Understanding Schrödinger's Cat Experiment and the Many Worlds Interpretation

[lj19]

Could someone please explain this experiment to me? And explain the "many world's interpretation" and the outcome of the experiment? Thank you.

 

[Steve Lajoie]

Hi! This is a quantum mechanics question. I think this subject should be moved.

Basically, you have a box from which no information can escape. It contains a cat and a quantum mechanical mechanism that would kill the cat if it goes to state Psi_D (dead), and the cat would live if it remained in state Psi_A (alive).

Since you can't know what happened inside the box, the quantum state of the quantum event, and thus the cat, is indeterminate and has a wave function 1/2 [Psi_A + Psi_D]. Thus, the cat is in an indeterminate state between alive and dead.

If you open the box, you're making a measurement, and the wave function collapses to either Psi_A or Psi_D.

Some would argue that the CAT makes the measurement, and knows as soon as the quantum event happens.

Some would say what difference does it make, YOU don't know until you open the box. I'm in that camp. We had to define our box in a way so you couldn't hear the cat's cry, or detect the drop in temperature with death, or smell the poison and all that - no possible information about the quantum event could escape. Thus, the question becomes unphysical.

AS for the many worlds interpretation, how can I test that? Show me how to detect many universes and I'll gleefully go with that one. But again, if you can't ever detect it in THIS universe, it is unphysical.

Did that help? Did I screw it up? Please let me know. Griffiths "Introductory Quantum Mechanics" explains it much better. It's a cute little text but even used copies are expensive.

 

[lj19]

Was the explanation of the "many worlds interpretation" explaining it through the cat being in parallel universes?
You say "We had to define our box in a way so" did you do this experiment?
Overall, I understand the experiment.
Physically, the cat's state of being was unknown therefore you can assume that the cat was dead AND alive, but really wouldn't it be one or the other? Even if you didn't open the box. I just researched this a bit, and came across someone [http://blogs.smithsonianmag.com/science/2009/06/02/what-is-schrodingers-cat/] who said the experiment was designed so that an atom had a 50/50 chance of decaying radioactively- is that why there was a 50/50 chance the cat was alive or the cat was dead therefore without having knowledge of if anything occurred, the cat was both alive and dead [not having to do with the many worlds theory]?

 

[Steve Lajoie]

Was the explanation of the "many worlds interpretation" explaining it through the cat being in parallel universes?
You say "We had to define our box in a way so" did you do this experiment?
Overall, I understand the experiment.
Physically, the cat's state of being was unknown therefore you can assume that the cat was dead AND alive, but really wouldn't it be one or the other? Even if you didn't open the box. I just researched this a bit, and came across someone [http://blogs.smithsonianmag.com/science/2009/06/02/what-is-schrodingers-cat/] who said the experiment was designed so that an atom had a 50/50 chance of decaying radioactively- is that why there was a 50/50 chance the cat was alive or the cat was dead therefore without having knowledge of if anything occurred, the cat was both alive and dead [not having to do with the many worlds theory]?

I believe in the many world interpretation, at the time you open the box, the event splits into two universes: one with the cat alive, and one with the cat dead.

No, I didn't do the experiment. I'm a dog person, but I like some cats, and I would never do that to any cat. I might do it to a cow, because I like to eat the poor things.

The idea is that there can be no way to determine if the quantum event killed the cat OUTSIDE the box.

Experiments have been done that show that the wave function doesn't collapse until you take the measurement. J.S. Bell put together a book of papers arranged in a sensible order called "Speakable and Unspeakable in Quantum mechanics" that touches on this subject. Griffiths also discusses it at the back of the book, after enough material has been covered that the reader could understand it.

 

[bcrowell]

I believe in the many world interpretation, at the time you open the box, the event splits into two universes: one with the cat alive, and one with the cat dead.
[...]
Experiments have been done that show that the wave function doesn't collapse until you take the measurement.

Mmm...not so sure that this is right. I wouldn't describe it as a split into two universes; the universe just happens to be in a certain wave state. There is only one wave, not two. The wave just doesn't happen to be a wave that describes a pure live cat or a pure dead cat. Sort of like a sound wave that had two different musical notes in it at the same time.

And I don't think wavefunction collapse is something that can be tested by experiment, nor is it a feature of the many-worlds interpretation. In fact, one of the main reasons to prefer MWI is that it avoids wavefunction collapse, which has foundational problems (since measurement is just a physical process like any other process).

