality - that there actually does exist another universe, (or a part of the same universe), where the experimenter is in every respect the same person but the experiment gave a different result?

Words like physical reality etc are very problematical because philosophers argue about what it means all the time without ever reaching a conclusion. Best to ban them. But each world has just as much validity as a world as any other.

Thanks
Bill

 

[atyy]

The interesting thing is that we have candidates for more complete theories in two different directions. dBB deals with what you write above and doesn't introduce new physics while beyond the Standard Model theories like String theory don't deal with what you write above and do introduce new physics. So my suggestion was that maybe the cut is here to stay in future theories involving new physics and we shouldn't picture the old theories as cut-free just because we can.

(However on second sight, things aren't so clear. dBB may be a different and more correct theory then QM, String theory has a hard time of predicting observable new physics, and maybe the two different directions aren't so different and progress on the measurement problem will lead to progress on quantum gravity. I just don't see it coming.)

My thinking was different - dBB and string theory both introduce new physics - and each is motivated by different cuts. dBB deals with the Heisenberg classical/quantum cut, and string theory deals with the Wilsonian UV cut. So having string theory as the next theory is not against dBB thinking. Actually, the only thing that is against dBB thinking is that Copenhagen is complete. I think it is completely consistent with the spirit of dBB to have MWI, if it works. It's the same as Asymptotic Safety and string theory both being consistent with Wilsonian thinking. As I understand it, considering Copenhagen complete would be like saying subtracting infinities is mathematically sound, ie. the Wilsonian idea is fundamentally wrong.

 

[Rajkovic]

"This is the quantum Bayesianism approach, or more generally “psi-epistemic” approaches. The idea is to simply deny that the quantum state represents anything about reality; it is merely a way of keeping track of the probability of future measurement outcomes. Is the particle spin-up, or spin-down, or both? Neither! There is no particle, there is no spoon, nor is there the state of the particle’s spin; there is only the probability of seeing the spin in different conditions once one performs a measurement."

This means that there is no collapse, there is no "quantum weirdness", right? Reality is fixed

 

[Rajkovic]

I got it ..This means that in MWI there is no collapse, there is no "quantum weirdness", right? nothing changes in reality. right?

and about this?
The “denial” strategy says “The idea of multiple worlds is so profoundly upsetting to me that I will deny the existence of reality in order to escape having to think about it.” Advocates of this approach don’t actually put it that way, but I’m being polemical rather than conciliatory in this particular post. And I don’t think it’s an unfair characterization. This is the quantum Bayesianism approach, or more generally “psi-epistemic” approaches. The idea is to simply deny that the quantum state represents anything about reality; it is merely a way of keeping track of the probability of future measurement outcomes. Is the particle spin-up, or spin-down, or both? Neither! There is no particle, there is no spoon, nor is there the state of the particle’s spin; there is only the probability of seeing the spin in different conditions once one performs a measurement. I advocate listening to David Albert’s take at our WSF panel.

(what he means by "There is no spoon")?
http://www.preposterousuniverse.com...ion-of-quantum-mechanics-is-probably-correct/

 

[bhobba]

This means that there is no collapse, there is no "quantum weirdness", right? Reality is fixed

No.

Quantum Bayesianism is a close relative of Copenhagen. The difference is it specifically states its interpretation of probability is Bayesian. Copenhagen doesn't say it outright, but in that interpretation the state is subjective, which is basically Bayesian anyway without spelling it out. I personally consider it the same as Copenhagen.

There is collapse, just like Copenhagen has collapse, it just doesn't really mean anything because it's purely subjective just like probabilities in Bayesian probability theory. When you update probabilities in that approach from new information it instantly changes from when that new information is available, but since its simply a subjective belief its of no concern at all.

The approach is based foundationally on POVM's as per post 136 in the following:
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

The Born rule is simply a consequence of its foundational axiom rather than a separate axiom.

