How can Schrödinger's Cat be both alive and dead?

[mathman]

For the last couple days the comic strip "Dilbert" has Schrodinger's cat as a character, having escaped from the box before it was inspected. The cat is half dead and half alive.

 

[JazzGuy]

Can some one explain to me how the cat can be both alive and dead, I get the principle that since we don't know it is both at the same time because we don't know but in reality it's either alive or alive we just don't know, it's the human factor of sentience just because we don't know doesn't make neither its one we just don't know. Following by that the universe exists because we observe it if we're not alive it's not real, just like the billions of other people you haven't seen aren't real. I'm not claiming anything i just want an explanation for this.

To interpret the Schrodinger's cat issue one first needs a basic primer in the orthodox postulates (the basics) of quantum mechanics. There is a very good presentation, for a general audience, at http://pirsa.org/displayFlash.php?id=12070006 This is one of the educational videos produced at the Perimeter Institute. It is well worth an hour and a half of watching as all the basic interpretations are mentioned. Rob Spekkens begins discussion of inconsistencies at 55:00 and goes on to Schrodinger's Cat. From this, one can glean the nature of the problem for the paradox of the cat being dead and alive. The heart of the issue is that we combine the history of a quantum level object with the history of a cat in a box. The unitary evolution of the quantum state is described in a way (linearly) that allows it to be summed with anything that is also linear. The assumption is that this can include the evolution of the cat. When you do this the cat is linked with the evolution of a quantum state. The defining function of the quantum state always includes the "square root of minus one" (i) which, itself is a paradoxical construction to the real world. We naively assume that some complex function (for linear evolution) should apply to the cat as well, simply by placing it in a box (so we can't see it). We also place a quantum-level particle in the box. We can't see its classical state either but ignore the fact that this is for an entirely different reason. By the way, it makes just as much sense to use cardboard for this box - which points out that there is something sadly lacking in our understanding of what constitutes quantum entanglement and our relationship to such a state. It is naive to assume a complex function applies to the cat because no one knows how to isolate the cat as such. Why this may not be possible is poorly understood. One obvious conclusion is that some sort of absolute boundary exists between the quantum state and the cat. In other words, between what is quantum and what is classical. Mathematics does not give any guidance on this issue which leads to the deeper question of whether or not mathematics is the final root of reality. Bell's inequality is universally interpreted to solve the issue of whether classical mathematics is the root because classical theory appears to fail the description of classical phenomena in its own basis of description. We are still missing something. Perhaps there is an absolute boundary across these paradoxical forms of description (classical and quantum). Then the universally accepted conclusion on Bell's inequality would also be wrong. We better call in the philosophers for this one - might as well include the musicians, the philosophers don't fair much better.

 

[alweiss]

This would be a good way to put it... except for a fact that having you be the observer changes the experiment too much. The cat as an observer in the original experiment knows whether its alive or dead. The cat is in a super position yet at some point it is dead. For the outside world, the cat is only dead when you send in a photon of light. So having you be "the cat" for this experiment is redundant, because it wouldn't help with the experiment

 

[Crazymechanic]

Well I don't want to sound too rude or whatever , but let's face it there is no half alive half dead cats or other creatures.All of this is just a physical limitation that we face in terms of knowing about the state of the cat at the very moment something happens beyond "our eyes".

Just like the guy buying a lottery ticket and later becoming the winner. He won the lottery actually in the moment he bought the "lucky" ticket because the right number combination was already in the computer but because it is a lottery he had no way of knowing that so it always feels like you won in the moment you get the information.

Now before you measure you cannot tell about the state of the cat but once you measure you have a great chance of setting the outcome and hence never knowing how long the cat would have been alive if you would have stayed aside and never touched the box.
That's that and that's all , sometimes I really don't get why people like to make this so mystical or sometimes the other way around , so complicated.

 

[BruceW]

maybe not a cat

there are various schemes,
between them

Ah, nice links. thanks dude. They seem to keep putting larger and larger objects into superposition. Although I guess a cat is a lot more difficult. Another thing I remembered is the 'Penrose interpretation' which is pretty interesting. If I understand correctly, this would predict that due to general relativity, any superposition of states with an energy difference greater than the Planck mass would undergo an objective collapse. So really, it is more than just an interpretation, since it gives predictions which are different to that of the standard QM. And as I understand it, no experiment has been done yet which uses a superposition of states with an energy difference greater than the Planck mass.

