Why is Schrodinger's Cat only a thought experiment?

[DaveC426913]

The explanation I've heard is that quantum superposition is an atomic-scale phenomenon, that it makes no sense to apply it to a macro-scale object such as a cat.

But that's not what the experiment is doing. The radioactive isotope is subject to quantum effects, and it seems to follow that the result can be detected (and thus acted upon) at a macro-level.

So, why would the cat not exist in two states?

 

[peter0302]

Well, it would according to the many-worlds interpretation. The worlds would split as soon as the cat interacted with anything else in a theremodynamically irreversible way.

In any other interpretation, you'd have to define what it means for the cat to "exist" in two states. The cat certainly knows whether it's alive or not, so from his perspective there's only one state. From the outside world's perspective, the state is one of ignorance. Mathematically, it's in superposition, and so the wave function as calculated by the outside observer would indeed reflect both states. So in a sense, the cat *does* exist in both states as far as the outside world is concerned. But are there literally two cats, or is the superposition of states nothing more than a fancy way of saying that we don't know the cat's state? It's a matter of interpretation.

 

[turbo]

Schrödinger was posing what he considered an absurdity to point out what he felt was a disconnect between deterministic classical physics and quantum theory. Clearly a cat cannot be both alive and dead at the same time, and opening the box after an hour to observe whether the cat is dead or alive does not collapse the wave-form of the cat (a macroscopic being), it simply tells us that the radioactive material either did or did not decay during the previous hour. Penrose uses this example in his popular lectures on the possibility of unifying quantum physics with classical physics.

 

[DaveC426913]

Schrödinger was posing what he considered an absurdity to point out what he felt was a disconnect between deterministic classical physics and quantum theory. Clearly a cat cannot be both alive and dead at the same time, and opening the box after an hour to observe whether the cat is dead or alive does not collapse the wave-form of the cat (a macroscopic being), it simply tells us that the radioactive material either did or did not decay during the previous hour.

I know, but why does it not work? Where does it fall apart?

Does it indicate that the isotope particle is not really in a superpsoed state?

 

[peter0302]

I know, but why does it not work? Where does it fall apart?

It falls apart when you try to assign physical meaning to the wave function. Only then do you have to ask the question whether the cat is "really" alive or dead. The wave function tells you the probability amplitudes of the cat's various possible states, and works perfectly well as long as you don't try to use it for anything other than calculating probabilities.

And again, if you believe in MWI, then there literally ARE two cats, with the universes splitting as the cats interact with the rest of the world.

Does it indicate that the isotope particle is not really in a superpsoed state?

The isotope is absolutely in a superposed state as far as the ignorant observer is concerned. As far as the cat is concerned, it's not. Now, you can start getting really philosophical and ask if the cat is intelligent enough to be considered an observer - that's really stretching the bounds of meaningful science if you ask me. Again, as long as you treat the wavefunction as nothing more than probability amplitudes, there is no paradox. If you try to assign deeper meaning to it, then you run into trouble, and I believe MWI is the only thing you can use to make any sense of it.

 

[DaveC426913]

Now, you can start getting really philosophical and ask if the cat is intelligent enough to be considered an observer

Well, observation has a specific meaning in this context, and it has nothing to do with intelligence. A camera could be an observer.

 

[jostpuur]

Schrödinger was posing what he considered an absurdity to point out what he felt was a disconnect between deterministic classical physics and quantum theory. Clearly a cat cannot be both alive and dead at the same time, and opening the box after an hour to observe whether the cat is dead or alive does not collapse the wave-form of the cat (a macroscopic being), it simply tells us that the radioactive material either did or did not decay during the previous hour. Penrose uses this example in his popular lectures on the possibility of unifying quantum physics with classical physics.

Clearly, according to the quantum mechanics, the cat will be in superposition of being alive and dead at the same time. Combining this with your claim, we arrive at the source of the paradox. Two claims, both clearly true, both contradictory. That's why we call it a paradox! IMO ignoring the paradox only tells about lack of understanding of quantum mechanics.

