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

[BruceW]

I'm not sure I see the issue. Again "in a superposition" is just relative to choice of observables.
A definite spin z-up electron, which we can quite clearly understand in terms of the classical analogue of a rotating mass, is also in a superposition of spin x-"up" and spin-x "down" states. Saying it is "in superposition" or "not" is simply a question of which component is being classically analogized.

Yes, so in this sense, the electron would be in a superposition of x-spin eigenstates. And also, the electron is in a single z eigenstate. What is wrong with these statements? It seems arbitrary to me to separate "state of knowledge of the system" and "state of the system". Why separate these two concepts? They are identical to me.

 

[BruceW]

analogously, vectors are used to describe the electric field. I can say the components of the electric field with respect to some basis are some values. And with respect to another basis, they are some other values. The physical situation can be described by either choice of coordinates, or any other choice.

Edit: I think I see your viewpoint though. In this analogy, would you say the only 'real' thing is the abstract vector (without reference to any basis)?

 

[capcom1983]

There is no cat if it isn't observed it doesn't exist. I love that (it also explains why I'm still 21). The point of this thought experiment is to remove observer with a result that is unknown and immeasurable. I prefer einsteins version with the bomb not poison. If you use a ka atom with a half life of 1600 years (and the cat amazingly lives that long) you still can't say that the atom decayed. So the cat would still be alive (old). Then when you look in the box this could cause the decay thus blowing up the cat.

 

[Omega0]

Edit: I think I see your viewpoint though. In this analogy, would you say the only 'real' thing is the abstract vector (without reference to any basis)?

I guess you got it. It does not matter if we speak about a "z-state". Once again this is just human thinking "oh, okay z-axis directed to heaven". That's it. Look at the description of the state of an electron. It is |UP> or |DOWN>. It's just naming. You can call it |fish> and |lemon>, it is the same, just convention. I believe it is wise to not call the spin of an electron "left" and "right" in the same sense (nevertheless I would say fish an lemon would be better for spin because then you don't get the idea that is has something to do with up and down)-

 

[jambaugh]

Yes, so in this sense, the electron would be in a superposition of x-spin eigenstates. And also, the electron is in a single z eigenstate. What is wrong with these statements? It seems arbitrary to me to separate "state of knowledge of the system" and "state of the system". Why separate these two concepts? They are identical to me.

Yes, I understand and vehemently disagree. The principle point is that what we know about e.g. an electron is how it will behave, its "actuality" not the "reality" of how it "is".

Objective state is to QM as the aether was to SR. Its exactly the excising of this component that "makes" the theory and advance. (And like the aether based SR equivalents you see popping up all the time on this forum you have the objective state based QM equivalents in the form of Many Worlds and Bohm's demonic pilot waves.)

Now just as you can do relativistic physics, carrying out Lorentz transformations properly while believing in an aether, you can likewise do quantum physics while believing the state vector you write down somehow is a representation of the state of reality of the quantum system. But at some points the very existence of these, aether and "state of reality" are articles of faith which cannot be directly known. You know system behavior through devices.

We define time by when a clock goes tick and we define an electron by when an electron detector goes click.

While the post modernists want to vanquish positivism, it is the appropriate paradigm for defining and carrying out science and most especially quantum physics.

 

[BruceW]

I think I see what you mean. In an ideal world, we would never mention the components of the state vector with respect to a basis. And it is only because we relate our theories to actual measurements, that it is useful to talk about the components.

I don't really see the connection to the aether/SR. I'm guessing you mean that when everything could be explained without the aether, then there is no longer a need to hold on to that concept. But this is not analogous to "component representation"/quantum theory because component representation is still useful to us, even though not really a necessary part of the theory. aether theory was no longer useful when SR became fully developed.

Or maybe you mean that QM has not fully developed yet, and when it does, the "component representation" will no longer be useful??!

 

[Crazymechanic]

@jambaugh according to how much I know myself and how much my logic tells me I agree to what you say mostly.This is also one of the things I questioned here before and some people have not yet responded to that.