 

[audioloop]

Ah, nice links. thanks dude. They seem to keep putting larger and larger objects into superposition. Although I guess a cat is a lot more difficult. Another thing I remembered is the 'Penrose interpretation' which is pretty interesting. If I understand correctly, this would predict that due to general relativity, any superposition of states with an energy difference greater than the Planck mass would undergo an objective collapse. So really, it is more than just an interpretation, since it gives predictions which are different to that of the standard QM. And as I understand it, no experiment has been done yet which uses a superposition of states with an energy difference greater than the Planck mass.

the second link, from penrose.

 

[bhobba]

That's that and that's all , sometimes I really don't get why people like to make this so mystical or sometimes the other way around , so complicated.

I have noticed that to. Beats me as well.

The solution to this within Copenhagen, the Ensemble interpretation and others is utterly trivial - the quantum weirdness happens at the detector - from then on everything is classical.

Although I have mentioned it many times I think with the way this thread keeps on continuing it needs to be said again - the import of Schrodinger's Cat is it points to the necessity of a fully quantum theory of measurement. That was a valid observation when it was first promulgated - but that has now largely been accomplished.

Thanks
Bill

 

[BruceW]

the second link, from penrose.

aha! oh yeah, I didn't even look at the authors. I should really get into the habit of that. Although, there is not much discussion about the possible implications for the 'Penrose interpretation', I guess probably because the energy difference would still not nearly be great enough to cause the 'objective collapse'.

Although I have mentioned it many times I think with the way this thread keeps on continuing it needs to be said again - the import of Schrodinger's Cat is it points to the necessity of a fully quantum theory of measurement. That was a valid observation when it was first promulgated - but that has now largely been accomplished.

I'm curious, but I don't really know what you mean.

 

[bhobba]

I'm curious, but I don't really know what you mean.

Ok - here it is again.

Schrodinger's Cat is trivial in Copenhagen that divides the world into two bits - classical and quantum. In Copenhagen we know about the quantum world when it makes its appearance here in the classical world which in Schrodinger's Cat is when the detector detects a particle - from that point on there is no mystery - every thing is honkey dorey.

But this dividing of the world into classical and quantum is a bit fishy - everything is really quantum. And if you look at it that way that's when you get issues - what we need is a fully quantum theory of observation. It was not available when Schrodinger proposed his thought experiment but a lot of work has been done on it since then and its pretty much solved.

Rather than me going over the decoherence explanation again (that's what in modern times we know a lot more about) you can either do an internet search on it or have a look at Susskinds Lectures:
http://www.newpackettech.com/Resources/Susskind/PHY30/QuantumEntanglementPart1_Overview.htm

I forget exactly which lecture he examines Schrodinger's Cat in but its probably a good idea to have a look at them all.

Thanks
Bill

 

[JazzGuy]

Well I don't want to sound too rude or whatever , but let's face it there is no half alive half dead cats or other creatures.All of this is just a physical limitation that we face in terms of knowing about the state of the cat at the very moment something happens beyond "our eyes".

Just like the guy buying a lottery ticket and later becoming the winner. He won the lottery actually in the moment he bought the "lucky" ticket because the right number combination was already in the computer but because it is a lottery he had no way of knowing that so it always feels like you won in the moment you get the information.

Now before you measure you cannot tell about the state of the cat but once you measure you have a great chance of setting the outcome and hence never knowing how long the cat would have been alive if you would have stayed aside and never touched the box.
That's that and that's all , sometimes I really don't get why people like to make this so mystical or sometimes the other way around , so complicated.

Thanks Crazymechanic. Here is my take on the difference between "not knowing" in quantum and then classical terms (for two possible outcomes). In quantum terms, "not knowing" means the outcomes are paradoxically simultaneous (before collapse occurs which destroys the quantum structure). In classical terms, it means that some action in time has simply not occurred yet (such as we are going to flip a coin to realize the outcomes in sequence). The quantum version structures "not knowing" paradoxically as simultaneous outcomes of events. Action in time does not apply. In the quantum structure, time is imaginary (and without direction) since it does not flow. In classical structure we will eventually see both outcomes but never simultaneously. My conclusion is that the two forms of "not knowing" are categorically different.

