# Schrödinger's Cat explanation

#### BruceW

Homework Helper
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

Mentor
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

Mentor
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

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#### stevendaryl

Staff Emeritus
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

Staff Emeritus
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

Mentor
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

Homework Helper
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

Homework Helper
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

Staff Emeritus
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

Homework Helper
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.

#### bhobba

Mentor
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.
Indeed it is.

The mixed state as a result of this has the FORM of a mixed state - because of this its called an improper mixed state - its not prepared the same way which is the very essence of the discussion of if decoherence solves the measurement problem or not.

(Entanglement prevents cross-terms such as \langle B_1 | O | B_2 \rangle)
This is the key physical process that's going on - it's entangled with the environment so off diagonal elements get suppressed. That how a pure state gets transformed to an improper mixed state.

Thanks
Bill

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#### bhobba

Mentor
What leaps? you haven't said what you disagree with.
To me when you used the term 'subjective' to describe collapse you were implying it is some kind of process. It isn't necessarily - and Copenhagen usually considers it isn't.

You have now clarified what you mean by subjective and we can proceed from there.

But just to be sure do you mean by subjective it can be placed at different places and because of that you consider it can not be made a working theory? That's what I am assuming in the following.

An observation occurs when it registers here in the classical world. Copenhagen didn't specify exactly what the boundary between classical and quantum was - it assumed we can always tell. For example at the particle detector when it clicks it has registered here in the classical world - no question. You can go back further and try and figure out exactly when it did occur and that's where you need a quantum theory of measurement which wasn't around at the time Schrodengers Cat was put forward. That was the real import of this thought experiment IMHO. Now we have a better understanding of decoherence and can push back a bit from that. What that tells us by interacting with the environment and the particle detector the state of system that emits the particle gets entangled with it and that causes decoherence to occur. Now here is where issues arise - my understanding is this only has been worked out for some simplified models and more work needs to be done on generalizing it - but what they show is - for it to be well below the level current technology can detect it happens very quickly (in the region of 10^-27 seconds I have read - and it continues to quickly drop even below that).

My view is if it's well below the level that current technology can detect, then, unaided by such technology it is most definitely describing the classical world we see around us - the world Copenhagen postulated when quantum 'observations' are registered.

If that isnt the sort of thing you had in mind let me know and we can chat about that.

Thanks
Bill

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#### bhobba

Mentor
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.
Undoubtedly everything we call classical is in some kind of superposition but at a level well below we can detect, even aided by technology.

When I say the cat, or other objects of everyday experience, is prevented from being in a superposition by decoherence obviously it is meant well below the ability to detect.

Thanks
Bill

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#### StarsRuler

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.
How would you feel being in a superposition of 2 states, for example, 1 being indoor and another being outdoor. Don´t you think is it paradoxical? :surprised

#### BruceW

Homework Helper
But just to be sure do you mean by subjective it can be placed at different places and because of that you consider it can not be made a working theory? That's what I am assuming in the following.
yeah. well, it can be placed at different places and it is a working theory (since we can always place the subjective collapse at a later time to get a more accurate answer). But it is not a nice theory.

bhobba said:
Now here is where issues arise - my understanding is this only has been worked out for some simplified models and more work needs to be done on generalizing it - but what they show is - for it to be well below the level current technology can detect it happens very quickly (in the region of 10^-27 seconds I have read - and it continues to quickly drop even below that).

My view is if it's well below the level that current technology can detect, then, unaided by such technology it is most definitely describing the classical world we see around us - the world Copenhagen postulated when quantum 'observations' are registered.
yes, I have heard of similar timescales (very fast). I agree really, decoherence explains why it would be very difficult to diffract a cat (for example). And I'm guessing this is essentially what you mean when you say "the classical world we see around us". So I agree on this. But the part of the Copenhagen interpretation that I don't like is the subjective non-unitary collapse. This is what draws a solid line between the classical and quantum worlds. And the irony is that since it is a subjective collapse, it has no physical meaning. Therefore we must place it at a time when it only changes the predictions of experiments by a very small amount, so that we still get approximately the same answer as we would have gotten without using the subjective collapse.

#### BruceW

Homework Helper
How would you feel being in a superposition of 2 states, for example, 1 being indoor and another being outdoor. Don´t you think is it paradoxical? :surprised
I would ask why do you think it is paradoxical. sure it would be a lot more difficult than doing the same thing for say, an electron. but difficult doesn't mean the same as paradoxical.