@BruceW """ "It seems arbitrary to me to separate "state of knowledge of the system" and "state of the system". Why separate these two concepts? They are identical to me."""

Bruce this is where i think it is not like that.
If our state of knowledge about the system would be the whole system then in the middle ages the Earth should have been flat and the sun orbited the Earth and when did that changed , when we made an observation? Now ofcourse you would disagree saying that quantum effects cannot be also the same effects on cosmological scales and yes you would be right but my analogy is more to point out that what we think is not always the whole truth , indeed in most of the cases it's not only half of it.
Now ofcourse it's my personal opinion as on this topic everyone has one of a kind but I do think that QM works just fine with no superpositions and other stuff and does so according to the laws nature has given it.Now the ones who need superpositions and other so called "quantum phenomenon" are us because we don't have he full access to scales so small and so a lack of full information and observation of what's going on.
Now physics and theories to me seems like people and debates if we would somehow have the ability to see through other peoples eyes and think like they do we would immediately understand them and the argument would be gone but because we can't we have to predict and analyze a man's opinion and the way he reacts to draw conclusions about the man and sometimes they are right sometimes not so and sometimes wrong, but the average conclusion about the average human is called psychology and yet no matter how good it is at describing ones behavior and etc you will never know the whole story of a person not being him.
Just like you can never know what it is to be an electron or so.
but ofcourse that doesn't mean we cannot atleast for 95% understand what one is and what it does.
Saying that we have the whole picture would be speculation and saying that what we see is the whole picture and there is nothing more to that would be unprovable hence another speculation.
i think saying that we not yet fully know would be a fair answer the thing is some people don't like these types of answer they get annoyed by them and angry. """ Or maybe you mean that QM has not fully developed yet, and when it does, the "component representation" will no longer be useful??! """

Do you think it is developed fully as of now when I hit the letters on this keyboard? :)

 

[f95toli]

I'm not sure I see the issue. Again "in a superposition" is just relative to choice of observables.
A definite spin z-up electron, which we can quite clearly understand in terms of the classical analogue of a rotating mass, is also in a superposition of spin x-"up" and spin-x "down" states. Saying it is "in superposition" or "not" is simply a question of which component is being classically analogized.

True, but my point was that if you e. g have a charge qubit the two states correspond to "0" or "1" electrons on the island these two states can be in a superposition, ¦0> and ¦1>is then most natural basis. There is a difference between this and the spin of an electron where the choice of basis is more arbitrary since spin is a fundamentally QM and also "classically" continous.

Note also that these two states (0 or 1 electron) that also exist classically; it is just that the charge qubit in the classical regime (e.g at high temperatures) is just (essentially) a fancy transitor.
Hence, a charge qubit (or a flux qubit) is a system that is binary in the classical regime. and where the most natural choice of basis in the quantum regime is a one which correponds to these two states.

You are of course free to change basis for whatever system you want, but to me as an experimentalist that is just math: when I design devices I will still think about single electrons moving in and out of an island, or currents flowing in different directions. These electrons and currents are "real" and something I can measure.

 

[bahamagreen]

It is unfortunate that a cat was chosen because the experimental design confounds the interaction between the half life of the radioactive trigger and the half life of the cat itself.

Intrinsic uncertainty can never be overcome as one may never know if a particular cat hasn't already spent some of its nine lives prior to being placed in the box.

The measurement problem occurs because if you repeated kill the cat until all its lives are consumed, you will have counted and verified how many lives it had left, but it's no longer suitable to meet the initial conditions assumed in the experimental design.

Hidden variables in QM arise from sloppy theory, design, and analysis, as when one cannot exclude the influence of past spent cat lives shortening the cat's present half life).

Wheeler's "Many-cats" interpretation of QM is an extreme example of how to address these issues.

 

[bhobba]

Objective state is to QM as the aether was to SR.

I am not a fan, but the MWI has an objective state and is very elegant mathematically. Same with BM - although to me its a kludge and not elegant. I too hold to an interpretation where the state is not objective however I think the issues with interpretation are a bit too subtle for blanket statements like that.