Why is Schrödinger's Cat only a thought experiment?

I believe I can answer this: Because a physical experiment would be useless. There is no interferences for a macroscopic objects, so you cannot prove the existence of the superposition.

Classical theory: The cat will be either dead or alive in the closed box. When you open the box, you see the cat being dead or alive.

Quantum theory: The cat will be in superposition of being dead and alive in the closed box. When you open the box, the cat's wave function collapses, and you see the cat being dead or alive.

The experimental result: When you open the box, the cat is dead or alive.

An actual experiment wouldn't tell us anything. That is why this is a thought experiment. Somebody might claim that the Occam's razor instructs us to abandon the hypothesis of cat being in superposition, since it is so complicated idea, and cannot be checked by experiment, but IMO this is invalid use of Occam's razor. This is a fact: Whenever the predictions of classical and quantum theory differ, the experimental result is that quantum theory is right. So IMO it seems simplest to assume, that the quantum theory is right also when it cannot be checked.

In any other interpretation, you'd have to define what it means for the cat to "exist" in two states. The cat certainly knows whether it's alive or not, so from his perspective there's only one state. From the outside world's perspective, the state is one of ignorance. Mathematically, it's in superposition, and so the wave function as calculated by the outside observer would indeed reflect both states. So in a sense, the cat *does* exist in both states as far as the outside world is concerned. But are there literally two cats, or is the superposition of states nothing more than a fancy way of saying that we don't know the cat's state? It's a matter of interpretation.

Wise words! IMO the solution to the paradox lies in the many worlds interpretation, and not in restricting the quantum theory to the microscopic objects only.

 

[lbrits]

I know, but why does it not work? Where does it fall apart?

Does it indicate that the isotope particle is not really in a superpsoed state?

One particular modern viewpoint is that the cat will be both alive or dead, but will unitarily evolve into a definite state because superimposed states tend to be unstable. Read up on Einselection ( http://en.wikipedia.org/wiki/Einselection ) and if you are familiar with density matrices, I invite you to take a look here: http://www.physics.thetangentbundle.net/wiki/Quantum_mechanics/einselection

 

[peter0302]

Well, observation has a specific meaning in this context, and it has nothing to do with intelligence. A camera could be an observer.

That's not exactly right. The pure form of the Copenhagen Interpretation is agnostic as to what qualifies as observation and what doesn't. Some people believe that intelligent observatoin is actually required for wave function collapse. I once accidentally offended someone on here quite seriously by calling those people nuts, but apparently it's not without its supporters.

 

[belliott4488]

The subject line of this thread made me think you were asking what's wrong with putting a cat in a box with a vial of cyanide with a random trigger ...

 

[DaveC426913]

An actual experiment wouldn't tell us anything.

I hadn't thought of it that way. The test is not falsifiable.

Although I think that's not the real reason why this is only a thought experiment.

 

[DaveC426913]

That's not exactly right. The pure form of the Copenhagen Interpretation is agnostic as to what qualifies as observation and what doesn't. Some people believe that intelligent observatoin is actually required for wave function collapse. I once accidentally offended someone on here quite seriously by calling those people nuts, but apparently it's not without its supporters.

I am of the pure camp.

 

[nanobug]

So, why would the cat not exist in two states?

Decoherence! The isotope needs to interact with the mechanism that breaks the vial. This mechanism is macroscopic. Entanglement with the particles of this mechanism will eliminate superposition, resulting in classical probabilities for the outcome.

 

[jostpuur]

Decoherence! The isotope needs to interact with the mechanism that breaks the vial. This mechanism is macroscopic. Entanglement with the particles of this mechanism will eliminate superposition, resulting in classical probabilities for the outcome.

Decoherence eliminates interference, not superposition.

 

[lbrits]

Decoherence eliminates interference, not superposition.

Well... actually... you can eliminate superposition by changing basis... so decoherence can also eliminate it, for what it's worth.

 

[vanesch]

So, why would the cat not exist in two states?

