# Does Schrodinger's Cat Paradox Suck?

• yuiop

#### yuiop

P.S. I am just a beginner in QM and these are just my initial impressions for discussion and corrections are welcome.

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Is Schrodinger's cat paradox a poor pedagogical example for students of QM?
Imho, yes.

Well in my opinion it shouldn't be labeled as a paradox but as an example how things can be in a superposition of states UNTIL someone or something makes an observation that breaks down the superposition.

For me all the cats of planet Earth that i don't or can't observe are in a superposition of states, i know that for any cat there is probably someone else (different for each cat) other than me observing that cat and he knows the state of the cat, but since he doesn't communicate with me to inform me, for me the cat is in superposition. I think when we intuitevely conclude that a cat can't be in superposition of dead and alive we kind of think of an invisible universal observer that knows the state of the cat, but that kind of observer doesn't necessarily exists.

I assume the 'anchor point' around which yuiop has built the argument in #1 seems to exactly reflect an entry by A. Neumaier I saw a while ago (basically that Decoherence 'rules'), but can't find. At any rate, suppose we follow the CI (Copenhagen Interpretation) rationale, and opening the box and viewing/recording the cat collapses the cat's wavefunction - 'causing' it to be dead or alive. What is actually being observed? The entire cat, or the minute fraction of photons reflecting off the surface fur of the cat? Obvious answer surely. And there is some clear theory explaining how such an extremely partial observation propagates instantly to effect the entire cat? What's more, even before opening the box, we note the cat is standing on the box, which is placed on a table or the floor etc. So what rule says 'cat wavefunction' is isolated from the box, and so on in and almost endless chain? There are so many loose ends to the whole notion of collapsing the wavefunction of some cleanly separate and internally coherent entity like 'cat' - imho anyway.

I think that it is a good way of representing quantum mechanics using familiar, macroscopical entities.
My interpretation of the thought experiment is that the superposition of quantum states has only broken down for the cat. From our perspective the events are still in superposition.

Imagine there is a detector which measures the spin of a photon and displays it to a human observer which is concealed in a box. If the photon has one spin, the human raises his right hand, if it has the other, he raises his left.
Once the spin is revealed to the human observer, the superposition breaks down for him. For any outside observers, unaware of the outcome, he, too, is in superposition of both states. Also; if the apparatus is removed, free from any observation by outside observers, the two events are entangled. If you look at which hand the human observer has up the superposition breaks down for the apparatus and the human and vice-versa.

That's how I understand it, anyway.
The breakdown of superposition will be independant and unique for each observer.

..Imagine there is a detector which measures the spin of a photon and displays it to a human observer which is concealed in a box. If the photon has one spin, the human raises his right hand, if it has the other, he raises his left.
Once the spin is revealed to the human observer, the superposition breaks down for him. For any outside observers, unaware of the outcome, he, too, is in superposition of both states. Also; if the apparatus is removed, free from any observation by outside observers, the two events are entangled. If you look at which hand the human observer has up the superposition breaks down for the apparatus and the human and vice-versa...
And here's where it really gets hazy and ambiguous imo. Raising a right hand or left hand will materially effect the momentum balance (as a temporal 'jerk' - overall momentum balance is preserved of course), and so 'which hand' is in principle easily inferred (not directly measured) by an outside observer. But if superposition of states applies, as you suggest, there will be no momentum imbalance from a clearly macroscopic act as 'raise hand', since as I understand it, superposition here implies a time averaged mix that leaves the box + person inside in a stable momnentum state - ie no shifts can be inferred. Is that really the case?

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Yes, unless you hate cats.

On a more pedological note: I don't think the observer need be sentient. The cat would begin to decay. Or perhaps bacteria are sentient?

But it is often the way of the world that teachers pull the leg of students. It teaches character.

Imagine there is a detector which measures the spin of a photon and displays it to a human observer which is concealed in a box. If the photon has one spin, the human raises his right hand, if it has the other, he raises his left.
Once the spin is revealed to the human observer, the superposition breaks down for him. For any outside observers, unaware of the outcome, he, too, is in superposition of both states. Also; if the apparatus is removed, free from any observation by outside observers, the two events are entangled. If you look at which hand the human observer has up the superposition breaks down for the apparatus and the human and vice-versa.