Thanks
Bill

 

[bhobba]

If our state of knowledge about the system would be the whole system then in the middle ages the Earth should have been flat and the sun orbited the Earth and when did that changed , when we made an observation?

You misunderstand state of knowledge. If you consider a quantum state to not be objective and merely an aid to describing the outcome of observations you consider it like probabilities in standard probability theory. Probabilities do not have objective existence like say an electric field but they also help in describing certain situations like rolling a dice. It has nothing to do with false views in the past actually being true.

Can I ask have you actually studied the details of QM? If not that would be a good start in actually understanding the issues involved.

Thanks
Bill

 

[bhobba]

You are of course free to change basis for whatever system you want, but to me as an experimentalist that is just math: when I design devices I will still think about single electrons moving in and out of an island, or currents flowing in different directions. These electrons and currents are "real" and something I can measure.

This is extremely important to modern physics and especially Quantum Mechanics. You are free to change basis, coordinates etc etc to whatever you want - they are simply man made constructs and the laws of nature should not depend on that choice. Certainly some choice often makes a situation easier to understand and analyse but in principle it can be anything.

Imagine a system and an apparatus to observe some property with a digital readout. List the possible outcomes as yi. This by definition is a vector and to bring this out write it as sum yi |bi>. Now we have a problem - the precise |bi> is arbitrary and can be changed to any other basis - but in doing that the yi will change - but the laws of nature can not depend on the choice of basis. To circumvent this problem QM replaces the |bi> by |bi><bi| to give the Hermitian operator sum yi |bi><bi|. This is basis independent and the possible outcomes of the observation are its eigenvalues. In fact this is the first axiom of Ballentines approach to QM found in his book - QM - A Modern Approach. The second axiom, the expected value of an observation is via the usual trace formula Tr(RP) where R is the observable defined above and P the state follows from Gleason's Theorem. It would seem that an arbitrary choice of basis is built right into the foundations of QM.

Thanks
Bill

 

[bhobba]

Hidden variables in QM arise from sloppy theory, design, and analysis, as when one cannot exclude the influence of past spent cat lives shortening the cat's present half life).

BM (Bohmian Mechanics) for example is not the product of 'sloppy theory, design, and analysis'. I don't hold to it but it's perfectly valid.

The issues with interpretation can not be resolved with throwaway lines like that.

Thanks
Bill

 

[akdude1]

Schrodingers was trying to show that the wave function might both collapse and keep going in separate universes but the experiment could be ruined if something as simple as cosmic radiation interacted with anything or if schrodinger were watching the whole experiment would be ruined. In summary Schrodinger said the wave function (in a perfect experiment) could both collapse and continue (again in a perfect world)

 

[bhobba]

Schrodingers was trying to show that the wave function might both collapse and keep going in separate universes

Don't think so - the MWI wasn't even around then.

What he was trying to show is the formalism if blindly followed leads to absurdities like a cat that is in a superposition of partly alive and partly dead. And he is correct - if you are not careful that's exactly the conclusion - but with appropriate care such as understanding exactly where it is observed in the macro world (at the particle detector) the issues vanish. For some reason however some want to draw a different conclusion - don't really know why. To me the issue is not that it can't be resolved, but, as I think it was Einstein that wryly remarked, the ways of doing it were all different. To Einstein this suggested what was happening was far from well understood and QM was incomplete. It is believed by some that Einstein rejected QM, and indeed his views did evolve, but most certainly in his later years he believed it was correct, and wasn't even really worried about its probabilistic nature, but rather it was incomplete. Thats the real import of Schrodinger's Cat - its not that the issue it raises can't be resolved - its there seems to be so many different takes on it.


Thanks
Bill

 

[akdude1]

@bhobba hey man my bad I totally spaced about when Hugh Everette postulated the MWI. Thanks for enlightening me!

 

[Crazymechanic]

@bhobba Nowhere I was saying or intended to say that everything we know about QM states is just a mind construct or mathematics I do believe that there are many so called "variables" that we do measure directly and assign meaning and numbers and states to them.
But all I was trying to say is that there is something we don't know because the way things work forbids us from direct chance of "seeing" it.