#### StarsRuler

Sorry, I wanted mean "don´t you think isn´t it paradoxical"

A person in a superposition of an state with the person indoor, and another state with the person in a middle of the street. What does the eye´s person watch??

#### bhobba

Mentor
But the part of the Copenhagen interpretation that I don't like is the subjective non-unitary collapse. This is what draws a solid line between the classical and quantum worlds. And the irony is that since it is a subjective collapse, it has no physical meaning. Therefore we must place it at a time when it only changes the predictions of experiments by a very small amount, so that we still get approximately the same answer as we would have gotten without using the subjective collapse.
Now I understand what you mean by subjective - yes its a problem - Copenhagen is very sketchy on exactly what classical is. I think its basically OK in that its easy to tell in any given set-up - but its not nice - and to be blunt a bit fishy.

But decoherence has cleared that up a lot - but without discussing the details not to everyone's satisfaction.

Thanks
Bill

#### stevendaryl

Staff Emeritus
The mixed state as a result of this has the FORM of a mixed state - because of this its called an improper mixed state - its not prepared the same way which is the very essence of the discussion of if decoherence solves the measurement problem or not.
Hmm. I'm not exactly sure what you mean by "improper mixed state". What's a "proper mixed state"?

This is the key physical process that's going on - it's entangled with the environment so off diagonal elements get suppressed. That how a pure state gets transformed to an improper mixed state.
Well, there are two different aspects to this: First, entanglement by itself leads to an effective mixed state, if you are only interested in one of the entangled subsystems. There is nothing special about "the environment" here. Second, there is the issue of whether it is possible to recover a pure state, and this is where the many degrees of freedom of the environment makes it practically impossible.

In principle, if you have an entangled state of the form

$|A_1\rangle |B_1 \rangle + |A_2\rangle |B_2 \rangle$

it is possible to "force" subsystem $B$ into a superposition by measuring subsystem $A$ in a particular way: Pick an operator $O$ on $A$ with eigenstates

$|A_1'\rangle = \dfrac{1}{\sqrt{2}} (|A_1\rangle + |A_2\rangle)$
$|A_2'\rangle = \dfrac{1}{\sqrt{2}} (|A_1\rangle - |A_2\rangle)$

and with corresponding eigenvalues $O |A_1'\rangle = +1 |A_1'\rangle$
$O |A_2'\rangle = -1 |A_2'\rangle$

Then measuring $O$ will force $B$ to be in a superposition of $B_1$ and $B_2$.

But if subsystem $A$ is the electromagnetic field and $B$ is a cat, there is no observable $O$ that can do this that is actually capable of being measured.

#### bhobba

Mentor
Hmm. I'm not exactly sure what you mean by "improper mixed state". What's a "proper mixed state"?
A proper mixture is one created by supplying a randomly selected pure state to be observed. It leads to a mixed state operator. The same operator results from decoherence but it was not physically created the same way. If it was measurement problem solved - what you measured was there prior to measuring - no collapse - no nothing - everything lily white in the quantum world. Trouble is it was not created that way and you can't say it had that state prior to observation. Now here is the kicker - you can't say it wasn't either - there is simply no way to tell the difference between the two observationally. So what you do is simply assume it is - no one can prove you wrong - measurement problem solved. This is what is meant by decoherence does not solve the measurement problem - it only gives the appearance of wavefunction collapse - but a small interpretational assumption allows it to.

Most good papers on decoherence and the measurement problem discuss it - eg:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf
'Postulating that although the system-apparatus is in an improper mixed state, we can interpret it as a proper mixed state superficially solves the problem of outcomes, but does not explain why this happens, how or when. This kind of interpretation is sometimes called the ensemble, or ignorance interpretation. Although the state is supposed to describe an individual quantum system, one claims that since we can only infer probabilities from multiple measurements, the reduced density operator SA is supposed to describe an ensemble of quantum systems, of which each member is in a definite state. Decoherence theorists have generally come to accept the criticisms above, and accept that decoherence alone does not solve the problems of outcomes, and therefore leaves the most essential question untouched.'

I personally hold to the ensemble interpretation - but as you can see it's not generally agreed it solves the measurement problem. This is what I mean when I write - it whispers in your ear something more may be going on. But it also IMHO strongly suggests this is the correct place to put the Von-Neumann regress cut - not at consciousness. I strongly suspect this is why Wigner abandoned consciousness causes collapse when he heard of some early work by Zurek.

Thanks
Bill

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