That's how I understand it, anyway.
The breakdown of superposition will be independant and unique for each observer.

Something I forgot to mention:

Seeing the human observer's hand raised can't tell you with certainty what spin the photon had. People lie, right?

The cat thought experiment is a little different.
The cat cannot fake death, but it may die of another cause.

So the two events are not completely entangled... but they are close.
Whether or not this is enough to preserve the superposition, I don't know.

But, hey! I'm only 16!

Of course Schrodinger's cat sucks. Schrodinger knew that right from the beginning. In fact it's pretty much the whole point. It illuminates two troubling issues in quantum mechanics, usually called the problem of measurement and the quantum classical transition (or Heisenberg's boundary).
You are certainly right that the cat will in fact be either alive or dead, but not both.
The problem is how to get there without violating the laws of quantum mechanics.
The most popular modern answer to that question is called decoherence.
But not everyone agrees that decoherence really solves the problem.
Best, Jim Graber

P.S.
Schrodinger's cat was originally invented to puzzle experts, not to instruct newbies.

Actually, the amplifier, capsule and cat form the classical part of the measuring equipment and the quantum system is the radioactive source. I think the "collapse" of the wavefunction of the nucleus happens just when we turn on the amplifier.

Besides, the collection of radioactive isotopes should be regarded as a system of non-interacting (as far as radioactivity is concerned, the decay constant does not depend on the concentration of atoms) identical particles. A particle that decays is best described by making the energy of the particles with a negative imaginary part:

$$E \rightarrow E - i \frac{\lambda}{2}$$

which makes the evolution of the single particle wave function:

$$\Psi(t) = \Psi(0) \exp\left[-\frac{i}{\hbar} (E - i \lambda/2) t\right] = \psi(0) \exp{\left[- \frac{\lambda t}{2}\right]} \, \exp{\left(-\frac{i}{\hbar} E t\right)}$$

and the square modulus is:

$$|\Psi(t)|^{2} = |\Psi(0)|^{2} e^{-\lambda t}$$

Yes, unless you hate cats.

On a more pedological note: I don't think the observer need be sentient. The cat would begin to decay. Or perhaps bacteria are sentient?

This is a good point. Let us say the cat has plentiful supply of food, water and air in the box and we leave it for a year before opening the box. Now if when we open the box we observe that the cat is a rotting corpse that is almost a skeleton with billions of bacteria feeding on it. Any reasonable observer would conclude that the cat died a long time before the box was opened and did not collapse into this state of decomposing corpse at the moment the box was opened. The QM interpretation is that not only is the cat in a superposition of living healthy state and decomposing corpse, but some of the bacteria are in a superposition of being alive and not yet born until the box is opened!

Also, does physics have a sufficiently clear definition of sentient? As far as physics is concerned, a sentient being is a computing device above a not clearly defined level of complexity and performance.

Yuiop, there are plenty of ways to make the thought experiment fit. But they are not simple and clear. Thus it sucks as a teaching tool.

It's still useful for other things like pulling the legs of students or dead cats.

To Delta2 & JDude13:

Cool, you guys are thinking along the same lines as I. This inspired me to think about this some more this evening. And JDude13, I think your understanding is very impressive for a 16 year old!

Yup, I agree with JDude13. The wavefunction is not a totally objective entity, it a tool which encodes one's information about a process, and quantum mechanics then provides the means to estimate probabilities of the future, given that information. If two people have different information, the wave functions they assign to a situation will be different. When the human in the box opens the cat in the box, his infomation set changes, and his wavefunction for the cat collapses, but to the scientist outside the double box, it does not. The scientist outside the box assigns a wave function for the human/cat combination which is a superposition of states, which then collapses when HE opens the box. Most quantum experiments assume multiple equivalent observers, so that the process of measurement by one affects the information of all. This extension to Schroedingers cat (I think its called Schroedinger's friend) is an example where this is not so. Every objection that I have heard to this idea finally boils down to distaste for the idea that the wave function is not absolute. But I am open to suggestion.