 

[BruceW]

@ bhobba - ah, OK. So the thing that has 'been accomplished' is the use of 'quantum decoherence' to explain how quantum effects become negligible when the original system becomes entangled with the 'environment'. And of course, most detectors can be classed as 'environment' in this context (since most detectors will have a huge amount of degrees of freedom). So really, as soon as the original quantum system gets entangled with the detector, quantum effects are then negligible.

On the surface, this is kindof obvious, since it is not practically possible to diffract something like a Geiger counter. But I know that there is also a lot of useful research into stuff like decoherence times, and how to try to reduce interaction of quantum systems with environment.

I agree about the Copenhagen interpretation. Using the Copenhagen interpretation, we impose a 'subjective collapse' of the state, at the boundary between the quantum and classical worlds. And this separation of the quantum and classical worlds is an arbitrary choice.

decoherence does not help us with this choice. It tells us that for an environment with a large number of degrees of freedom, there will be negligible quantum effects. But the key is the word negligible. There is no exact cut-off which we might use to define the quantum and classical worlds. We are still stuck with the problem that the separation between quantum and classical according to the Copenhagen picture is essentially an arbitrary choice.

That's why the Copenhagen interpretation doesn't really answer the Schrodinger's cat problem. We can use the 'subjective collapse', but we have no definitive way to say when we are allowed to use it and when we cannot.

edit: p.s. thanks for the link. everyone seems to love this Susskind guy. so I will be interested to hear him talking about QM.

 

[bhobba]

There is no exact cut-off which we might use to define the quantum and classical worlds.

Errrrr. So you think a cat isn't classical?

Thanks
Bill

 

[akhmeteli]

Errrrr. So you think a cat isn't classical?

So you think a cat isn't quantum?

 

[stevendaryl]

Well I don't want to sound too rude or whatever , but let's face it there is no half alive half dead cats or other creatures.All of this is just a physical limitation that we face in terms of knowing about the state of the cat at the very moment something happens beyond "our eyes".

Just like the guy buying a lottery ticket and later becoming the winner. He won the lottery actually in the moment he bought the "lucky" ticket because the right number combination was already in the computer but because it is a lottery he had no way of knowing that so it always feels like you won in the moment you get the information.

Now before you measure you cannot tell about the state of the cat but once you measure you have a great chance of setting the outcome and hence never knowing how long the cat would have been alive if you would have stayed aside and never touched the box.
That's that and that's all , sometimes I really don't get why people like to make this so mystical or sometimes the other way around , so complicated.

Yes, there is nothing at all mysterious about quantum mechanics if you believe that the questions you might ask, such as "Is the cat alive, or dead?" all have definite answers, regardless of whether we know those answers, and that measurement merely allows us to know about a pre-existing fact. But it's hard to see how to make this idea consistent with what we know about quantum mechanics. For example, if we prepare a electron in a state that is an eigenfunction of the x-component of spin, then the z-component of the spin is simply undefined, according to our current understanding of quantum mechanics. It's not that we don't know what it is, but that it just doesn't have a value.

There is no reason, in principle, that this particularly quantum type of uncertainty can't scale up to the level of cats and people.

 

[Crazymechanic]

Well I could agree that for a single electron there really is a "guess what" thing involved but as you just said not for a cat or a human , not at that level , so the main thought of the cat in the box thing is correct but if we really speak about a cat then no there is no superposition there is just a lack of knowledge or rather I should say a lack of a physical way to get the information without "writing history"

Now as for the single quantum particle , here we can speak about superposition and still then the next discussion appears , is it a fundamental rule of nature to let us or any conscious observer know any of the two variables while hiding the other or is it again our lack of knowledge or lack of a way to access that knowledge even if it's there somewhere to which i want to believe it is.

 

[audioloop]

aha! oh yeah, I didn't even look at the authors. I should really get into the habit of that. Although, there is not much discussion about the possible implications for the 'Penrose interpretation', I guess probably because the energy difference would still not nearly be great enough to cause the 'objective collapse'.

they base it from:
(and refer also to gravitationally induced collapse)

Scheme to probe the decoherence of a macroscopic object
S. Bose, K. Jacobs, P. L. Knight
Optics Section, The Blackett Laboratory, Imperial College, London SW7 2BZ, England
http://pra.aps.org/abstract/PRA/v59/i5/p3204_1