 

[lj19]

I think this experiment, as they said in the video link, was a "thought experiment". But the interpretations of the theory can be different, like the many world theory versus other interpretations. Wouldn't it be that once the box is opened, then the experiment theoretically could be psychically observed so the cat could either be dead or alive, and then not both according to the experiment? But before it is opened, then, the multiple world theory if used or considered, can develop that the cat is both dead and alive [before the box is opened]? Or is it something different? How could the m.w.i. occur once opened if then the cat is alive or dead?..and not both anymore.
Could someone explain how waves correspond to this? I didn't understand that, thanks.

 

[Upisoft]

You open the box. There is a cat. After some examination you find it is dead. After closer examination you find it was dead for at least 2 hours. If everything happens at the moment when you open the box how it is possible that the cat has been dead for 2 hours?

 

[Fredrik]

The point of the Schrödinger's cat thought experiment is to show that the linearity of the Schrödinger equation implies that if microscopic systems can be in superpositions, then so can macroscopic systems. However, the Schrödinger equation applies only to systems that are isolated from their environments, so it doesn't apply to a cat. It's not that the cat isn't quantum mechanical, it's that when it interacts with its environment, we can't apply the Schrödinger equation just to the cat. We need to apply it to the combined system cat+environment, and if we do, we see that the quantum properties of the system are very quickly moved into the environment where they are practically unobservable. This phenomenon is called decoherence.

A measurement in QM is an interaction between a system (which has been kept isolated from its environment) and a measuring device (which can't be isolated from the environment) that correlates the eigenstates of some observable with the eigenstates of the measuring device. No such correlations are developed betweeen the cat and the observer when you open the box and look inside, because the cat has been interacting strongly with its environment for a long time, so the states of the cat are already correlated with the states of the environment, and as a result, the cat is effectively classical. The environment is the observer here, not the physicist.

 

[Jobrag]

Read Dirk Gently's Holistic Detective Agency by Douglas Adams there is a very clear description fairly close to the start of the book.

 

[Upisoft]

I'm trying to make distinction between a cat having defined state and we not knowing it, and a cat having undetermined state.

Many world interpretation means that the cat has defined state (in this world) but we cannot know which is our wold until we open the box.

If the state of the cat is truly undefined, then a lot of things happen in the instant when you open the box. (i.e. the time is not ticking in a closed box). That does not sound realistic.

At last the cat has defined state all the time, the time is ticking inside the box. We don't know what happens in the box until we open it.

 

[Fredrik]

I'm trying to make distinction between a cat having defined state and we not knowing it, and a cat having undetermined state.

Mathematically, the second option is represented by the state operator $|\psi\rangle\langle\psi|$ where $|\psi\rangle$ is the superposition $$\frac{1}{\sqrt{2}}(|\text{dead}\rangle+|\text{alive}\rangle)$$, and the first option by $\frac{1}{2}|\text{dead}\rangle\langle\text{dead}|+\frac{1}{2}|\text{alive}\rangle\langle\text{alive}|$. But you have to study state operators (a.k.a as density operators or density matrices) to understand that. The Wikipedia page is a good start. Link.

 

[pallidin]

You open the box. There is a cat. After some examination you find it is dead. After closer examination you find it was dead for at least 2 hours. If everything happens at the moment when you open the box how it is possible that the cat has been dead for 2 hours?

Exactly! Direct proof that the experiment is non-sensical and invalid.
I read somewhere that the experiment was never intended to be considered real, rather to demonstrate that we can complicate things beyond common sense and reality.

 

[pallidin]

The point of the Schrödinger's cat thought experiment is to show that the linearity of the Schrödinger equation implies that if microscopic systems can be in superpositions, then so can macroscopic systems. However, the Schrödinger equation applies only to systems that are isolated from their environments, so it doesn't apply to a cat. It's not that the cat isn't quantum mechanical, it's that when it interacts with its environment, we can't apply the Schrödinger equation just to the cat. We need to apply it to the combined system cat+environment, and if we do, we see that the quantum properties of the system are very quickly moved into the environment where they are practically unobservable. This phenomenon is called decoherence.

A measurement in QM is an interaction between a system (which has been kept isolated from its environment) and a measuring device (which can't be isolated from the environment) that correlates the eigenstates of some observable with the eigenstates of the measuring device. No such correlations are developed betweeen the cat and the observer when you open the box and look inside, because the cat has been interacting strongly with its environment for a long time, so the states of the cat are already correlated with the states of the environment, and as a result, the cat is effectively classical. The environment is the observer here, not the physicist.

Nice post!