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Seeing the human observer's hand raised can't tell you with certainty what spin the photon had. People lie, right?

The cat thought experiment is a little different.
The cat cannot fake death, but it may die of another cause.

So the two events are not completely entangled... but they are close.
Whether or not this is enough to preserve the superposition, I don't know.

But, hey! I'm only 16!

Another observation:
If we see the human with his left had raised does it increase the likelyhood of the associated outcome? As in... He may lie and make the information invalid but then again, he may not. The wave-function becomes a measure of his trustworthy-ness or his ability to read the measurement made by the apparatus (without telling us). What if another scientist tells him to only raise his left hand? Does that mean that our model of superposition in the box has no value as the other scientist has already determined the outcome. Perhaps there are subtle differences in the two different outcomes of the tainted experiment. Maybe the human has a different facial expression, depending on what he sees. Our simplification of the two out comes (left hand raised/ right hand raised) doesn't cover the wide range of things which would change.
Left for a longer and longer period of time, the outcomes will become more and more dis-simmilar.

For example: in the two outcomes, 1) & 2),
1)The observer raises his right hand.
2)The observer raises his left hand.

1)The observer is right-handed and so he is able to keep his arm up for a substantial amount of time.
2)The observer is right-handed so he is less able to keep his hand up for a substantial amount of time.

1)The observer's right hand is still raised.
2)The observer's left arm becomes tired and he lowers his hand. He becomes frustrated.

1)The observer's right arm becomes tired and he lowers it.
2)The observer feels he has been left in the box and begins beating on the sides trying to gain the attention of the scientists.

This is a rather rough and not-well-thought-out scenario of the two outcomes which shows us that time affects the differences in scenarios.

Now pretend that the observer doesn't need to do anything but look at the screen which reveals an up arrow or a down arrow when confronted with one of the two spin directions.

1)The arrow points down.
2)The arrow points up.

1)The observer's eyes are subconciously drawn down.
2)The observer's eyes are subconciously drawn up.

And on and on and on... Changing more wildly with each step.

This shows that superposition will be achieved macroscopically with any obsever, whether or not you give conditions and instructions to the observer.

Another observation:
If we see the human with his left had raised does it increase the likelyhood of the associated outcome? As in... He may lie and make the information invalid but then again, he may not. The wave-function becomes a measure of his trustworthy-ness or his ability to read the measurement made by the apparatus (without telling us). What if another scientist tells him to only raise his left hand? Does that mean that our model of superposition in the box has no value as the other scientist has already determined the outcome. Perhaps there are subtle differences in the two different outcomes of the tainted experiment. Maybe the human has a different facial expression, depending on what he sees. Our simplification of the two out comes (left hand raised/ right hand raised) doesn't cover the wide range of things which would change.
Left for a longer and longer period of time, the outcomes will become more and more dis-simmilar.

[shortened]

This shows that superposition will be achieved macroscopically with any obsever, whether or not you give conditions and instructions to the observer.

But remember that your lack of knowledge about a system does not itself mean that quantum superpositions between states representing different outcomes appear. Some of those you mention are uncertainties due to lack of information, not uncertainties due to quantum behaviour.

E.g. as you said, the observer might lie. But it might be the case that the microscopic quantum wavefunction description of the observer inside the box will not develop to make that possible, i.e. like a wavefunction that cannot develop into "spin up". This can be the case even though we as outside observer arent' aware of it. In that case, the observer will not be in a superposition of states "lie + no-lie", so it would be incorrect of us to describe him/her in that way.

If you knew the full quantum description of the intenal observer, you would know exactly which superposition of states the composite system (internal observer + experimental quantum system) was in after their mutual interaction occured. Otherwise you must describe the composite system usinga density matrix which includes classical uncertainties, not only a wavefunction.

The best that can be said of measurement in postulatory quantum mechanics is that the information obtained or ignorance removed upon measurement (partially determined according to prescription) is not the same http://en.wikipedia.org/wiki/Information_theory" [Broken] obtainable before a measurement is made.

