Does Schrodinger's Cat Paradox Suck?

yuiop

Is Schrodinger's cat paradox a poor pedagogical example for students of QM? In the traditional formulation of the paradox, the cat is declared to be both alive and dead at the same time, but no proof is offered of how the paradox can not be resolved by simply assuming the cat is either dead or alive but not both, before a human observer opens the box. This might give a new student to QM the (incorrect) impression that the non classical properties of quantum states is simply a non standard interpretation of results that can be perfectly explained by classical assumptions. Secondly, the cat paradox implies the whole radioactive source, detector, amplifier, poison capsule and cat system is in a superposition of states, until a human opens the box and makes an observation. This (in my opinion) is misleading, because the superposition breakdown probably occurs much earlier. For example the cat observing the poison capsule breaking is an observation (although brief) by a sentient being, but the Schrodinger cat paradox implies that a living creature such as a cat is not sufficiently sentient to qualify as an observer. Even this is misleading, because an observation does not have to be an observation by a sentient being and can simply be a measurement by a machine such as the detection and amplification of the decay particle by a Geiger counter. In my opinion, even observation or detection is not totally necessary for the superposition to collapse. For example some experiments seem to suggest that passing a photon through a special kind of prism that deflects the photon one way or another according to its polarisation, is sufficient to collapse the superposition because there is potential to make a measurement of the polarisation based on "which way" information, even if there is no detection equipment present. All in all, I get the impression that the Schrodinger's cat paradox does nothing other than potentially confuse newcomers to QM.

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

ThomasT

Imho, yes.

Delta²

Well in my opinion it shouldnt 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 dont or cant 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 doesnt communicate with me to inform me, for me the cat is in superposition. I think when we intuitevely conclude that a cat cant 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 doesnt necessarily exists.

Q-reeus

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.

JDude13

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 aparatus 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 aparatus 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.

Q-reeus

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?

DmplnJeff

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.

JDude13

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!

jimgraber

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

jimgraber

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

Dickfore

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:

[tex]
E \rightarrow E - i \frac{\lambda}{2}
[/tex]

which makes the evolution of the single particle wave function:

[tex]
\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)}
[/tex]

and the square modulus is:

[tex]
|\Psi(t)|^{2} = |\Psi(0)|^{2} e^{-\lambda t}
[/tex]

yuiop

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.

DmplnJeff

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.

torquil

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!

Rap

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.

JDude13

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 aparatus (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 ammount of time.
2)The observer is right-handed so he is less able to keep his hand up for a substantial ammount 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 wich 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.

torquil

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.