Schrödinger's cat question

[Fozzie]

I have only recently become familiar with this concept, so please forgive me if my question seems daft. Schrödinger wrote "Until the box is opened at the end of the hour, we will not know what has happened. According to quantum law then, the cat is both dead and alive, in a superposition of states. It is only when we break open the box and learn the condition of that cat that the superposition is lost, and the cat becomes either dead or alive.

 

It's the "both dead AND alive" bit that I cannot grasp. Why not "dead OR alive" because at that stage, we still don't know, so the answer has to be OR, as there are two possibilities.

 

To take another example, before a tin of beans it opened, it will either contain beans, OR it won't. It can't be full and empty at the same time. So why is it necessary to use this play on words?

[swansont]

Because that's the way it is in quantum mechanics. When a system is in a superposition of states, it behaves like it is in both states at once. It isn't in just one state until you actually measure it to be in that state.

[Fozzie]

So I presume a superposition of states must be purely theoretical, because once you take a measurement, as you say, it isn't in just one state until you actually measure it to be in that state.

 

So was this superposition theory derived mathematically?

[ajb]

So I presume a superposition of states must be purely theoretical, because once you take a measurement, as you say, it isn't in just one state until you actually measure it to be in that state.

 

It is all theoretical in the sense that we have a mathematical description. The only real things are what can be measured.

 

Anyway, It seems that the idea of superposition of states is unavoidable in quantum mechanics. Quantum mechanics has passed all experimental tests asked of it. There is plenty of experimental work evolving superposition of states and entangled states.

 

So was this superposition theory derived mathematically?

 

If a system has, lets say two states which we will call [math]|alive\rangle[/math] and [math]|dead\rangle[/math], then a general state is

 

[math]|general \rangle = |alive\rangle + |dead \rangle[/math],

 

(up to some linear coefficents).

 

The point is that when a measurement is made one of the alive and dead states is "selected" and that is what you see.

[swansont]

If a system has, lets say two states which we will call [math]|alive\rangle[/math] and [math]|dead\rangle[/math], then a general state is

 

[math]|general \rangle = |alive\rangle + |dead \rangle[/math],

 

(up to some linear coefficents).

 

The point is that when a measurement is made one of the alive and dead states is "selected" and that is what you see.

 

The "linear coefficients" including a possible - sign, which has certain ramifications. But probably beyond the scope of discussion here.

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So I presume a superposition of states must be purely theoretical, because once you take a measurement, as you say, it isn't in just one state until you actually measure it to be in that state.

 

No, the superposition has actual consequences — the states can interfere. An ensemble in a linear superposition of states is not simply a mixture of particles with half in one state and half in another.

 

http://electron6.phys.utk.edu/QM1/modules/m5/interference.htm

 

This has implications on what results one can see, and these can be (and have been) measured.

[swaha]

ok if the cat is both alive and dead y cant we see it that way? y do we only measure after opening the box that its dead or alive? i asked something like this regarding photons where Mr swanshot said that this is how there trajectory is defined. but my question is if something can simultaneously be in two states or places how can we say it's the same thing which is present? whenever there is a difference in position at the same time how can we ever consider the things same? please reply.

[cameron marical]

I think that the double split experiment can help you understand this.

 

And it is not just us measuring it, it can be any interaction were information is exchanged. whether a photon bumps into the subject, or a molecule etc...

[swansont]

I suppose you could come up with an experiment where the alive/dead superposition could interfere and have some result that could be measured, but I can't think of one right now. We can only measure alive or dead because those are the eigenstates of the system; once we open the box, we collapse the wave function. But until we've done that, or there has been some other interaction that does it, we have a superposition of states.

 

The purpose behind this thought experiment is to illustrate the weirdness of quantum mechanics.

[Lightingbird]

OK Here is my question.

 

What does it mean? Why would you need to answer this question? Now from my understanding this is in some sort of relation to superstring theory. Bear with me, I admit I'm not sure. It has always been my thought the point of this was for our living determination.

 

I mean that I see a guy a bus alive. The girl next to me sees me. Kids at a playground see the bus go by the school. A person in a business office looks down at the kids. A passenger on a plan is looking at the buildings. Then from the space some astronauts looks down at the small plans traveling about. This goes on and on until at some point who look at all of us to know we are actually alive.

 

Again.. I'm stretching. Correct me please. I've always been confused about this.

[J.C.MacSwell]

I suppose you could come up with an experiment where the alive/dead superposition could interfere and have some result that could be measured, but I can't think of one right now. We can only measure alive or dead because those are the eigenstates of the system; once we open the box, we collapse the wave function. But until we've done that, or there has been some other interaction that does it, we have a superposition of states.

 

The purpose behind this thought experiment is to illustrate the weirdness of quantum mechanics.

 

Here's my attempt from a few years back (2005):

 

What if you had two cats in the box, one male and one female. After, say, 10 minutes a decay device will trigger one of them dead in a way that won't effect the other. (Say it triggers a cyanide capsule to rupture in the stomach).

 

So you have a live/dead cat and another live/dead cat. Can they interfere with each other?

 

Assume there is enough food and water in the box/system and half the box was isolated/compartmented so the cats can't get to it because of a trap door than wasn't (quite) big enough.

 

After a year the trap door is sealed and the isolation/compartment is saved and the remaining half is jettisoned into a black hole.

 

When the isolation/compartment is opened could it contain any kittens?

[emcelhannon]

In the single cat thought experiment would it make a difference if the measurement were initiated by the cat?

[swansont]

In the single cat thought experiment would it make a difference if the measurement were initiated by the cat?

 

That's a topic of discussion by some, but it goes well beyond the scope of the original thought experiment.

[cameron marical]

what decides what?

 

What is the cause of one wave function to collapse and the other not?

[emcelhannon]

That's a topic of discussion by some, but it goes well beyond the scope of the original thought experiment.

 

Well, that's tantalizing. Who would I read if I wanted see some theories on the subject?

Thanks

[J.C.MacSwell]

Well, that's tantalizing. Who would I read if I wanted see some theories on the subject?

Thanks

 

If you want an entertaining non technical overview I recommend this:

 

http://en.wikipedia.org/wiki/In_Search_of_Schr%C3%B6dinger%27s_Cat

[emcelhannon]

Thank you J.C.,

It was an interesting book, but I meant the "well beyond the scope of the original thought experiment" part.

I thought I understood it as far as I was capable, so I expected a cat initiated test, (although I didn't know why) would likely have the same results as every other similar thought experiment. If there's more to be considered along these lines, I'm terribly interested, but I don't want to change the subject of this thread.

[swansont]

Google on terms like 'schrodinger cat consciousness' or 'schrodinger cat observer.' But be warned — there is a lot of chaff and little wheat, i.e. there is often little physics in he discussion.

[emcelhannon]

But be warned — there is a lot of chaff and little wheat, i.e. there is often little physics in he discussion.

 

Perhaps you could reccomend a reputalbe author.

thanks

[swansont]

Since it's not a topic I've pursued, nobody comes to mind.

[iNow]

Perhaps you could reccomend a reputalbe author.

thanks

 

I'd suggest reading this, then exploring the references and external links. You never know where the pinball effect will take you when trying to teach yourself something new.

 

http://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_Cat

[swaha]

if we always collapse the wave function while measuring it how can we say that it was at the superposition of some states & not that state themselves?

[swansont]

if we always collapse the wave function while measuring it how can we say that it was at the superposition of some states & not that state themselves?

 

Because there are experiments you can do with superpositions that show interference of the states, which would not occur if the system were in just one state.