Added Later:
If you want more detail on the approach check this out:
http://arxiv.org/pdf/1301.3274.pdf

As you can see its simply some stuff with POVM's as the foundational thing in QM and the Born rule is a consequence of that. As it says:
'The most important point of this exercise is that with such a mapping established, one has every right to think of a quantum state as a probability distribution full stop.'Thanks
Bill

 

[bhobba]

The “denial” strategy says “The idea of multiple worlds is so profoundly upsetting to me that I will deny the existence of reality in order to escape having to think about it.” Advocates of this approach don’t actually put it that way, but I’m being polemical rather than conciliatory in this particular post.

Don't get caught up in philosophical semantics that really just expresses the person that is putting it forward personal belief in the form of some kind of dialectic. That isn't what science is about. If you find it weird, its because MW is weird. If its too weird for you to stomach, and it is for me, just say it, without the philosophical waffle about denying reality yada, yada, yada.

The reason is it may be true. Future progress may figure out some way of testing it experimentally - then you end up with egg on your face and understand your dialectic is a crock. It has happened heaps of times. Kant for example had a dialectic that purported to show Euclidean geometry must a-prori be true. Gauss proved him wrong by expressing the problem mathematically, and showed, logically, non euclidean geometries are just as valid. He however didn't publish because Kant held such a strong intellectual sway. Math and physics have thankfully moved on since then.

Thanks
Bill

 

[kith]

My thinking was different - dBB and string theory both introduce new physics

dBB is widely considered to be an interpretation of QM, so its predictions are considered to be identical to Copenhagen's. If this is the case then dBB doesn't introduce new physics. If not, dBB is a different theory. This is possible but my impression so far is that whenever dBB deviates from QM, the effects are ultimately not observable.

dBB deals with the Heisenberg classical/quantum cut, and string theory deals with the Wilsonian UV cut. So having string theory as the next theory is not against dBB thinking.

This is an interesting analogy. Unfortunately, I don't know much about renormalization and String theory. To me, the motivation and accomplishments of String theory seem to be mostly physical by being able to make predictions for physical situations where previous theories break down. But since actually making these predictions -let alone verifying them- seems to be very difficult, you may be right that the main advancement is conceptual.

I think it is completely consistent with the spirit of dBB to have MWI, if it works.

That doesn't make sense to me. In dBB, there's only one world. Wrt to Copenhagen, the hidden variables of dBB represent a more fundamental reality. Wrt to MWI, the hidden variables specify which world is the real one. So the hidden variables give a more complete picture for both interpretations.

As I understand it, considering Copenhagen complete would be like saying subtracting infinities is mathematically sound, ie. the Wilsonian idea is fundamentally wrong.

This doesn't seem to fit into what you wrote above: your analogy was Copenhagen<->Wilson, dBB<->String theory. So wouldn't considering Copenhagen complete correspond to the Wilsonian idea being fundamental?

 

[kith]

Are they not just possible outcomes though?, and only one of them actually IS realized?

bhobba already answered this but just to be clear: we were talking specifically about the Many Worlds interpretation. In the Copenhagen interpretation, only one outcome is realized.

 

[atyy]

dBB is widely considered to be an interpretation of QM, so its predictions are considered to be identical to Copenhagen's. If this is the case then dBB doesn't introduce new physics. If not, dBB is a different theory. This is possible but my impression so far is that whenever dBB deviates from QM, the effects are ultimately not observable.

Yes, here I am assuming that dBB points to the possibility of "quantum non-equilibrium" and so it is a different theory. I consider pure dBB to be not real, just as the ensembles of statistical mechanics are not real.

This is an interesting analogy. Unfortunately, I don't know much about renormalization and String theory. To me, the motivation and accomplishments of String theory seem to be mostly physical by being able to make predictions for physical situations where previous theories break down. But since actually making these predictions -let alone verifying them- seems to be very difficult, you may be right that the main advancement is conceptual.