 

[Upisoft]

Exactly! Direct proof that the experiment is non-sensical and invalid.
I read somewhere that the experiment was never intended to be considered real, rather to demonstrate that we can complicate things beyond common sense and reality.

The result is consequence of the assumption there is a box that can fully isolate quantum system from the external world. Such thing simply does not exist, hence stupid results follow.

 

[Ken Natton]

I read somewhere that the experiment was never intended to be considered real, rather to demonstrate that we can complicate things beyond common sense and reality.

My understanding is that Schrödinger himself never intended the experiment to be taken seriously. He intended it to highlight what he saw as the absurdity of the Copenhagen interpretation. It may well be the case that Schrödinger would have been horrified by the sheer volume of earnest discussion his thought experiment has generated over the years since he first dreamed it up. History records the uneasy relationships that existed between the various major players at that time, between the likes of Einstein and Schrödinger who passionately rejected the Copenhagen interpretation, and the likes of Niels Bohr and Werner Heisenberg who doggedly defended it.

I think the modern explanation for why the cat is not, in fact, ever both alive and dead at the same time is something called ‘decoherence’, by which the superpositions of the quantum world ‘decohere’ in the interface with the macro world, detectable and understandable by human physicists.

And for me, the better route into understanding the rationale behind the many worlds interpretation is the double slit experiment rather than Schrödinger’s Cat. The whole mystery of how it appears to be that the detected particle seems to have known ahead of time that it was going to be observed is the idea that there are actually infinite parallel universes in which the particle took every possible path between the emitter and the detection screen, including many in which it made it through neither slit, and large numbers in which it made it through one or the other slit, and when we observe the particle showing up at a particular point on the display screen and read the detector telling us which slit it went through, all we do is confine ourselves to that one universe in which that was the result.

For me, the many worlds interpretation is so much hokum, but I accept that opinion is no more scientific than is any other belief stated on this thread.

 

[lj19]

I remember learning that a scientist recently was able to create a particle in a parallel universe. http://homeboyastronomy.com/2008/07/27/do-parallel-universes-really-exist-new-evidence/ Could anyone explain thoroughly anything from this video?

Is the universe finite but always expanding?

Also, in Schrödinger's experiment was a thought experiment, and is the many world's interpretation is stating that the cat is physically dead and alive, or not? Is it saying that the cat exists alive in one universe and dead in the other?

 

[Steve Lajoie]

Experiments have verified that the Copenhagen interpretation is correct.

 

[Fredrik]

I remember learning that a scientist recently was able to create a particle in a parallel universe. http://homeboyastronomy.com/2008/07/27/do-parallel-universes-really-exist-new-evidence/ Could anyone explain thoroughly anything from this video?

I'm not going to watch the video, but there is certainly no evidence that many worlds actually exist.

Is the universe finite but always expanding?

No one knows if it's infinite or just enormous. It's likely that it will continue to expand forever even if it's finite.

Is it saying that the cat exists alive in one universe and dead in the other?

Yes, that's one possible interpretation of the mathematics.

Experiments have verified that the Copenhagen interpretation is correct.

Different interpretations make the same predictions about results of experiments, and experiments can only tell you how accurate a theory's predictions are, so what you're saying is impossible.

 

[Ken Natton]

Experiments have verified that the Copenhagen interpretation is correct.

It is abundantly clear that the Copenhagen interpretation remains just that – an interpretation. Certainly, in the historical context of the intellectual (and actually quite amicable) battle between Bohr and Einstein, it is Einstein who eventually faded into the background and Bohr’s basic approach that went on to dominate the subsequent development of quantum mechanics and its progeny, quantum electrodynamics.

The modern version of the debate centres around the famous imperative to ‘shut-up and calculate’. There are those, essentially the descendants of the supporters of the Copenhagen interpretation, who hold that we will never know the truth of what happens at the quantum level, because it is unknowable, because it is beyond our ability to experience it, or to relate it to anything we can experience, but that the utility of the mathematical formalism is proven and therefore, we should just shut-up and calculate. On the other side there are those who see that as a very sterile viewpoint, one with which they will always remain dissatisfied. They believe that, however impossible it might seem, we should never give up the quest to at least try to understand. It is by that very quest that we have come as far as we have. The trouble is, for the moment at least, ideas such as the many worlds interpretation have a very shaky scientific basis.

 

[Steve Lajoie]

Well... Griffiths, "Introduction to Quantum Mechanics", 3rd ed, page 4 does point out that the Copenhagen interpretation has been verified experimentally and dispels the agnostic "shut up and calculate" view. Griffiths points to J.S. Bell's excellent book "Speakable and Unspeakable in Quantum Mechanics".

