Undergrad Schrodinger's cat, the multiverse and isolated systems

[Feeble Wonk]

Here is one way to create a mixed state. Randomly select a pure state. There is a pure state there - but its unknown what it is. Such are called proper mixed states.

Ugh... I'm getting MORE confused rather than less.

My previous understanding was that the "pure" state was in actual superposition... still in the "and" state, so to speak. In contrast, I thought the "proper mixture" was in an "either/or" state. It's admittedly a subtle difference, but logically significant.

 

[Feeble Wonk]

Or... are you saying that the "proper" mixed state actually contains a "pure" state in addition to a null (nonexistent) state? Nonexistent, in the sense that it MIGHT have been, but it's not.

 

[bhobba]

Or... are you saying that the "proper" mixed state actually contains a "pure" state in addition to a null (nonexistent) state? Nonexistent, in the sense that it MIGHT have been, but it's not.

Its what I said. Imagine you have a heap of pure states that are the possible outcomes of an observation. You randomly select one. There is a pure state there - but because it was randomly selected you don't know which one - only the probability of what it is. That is a proper mixed state.

Thanks
Bill

 

[quantumfunction]

I think the real question is about decoherence and isolated systems.

If the box is an isolated system doesn't the cat and everything in the box become observable states of that isolated system (the box)? If I understand Tegmark and Everett's postulate about isolated systems, it's saying that decoherence doesn't occur if there's nothing external to the isolated system. In this case all observable states of the isolated system would be realized.

So if the universe is an isolated system then our universe would be an observable state of that isolated system because there's nothing external to the universe to interact with so no decoherence.

The reason we can see the wave nature of particles is because they can remain isolated for long periods of time. So in a sense these particles have free will according to the Free Will Theorem.

The free will theorem of John H. Conway and Simon B. Kochen states that, if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006.[1] They published a stronger version of the theorem in 2009.[2]

https://en.wikipedia.org/wiki/Free_will_theorem

A baseball can't remain isolated from it's environment so it's always in one observable state. This would mean classical objects don't have free will. There different states can't exist in the same environment so they're in different universes.

On a side note, this could mean if we have free will it's due to a quantum mind. So on a classical level you have no choice but to go to medical school instead of law school because you're in this observable state of an isolated system. Your quantum mind would be like the isolated particle and experiences a choice between law school and medical school.

I think Tegmark understood this dilemma and he recently proposed that consciousness was a state of matter. I think it makes more sense if consciousness is quantum because that would mean the mind could remain isolated from the environment and could make choices or appear to make choices because it would have a wave nature like an isolated particle.

 

[bhobba]

If the box is an isolated system doesn't the cat and everything in the box become observable states of that isolated system (the box)?.

If the box is an isolated system its the same story. The observation happens at the particle detector - everything is common-sense classical from that point on. The cat lives or dies regardless of if the box is opened, is isolated etc.

Thanks
Bill

 

[quantumfunction]

If the box is an isolated system its the same story. The observation happens at the particle detector - everything is common-sense classical from that point on. The cat lives or dies regardless of if the box is opened, is isolated etc.

I think the point is, there is no common sense classical for an isolated system. You will always be observing one observable state or the other of that system. So it's kind of an illusion that stems from the fact we can't be isolated from the environment long enough to experience or see these other observable states of the isolated system.

So live cat/dead cat or Law School/Medical School would be observable states of an isolated system and there's no decoherence. So decoherence occurs as a system grows in size and can't remain isolated from it's environment for long periods of time. So everything would essentially be quantum and classical objects are just quantum systems that can't be isolated from their environment.

There was a recent study of cesium atoms that showed they don't follow a well defined path. There needs to be more tests done but it could essentially show that what we call common sense classical is really just and observable state of an isolated system and it appears classical because we can't remain isolated from the environment long enough to see other observable states of the isolated system.

http://www.eurekalert.org/pub_releases/2015-01/uob-acb012015.php

Here's another article on the subject

Macrorealism Violated By Cs Atoms

http://www.itec-sde.net/en/posts/macrorealism-violated-by-cs-atoms

Like I said, more tests need to be done but I do think Tegmark is on the right track.

 

[bhobba]

I think the point is, there is no common sense classical for an isolated system.

I have no idea why you would think that. For example astronauts circling the Earth in a space capsule is for all practical purposes an isolated system - everything that goes on there is classical.

Thanks
Bill

 

[quantumfunction]

I have no idea why you would think that. For example astronauts circling the Earth in a space capsule is for all practical purposes an isolated system - everything that goes on there is classical.