"We propose a quantum optical version of Schrödinger’s famous gedanken experiment in which the state of a microscopic system (a cavity field) becomes entangled with and disentangled from the state of a massive object (a movable mirror). Despite the fact that a mixture of Schrödinger cat states is produced during the evolution (due to the fact that the macroscopic mirror starts off in a thermal state), this setup allows us to systematically probe the rules by which a superposition of spatially separated states of a macroscopic object decoheres. The parameter regime required to test environment-induced decoherence models is found to be close to those currently realizable, while that required to detect gravitationally induced collapse is well beyond current technology"

I know that there is also a lot of useful research into stuff like decoherence times, and how to try to reduce interaction of quantum systems with environment.

right, decoherence times vs superposition times and cooling near zero deegres.

keith schwab
http://www.kschwabresearch.com/
The Schwab Group pursues the development and applications of the most advanced measurement techniques to both probe the fundamental quantum nature of the physical world, and to further nanoscience and nanotechnology. Currently our work has been focused on the exploration of the quantum properties of nanoscale electro-mechanical structures at ultra-low temperatures, and the applications of nanofabrication to atomic and quantum optics experiments.


Aspelmeyer, Schwab, Zeilinger.
Quantum Upsizing
http://fqxi.org/data/articles/Schwab_Asp_Zeil.pdf

Quantum effects are mysterious, says Schwab. “Why do they work on a small
scale but not at a big scale?”



.

 

[BruceW]

Errrrr. So you think a cat isn't classical?

Thanks
Bill

just because it would be very difficult (in practice) to diffract a cat, then does that mean in principle it can't be done? I'm guessing when you say "a cat is classical", you mean that it is impossible (even in principle) to diffract a cat. But there is no experimental evidence to back that up. There is no evidence either way.

 

[stevendaryl]

Well I could agree that for a single electron there really is a "guess what" thing involved but as you just said not for a cat or a human

I don't agree. There is nothing in principle different about a cat than an electron, other than the enormous complexity.

 

[bhobba]

just because it would be very difficult (in practice) to diffract a cat, then does that mean in principle it can't be done? I'm guessing when you say "a cat is classical", you mean that it is impossible (even in principle) to diffract a cat. But there is no experimental evidence to back that up. There is no evidence either way.

That's exactly what I am NOT saying. I believe everything is quantum and in principle you can demonstrate quantum effects at all levels - and indeed some strange quantum effects have been demostrated for macro objects.

What I am saying, and exactly what Copenhagen assumes, is objects of everyday experience that in everyday use behaves in a classical manner exist, and it is from this our classical intuition has developed. That is the sense I mean and Copenhagen means, and Bohr opined about in his vague but usually correct commentary about the quantum world.

This is the Achilles heel of Copenhagen in that while cats etc are obviously classical it does not explain why the classical world exists and behaves the way it does. There are some obvious basic theorems such as Ehrenfest's theorem and other stuff you find in all QM textbooks, but it was not until decoherence was better understood it was really resolved and even then some issues still remain - but most think its along the lines of dotting the i's and crossing the t's - but one never knows - there may be a deep truth waiting here - only time will tell.

Thanks
Bill

 

[bhobba]

I don't agree. There is nothing in principle different about a cat than an electron, other than the enormous complexity.

There isn't. But everyday experience shows they do not behave like quantum objects do but have a well defined momentum and position and do not interfere. It is in that sense Copenhagen means when they speak of a classical world.

Exactly why such a world exists is an area of active research - most of the issues have been resolved but a few do remain. However it is an indisputable fact from everyday experience it exists, live and dead cats behave in a classical way and do not interfere - at least the the limits of our current technology - and probably even well beyond that. But that is with the aid of technology - from everyday experience there is no such issue.

Thanks
Bill

 

[BruceW]

That's exactly what I am NOT saying. I believe everything is quantum and in principle you can demonstrate quantum effects at all levels

right, OK so when you say "a cat is classical" you essentially mean that due to decoherence, quantum effects (like diffraction of the cat) are much more difficult. and the interference between alive and dead states of the cat becomes very small. The problem is that still, the interference is non-zero. And the Copenhagen interpretation 'solution' to this problem is that we impose a subjective collapse which makes the interference between alive and dead states exactly equal to zero. This gives us a way to say "what probability is the cat alive?" (in other words, we impose the subjective collapse so that we can give meaning to the probabilities of certain states).