There are not dead cats and live cats existing in some odd superposition except by interpretation of the measure of subjective knowledge, nor multiple worlds, nor pilot waves, etc. except as interpretations to make sense of it.

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I think that its a great example, eventhough I didn't have the actual subject yet. (so maybe I don't really am entitled to have a say on this :P) But I really like to have imaginable examples for theories, things that i can visualise. And Schrodingers cat does just that.

I think that its a great example, eventhough I didn't have the actual subject yet. (so maybe I don't really am entitled to have a say on this :P) But I really like to have imaginable examples for theories, things that i can visualise. And Schrodingers cat does just that.

Yes. I don't disagree at all. These things are indispensable to some form of mental imagery or deductive chain.

Part of the purpose of the cat experiment is to seek enlightenment about what superposition really is. While this might not be useful to the introductory student, it does reveal a deeper truth about the universe:

There are facts in the universe that are unknowable by experiment. One of these seems to be the nature of superposition. There are several prominent interpretations of superposition that are experimentally identical but show wildly differing views of the universe. http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics" [Broken]

Initially these serve as distractions to learning the math because each interpretation seems to lead students to err. Later on, contrasting them provides insights. Perhaps some of these might even be disproved by clever scientists. But that's why quantum physics isn't easy like rocket science.

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Came across the following link which in laymen's terms seems to set the right perspective:
http://factoidz.com/understanding-schrodingers-cat-and-quantum-uncertainty/
Makes it plain why Schrodinger's cat or hand waving humans etc inside boxes with detectors can never in reality be in a superposed state. Experimentalists understand what's really required - even for a ~10um sized mirror, cooling to millikelvin levels and delicate suspension in a vacuum are absolute prerequisites. Compare that to a room-temperature cat/human-in-a-box! Hence the OP's premise is more than confirmed - a very poor and misleading thought experiment, imho.

Of course Schrodinger's cat sucks. Schrodinger knew that right from the beginning. In fact it's pretty much the whole point. It illuminates two troubling issues in quantum mechanics, usually called the problem of measurement and the quantum classical transition (or Heisenberg's boundary).
You are certainly right that the cat will in fact be either alive or dead, but not both.
The problem is how to get there without violating the laws of quantum mechanics.
The most popular modern answer to that question is called decoherence.
But not everyone agrees that decoherence really solves the problem.
Best, Jim Graber

Exactly. The point of Schrodinger's cat is not to say that the can can indeed be both dead and alive, but instead to illustrate the connection between, measurement, decoherence, and the emergence of classical laws.

There was a recent thread whose discussion was along these lines. Check out my post, as well as Tiny Tim's:

No doubt that is true for serious students of QM who are taught the right perspective(s), but do a web search using "Schrodinger's cat" and just see how many links present the 'classical interpretation' of alive+dead cat! It's the perpetuation of a popular myth that the non-specialist/general public accept as 'weird fact' that bugs me.

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It's the perpetuation of a popular myth that the non-specialist/general public accept as 'weird fact' that bugs me.

Add it to the list. It's not the first time public perception has misunderstood science.

But remember that your lack of knowledge about a system does not itself mean that quantum superpositions between states representing different outcomes appear. Some of those you mention are uncertainties due to lack of information, not uncertainties due to quantum behaviour.

E.g. as you said, the observer might lie. But it might be the case that the microscopic quantum wavefunction description of the observer inside the box will not develop to make that possible, i.e. like a wavefunction that cannot develop into "spin up". This can be the case even though we as outside observer arent' aware of it. In that case, the observer will not be in a superposition of states "lie + no-lie", so it would be incorrect of us to describe him/her in that way.

If you knew the full quantum description of the intenal observer, you would know exactly which superposition of states the composite system (internal observer + experimental quantum system) was in after their mutual interaction occured. Otherwise you must describe the composite system usinga density matrix which includes classical uncertainties, not only a wavefunction.

I realize that. I was just exploring whether or not seeing the observer with one hand up was enough to break the superposition given that he may put that hand up regardless of the outcome. I then went on to say that even seeing him, regardless of his decision, shows slight differences between each state which is in superposition and that the entanglement will break down apon seeing the observer regardless of whether or not you told him to do something different for each outcome. There will be subtle differences in the behaviour of the observer in each outcome. Such is the nature of the human brain.