No they're not. Everything classical in size in our universe can't remain isolated like subatomic particles. I would like to see the article that says Humans in space are just like photons or electrons. So for larger objects in an observable state of an isolated system your wave nature is essentially zero. As large objects, the wave function can't become large enough for us to see other observable states of the isolated system like for instance an electron.

Here's an article from Nature that talks about this:

Physics: Quantum all the way

Decoherence also predicts that the quantum–classical transition isn't really a matter of size, but of time. The stronger a quantum object's interactions are with its surroundings, the faster decoherence kicks in. So larger objects, which generally have more ways of interacting, decohere almost instantaneously, transforming their quantum character into classical behaviour just as quickly.

http://www.nature.com/news/2008/080430/full/453022a.html

 

[Feeble Wonk]

Its what I said. Imagine you have a heap of pure states that are the possible outcomes of an observation. You randomly select one. There is a pure state there - but because it was randomly selected you don't know which one - only the probability of what it is. That is a proper mixed state.

So, it's more or less what I was thinking. It seems to be a semantic issue, but of fundamental significance.

By this definition, the "proper" MIXED state is not really a "mixture" at all... IF the pure state actually exists, and the previously potential states no longer do. Or, maybe a better way of saying it is... A proper mixed state is a mixture of what IS, and what MIGHT HAVE BEEN, prior to observation of what IS... the "mixture" is completely (and only) a statistical description, and not an ontological depiction of what exists (assuming that ANYTHING actually exists).

I recognize that this phrasing of the issue is probably a little too "metaphysical" for your tastes, but aside from that, is the general idea correct?

 

[bhobba]

I would like to see the article that says Humans in space are just like photons or electrons.

I never said they were - in fact since they behave classically they are nothing like photons and electrons.

And yes everything is quantum - but that doesn't mean objects can't behave classically since its obvious from everyday experience the world around us does.

Thanks
Bill

 

[bhobba]

I recognize that this phrasing of the issue is probably a little too "metaphysical" for your tastes, but aside from that, is the general idea correct?

Its called a mixture for technical reasons to do with generalised probability theory - but what you said is about as good as you will et at the lay level.

Thanks
Bill

 

[DennisN]

Reading this thread made me look around a bit, and I stumbled upon this paper which I had not seen before, which I found interesting enough to mention here, and it may perhaps also be interesting to thread readers... (I have not read the whole paper yet, but I will).

It is about "many worlds of [so-called] causal diamonds", decoherence, eternal inflation, "pocket universes", isolated/closed systems etc:

The Multiverse Interpretation of Quantum Mechanics
Raphael Bousso, Leonard Susskind
(Submitted on 19 May 2011 (v1), last revised 22 Jul 2011 (this version, v3))
Arxiv link: http://arxiv.org/abs/1105.3796
Pdf: http://arxiv.org/pdf/1105.3796v3

Abstract:
We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics.

Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment". In fact decoherence is absent in the complete description of any region larger than the future light-cone of a measurement event. However, if one restricts to the causal diamond - the largest region that can be causally probed - then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many-worlds (all possible decoherent causal diamond histories) in a single geometry.

We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in "hats" (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.

 

[alexepascual]

I think the point is, there is no common sense classical for an isolated system. You will always be observing one observable state or the other of that system. So it's kind of an illusion that stems from the fact we can't be isolated from the environment long enough to experience or see these other observable states of the isolated system.

Well, we know already what bhobba thinks. He thinks that the isolated system-detector is in a definite state once the detector has interacted with the quantum system. If I am correct, you (Quantumfuction) and Feeble are more inclined to think that these systems remain in a superposition state.
But another way to interpret the way decoherence takes place (besides the one you describe in the quote above) would be that the inside of the box does not collapse to a definite state just because of uncontrolable leakage of information. The collapse would not be an absolute thing but relative to another system. If you were sitting inside the box (even if you are not a friend of Wigner) you would say that there has been collapse, because you have split into two copies of yourself and have become entangled with the two possible states of the system-detector-cat. So for you inside the box the cat is dead or alive. For someone outside the box as they have not become entangled with the inside of the box, the inside is still in an indefinite state. But we have to consider that a preferred basis has already been chosen and we could represent this as a density matrix with all the element there (two in this case) but to the outside observer which of these diagonal elements will become his/her "reality" remains undefined (not just unknown). The outside observer does not need to be a sentient/conscious being but could just be a measurement device. What do you think Quantumfunction about his way of looking at it?