I think the obvious answer is that we all like cats, and we are not going to do cruel things to them

Seriously, MWI-people claim that the cat DOES exist in two states, of which we are only aware of one of them (and other "we's" are aware of the other state).

 

[Hurkyl]

To my knowledge, only three options are offered by all of the main interpretations of quantum mechanics are:

(1) You see a cat that's dead, or you see a cat that's alive.
(2) You are actually in a superposition of states, some of which see a dead cat, some of which see a live cat, and none of which see any sort of ambiguity.
(3) Both (1) and (2) are valid analyses.

 

[LURCH]

I hadn't thought of it that way. The test is not falsifiable.

Although I think that's not the real reason why this is only a thought experiment.

I notice that you posted this last night. Having had a chance to sleep on it, do you still have the same opinion? I myself am quite convinced that this is exactly the reason this test is not performed in reality (using something other than a live cat, of course).

 

[lbrits]

The test is very falsifiable... Take a beam splitter and shine one part of the beam on the alive/dead cat and allow the other to pass straight through. Recombine the beams onto a detector. I believe you should get a different interference pattern based on whether the cat is alive/dead/superposition.

I didn't say the test was practical, though.

 

[jostpuur]

The subject line of this thread made me think you were asking what's wrong with putting a cat in a box with a vial of cyanide with a random trigger ...

I think the obvious answer is that we all like cats, and we are not going to do cruel things to them

this is exactly the reason this test is not performed in reality (using something other than a live cat, of course).

You are so excessively ethical! The medical industry already uses animal experiments for scientific purposes. Why not theoretical physics too!?

 

[jostpuur]

Well... actually... you can eliminate superposition by changing basis...

Like instead of using basis

<br /> |\psi\rangle_{\textrm{cat is alive}},\;|\psi\rangle_{\textrm{cat is dead}}<br />

we choose a new basis

<br /> |\psi\rangle_1 = |\psi\rangle_{\textrm{cat is alive}} + |\psi\rangle_{\textrm{cat is dead}}<br />

<br /> |\psi\rangle_2 = |\psi\rangle_{\textrm{cat is alive}} - |\psi\rangle_{\textrm{cat is dead}}?<br />

Now the cat won't be in superposition of two basis vectors, but this is not a very convincing trick if you wanted to solve the Schrödinger's paradox!

so decoherence can also eliminate it, for what it's worth.

You put the word "so" there, as if the previous comment somehow explained how decoherence removes superposition

The test is very falsifiable... Take a beam splitter and shine one part of the beam on the alive/dead cat and allow the other to pass straight through. Recombine the beams onto a detector. I believe you should get a different interference pattern based on whether the cat is alive/dead/superposition.

This is only a complicated way of opening the box.

 

[lbrits]

Like instead of using basis

<br /> |\psi\rangle_{\textrm{cat is alive}},\;|\psi\rangle_{\textrm{cat is dead}}<br />

we choose a new basis

<br /> |\psi\rangle_1 = |\psi\rangle_{\textrm{cat is alive}} + |\psi\rangle_{\textrm{cat is dead}}<br />

<br /> |\psi\rangle_2 = |\psi\rangle_{\textrm{cat is alive}} - |\psi\rangle_{\textrm{cat is dead}}?<br />

Now the cat won't be in superposition of two basis vectors, but this is not a very convincing trick if you wanted to solve the Schrödinger's paradox!



You put the word "so" there, as if the previous comment somehow explained how decoherence removes superposition



This is only a complicated way of opening the box.

My first statement elucidates the fact that it isn't the superposition that gets people in knots, but the direction the state is pointing in. So either all states are equally good, and detractors should just shut up, or that some states seem "preferred", and we should figure out why. (Said differently, if you buy the whole wavefunction collapse argument, why can't we simply collapse it into \left|\psi\right\rangle_1 etc.?) Personally I believe that environmental eigenstate selection gives a decent explanation.