I think they are mainly conceptual. And both still have ways to go in describing known reality. String theory is shaky for cosmology, especially with positive cosmological constant, and dBB is shaky for chiral fermions interacting with non-Abelian gauge fields. An interesting point here is that one idea for getting chiral fermions in lattice gauge theory is by introducing extra dimensions. If that actually works, then dBB and string theory will both introduce extra dimensions.

That doesn't make sense to me. In dBB, there's only one world. Wrt to Copenhagen, the hidden variables of dBB represent a more fundamental reality. Wrt to MWI, the hidden variables specify which world is the real one. So the hidden variables give a more complete picture for both interpretations.

Yes, I should elaborate. It is not so much that dBB is directly consistent with MWI, rather dBB and MWI are both motivated by naive realism and the assumption that Copenhagen is complete. Each introduces an additional assumption (hidden variables or multiple outcomes) to complete Copenhagen.

(Perhaps BM is in a very technical sense consistent with MWI, since we can imagine Bohmian Many-Worlds, which seems to make all the difficulties of MWI go away.)

This doesn't seem to fit into what you wrote above: your analogy was Copenhagen<->Wilson, dBB<->String theory. So wouldn't considering Copenhagen complete correspond to the Wilsonian idea being fundamental?

Copenhagen <-> Subtracting infinitities (It works FAPP!)
Naive realism, incompleteness of Copenhagen <-> Wilsonian framework, incompleteness of QED, quantum general relativity
dBB <-> string theory (new physics)
MWI <-> Asymptotic Safety (no new physics)

 

[kith]

I like your point of view but I don't share it yet. ;-) I still tend to think that Copenhagen tells us something important about physics and that although dBB is valuable it won't lead to new physics. But my current thinking is strongly rooted in non-relativistic QM and I will definitely have your analogies in the back of my head when I explore QFT and physics beyond the Standard Model more.

 

[atyy]

I like your point of view but I don't share it yet. ;-) I still tend to think that Copenhagen tells us something important about physics and that although dBB is valuable it won't lead to new physics. But my current thinking is strongly rooted in non-relativistic QM and I will definitely have your analogies in the back of my head when I explore QFT and physics beyond the Standard Model more.

I do think Copenhagen is telling us something. But what? There are two ways to go. The first is that naive realism always holds, but at some point we need a cut (or MWI), because the aim of physics is to predict the future, whereas as the Wiener saying goes - the best model for a cat is another cat, preferably the same cat - at some point we cannot model the whole universe and our theories must necessarily be incomplete. So perhaps all useful post-quantum theories will have a cut, maybe something like http://arxiv.org/abs/1105.4464. I think dBB is consistent with this view, since naive realism is privileged by assumption. However, dBB also suggests that we are not necessarily at this stage yet by providing a toy counterexample in the case of a universe in which non-relativistic quantum mechanics is a good approximation.

The second view is that there is something fundamentally wrong with naive realism. Maybe consistent histories in the Griffiths's style or Wheeler's universe observing itself or Penrose's consciousness is a fundamental element (Penrose is usually considered a naive realist, so he wouldn't put himself here, but I do). Let's call this the Wheeler-Penrose-Chopra approach :)

Is your view about what Copenhagen is teaching us one of the above, or something else entirely? Myself I do Copehagen on weekdays, dBB on Sundays (Bell: "I am a Quantum Engineer, but on Sundays I have principles") and Wheeler-Penrose-Chopra on Friday and Saturday evenings.

A bit more seriously, here is an analogy for naive realism in mathematics. In mathematics we have the intuitive natural numbers and Peano's axioms. Goedel's incompleteness theorem says that there will always be statements that are true about the intuitive natural numbers that cannot be captured by any axiomatic system. Here the intuitive natural numbers live in naive reality. Well, can we get rid of naive reality? We can at least try to get rid of the intuitive natural numbers. Instead of using the intuitive natural numbers, we can formalize the natural numbers in ZFC. Then we assert that the intuitive natural numbers do not exist, and we only ever mean the natural numbers in ZFC. However, naive realism still survives, because to define ZFC itself, we need a metalanguage which lives in naive realism.