Now this 'solution' raises the further question: "how small does the interference between alive and dead states need to be, when we impose the subjective collapse?" the answer of course, is that it just needs to be small enough to be within the experimental error of our specific experiment. In other words, we must make sure that any consequence of the subjective collapse is not detectable in the given experiment. There is nothing fundamental about this choice. The system has unitary evolution as far as we know from experiment, therefore we must impose this subjective (non-unitary) collapse at a time where it will not cause the predictions to change by more than the experimental error. So the Copenhagen interpretation 'works', but it is definitely not what we would hope for in a physical theory.

 

[JazzGuy]

I don't agree. There is nothing in principle different about a cat than an electron, other than the enormous complexity.

One point of clarification for comment. If the cat could actually be down-converted to a collection of entangled atoms and molecules. I would no longer be a cat. None of the complex (classically based) functions of the body would be possible. We would just have some very complex new experiment on a bunch of atoms we collected together from the cat.
If there actually is some entangled state that has meaning for cats, humans and the entire universe then we will have to solve the issue of quantum gravity first, and since we will also be in this very large entangled state we certainly will not be aware of it or able to do experiments based on it.

 

[StarsRuler]

But while the decoherence time, in spite of being very short, the cat can´t be in a superposition. ¿ How did the cat feel in a superposition? If the superposition is in external objects, no matter because we are not in a superposition, but with alive being, it is paradoxical, the collapse must be instantaneous

 

[JazzGuy]

But while the decoherence time, in spite of being very short, the cat can´t be in a superposition. ¿ How did the cat feel in a superposition? If the superposition is in external objects, no matter because we are not in a superposition, but with alive being, it is paradoxical, the collapse must be instantaneous

I think I understand your point. Rephrasing from a different perspective - the cat is, after all, no different that the scientist, as an observer. There is no distinction between their positions inside versus outside a box (cement, cardboard, or equally, the scientist closing his or her eyes ... etc.). Forming something as entangled requires a true down-conversion mechanism (not a box!) which creates a boundary between the classical and quantum state. The functional mechanism of this "boundary" has, to date, not been identified and consequently we have no idea what our relationship to it is, at the classical level.

 

[bhobba]

How did the cat feel in a superposition?

The cat was never in a superposition - decoherence prevents that for the cat or any classical object we experience day to day - ever. I have read even one oxygen atom or a few photons is enough to decohere and there is MUCH MUCH more than that about.

In Schrodinger's Cat everything after the detector is bog standard stuff we see around us every day and behaves exactly like every other object we experience. Claims otherwise are simply CRAZY.

I seem to recall all this has been discussed earlier in the thread - don't know why there is a desire to rehash it.

Thanks
Bill

 

[bhobba]

And the Copenhagen interpretation 'solution' to this problem is that we impose a subjective collapse which makes the interference between alive and dead states exactly equal to zero. This gives us a way to say "what probability is the cat alive?" (in other words, we impose the subjective collapse so that we can give meaning to the probabilities of certain states).

Wow. Many leaps being made here. First, while there is a bit of variation in Copenhagen, most would side with the idea collapse is simply something that occurs in theorists calculations since a state is simply something that aids in those calculations. What exists out there is if the particle detector detects a particle or not. The atom is in a superposition - but that's it - that's all.

There seems to be a bit of confusion about this and I seem to simply rehash the same stuff all the time. I shoud really refer people to the Wikipedia article - it has it right:
http://en.wikipedia.org/wiki/Schrödinger's_cat
'However, one of the main scientists associated with the Copenhagen interpretation, Niels Bohr, never had in mind the observer-induced collapse of the wave function, so that Schrödinger's cat did not pose any riddle to him. The cat would be either dead or alive long before the box is opened by a conscious observer. Analysis of an actual experiment found that measurement alone (for example by a Geiger counter) is sufficient to collapse a quantum wave function before there is any conscious observation of the measurement. The view that the "observation" is taken when a particle from the nucleus hits the detector can be developed into objective collapse theories. The thought experiment requires an "unconscious observation" by the detector in order for magnification to occur. In contrast, the many worlds approach denies that collapse ever occurs.'

Thanks
Bill

 

[stevendaryl]

One point of clarification for comment. If the cat could actually be down-converted to a collection of entangled atoms and molecules. I would no longer be a cat. None of the complex (classically based) functions of the body would be possible. We would just have some very complex new experiment on a bunch of atoms we collected together from the cat.
If there actually is some entangled state that has meaning for cats, humans and the entire universe then we will have to solve the issue of quantum gravity first, and since we will also be in this very large entangled state we certainly will not be aware of it or able to do experiments based on it.