 

[bhobba]

But all I was trying to say is that there is something we don't know because the way things work forbids us from direct chance of "seeing" it.

What precisely don't you know if you can't see it? The cat is either alive or dead regardless. Is it the knowledge the cat is alive or dead? Of course you can't see the cat to determine that until you open the box - and the experiment is designed precisely for that - but that's utterly trivial. The issue with Schrodinger's cat is to point out issues of the formalism - its not to show that you have to resort to some weird ideas like 'then in the middle ages the Earth should have been flat and the sun orbited the Earth and when did that changed , when we made an observation?' to resolve it. If you had a machine in their that flipped a coin and you had to open a box to see if it was heads or tails would you evoke similar arguments? To be specific what it highlighted is the need for a quantum based theory of measurement - since then a lot of work has been done on just that - and research is ongoing.

There are many ways to resolve Schrodinger's Cat - I gave one - namely to realize the weirdness resides at the particle detector and not at the cat. Here is another one - in Copenhagen the state is simply a theoretical device to determine the probability of outcomes here in the macro world - it allows us to determine the probability of the cat being dead or alive - but the cat at any time is either dead or alive. The issue with Copenhagen though is it splits the world into a classical macro world and a quantum world - but since the classical macro world is still governed by QM why does it appear to behave differently? Modern research has shown decoherence is the reason. You can have a look at further ways to resolve it here:
http://en.wikipedia.org/wiki/Schrödinger's_cat

Of modern times decoherence is often directly invoked to resolve it (it was not known about at the time it was propsed) - that shows the live and dead states never interfere so it behaves clasically:
http://en.wikipedia.org/wiki/Quantum_mind%E2%80%93body_problem
'Decoherence does not generate literal wave function collapse. Rather, it only provides an explanation for the appearance of wavefunction collapse, as the quantum nature of the system "leaks" into the environment. That is, components of the wavefunction are decoupled from a coherent system, and acquire phases from their immediate surroundings. A total superposition of the universal wavefunction still exists (and remains coherent at the global level), but its fundamentality remains an interpretational issue. "Post-Everett" decoherence also answers the measurement problem, holding that literal wavefunction collapse simply doesn't exist. Rather, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive. Moreover, our observation tells us that this mixture looks like a proper quantum ensemble in a measurement situation, as we observe that measurements lead to the "realization" of precisely one state in the "ensemble".'

Indeed that link examines the whole mind body thing - it explains while some hold to consciousness being part of QM, it most definitely is not required, not required at all.

Thanks
Bill

 

[Crazymechanic]

@bhobba I don't know why you interpret me again maybe because of the way I word my phrases but I used the flat Earth just as an analogy although I agree in the times of flat Earth it was not because we didn't know which of the scenarios will play out but we just didn't knew and had no devices and maths to prove either one.

The research may be ongoing but it's not like our research will change the laws with which QM plays out , in this case the fact that we already know very well that wave function collapse at measurement.
To say that nature knows what she will "spit out" what state there is going to be and is even before we ever made the "eye contact" well I don't know that would have to mean that nature is self aware. That would be philosophy.
Maybe there is a God behind all of this.Again philosophy.
Well I think this thread is maxed out as there is nothing more fundamental to Schroedingers cat right now that we could add to what we already know.

 

[Charles Wilson]

http://www.nobelprize.org/nobel_prizes/physics/laureates/1954/born-lecture.pdf

I wasn't going to post anymore in fear of the Hounds of Hell nipping at my heels (How can quoting someone's position to develop a point without asserting whether it is your own position be one of the dreaded Thought Crimes in QM-Land?...)

Maybe this might help.

Born gives a great deal of useful historical info, especially at the beginning. The development of |Psi|^2 is worth the price of admission all by itself.

CW

 

[alweiss]

I know that so far as we know, it's impossible to figure this out, but is it possible that in a superposition, the atom(or whatever particle, in this case a cat) becomes two atoms once interaction with anything is blocked off, and then once a photon of light is sent some type of force pushed one cat away, leaving just the one cat in one state?