 

[bhobba]

For someone outside the box as they have not become entangled with the inside of the box, the inside is still in an indefinite state.

In the early days of QM Von Neumann sorted this all out. He showed the cut can be placed anywhere in the Von-Neumann chain. This is nothing new. The question is why do you choose not to place it right after decoherence and instead proceed to espouse such a complicated weird view of the world with information leaking out etc etc.

But regardless of that once the collapse has occurred and inside the box the cat is dead or alive it has occurred period - for observers outside the box - for anyone.

Quantum Darwinism takes a view somewhat like that - but Zureck takes the quantum state as primary and uses it to derive the Born rule via evarience. Because of that he has to be rather tricky about what an observation is - however once you accept the Born rule there is no need for such sophistry.

Personally I take observations as primary and the state emerges from that - see post 137:
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

Thanks
Bill

 

[alexepascual]

In the early days of QM Von Neumann sorted this all out. He showed the cut can be placed anywhere in the Von-Neumann chain. This is nothing new. The question is why do you choose not to place it right after decoherence and instead proceed to espouse such a complicated weird view of the world with information leaking out etc etc.

Information leaking out is just the way most environmental decoherence proponents present it, including Zurek. So for these peple, if information "leaks out" and let's say travels away towards some other galaxy, then there is decoherence even if there is no entanglement with the observer. The way I see it is a little diferent. For me is not just the fact that information has gotten out of control by leaking out but that the system has become entangled with the observer.
Is it weird? Maybe, but in my view there is no model (interpretation) that solves all the paradoxes. You may say that the ensemble interpretation solves most paradoxes, but if there is one paradox left, that may be very important.

 

[bhobba]

Information leaking out is just the way most environmental decoherence proponents present it, including Zurek.

I disagree with that.

My bible on this, and many consider it THE book, is Schlosshauer's text:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

That is NOT what generally happens in decoherence - some models yes - but in general no. For example in Schroedingers Cat the decoherence occurs in the particle detector - everything is classical after that.

As I explained previously you are likely thinking of Quantum Darwinian which is a particular interpretation using decoherence and uses ideas like that - it's not a general requirement - not by a long shot.

Thanks
Bill .

 

[alexepascual]

I disagree with that.
My bible on this, and many consider it THE book, is Schlosshauer's text:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20
That is NOT what generally happens in decoherence - some models yes - but in general no. For example in Schroedingers Cat the decoherence occurs in the particle detector - everything is classical after that.
As I explained previously you are likely thinking of Quantum Darwinian which is a particular interpretation using decoherence and uses ideas like that - it's not a general requirement - not by a long shot. Thanks
Bill .

I have not read Schlosshawer's book, but some years ago I had read a very complete and long article by him. I though it was a very comprehensive review of the subject. With respect to Quantum Darwinism, I didn't remember much about that concept as I haven't read Zurek's articles for a while, but I just read a little about it and it looks like it refers more to the selection of a preferred pointer basis rather than the selection of a particular eigenvalue of the selected measurement operator involved in the decoherence process. So from what you are saying, you think that Zurek's ideas are not the most popular within the environmental decoherence school right?
At this point Bill I wonder if you think your interpretation solves all the paradoxes of quantum mechanics or you think that there is still something important that is not resolved. I don't mean some technicality but some paradox that is still unexplained. If that's the case, what is that unresolved paradox?

 

[bhobba]

So from what you are saying, you think that Zurek's ideas are not the most popular within the environmental decoherence school right?

I have no idea how popular they are. Its just he makes use of ideas similar to what you are talking about in his development evarience.

At this point Bill I wonder if you think your interpretation solves all the paradoxes of quantum mechanics or you think that there is still something important that is not resolved. I don't mean some technicality but some paradox that is still unexplained. If that's the case, what is that unresolved paradox?

QM has no paradoxes - just blemishes. By blemishes I mean things like Copenhagen assumes the existence of a commom-sense classical world observations appear in. That means it can't explain such a world because it assumes it from the start. It doesn't invalidate it or anything like that but it is a blemish. Refinements like my ignorance interpretation and decoherent histories fix that particular blemish, but some still remain like why do we get any outcomes at all. Some like BM resolves that one but most interpretations stand powerless before it. I simply assume they exist by interpreting an improper mixed state as a proper one - it doesn't invalidate it or anything like that - and every theory has undefined primitives - again its just nice if there was an explanation.