I don't find the many world's hypothesis to be a scientific hypothesis, and that is probably why it is not taught at the university level and you can only find it in pop-Fiziks books.

The thing about the Schrödinger's cat experiment is that you can't prove that the cat is alive, dead or in a mixed quantum state of alive and dead when it is inside the box, by definition. Thus, the question is unphysical.

 

[Ken Natton]

Okay, I’m not looking to get into some little ’who can prove their viewpoint the best' exchange with you. My understanding is that this chap is one of the key proponents of the many worlds theory, and you should be able to see that he is a bit more of a heavyweight than your ‘pop-Fiziks’ suggests. He is also a strong opponent of the ‘shut-up and calculate’ view.

http://en.wikipedia.org/wiki/David_Deutsch


I have not read the titles you mention, the person that I have found particularly good at making the subject compelling and accessible for me is this man:

http://en.wikipedia.org/wiki/Jim_Al-Khalili

He tries to take a moderating stance by advocating ‘shut-up while you calculate’. That is, certainly you should use the existing mathematical formalism for the serious work, but that doesn’t mean that you can’t find some time for something that pushes a little harder at the boundaries.


And I’m not sure that even Niels Bohr ever suggested that it was hard and fast that the particle really does pass through both slits. Only that we don’t know otherwise, objecting to that idea doesn’t get us anywhere, and proceeding on the assumption that it does, does get us somewhere. On that point, I suppose it is unarguable that he was right. Quantum Physics has achieved all that it has achieved with its probabilistic approach.

There are some who assert that the problem with the Copenhagen interpretation is that it has taken over too completely and now actually serves to stifle original thinking. I don’t think that even its staunchest supporters ever ruled out the possibility of some deeper explanation emerging to supersede it at some point in the future. So whence comes the idea of such an absolute as ‘the Copenhagen interpretation is correct’ I don’t know.

I see no value in wasting any further energy on Schrödinger’s cat. My point is that neither would Schrödinger.

 

[Upisoft]

Someone please entangle cup of (1/2 cat food + 1/2 empty) with the poor animal put it in the box and close the thread.

 

[Steve Lajoie]

Experiments show that the particle does pass through both slits, before the wave function has been collapsed by a measurement. It was done by noting that it produces interference, which it wouldn't do if it passed through one slit. Copenhagen doesn't stifle thought. Of the alternatives, it is the best interpretation. It has 'take over' because it works.

The problem I see with many worlds is that it is unphysical: you cannot test events in the alternative universe where you got a different measurement.

I agree that asking what happens inside a box from which you can tell what happens inside is a bit absurd.

 

[Steve Lajoie]

Someone please entangle cup of (1/2 cat food + 1/2 empty) with the poor animal put it in the box and close the thread.

What is wrong with this thread that you want it closed?

 

[StevieTNZ]

If the wavefunction is describing the 'cat', then wouldn't it have collapsed to say the object is a cat? For all we know the wavefunction could have possibilites that it's a dead-cat or alive-cat, or even a dead-frog or alive-frog... the list goes on?

 

[StevieTNZ]

Experiments have verified that the Copenhagen interpretation is correct.

But can a macroscopic object really measure? Its saying that if the macroscopic object is Classical, then it's deterministic, and whatever result you get on the object would correlate to the microscopic object, which logically be deterministic as well. I thought the quantum world is indeterministic?

 

[pallidin]

The thing about the Schrödinger's cat experiment is that you can't prove that the cat is alive, dead or in a mixed quantum state of alive and dead when it is inside the box, by definition. Thus, the question is unphysical.

Exactly. And non-sensical.
THAT was the intent of the thought-experiment!
To demonstrate nothing about the cat, but to demonstrate that some types of experimentation can be bizarre enough to be non-sensical; wholly invalid.

In other words... THE CAT IS DEAD OR ALIVE REGARDLESS OF OBSERVATIONAL INFLUENCE.
That was his point; that humans can envision a scenario that simply does not exist.

 

[Elvin12]

I know its late but i just this thread now.
Anyway, no Schrodinger didn't mean the "thought experiment" seriously. The whole point was to show the absurdity of the Copenhagen interpretation. The fact that it is a thought experiment means that it hasn't and can't be conducted. The reason is obvious, despite the obvious animal cruelty, it's impossible to observe the experiment as the fact that the cat is observed would ruin the whole purpose of it.
However, going back to the proof of superposition, it does actually exist which has been proven through the double-slit experiment. When the particles (as large as bucky-balls) are fired they show an interference pattern. That is the particle interfering with itself as it passes through each point in space-time taking each path (sum-ver histories by Feynman), meaning that that some paths cross and particles interfere. However, when a particle detector is used the wave-function collapses and the interference is gone.
I hope this helps

 

[Fredrik]

Exactly. And non-sensical.
THAT was the intent of the thought-experiment!
To demonstrate nothing about the cat, but to demonstrate that some types of experimentation can be bizarre enough to be non-sensical; wholly invalid.