My second statement, a "complicated way of opening the box", eliminates the possibility that the act of measurement will cause a) collapse or b) decoherence, e,g, by a macroscopic observer. Of course, the cat could still observe itself (thereby violating linearity/unitarity of QM), but I digress... See statement 1.

 

[Manchot]

I regularly use http://www.randomnumbers.info/ as a type of "quantum coin flip." In other words, I am a type of living Schrödinger's cat. :-D

 

[minimal]

Wise words! IMO the solution to the paradox lies in the many worlds interpretation, and not in restricting the quantum theory to the microscopic objects only.

Doesn't the many worlds interpretation SERIOUSLY violate the first law of thermodynamics though? The only way I think you can get around that is to argue that time doesn't exist (as the common conception) and all possible states ever exist simultaneously.

 

[Ken G]

Clearly, according to the quantum mechanics, the cat will be in superposition of being alive and dead at the same time.

Quantum mechanics does not say that because a combined cat/apparatus state does not have to project onto a pure (or "superposition") state for the cat alone. This is a common misconception you see in a lot of places. But as Hurkyl said, the real issue is whether or not the entire system (including you, importantly), can be in a superposition state or not. That is not at all the same as asking if the cat can be.

Combining this with your claim, we arrive at the source of the paradox. Two claims, both clearly true, both contradictory. That's why we call it a paradox!

But it isn't a paradox, there is no difficulty in resolving it-- the real problem is we have multiple choices of how to do it! (Again see Hurkyl's post.)

Quantum theory: The cat will be in superposition of being dead and alive in the closed box. When you open the box, the cat's wave function collapses, and you see the cat being dead or alive.

Again, this is not what quantum theory says. Quantum theory says that "opening the box" means projecting the cat onto a state you can label "alive" or "dead", that's just what you mean by opening the box, however you do it. For simple systems, that involves "collapsing the wave function", but a cat doesn't have a wave function. Even for quantum systems, however (which are "systems usefully treated using wave functions"), collapse occurs for a particular reason-- you intentionally forced them to project onto a certain basis. You collapsed it on purpose, in other words, it wasn't anything mysterious. What is mysterious is why all we can get is a statistical prediction of how that collapse will play out, but there may not be any resolution of that problem-- it may be all we can do (it certainly is so far).

Somebody might claim that the Occam's razor instructs us to abandon the hypothesis of cat being in superposition, since it is so complicated idea, and cannot be checked by experiment, but IMO this is invalid use of Occam's razor.

It can be checked. If the alive cat is standing, and the dead cat is lying down, then you can easily check for interference between the two states. The beamsplitter approach has already been mentioned by lbrits.

This is a fact: Whenever the predictions of classical and quantum theory differ, the experimental result is that quantum theory is right. So IMO it seems simplest to assume, that the quantum theory is right also when it cannot be checked.

But a standing/lying cat that you could send a light beam through is not the prediction of quantum mechanics. To use that language, you would have to be talking about the projected state of the cat, and any such projection will destroy the superposition you are claiming to exist.

Wise words! IMO the solution to the paradox lies in the many worlds interpretation, and not in restricting the quantum theory to the microscopic objects only.

I would go the opposite direction-- restrict quantum theory to the realm of wherever wave functions are actually useful, which excludes the realm of the experimenter and suggests Hurkyl solution #1. Anything else just seems like semi-magical philosophical baggage to me.

 

[Hurkyl]

Anything else just seems like semi-magical philosophical baggage to me.

Actually, #1 is the one with extra baggage. #1 postulates that, in addition to the framework that QM requires to describe reality, there is an ill-defined and essentially untestable process that magically transitions the universe out of a generic quantum state and into one that more closely resembles certain pre-conceived philosophical notions about how the universe should behave.

If you like sticking to pre-conceived notions, or simply believe that quantum mechanics has not yet stood the test of time, then #1 is good. But, alas, it's the least desirable if you believe that scientific theories should be the primary motivator of natural philosophy.

 

[Ken G]

Actually, #1 is the one with extra baggage. #1 postulates that, in addition to the framework that QM requires to describe reality, there is an ill-defined and essentially untestable process that magically transitions the universe out of a generic quantum state and into one that more closely resembles certain pre-conceived philosophical notions about how the universe should behave.