What is interesting about the above argument is that it both argues that we need naive realism, and that mathematics has an unavoidable cut. But I don't know how that cut relates to the Heisenberg cut of Copenhagen, since I think the cut of mathematics should also be in a classical theory like GR. Maybe, as you say, even the old theories have a observer/system cut?

 

[zonde]

No, all outcomes are realized in some universe. So after a spin experiment, there is one universe where the spin has been measured as up and one where it has been measured as down.

Newer understood this about MWI. Take Mach–Zehnder interferometer, photons are detected only at one output in case of interference. If you say that all outcomes are realized then you contradict experiment.

 

[StevieTNZ]

Newer understood this about MWI. Take Mach–Zehnder interferometer, photons are detected only at one output in case of interference. If you say that all outcomes are realized then you contradict experiment.

But there is only one possible outcome? How does that contradict Many Worlds?

 

[zonde]

But there is only one possible outcome? How does that contradict Many Worlds?

Obviously there are two possible outcomes (beamsplitter has two outputs) but we observe only one in idealized case.
There are two possible outcomes after the first beamsplitter. And then there are two possible outcomes after second beamsplitter if we consider only single path.
Basically two worlds have to interact to determine outcome or the "wrong" worlds have to cease to exist (after they somehow discover that they are wrong).

 

[GasolineRainbow]

I am a bit ignorant about all this so can people clear something up for me...
You can see the interference pattern in the double slit experiment until you try to measure it with, for example, polarised light.
This is because the 2 part wavefunction becomes one part once you measure which slit the light photon has gone through, i.e. it's no longer in a superposition state
Surely that doesn't actually mean there is no interference pattern?? Of course you can't observe it when you're measuring which photons went through which slit since where they end up, aside from some places being more likely than others, is essentially random. So the interference pattern hasn't gone, you're just not observing it? If you marked on all the photons that, from your measurements, passed through the right, and then all the photons that passed through the left, would you not be able to see the interference pattern again? Or can you not?
I think I'm just confused by superposition states. I can't help but think of wavefunctions as hypothetical descriptions of where the photon might pass, rather than the photon passing through both slits at once. So the superposition state, by my definition, does not collapse. It's an imaginary state that describes a possibility rather than a reality and when you measure the realities you can't see the interference pattern, but when you look at the photons without knowing which slit they passed through, you see the possibilities, and that equates to the interference pattern. I don't think I'm explaining myself very clearly but if anyone gets my point, can they help me out?

 

[StevieTNZ]

Obviously there are two possible outcomes (beamsplitter has two outputs) but we observe only one in idealized case.
There are two possible outcomes after the first beamsplitter. And then there are two possible outcomes after second beamsplitter if we consider only single path.
Basically two worlds have to interact to determine outcome or the "wrong" worlds have to cease to exist (after they somehow discover that they are wrong).

I'm pretty sure after the 2nd beam splitter one of the paths has zero probability for the system to go along.

 

[zonde]

I'm pretty sure after the 2nd beam splitter one of the paths has zero probability for the system to go along.

Yes, this is QM prediction in idealized specific case. But this prediction is non trivial and you have to explain it if you claim that you have meaningful QM interpretation.

 

[StevieTNZ]

Things with 0 probability of happening don't make the universe branch out so it does happen, only then to realize it shouldn't and cease to exist.
No branching occurs to make a universe where the particle goes along that 0 probability path. (I would have thought?)

 

[Feeble Wonk]

I know that I shouldn't pursue this, but I can't help myself. I am sometimes confused as to whether (and why) decoherence is consistently as limiting to potential quantum states as I've often heard it argued. I think I understand the general decoherence concept... the interaction between the environment, the prepared system and the "apparatus" by which potential quantum states are differentiated. But, it seems to me that IF we consider that the quantum state in question as being that describing the entire universe, and no effort is made to manipulate (prepare) the system, then the definition of "environment" becomes somewhat arbitrary and/or ambiguous.

