What is Decoherence and How Does It Solve Schrodinger's Cat Paradox?

[scilover89]

A cat and a flask of poison are enclosed together in a hermetically sealed opaque container. If the flask is broken, the cat is killed by the poison. Breakage of the flask is triggered by the discharge of a Geiger placed behind one of two holes made in a screen which is irradiated at the front by abeam of electrons. It is supposed that the beam is so weak that only one electron passes through the screen during the experiments.

According to QM, the cat should be dead-alive before the experimenter observe it

But, can't the cat observe the flow of electrons and make every possible route collaspe into one? Then the cat will not be dead-alive.

I hope you guys can give me some advice. Thank you.

 

[dextercioby]

A cat and a flask of poison are enclosed together in a hermetically sealed opaque container. If the flask is broken, the cat is killed by the poison. Breakage of the flask is triggered by the discharge of a Geiger placed behind one of two holes made in a screen which is irradiated at the front by abeam of electrons. It is supposed that the beam is so weak that only one electron passes through the screen during the experiments.

According to QM, the cat should be dead-alive before the experimenter observe it

But, can't the cat observe the flow of electrons and make every possible route collaspe into one? Then the cat will not be dead-alive.

I hope you guys can give me some advice. Thank you.

That would be one hell of a cat!

I guess the last chapter of David J.Griffiths' book "Introduction to Quantum Mechanics" would give you an insight into Erwin Schroedinger's (hopefully) "Gedankexperiment".

Daniel.


PS.Are u sure the box is hermetically ceiled??What if it's hermiteanly ceiled?? Would that change the outcome??

 

[humanino]

But, can't the cat observe the flow of electrons and make every possible route collaspe into one? Then the cat will not be dead-alive.

yes actually you are right : the cat is an observer, as you are. It is a huge macroscopic body, full of fluids and thermodynamics exchanges. As a result, separated parts of the cat's body cannot be coherent and there is no superposition. QM is not violated though. It is just that the phases of the off-diagonal element of the density matrix are random-like so they quikly average to zero. One could even in principle measure this decoherence time, it has been done and is in accordance qith the expected result (up to a certain accuracy, which is probably quite good, I do not remember )

Anyway, Schrödinger's cat was intended to be schematic. Like saying "In QM, doors can be open and close at the same time". No really they can't, because it is too improbable.

 

[tribdog]

I hate the cat.
I never liked the whole scenario, but I think what you need to realize is that this isn't meant to be a real experiment. It was originally meant to show how ridiculous quantum mechanics can be, by someone who didn't believe in it in the first place. cats don't behave quantum mechanically. forget about the cat. trying to learn qm using cats will only hurt your understanding

 

[tribdog]

dogs on the other hand...

 

[humanino]

You may like to check those two threads :
[thread=39547]Schrödinger's Cat[/thread]
[thread=46972] Decoherence, Unitary Evolution and Information[/thread]
as well as Stanford's Encyclopedia of Philosophy on The Role of Decoherence in Quantum Theory

 

[Galileo]

I hate this experiment.

I love cats.

 

[DaveC426913]

I want to bring this thread back on track because there is an elegant solution to the apparent paradox.

"...can't the cat observe the flow of electrons and make every possible route collaspe into one?..."

Yes.
Within the confines of the box, the cat observes the flow of electrons, sees the vial break, and dies. Because it's being observed, those states collapse and there is only one state.

Also, within the confines of the box, the cat observes the flow of electrons, sees the vial NOT break, and lives. Because it's being observed, those states collapse and there is only one state.

But outside the box, both events are *still superposed*. The two of them do not collapse into one until the box is opened.


Note that this is regressive. *We* open a box with a dead cat in it. Simultaneously, we open a box with a live cat in it. Both those events are superposed, though we in this universe only experience one. Not until someone observes *us* do those two states collapse into one.

 

[Macgyver]

The only thing this experiment definitively proves is that Schrödinger was more of a dog person, like Pavlov.

 

[selfAdjoint]

The only thing this experiment definitively proves is that Schrödinger was more of a dog person, like Pavlov.

Not so. Schroedinger was a cat person to the max. He used a cat in his gedankenexperiment just because the thought of doing that to a cat was so horrible, and he wanted to attract people's attention.

 

[Macgyver]

Not so. Schroedinger was a cat person to the max. He used a cat in his gedankenexperiment just because the thought of doing that to a cat was so horrible, and he wanted to attract people's attention.

I suppose a cat would get a great deal more attention that the standard lab rat.