I don't agree there. That process is neither ill-defined nor magical-- it is the process of science. If you look at how quantum mechanics is actually tested, absent of all philosophical baggage, you find that it involves the setup of an apparatus that ignores, neglects, or averages over all information that is not deemed important for the experiment at hand (we, for example, might use light from the Sun, or a laser, never worrying about the history of that light or its entanglements-- we pretend our apparatus is a closed system with known inputs, which it is not). This very setup of the apparatus means we do not have a "total pure state" on which we are carrying out our observations, but we don't care-- we only wish to treat what we are testing, so we may, for example pretend that our initial state is a statistically mixed state (like a cat).

Then, if that wasn't untrue enough to the axioms of quantum mechanics, the next thing we do (after time evolving the initial conditions, that part we might expect to unfold quantum mechanically) is to intentionally couple the quantum system to something we can rely on to behave classically-- the detection apparatus. What is "ill-defined" or "magical" about that? We chose to do it, and then get all bothered when the results appear paradoxical when viewed quantum mechanically! If you can name an experiment that tests quantum mechanics that never invokes the use of a classical apparatus that is chosen expressly to behave classically, then I can agree with your stance.

Physically, what is happening when we choose such a "classical apparatus" is that we are coupling in all kinds of untraceable noise modes that intentionally decohere the quantum system we are testing, and project it onto a statistically mixed array of possible outcomes. But the point is, we very intentionally decided to do that, and we always do-- because science is at its heart a classical endeavor. A quantum scientist might do things very differently, but we don't know how such a scientist could be intelligent...

 

[Hurkyl]

That process is neither ill-defined nor magica

The unitary part of quantum mechanics predicts:
(1) Classical apparatuses cannot exist
(2) Quantum apparatuses can simulate classical ones
(3) Thermodynamics can make the simulation's flaws essentially undetectable

The Copenhagen interpretation postulates that the actual, physical state of the universe undergoes an effectively undetectable 'collapse', which violates both the unitary and relativistic parts of quantum mechanics. To the best of my knowledge, the CI does not give any hints about the mechanism of collapse, nor any theoretical indication about where and when a collapse should occur. If there has been progress in these respects, please share.


In my opinion, the primary mistake in the CI is the insistence upon using unconditional probabilities. Consider the classical setup where Alice and Bob each have half of an entangled pair of qubits. If Bob measures his qubit and gets a |1>, then it is impossible, even in principle, for the experiment to give any information about

P(Alice gets a |0>, given that Bob gets a |0>),

from which it follows that it is impossible for this experiment to give any empirical evidence regarding

P(Alice gets a |0>).

However, this is precisely the probability that the CI insists is being tested when it concludes that wavefunction collapse must occur! This is based upon an assumption of statistical independence, which the CI prefers to retain, even at the cost of sacrificing the best tested laws of nature in the history of mankind.

 

[Ken G]

The unitary part of quantum mechanics predicts:
(1) Classical apparatuses cannot exist
(2) Quantum apparatuses can simulate classical ones
(3) Thermodynamics can make the simulation's flaws essentially undetectable

I would say that this argument inverts the process of how science is done. Science is not done by asserting axioms and seeing how their ramifications connect to reality, monkeying with our understanding of reality as necessary. Instead, it starts with real phenomena, like the way we interact with our measuring devices and how we rely on those devices to behave when we formulate the meaning of "objective observation". Then we take that interaction as the fundamental reality that we wish to understand, and we form axiomatic structures to attempt to simulate it. So prediction (1) is ascientific, and prediction (2) is the purpose of quantum mechanics, so it is not a prediction of quantum mechanics. You will need to cite an experiment done with a "quantum apparatus" to show the logic in the direction you are applying it (the main problem being, the human mind has built science around classical behavior). I don't know what you mean by prediction (3), perhaps elucidating that would help.