Thanks
Bill

 

[quantumfunction]

Well, we know already what bhobba thinks. He thinks that the isolated system-detector is in a definite state once the detector has interacted with the quantum system. If I am correct, you (Quantumfuction) and Feeble are more inclined to think that these systems remain in a superposition state. But another way to interpret the way decoherence takes place (besides the one you describe in the quote above) would be that the inside of the box does not collapse to a definite state just because of uncontrolable leakage of information. The collapse would not be an absolute thing but relative to another system. If you were sitting inside the box (even if you are not a friend of Wigner) you would say that there has been collapse, because you have split into two copies of yourself and have become entangled with the two possible states of the system-detector-cat. So for you inside the box the cat is dead or alive. For someone outside the box as they have not become entangled with the inside of the box, the inside is still in an indefinite state. But we have to consider that a preferred basis has already been chosen and we could represent this as a density matrix with all the element there (two in this case) but to the outside observer which of these diagonal elements will become his/her "reality" remains undefined (not just unknown). The outside observer does not need to be a sentient/conscious being but could just be a measurement device. What do you think Quantumfunction about his way of looking at it?

Good points.

Like I said, this is more about isolated systems than it is about decoherence. Decoherence can occur in the box but if the box is an isolated system, then live cat/dead cat both exist in the box.

If the box is all there is, there's nowhere for the wave function to go that's external to the box. The cat isn't in a pure state of live cat/dead cat but a mixed state of life cat or dead cat but both observable states exist in the box if the hypothetical box is isolated and there isn't any space external to the box to interact with.

When the Scientist opens the box, he's in an observable state of either live cat/happy Scientist or dead cat/sad Scientist. This extends to the guy on the highway whose happy cause girlfriend said yes to Marriage or sad guy on the highway cause girlfriend said no. This just means the state of the cat becomes entangled with the entire universe.

So for an isolated system there is no deoherence. Within the isolated system you have observable states that become large enough to where there's decoherence that occurs relative to each system in that observable state like cats, dogs, humans and planets.

So you have a global wave function that evolves according to Schrodinger's equation and never "collapses" because there's nothing external to the universe that can interact with it. So it goes back to Everett's postulate.

All isolated systems evolve according to the Schrodinger's equation.

Now, Penrose understands this and Tegmark and Penrose agree in principle. Penrose just thinks there's a self collapse or what he calls Objective Reduction which simply says that instead of all of these possible states evolving, they reach a threshold he calls the one graviton level and at this threshold all states collapse except 1. So you have one state that's cyclical instead of many states that are parallel. I think Penrose will run into trouble if they keep doing test with Cs atoms and larger objects that violate macrorealism. Penrose depends on classical objects having a definite path.

 

[bhobba]

Decoherence can occur in the box but if the box is an isolated system, then live cat/dead cat both exist in the box.

That's impossible.

Cats can not be in a superposition of alive/dead. For example to be alive it must breath air that quickly decoheres it. The differences in the processes going on in a live and dead cat are such that its impossible for them to be in superposition any more than you can be in a superposition with the person next to you in a checkout line. This is the efficiency of a measurement device issue - some macroscopic states due to their nature will give unambiguous results - a live and dead cat is one of those - like a 1 or 0 appearing on a computer screen.

Thanks
Bill

 

[quantumfunction]

That's impossible.

Cats can not be in a superposition of alive/dead. For example to be alive it must breath air that quickly decoheres it. The differences in the processes going on in a live and dead cat are such that its impossible for them to be in superposition any more than you can be in a superposition with the person next to you in a checkout line. This is the efficiency of a measurement device issue - some macroscopic states due to their nature will give unambiguous results - a live and dead cat is one of those - like a 1 or 0 appearing on a computer screen.

Thanks

It's not impossible if the system is isolated. You're looking at it as if the Cat has an object classical existence separate from the isolated system. The observable states of the isolated system just have a wave function that's essentially zero. There isn't any evidence that these observable states of an isolated system just vanish and that's why you have these debates between people like Tegmark, Penrose and Deutsch.

 

[bhobba]

All isolated systems evolve according to the Schrodinger's equation.

Yes - but that does not stop mixed states appearing. The interpretation is the mixed state is a proper mixed state. That's the interpretive assumption so we actually get outcomes. Without that, or a similar assumption, outcomes are not possible.

Thanks
Bill

 

[bhobba]

It's not impossible if the system is isolated

It doesn't matter how you cut and dry it there is no way for a cat to be in a superposition of alive and dead - its impossible.