It's been touched on already... but Schrodinger's paradox was originally formulated by Einstein as a reductio ad absurdum argument against the completeness of QM.

Einstein, in a letter to Schrodinger:
The system is a substance in chemically unstable equilibrium, perhaps a charge of gunpowder that, by means of intrinsic forces, can spontaneously combust, and where the average life span of the whole setup is a year. In principle this can quite easily be represented quantum-mechanically. In the beginning the psi-function characterizes a reasonably well-defined macroscopic state. But, according to your equation [i.e., the Schrödinger equation], after the course of a year this is no longer the case. Rather, the psi-function then describes a sort of blend of not-yet and already-exploded systems. Through no art of interpretation can this psi-function be turned into an adequate description of a real state of affairs; in reality there is just no intermediary between exploded and not-exploded.

And Schrodinger's version of the paradox begins, by the way, with:
One can even set up quite ridiculous cases. A cat is penned up...
Even Schrodinger didn't buy one bit of the the alive+dead cat thing... it was exactly the opposite.

If the paradox is used to teach anything it should be the inadequacy of many explanations of QM.

See http://plato.stanford.edu/entries/qt-epr/#1.3 for the Einstein quote. http://www.tu-harburg.de/rzt/rzt/it/QM/cat.html is Schrodinger's paper. You'll have to excuse me for bringing history and philosophy into a physics discussion :).

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The point of Schrodinger's cat is not to say that the can can indeed be both dead and alive, but instead to illustrate the connection between, measurement, decoherence, and the emergence of classical laws.

The point of Schrodinger's cat is also not to illustrate decoherence (a concept developed 50 years after the paradox) or the emergence of classical laws from quantum things. Schrodinger is very explicitly an instrumentalist. From his cat paradox paper:
Reality resists imitation through a model. So one let's go of niave realism and leans directly on the indubitable proposition that actually (for the physicist) after all is said and done there is only observation, measurement. Then all our physical thinking thenceforth has as sole basis and as sole object the results of measurements which can in principle be carried out, for we must now explicitly not relate our thinking any longer to any other kind of reality or to a model.
For Schrodinger and his cat, there is no emergence of the classical from the quantum, because there are no such things as quantum states. Again, the whole point of the paradox is to show the impossibility of quantum states. It's an argument for instrumentalism in QM.

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The point of Schrodinger's cat is also not to illustrate decoherence (a concept developed 50 years after the paradox) or the emergence of classical laws from quantum things. Schrodinger is very explicitly an instrumentalist. From his cat paradox paper:For Schrodinger and his cat, there is no emergence of the classical from the quantum, because there are no such things as quantum states. Again, the whole point of the paradox is to show the impossibility of quantum states. It's an argument for instrumentalism in QM.

Exactly. The superposition of dead cat/alive cat does not mean the cat is both dead and alive. It means there is a certain probability of opening the box and finding the cat dead and one minus that probability of finding it alive. Before we open the box, we just don't know and cannot know. To be very strict about it, even the statement that the cat is either dead or alive before we open the box is improper, because "is" implies a reality that cannot be measured or accessed.

Exactly. The superposition of dead cat/alive cat does not mean the cat is both dead and alive. It means there is a certain probability of opening the box and finding the cat dead and one minus that probability of finding it alive. Before we open the box, we just don't know and cannot know. To be very strict about it, even the statement that the cat is either dead or alive before we open the box is improper, because "is" implies a reality that cannot be measured or accessed.

I would gracefully decline this. Define a dead system. You would see what I mean.
Life is chemistry, and when some critical functionalities stop in the brain, we call it brain dead or dead for short. That is the only definition of dead. As a result of micro state change - the macro state of dead appears. For smaller organisms like a virus, there is no *dead*.

Are viruses dead or alive? The dead body and alive body might be interchangeable from a pure chemistry perspective. Like a dead virus and an alive virus is.

There is no paradox here, never was.
I think ERP is a better one, at that.