Even a few stray photons from the CMBR is enough to decohere a dust particle...

Yet, does anything change if the quantum state of the "few stray photons" are also unresolved? Again, if what we are considering is the quantum state of the cosmos as a whole, and no experimental controls are in place, does that change anything. Is every subatomic particle necessarily an apparatus by which a measurement is made?

 

[atyy]

I know that I shouldn't pursue this, but I can't help myself. I am sometimes confused as to whether (and why) decoherence is consistently as limiting to potential quantum states as I've often heard it argued. I think I understand the general decoherence concept... the interaction between the environment, the prepared system and the "apparatus" by which potential quantum states are differentiated. But, it seems to me that IF we consider that the quantum state in question as being that describing the entire universe, and no effort is made to manipulate (prepare) the system, then the definition of "environment" becomes somewhat arbitrary and/or ambiguous.

I think this is a problem for pure decoherence. It is often said that decoherence has rephrased the measurement problem, and removed the need for a subjective observer-dependent cut, and that the measurement problem is mainly one of why there are definite outcomes. In simple systems, it may be that pure decoherence plus an additional criterion can give an "objective" cut, in the sense the all observers who use the criterion will place the cut in the same location. However, a hallmark of the Copenhagen interpretation is that different observers can place the cut in different places, and the cut is not objective. Because decoherence plus an additional criterion is too objective, I don't think decohence can place an objective cut - or rather if it can, the cut will be wrong for some observer.

Schlosshauer's very good review on decoherence http://arxiv.org/abs/quant-ph/0312059 does phrase the measurement problem mainly as one of definite outcomes, but he does mention (p15): "Finally, a fundamental conceptual difficulty of the decoherence-based approach to the preferred-basis problem is the lack of a general criterion for what defines the systems and the “unobserved” degrees of freedom of the environment (see the discussion in Sec. III.A). While in many laboratory-type situations, the division into system and environment might seem straightforward, it is not clear a priori how quasiclassical observables can be defined through environment-induced superselection on a larger and more general scale, when larger parts of the universe are considered where the split into subsystems is not suggested by some specific system-apparatus surroundings setup."

 

[harrylin]

[..] Those that go on about this conciousness stuff often are influenced by gutter trash like What The Bleep Do We Know Anyway:


Its junk of the first order trying to justify new age stiff like The Secret. [..]

That one I have seen completely - not because I wanted to, but because my sister saw it on TV and asked my opinion about it. It's obviously manipulated by some kind of sect, making it appear as if serious physicists support wacky ideas.
See: https://en.wikipedia.org/wiki/What_the_Bleep_Do_We_Know!?#Featured_individuals

 

[Feeble Wonk]

Schlosshauer's very good review on decoherence http://arxiv.org/abs/quant-ph/0312059 does phrase the measurement problem mainly as one of definite outcomes, but he does mention (p15): "Finally, a fundamental conceptual difficulty of the decoherence-based approach to the preferred-basis problem is the lack of a general criterion for what defines the systems and the “unobserved” degrees of freedom of the environment (see the discussion in Sec. III.A). While in many laboratory-type situations, the division into system and environment might seem straightforward, it is not clear a priori how quasiclassical observables can be defined through environment-induced superselection on a larger and more general scale, when larger parts of the universe are considered where the split into subsystems is not suggested by some specific system-apparatus surroundings setup."

This appears to be precisely the point of my question. So, in the absence of a definitive "line in the quantum sand" determined by an obvious system-apparatus-environment situation, how open can the cosmological quantum state remain? At the risk of extending this question to the seemingly absurd, can we return to the unobserved moon scenario for a moment? If the presence of the moon on a macroscopic level is manifested by various parameters such as gravitational effects and visual identification among others, without any additional manipulation of apparatus-system-environment relationships in place, would the EXACT location of the moon become infinitesimally less determined if no one was looking?