 

[tribdog]

I want to say something, and it sounds like a joke but it isn't. I know the Cat is just a way to wrap someone's mind around QM, but it never worked for me. I can only think of one case where quantum mechanics is seen in the macro world. Every week I buy a lottery ticket. When I go to the Circle K the next day to see what the winning lottery numbers were there is a moment where I can look at my ticket and it is juxtaposed might be a winner, might be a loser. It is only when I see the actual winning numbers that my ticket collapses into the losing state. there is a moment there though when it is a winner.
Isn't that a better thought experiment than the damn Cat?

 

[scilover89]

I want to bring this thread back on track because there is an elegant solution to the apparent paradox.

"...can't the cat observe the flow of electrons and make every possible route collaspe into one?..."

Yes.
Within the confines of the box, the cat observes the flow of electrons, sees the vial break, and dies. Because it's being observed, those states collapse and there is only one state.

Also, within the confines of the box, the cat observes the flow of electrons, sees the vial NOT break, and lives. Because it's being observed, those states collapse and there is only one state.

But outside the box, both events are *still superposed*. The two of them do not collapse into one until the box is opened.

Thanks. According to your statement, there are only one state for the cat, but two state for the observer before the observer observed it.
So let say the observer can hear the cat's sound.
If the cat alive, it will make noise and alert the observer.
Oppositely, the cat is dead and it will not make any noise.
So where is the paradox?

 

[matt.o]

hearing the cat is a way of "observing " it.

 

[tribdog]

Thanks. According to your statement, there are only one state for the cat, but two state for the observer before the observer observed it.
?

dude, you got to forget the cat or you're going to get lost.
it is not the observer seeing two states, the "cat" exists in two states. that's what makes qm so different than what we're used to.

 

[TheDonk]

So seeing the cat, hearing the cat, knowing anything about the cat is an observation. If you throw a rock at the cat and never see what happens then did the rock observe the cat? What isn't an observation!? I think I understand just want to hear what someone else says to get a different perspective.

 

[humanino]

If you throw a rock at the cat and never see what happens then did the rock observe the cat?

you make it even clearer than Schrödinger himself : yes, throwing a rock on a cat is indeed a way of measuring it
Indeed, you will know very vell its position after that

Say one photon is thrown on two slits and you observe it on a screen. Which path did it took ? If you could have known in principle, you have to add the probability for eaach path to obtain the probability of hiting on the screen. If there is no way you can guess which path, then you must add amplitudes which are complex numbers, to get the amplitude for hiting the screen.

The probability is the length of the complex number, so knowing the probability you loose the information about the direction of the complex number, its phase.

In which case one adds amplitude (quantum coherence), in which case one adds probability (classical, incoherent=no fixed phase between two waves) ?
There is a transition from one to the other, through decoherence. There is an interpretation that says decoherence is due to the interaction with environment. Any measurement is usually a "strong" interaction with the "environment".

Decoherence, transition from quantum to classical

 

[caribou]

I was reading about Schrödinger's Cat in Robert Griffith's book Consistent Quantum Theory.

He points out that it's generally a mistake to think of the physical meaning of a superposition state like Schrödinger's Cat as being some kind of combination of the physical meaning of the individual live and dead cat states.

An x+ spin state is a linear combination of z+ and z- spin states but means something quite different from either z spin state that makes up the x+ spin state. I think this suggests what a "live and dead cat" superposition state means in a physical sense might be quite different from a "live cat" and "dead cat" we imagine, if the superposition can be given any meaning at all.

Also, a state C can be a linear combination of not just states A and B but also combinations of other states -- I + J or K + L and so on -- in the same way as a vector in three dimensions can be made by any of a countless number of pairs of perpendicular vectors. I take this to mean that a "live and dead cat" superposition state can be made from states other than "live cat" and "dead cat" and so why interpret it as being some mixture of the physical meanings of "live" and "dead" states?

It all seems to mean that we can talk about a superposition state, but it's not at all easy to say what it actually means in a physical sense.

Anyhow, as suggested by others, the solution to Schrödinger's Cat paradox is now believed to be that that the interaction between the cat and the contents of the box with the rest of the universe causes the superposition state to decohere in an unimaginably quick time. The fate of the cat become entangled with the fate of things outside of the box and the superposition state is destroyed.

The famous example of how common and fast decoherence is that even a tiny dust grain in deep space will decohere in a billionth of a second from a superposition of two positions by interactions with just the countless photons left over from the Big Bang.

Decoherence is not easy to escape, even for hypothetical cats.