I would gracefully decline this. Define a dead system. You would see what I mean.
Life is chemistry, and when some critical functionalities stop in the brain, we call it brain dead or dead for short. That is the only definition of dead. As a result of micro state change - the macro state of dead appears. For smaller organisms like a virus, there is no *dead*.

Are viruses dead or alive? The dead body and alive body might be interchangeable from a pure chemistry perspective. Like a dead virus and an alive virus is.

There is no paradox here, never was.
I think ERP is a better one, at that.

I don't think the problem is whether the macro states of dead/alive are well defined but that when we measure(observe the cat in this case) we can only have one of these states and not a superposition. To say that the cat is in superposition of dead and alive is , for me, another way to say that i don't know in which of these states the cat is until i do a measurement.

I don't think the problem is whether the macro states of dead/alive are well defined but that when we measure(observe the cat in this case) we can only have one of these states and not a superposition. To say that the cat is in superposition of dead and alive is , for me, another way to say that i don't know in which of these states the cat is until i do a measurement.

Classical uncertainty is not the same as quantum superposition. Lack of knowledge about quantum state is not equivalent to a quantum superposition.

Also, everyone agrees that the measurement cannot tell us that the cat is both alive and dead simulaneously. This problem is about which quantum wavefunction describes the cat prior to the measurement. I though everybody agreed that all physical objects are described by wavefunctions, since QM encompasses classical mechanics. QM does not have restricted domain of validity according to current physics.

It is a matter of principle: Even if e.g. interactions with the environment causes the cat to be in a superposed state for only 10^-10000000 seconds, it is still a matter of principle that QM predicts that at some point it is a superposition. At least for an "idealized cat" that can be correctly described by two such quantum states.

Exactly. The superposition of dead cat/alive cat does not mean the cat is both dead and alive. It means there is a certain probability of opening the box and finding the cat dead and one minus that probability of finding it alive. Before we open the box, we just don't know and cannot know. To be very strict about it, even the statement that the cat is either dead or alive before we open the box is improper, because "is" implies a reality that cannot be measured or accessed.

Well, in the two-slit experiment we often say that one particle is two places at once. That's is another example of classical terminology used in quantum situations. I have no problem with that, and think it is a natural description due to the wave nature of the particle. Also, the path-integral QM formalism ties in nicely with this as well.

Feynman was critizied for using such terminology by Bohr when he presented his path-integral formalism (particle paths is classical terminology). But there is no problem with it if it is used correctly.

The point of Schrodinger's cat is also not to illustrate decoherence (a concept developed 50 years after the paradox) or the emergence of classical laws from quantum things. Schrodinger is very explicitly an instrumentalist. From his cat paradox paper:For Schrodinger and his cat, there is no emergence of the classical from the quantum, because there are no such things as quantum states. Again, the whole point of the paradox is to show the impossibility of quantum states. It's an argument for instrumentalism in QM.

Let me reword what I said above and focus it on the OP's original question:

The modern day pedagogical usefulness of the Schrodinger's cat experiment is that it helps to illustrate the connection between measurement, decoherence, and the emergence of classical laws.

This is my answer to the OP original question. It may not be the original purpose of the thought experiment, but I think this is why Schrodinger cat is still a useful pedagogical tool.

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I don't think the problem is whether the macro states of dead/alive are well defined but that when we measure(observe the cat in this case) we can only have one of these states and not a superposition. To say that the cat is in superposition of dead and alive is , for me, another way to say that i don't know in which of these states the cat is until i do a measurement.

No, its not a question of which state the cat is in before the measurement. You know what state it is in before the measurement, and that state is a superposition of dead and alive, which means that upon measurement, it will be found either dead or alive. To say that it is either dead or alive before the measurement is equivalent to a "hidden variables" approach to QM which has been proven wrong.

The fact that classically it makes sense to think of the cat as dead or alive before the measurement is because the act of measurement has a ridiculously small probability of affecting the outcome of the measurement. In the microscopic regime this is not always the case, and then it DEFINITELY makes no sense to think of what a superposed microscopic system is "really" like before measurement, beyond that given by the superposed wave function itself. Strictly speaking, it makes no sense in either case.