You might be right about that, but I don't see why it's necessarily true that we have to solve quantum gravity in order to understand how an apparently classical world emerges from quantum mechanics. I don't expect quantum gravity to be important in mild gravitational conditions such as those found near the Earth.

 

[stevendaryl]

The cat was never in a superposition - decoherence prevents that for the cat or any classical object we experience day to day - ever.

I think this point needs some clarification. The way that I understand decoherence (which probably isn't very well) is that it's not a matter of destroying superpositions, but a matter of superpositions spreading to affect the whole universe. So, rather than having the cat be in a superposition of $|$dead cat$\rangle$ and $|$live cat$\rangle$, you have the whole world in a superposition of $|$world with dead cat$\rangle$ and $|$world with live cat$\rangle$. There is still a superposition involved, but it's not the cat in the superposition.

 

[bhobba]

I think this point needs some clarification. The way that I understand decoherence (which probably isn't very well) is that it's not a matter of destroying superpositions, but a matter of superpositions spreading to affect the whole universe. So, rather than having the cat be in a superposition of $|$dead cat$\rangle$ and $|$live cat$\rangle$, you have the whole world in a superposition of $|$world with dead cat$\rangle$ and $|$world with live cat$\rangle$. There is still a superposition involved, but it's not the cat in the superposition.

Intuitively the coherence leaks out to the environment - it interacts with with other objects that scrambles its phase so you end up with a phase of zero - that being the average of the phase of the objects that randomly changes it.

Technically you do what is called tracing over the environment which transforms a pure state to an improper mixed state.

Thanks
Bill

 

[JazzGuy]

I think this point needs some clarification. The way that I understand decoherence (which probably isn't very well) is that it's not a matter of destroying superpositions, but a matter of superpositions spreading to affect the whole universe. So, rather than having the cat be in a superposition of |dead cat⟩ and |live cat⟩, you have the whole world in a superposition of |world with dead cat⟩ and |world with live cat⟩. There is still a superposition involved, but it's not the cat in the superposition.

Intuitively the coherence leaks out to the environment - it interacts with with other objects that scrambles its phase so you end up with a phase of zero - that being the average of the phase of the objects that randomly changes it.

Technically you do what is called tracing over the environment which transforms a pure state to an improper mixed state.

Thanks
Bill

Getting more complicated for sure. I think I see your points is this correct? - Many worlds assumes the cat is in a state of superposition in the box. We decohere the state and the cat becomes either dead or alive - say alive. In some other world the cat is dead ... on and on it goes for everything. In every classical event this entangled coherence of all possible entangled states takes on some new direction and our classical experience builds. The universe is an infinity resource of unexpressed complexity and classical reality causes its expression to develop lines expression. Here is a question. Before we put the cat in the box it was alive, so in a state of decoherence. By putting it in the box we were able to reverse the process for both the real cat and observer back to one of coherence before collapse. There is also a future state in which the cat is again coherent. We never see his reversal in any larger classical context. This phenomenon of time reversal is purely quantum. This means that a much larger structure of possible quantum states exists that encompasses everything in which the reversal (as for the cat) could also be initiated. Thus the universe must have a "largest of all" quantum description that includes all we have decohered in our paths (which allows time reversal for this evolved decoherence). We are back to the problem of accounting for all time and gravity - where does the description end that encompasses all this potential.

 

[BruceW]

Wow. Many leaps being made here. First, while there is a bit of variation in Copenhagen, most would side with the idea collapse is simply something that occurs in theorists calculations since a state is simply something that aids in those calculations. What exists out there is if the particle detector detects a particle or not. The atom is in a superposition - but that's it - that's all.

What leaps? you haven't said what you disagree with. The Copenhagen interpretation is a 'subjective non-unitary collapse' interpretation. subjective does not mean a human needs to be involved. It means that the state does not actually collapse for any physical reason, but we must place in the collapse 'by hand'. For example, we might choose to add in the 'subjective non-unitary collapse' at some short time interval after the Geiger counter has interacted with the particle. And conversely, the Penrose interpretation is an objective collapse because there is a physical cause for the collapse of the state, which we will one day hopefully be able to test experimentally.