 

[ZapperZ]

I know that so far as we know, it's impossible to figure this out, but is it possible that in a superposition, the atom(or whatever particle, in this case a cat) becomes two atoms once interaction with anything is blocked off, and then once a photon of light is sent some type of force pushed one cat away, leaving just the one cat in one state?

Then you have misunderstood the superposition principle. What is in superposition is NOT the cat, or the atom, but rather a property of the cat or atom. This property, described by an observable, is the one that is in superposition, not the whole cat or atom.

By creating a duplicate system, you've created a whole slew of problems, including several conservation violations.

Zz.

 

[alweiss]

Thanks for the clarification !

 

[StarsRuler]

The cat is a macroscopical system with the precision for decide if he is alive. He is an observer, alive or dead, the system decohere in a very short time. There is no superposition with the cat. We can let an isolated closed box but the cat is alive or dead . It is question to do the calculations

 

[audioloop]

the pertinent question is if persist superposition (a linear principle, i.e. not change)
on macroscopic objects ?
to answer that, what is need is experimental testing.

 

[bahamagreen]

BM (Bohmian Mechanics) for example is not the product of 'sloppy theory, design, and analysis'. I don't hold to it but it's perfectly valid.

The issues with interpretation can not be resolved with throwaway lines like that.

Thanks
Bill

Why do I get the idea that you did not read my post? (#79) ;)

 

[bhobba]

Why do I get the idea that you did not read my post? (#79) ;)

Well let's see:

The measurement problem occurs because if you repeated kill the cat until all its lives are consumed, you will have counted and verified how many lives it had left, but it's no longer suitable to meet the initial conditions assumed in the experimental design.

All its lives consumed? Hmmmmm.

Maybe its not me reading it, which I did, maybe its what you are saying.

Thanks
Bill

 

[bhobba]

The cat is a macroscopical system with the precision for decide if he is alive. He is an observer, alive or dead, the system decohere in a very short time. There is no superposition with the cat. We can let an isolated closed box but the cat is alive or dead . It is question to do the calculations

In QM an observation does not require an observer. An observation is whenever a quantum process makes its mark here in the macro world, which in this setup occurs at the particle detector. Schrodinger's Cat never was an issue for Copenhagen - its solution within Copenhagen was utterly trivial. The issue with Schrodinger's Cat was, and always has been, pointing to the need of a fully quantum theory of measurement rather than the fundamental split Copenhagen makes between the quantum and the macro world.

I suspect you know that though and it was just the way you expressed it.

Your observations about decoherence are spot on - and is part of the modern view of Schrodengers Cat that reflects the work that has been done with developing that quantum theory of measurement since Schrodinger proposed his famous (infamous?) thought experiment.

Pop Sci accounts IMHO are responsible for much of the misunderstanding about this thought experiment.

Thanks
Bill

 

[bhobba]

the pertinent question is if persist superposition (a linear principle, i.e. not change) on macroscopic objects ? to answer that, what is need is experimental testing.

The cat is obviously not in a superposition of alive and dead.

However it is well known that once entanglement with the environment is removed, which is difficult, but not impossible, to do, (it usually means it must be kept ultra cold - most entanglement is via some kind of 'heat bath') quantum effects reassert themselves even for macro objects. And indeed some strange quantum effects have been observed with macro objects, and undoubtedly future experiments will reveal even more eg:
http://www.scientificamerican.com/article.cfm?id=quantum-microphone

Although I have a bone to pick with the article:
'As to how the day-to-day reality of objects that we observe, such as furniture and fruit, emerges from such a different and exotic quantum world, that remains a mystery'.

That's not quite true - how classical behavior emerges is pretty well understood - environmental decoherence has shed a lot of light on it - but some issues do remain such as the so called factoring problem (there are others as well, and most good textbooks allude to them - but strangely, and I am not quite sure why this is, it may be for a deep reason or evidence of nothing at all, they do not talk about the factoring problem - I have only seen discussions here about it - interesting). I believe, and I think most physicists also believe, this is more along the lines of dotting the i's and crossing the t's so to speak and they will be resolved - but really who knows what the future will bring.