The Copenhagen interpretation postulates that the actual, physical state of the universe undergoes an effectively undetectable 'collapse', which violates both the unitary and relativistic parts of quantum mechanics.

I would call that the "Heisenberg skew" to the Copenhagen interpretation, but Heisenberg was engaging in philosophy-- I much prefer the approach Bohr finally settled on, which to me is that we were never talking about the "physical state of the universe", for all we have access to is science. The scientific approach is to engage in behaviors that intentionally accomplish the "collapses" you refer to, but these are not collapses in the "state of the universe", they are simply collapses in the information that we have chosen to track. The fingerprints of the physicist is all over the result, as is always the case in science-- treating it like an abstract event happening to the "state of the universe" is to turn science into philosophical baggage, forgetting along the way what defines science in the first place (i.e., Galileo not Plato).

As for "nonunitariness", the unitarity applies only to the complete system, which includes us, as you yourself pointed out. As we have no way to step outside that system to test its unitariness, we find that unitariness is actually only an effective concept-- a concept that applies imperfectly to subsets only to the extent that they are treatable as closed systems. Measurement violates that closure requirement, so we do not expect measurement to be unitary, when projected onto the state of the system being measured (which is what science does). That holds unless we subsume our apparatus into a larger one that includes us-- betraying the entire point of objective science as something to be distinguished from untestable philosophy.

To the best of my knowledge, the CI does not give any hints about the mechanism of collapse, nor any theoretical indication about where and when a collapse should occur. If there has been progress in these respects, please share.

It is nothing new in science to note that we cannot access the details of a process that we are treating statistically. It is no less true in classical physics than quantum mechanics-- we never had any idea that wasn't purely statistical about how to predict the weather next January. So I don't see why we should be bothered that quantum mechanics yields inherently statistical results when we project our predictions onto real or hypothetical observations in the future. No one ever promised we could predict everything-- I find it much more amazing that we do so well, than am I bothered by our need to resort to statistical predictions in quantum mechanics. Who said reality was deterministic? Even in classical mechanics, that was always just a philosophical pretense-- it never came from science, again because that would be inverting the proper logic of how we choose axioms to describe reality, not interpreting reality to fit our axioms.

In my opinion, the primary mistake in the CI is the insistence upon using unconditional probabilities. Consider the classical setup where Alice and Bob each have half of an entangled pair of qubits. If Bob measures his qubit and gets a |1>, then it is impossible, even in principle, for the experiment to give any information about

P(Alice gets a |0>, given that Bob gets a |0>),

from which it follows that it is impossible for this experiment to give any empirical evidence regarding

P(Alice gets a |0>).

I don't understand your point here-- the CI allows for joint wave functions, and joint wave functions successfully pass every experimental test you can name in regard to Alice and Bob-- even ones where Alice and Bob are using different wave functions to reflect different information. The desire to make the wave function "something real" that has a unique existence outside of how Alice or Bob is using theirs is pure philosophical baggage, quantum mechanics works fine without that.

However, this is precisely the probability that the CI insists is being tested when it concludes that wavefunction collapse must occur! This is based upon an assumption of statistical independence, which the CI prefers to retain, even at the cost of sacrificing the best tested laws of nature in the history of mankind.

The CI does not make any incorrect predictions in any known experiments, I think you are misinterpreting what a wave function collapse is. It is a reflection of the change in information in some physicists head-- that's what it is, anything more is something you may choose to add if you have a philosopical bent, but the science doesn't care, in regard to testing predictions. I'm saying that if you look at what science is, rather than philosophize about what reality is, the problems vanish and the CI works swimmingly (the minimal Bohr version).

 

[Hurkyl]

Science is not done by asserting axioms and seeing how their ramifications connect to reality, monkeying with our understanding of reality as necessary.

To further our understanding of reality is one of the primary reasons we have the natural sciences, is it not? The bulk of your post appears to insist the opposite -- we force science to conform with some a priori notion of how reality is supposed to behave. I suppose attitudes like that are why we have the famous quote, "Science progresses one death at a time."