In the Copenhagen interpretation, the 'subjective non-unitary collapse' by definition cannot be experimentally tested (that's why it is called subjective). For this reason, we must choose the subjective collapse to occur only when it does not change the results of the experiment by a significant amount. For example, when the entire Geiger counter becomes entangled with the particle, we can choose the subjective collapse to occur, since the interference between the states "particle has been detected" and "particle has not been detected" of the Geiger counter is incredibly small. Therefore for the vast majority of experiments, adding in the subjective collapse does not change the predicted outcome.

The use of this 'subjective non-unitary collapse' does make a working theory. But conceptually it is not very nice. Also, we must always be careful to put in the subjective non-unitary collapse only when it makes a negligible difference to the outcome of the experiment. And our choice of when it happens is arbitrary in the sense that we can always make our predictions more accurate by putting in the 'subjective non-unitary collapse' later in the experiment. And of course, we will want a different accuracy depending on the experiment, so we must consider each experiment individually before we decide when to put in the 'subjective non-unitary collapse'. So for these reasons, we would hope for a better explanation of measurement.

 

[BruceW]

But while the decoherence time, in spite of being very short, the cat can´t be in a superposition. ¿ How did the cat feel in a superposition? If the superposition is in external objects, no matter because we are not in a superposition, but with alive being, it is paradoxical, the collapse must be instantaneous

Intuitively it seems strange, but there is nothing paradoxical about a cat (or a person) being in a superposition. Whether it is in principle possible to do this is up for debate, since there is no experimental evidence either way.

 

[stevendaryl]

Intuitively the coherence leaks out to the environment - it interacts with with other objects that scrambles its phase so you end up with a phase of zero - that being the average of the phase of the objects that randomly changes it.

Technically you do what is called tracing over the environment which transforms a pure state to an improper mixed state.

Sorry for being nitpicking, but I think that needs a little clarification, as well. The tracing over the environment is something WE do in analysis, it's not a physical process.

Mathematically, what's going on is illustrated by this simplified picture:

Suppose you have a system composed of two subsystems, A and B (for example, cat + environment), in an entangled state:

$| \Psi \rangle = c_1 | A_1 \rangle | B_1 \rangle + c_2 | A_2 \rangle | B_2 \rangle$

Now, suppose that you have some observable $O$ that only depends on the second subsystem. In that case, its expectation value will be given by:
$\langle \Psi | O | \Psi \rangle = |c_1|^2 \langle B_1 | O | B_1 \rangle + |c_2|^2 \langle B_2 | O | B_2 \rangle$

(Entanglement prevents cross-terms such as \langle B_1 | O | B_2 \rangle)

This expectation value is the same as if you had used system B alone and used the mixed state with density matrix
$\rho = |c_1|^2 | B_1 \rangle \langle B_1 | + |c_2|^2 | B_2 \rangle \langle B_2 |$

So the use of mixed states from this point of view (this is from Everett's original paper on the Many Worlds Interpretation) reflects (1) Entanglement, and (2) observations/measurements that only depend on a subsystem. So when you have a system entangled with the environment, since it is very difficult to directly measure anything about the environment, you can ignore it for most purposes by using mixed states.

 

[audioloop]

The use of this 'subjective non-unitary collapse' does make a working theory. But conceptually it is not very nice. Also, we must always be careful to put in the subjective non-unitary collapse only when it makes a negligible difference to the outcome of the experiment. And our choice of when it happens is arbitrary in the sense that we can always make our predictions more accurate by putting in the 'subjective non-unitary collapse' later in the experiment. And of course, we will want a different accuracy depending on the experiment, so we must consider each experiment individually before we decide when to put in the 'subjective non-unitary collapse'. So for these reasons, we would hope for a better explanation of measurement.

yes i agree, talk about a subjective collapse is useless, futile, inane, so it is better the objective reduction models, be trace dynamics model by Adler or the gravity inspired models of Diosi or Penrose or Karolyhazy (K-Model).

Models of Wave-function Collapse, Underlying Theories,
and Experimental Tests
Rev. Mod. Phys. 85, 471–527 (2013)
http://rmp.aps.org/abstract/RMP/v85/i2/p471_1
http://arxiv.org/pdf/1204.4325.pdf

 

[BruceW]

ah wow, excellent link. they give a nice introduction and description of this collapse problem, and ideas that have been put forward to explain it.