Thanks
Bill

 

[quantumfunction]

Yes - but that does not stop mixed states appearing. The interpretation is the mixed state is a proper mixed state. That's the interpretive assumption so we actually get outcomes. Without that, or a similar assumption, outcomes are not possible.

Thanks
Bill

It's an assumption based on the fact that we don't have any evidence of that there's anything external to the universe. If there's some evidence that shows this I would like to see it. So yes, if the hypothetical box is an isolated system then both live cat/dead cat exist in the box. In this case the box is the universe. If the universe can never be observed (externally) then you have a superposition of states including live cat/dead cat.

 

[bhobba]

It's an assumption based on the fact that we don't have any evidence of that there's anything external to the universe.

Its got nothing to do with that. Its got to do with the physical nature of live and dead cats. A live cat wanders around, has a heart pumping etc etc. A dead cat just lies there - dead. They are both decohered by their environment to have those classical properties - they can't be in superposition any more than the two end points on a line can be in superposition - its impossible by the definition of what a line is.

Thanks
Bill

 

[quantumfunction]

Its got nothing to do with that. Its got to do with the physical nature of live and dead cats. A live cat wanders around, has a heart pumping etc etc. A dead cat just lies there - dead. They are both decohered by their environment to have those classical properties - they can't be in superposition any more than the two end points on a line can be in superposition - its impossible by the definition of what a line is.

Thanks
Bill

Again, they both decohered by their environments because they're not isolated from their environment. Their still observable states of an isolated system. The way you described it in an older post is exactly what I'm saying. You said:

In MW an observation does nothing - everything keeps evolving as is but each outcome is considered a world. Its very very neat mathematically and extremely beautiful - but not to everyone's taste so to speak.

Actually the beauty and allure of MW is no collapse occurs. Everything just keeps evolving - but after decoherence occurs the system is in a mixed state that is the sum of the possible outcomes. Noting at all happens - the universe keeps on evolving - but is now able to be conceptually separated into a number of 'parts' where each part is the outcome of the observation and considered a separate world.

Thanks
Bill

This is what I'm saying but maybe you're still doubt these issues. I agree it's extremely beautiful and you don't run into some of the same problems that a lot of other interpretations run into. So again, you can't think of the live cat/dead cat as two separate classical environments but two environments that exist because their observable states of an isolated system.

Here's an older video of Sean Carroll explaining why he favors MWI and he says some of the same things I'm saying here.

 

[bhobba]

The way you described it in an older post is exactly what I'm saying.

You are not understanding what I said which is different to what you said.

In any interpretation the cat is never in a superposition. The system - cat and particle are entangled so by construction the cat not be in superposition.

Here is the math. The cat can be in two states |a> - alive |d> for dead. The particle is in two states |pn> - particle not detected and |pd> - particle detected. Now due to the setup the cat is alive if the particle is not detected and dead if it is. We will for simplicity assume it is 50-50 which happens. The system is in the entangled state 1/√2 |pd>|d> + 1/√2 |pn>|a>. Because of the entanglement the cat can't be in a pure state hence can't be in a superposition. Only pure states can be in a superposition. It turns out the cat is in the mixed state 1/2|pd><pd| + 1/2 |pa><pa|.

The above is independent of interpretation. In MW each part of the mixed state |pd><pd| and |pa><pa| are interpreted as a separate world so the superposition 1/√2 |pd>|d> + 1/√2 |pn>|a> remains intact. In ignorance ensemble it is interpreted as a proper mixed state so the cat is either alive or dead. What happens there to the original superposition is slightly more complicated but can't be distinguished from the MW version.

Sean Carroll beieves in many worlds - I don't - big deal. Neither do a number of people in the following discussion:


As far as interpretations go none is better than the other.

Thanks
Bill

 

[bahamagreen]

Is there a QM interpretation that formally ascribes that the past is strictly counterfactual definite?

 

[bhobba]

Is there a QM interpretation that formally ascribes that the past is strictly counterfactual definite?

It obviously is. In QM we can always speak with definiteness about observations that occurred in the past.

Thanks
Bill

 

[bahamagreen]

What if when you open the box you observe that it is empty with neither mechanism nor cat...?
If what a past record of observation entails about the present is in conflict with a present observation, do we not take the present observation over the past record?
Maybe I'm using the wrong term. QM seems to be classically acausal and nondynamical... if a present observation is a primitive of theory, it seems the present observation of the record of an alleged past observation would be a primitive, but the object of that present observation (the record of the past observation) might not hold the same warrant with respect to the present.