But that is not what is going on here. The cat and the rest of the paraphernalia of this thought experiment are entangled with each other and the environment - specifically its not done at an ultra cold temperature near absolute zero.

Thanks
Bill

 

[audioloop]

quantum effects reassert themselves even for macro objects.

That's not quite true - how classical behavior emerges is pretty well understood

valid to 430 atoms (experimental limit).

i am talking about 10 ²⁰ atoms.

 

[bhobba]

i am talking about 10 ²⁰ atoms.

Precisely what are you claiming that number of atoms demonstrate and exactly how does it deviate from the standard treatments found in virtually every QM textbook?

Thanks
Bill

 

[BruceW]

There are quantum systems (in the sense that they can only be described quantum-mechanically) of much more than just 430 particles. for example:
http://en.wikipedia.org/wiki/Macroscopic_quantum_phenomena
http://en.wikipedia.org/wiki/Bose-Einstein_condensation
In some of these situations, there are a very large number of particles (or atoms) in the same quantum state (i.e. all in superposition). And they are definitely macroscopic phenomena. So it is clear that QM can work for macroscopic phenomena. What is not clear is if QM works for a system like a cat, i.e. can we describe the entire cat as a single quantum state? No-one knows because such an experiment has not been done to find out. You would have to do something equivalent to diffracting a cat, which is experimentally going to be *very* difficult, definitely beyond current technology.

We can be fairly confident that the individual components of the cat (i.e. its atoms) can each be described approximately (i.e. considering each atom independently of the others). But this is an approximation. So I don't think it is justified to say a priori that we must be able to describe a cat as a single quantum state. Maybe we can. Maybe we can't. But we don't have the technology to test this. (I personally think that a cat could be diffracted if we had the technology to do such an experiment, but who knows).

 

[bhobba]

We can be fairly confident that the individual components of the cat (i.e. its atoms) can each be described approximately (i.e. considering each atom independently of the others). But this is an approximation. So I don't think it is justified to say a priori that we must be able to describe a cat as a single quantum state. Maybe we can. Maybe we can't. But we don't have the technology to test this. (I personally think that a cat could be diffracted if we had the technology to do such an experiment, but who knows).

All true. The point here however is the alive and dead states show no interference and each state to the limit of our current technology behaves entirely classically.

Thanks
Bill

 

[BruceW]

yeah, or I would word it as: we can't probe the (possible) interference between alive and dead states because a cat is darn complicated. (unlike a Bose-Einstein condensate which is relatively simple).

 

[audioloop]

So I don't think it is justified to say a priori that we must be able to describe a cat as a single quantum state. Maybe we can. Maybe we can't. But we don't have the technology to test this. (I personally think that a cat could be diffracted if we had the technology to do such an experiment, but who knows).

maybe not a cat

there are various schemes,
between them

http://eprints.gla.ac.uk/32707/1/ID32707.pdf
"We introduce a novel cooling technique capable of approaching the quantum ground state of a kilogram-scale system"


http://web.physics.ucsb.edu/~quopt/tow.pdf
"We have performed a detailed study of the experimental requirements for the creation and observation of quantum superposition states of a mirror consisting of 10¹⁴ atoms, approximately 9 orders of magnitude more massive than any superposition observed to date. Our analysis shows that, while very demanding, this goal appears to be within reach of current technology"


http://arxiv.org/pdf/1201.4756v2.pdf
http://link.springer.com/article/10.1007/s10686-012-9292-3
"Testing the predictions of quantum theory on macroscopic scales is one of today's outstanding challenges of modern physics and addresses fundamental questions on our understanding of the world. Specically: will the counterintuitive phenomena of quantum theory prevail on the scale of macroscopic objects? This is at the heart of the so-called \quantum measurement problem", also known as Schrodinger's cat paradox. Another question is whether quantum superposition states of massive macroscopic objects are consistent with our notion of space-time or whether quantum theory will break down in such situations"


.