 

[atyy]

This appears to be precisely the point of my question. So, in the absence of a definitive "line in the quantum sand" determined by an obvious system-apparatus-environment situation, how open can the cosmological quantum state remain? At the risk of extending this question to the seemingly absurd, can we return to the unobserved moon scenario for a moment? If the presence of the moon on a macroscopic level is manifested by various parameters such as gravitational effects and visual identification among others, without any additional manipulation of apparatus-system-environment relationships in place, would the EXACT location of the moon become infinitesimally less determined if no one was looking?

Are you asking in the context of a particular interpretation?

 

[Feeble Wonk]

Well... I'm open to in-put from any interpretation I guess. But I suppose the question was specifically with regard to standard Copenhagen interpretation, and the limitations imposed by decoherence.

 

[atyy]

Well... I'm open to in-put from any interpretation I guess. But I suppose the question was specifically with regard to standard Copenhagen interpretation, and the limitations imposed by decoherence.

That's easy. Copenhagen says nothing about the moon when you don't look. Copenhagen has 3 things it needs the observer to do

(1) Choose a system/apparatus divide (ie. the Heisenberg cut or the classical/quantum cut)
(2) Choose an observable (ie. a preferred basis)
(3) Choose when the observable is measured

In simple cases, it does seem that decoherence plus additional objective criteria (eg. the probability sieve) can do all 3, so there is some advance in the sense that although we still have bizarre things like a Heisenberg cut and wave function collapse, we no longer need an observer to subjectively do these jobs. This is why it is often said that decoherence rephrases the measurement problem. However, as we discussed above in posts #83 and 84, decoherence cannot do (1) one in general, because a hallmark of Copenhagen is that the cut is not objective, and can be shifted. (Schlosshauer uses different terminology in his review. What I am calling Copenhagen with a movable cut is called the "standard interpretation" by him, while he uses "Copenhagen" for an objective unmovable cut.)

 

[Rajkovic]

In Qbism, the interpretation of the state is subjective, right.. then what changes in the macro world?

 

[bhobba]

Yet, does anything change if the quantum state of the "few stray photons" are also unresolved? Again, if what we are considering is the quantum state of the cosmos as a whole, and no experimental controls are in place, does that change anything. Is every subatomic particle necessarily an apparatus by which a measurement is made?

Scratching head here. Why exactly do you think the state of the photons will not be changed by the interaction?

And not every object in the universe is not an observational apparatus - only those capable of causing decoherence eg a single photon is not enough to decohere a dust particle - you evidently need a few.

.Thanks
Bill

 

[bhobba]

In Qbism, the interpretation of the state is subjective, right.. then what changes in the macro world?

The outcome of the observation.

Thanks
Bill

 

[zonde]

Things with 0 probability of happening don't make the universe branch out so it does happen, only then to realize it shouldn't and cease to exist.
No branching occurs to make a universe where the particle goes along that 0 probability path. (I would have thought?)

Let me use analogy.

Say you are standing on a street corner and you want to get to the diagonally opposite corner of the block. You can go around the block by going left (L path) or right (R path). And as you go by either path you have to count front doors of the buildings that you pass. So if you choose L path you will count X number of doors but if you choose R path you will count Y number of doors.
But the trick is that I want you to tell me at the end if the difference between X and Y is odd or even number (that will decide which one of the further paths will be 0 probability path and which one - 1 probability path).

Can you do that if you are allowed to make two copies of the world?
Say two worlds - L and R. In L world you take L path but at the end you know X but don't know Y. And vice versa for R world. And if you do not allow worlds to communicate some time after splitting you can't tell me the quantity I am asking, right?

 

[kith]

Newer understood this about MWI. Take Mach–Zehnder interferometer, photons are detected only at one output in case of interference. If you say that all outcomes are realized then you contradict experiment.