In other words... THE CAT IS DEAD OR ALIVE REGARDLESS OF OBSERVATIONAL INFLUENCE.
That was his point; that humans can envision a scenario that simply does not exist.

As a thought experiment it's certainly not nonsense, unless quantum mechanics is. QM clearly states that the cat will be in a superposition of dead and alive. We now know the the cat's interactions with the environment will move all the quantum weirdness into the microscopic properties of the matter around it, but this doesn't completely answer the question of what actually happens to the cat, since there's always some quantum weirdness left, even when the effects of that weirdness on predictions of results of experiments are too small to be measured.

 

[TrickyDicky]

As a thought experiment it's certainly not nonsense, unless quantum mechanics is.

This is a non-sequitur. It doesn't follow logically that if a particular thought experiment is absurd (and the Schrodinger's cat is, it was intendend by Schrodinger to be as previously pointed out), that Quantum mechanics is also nonsense (wich obviously isn't).

It was some type of physicists joke or even a sort of a zen koan, merely to suggest that QM might be incomplete, in the midst of the debates between Bohr and Einstein.

It's certainly kind of bizarre the amount of printed pages that this originated that missed the point.

See for instance the chapter five about this by Bob Laughling in his book "A different universe" :http://books.google.com/books?id=I5kbyB-yfB4C&printsec=frontcover&dq=laughlin+a+different+universe&hl=en&src=bmrr&ei=pKPyTJ7sGpH-4waUh7jcAw&sa=X&oi=book_result&ct=book-preview-link&resnum=1&ved=0CDYQuwUwAA#v=onepage&q&f=false

 

[pallidin]

QM clearly states that the cat will be in a superposition of dead and alive.

So, has that clearly easy experiment been done? Let's say 4 weeks, no food or water.
Superposition would DEMAND that if the cat were found dead, that the death would be medically proven to be at the time of observation.

But if medical examination of the cat clearly shows that death occurred BEFORE observation(tissue dehydration, putrification, etc...) it would throw superposition out of the water.

Superposition would demand that morbid dehydration or putrification COULD NOT EXIST.

 

[pallidin]

To continue with my rant, WOULD SOMEONE PLEASE PERFORM THE EXPERIMENT, using an ant if PETA is a problem, to settle this once and for all?

This is WELL within current and available capabilities.

 

[Elvin12]

Superposition would DEMAND that if the cat were found dead, that the death would be medically proven to be at the time of observation.
Superposition would demand that morbid dehydration or putrification COULD NOT EXIST.

No, if a particle is in superposition all it means is that it occupies all the possible states simultaneously but it doesn't mean it will stay like that infinitely long until it is observed by the environment. The wave function of the particle will constantly progresses into new and different wave functions. So in other words there still would be different outcomes but they would be "cat died on day 2 and stayed like that for two days" or "cat survived" and maybe even different timings of cat's death (if the timing would be defined by a random event".

Moreover, cat is macroscopic and is always in touch with its environment which means it cannot be in a superposition state as its particles are always "observed" (are interacting) with the particles of the box, air and even itself, therefore leading to wave function collapse.

Lastly, i doubt such an experiment would be permitted by the authorities :)

 

[pallidin]

No, if a particle is in superposition all it means is that it occupies all the possible states simultaneously but it doesn't mean it will stay like that infinitely long until it is observed by the environment. The wave function of the particle will constantly progresses into new and different wave functions. So in other words there still would be different outcomes but they would be "cat died on day 2 and stayed like that for two days" or "cat survived" and maybe even different timings of cat's death (if the timing would be defined by a random event".

Moreover, cat is macroscopic and is always in touch with its environment which means it cannot be in a superposition state as its particles are always "observed" (are interacting) with the particles of the box, air and even itself, therefore leading to wave function collapse.

Lastly, i doubt such an experiment would be permitted by the authorities :)

Well, it could be done with an ant. What authorities would be against that.

 

[pallidin]

So, this type of experiment has not been done?
I find it quite odd that an actual experiment has not been done.
Doesn't seem right. VERY easy to do.

Seems more like an agenda push than a scientific one.