No. If the probability to detect the photons at one detector is 100%, then there is only a single possible outcome and therefore only a single world.

The MWI doesn't simply assign worlds to all terms in a superposition. This wouldn't make sense because whether a state is a superposition or not depends on the basis and every state is a superposition of eigenstates of some observable.

In the most basic version, the splitting into different worlds occurs whenever you have different possible outcomes in a measurement. More sophisticated, the splitting occurs whenever a superposition is turned into the corresponding mixed state by decoherence.

 

[Feeble Wonk]

Scratching head here. Why exactly do you think the state of the photons will not be changed by the interaction.

And, again, how does the environment know if the photon(s) interacted with the dust particle? My question was making the assumption that the dust particle is not being observed in anyway other than through its "potential" random environmental interaction, with no system preparation and no experimental controls. Furthermore, the dust particle and the photon(s) are only being considered as part of the entire cosmological quantum state. So, would the quantum state of both the photons and the dust particle be less "determined" in such a way as to delay the environmentally induced collapse secondary to decoherence?
I

 

[Feeble Wonk]

Apologies... I botched that lady posting. I'll try again.

And not every object in the universe is not an observational apparatus - only those capable of causing decoherence eg a single photon is not enough to decohere a dust particle - you evidently need a few.

.Thanks
Bill

I'm sorry to be dense about this, but that's what I'm trying to understand. Which subatomic particles perform as an observational apparatus, and why sometimes rather than others. Is it totally dependent on the preparation state of the system being observed? And if the system is not "prepared", and there are no experimental controls in place, such that both system and "environment" are maximally "open", does this change things? It seems that under certain circumstances quantum superpositions can be maintained for a functional period of time, even in warm and "noisy" environments. At least, the demonstration of quantum effects in photosynthesis would appear to suggest that.
http://m.phys.org/news/2012-01-role-quantum-effects-photosynthesis.html

 

[Feeble Wonk]

Scratching head here. Why exactly do you think the state of the photons will not be changed by the interaction?

But, how does the environment know if the photon(s) interacted with the dust particle? My question was making the assumption that the dust particle is not being observed in anyway other than through its "potential" random environmental interaction, with no system preparation and no experimental controls. Furthermore, the dust particle and the photon(s) are only being considered as part of the entire cosmological quantum state. So, would the quantum state of both the photons and the dust particle be less "determined" in such a way as to delay the environmentally induced collapse secondary to decoherence?

 

[bhobba]

Which subatomic particles perform as an observational apparatus, and why sometimes rather than others.

It depends on the situation - specifically if the object or objects interact with what is being observed and the degree of interaction. You must analyse each situation in detail to determine if the decoherence (ie interaction) is enough to give a definite outcome in some observable. Of course its a bit arbitrary what is counted as a definite outcome eg what precision we count the position to be known before we say it has that position. It turns out to nearly always be the position observable and when you chug through the math the reason is virtually all interactions are of the radial type.

Thanks
Bill

 

[bhobba]

But, how does the environment know if the photon(s) interacted with the dust particle?

The environment has nothing to do with it in that situation ie the few stray photons is the environment.

Thanks
Bill

 

[zonde]

No. If the probability to detect the photons at one detector is 100%, then there is only a single possible outcome and therefore only a single world.

The MWI doesn't simply assign worlds to all terms in a superposition. This wouldn't make sense because whether a state is a superposition or not depends on the basis and every state is a superposition of eigenstates of some observable.

In the most basic version, the splitting into different worlds occurs whenever you have different possible outcomes in a measurement. More sophisticated, the splitting occurs whenever a superposition is turned into the corresponding mixed state by decoherence.

Yes, with a bit of help from Wikipedia I understand what I missed about MWI - world splits only at measurement and not before.

And it makes MWI even more bizarre. Quantum system in MWI actually is a wave. So it is non-local.
And then the split. It is non-local - how else if the quantum system is non local?
And it creates only appearance of particle. So there is no such a thing as particle in MWI, right?