Is the Born Rule the Key to Understanding Schrodinger's Cat Experiment?

[moriheru]

Greetings,
Concider the classical setup for the Schrodingercat equation, that is cat in a box some deadly gas or acid isolated in a glas and a hammer that destroys the glas after an uncertain time.
Just for some fun consider a new setup: Cat in a box, deadly gas or acid(I think it's blausauere for all the germans) in a glass or any breakable isolator, a hammer that is connected to a second Schrodingerscat box and that shall destroy the isolator of the first Schrodingerscat box if the isolator in the second Schrodingerscat box is destroyed...
any thoughts,where the maths is concerned?

 

[Matterwave]

Since the two boxes are connected through a detection channel, I see no difference between this experiment and the original Schrodinger cat experiment...except for where you say use a glass box. Obviously we can see inside a glass box (photons will get inside and make it no longer an isolated environment), so that sort of ruins the point of the experiment.

 

[Nugatory]

except for where you say use a glass box. Obviously we can see inside a glass box (photons will get inside and make it no longer an isolated environment), so that sort of ruins the point of the experiment.

I think OP was trying to say that the poison was isolated in a glass vial, as in the traditional form of the experiment. But your answer still stands - as stated, this is no different from the standard one-cat experiment.

 

[Matterwave]

I think OP was trying to say that the poison was isolated in a glass vial, as in the traditional form of the experiment. But your answer still stands - as stated, this is no different from the standard one-cat experiment.

Ah, I read that as the cat was in a glass box. My bad. Then yea, just go with the first part of my statement.

 

[bhobba]

any thoughts,where the maths is concerned?

Like the original Schroedinger's Cat its not really a math problem - its an understanding problem.

QM is a theory about observations that appear in an assumed common-sense classical world. In Schroedinger's cat, or your variation, that occurs at the particle detector. Everything is common-sense classical from that point on.

The purpose of Schrodinger's Cat was not what you read in popularisations - it was to highlight an issue with QM - namely the need for a fully quantum theory of measurement without this need for assuming a classical world that the theory should really explain. Since then a lot of progress has been made, but a few issues remain.

Lubos wrote a nice article on it:
http://motls.blogspot.com.au/2011/05/copenhagen-interpretation-of-quantum.html

Thanks
Bill

 

[David Carroll]

What's in the all these isolators? All poisons? Or radioactive sources?

 

[David Carroll]

Is this what you're saying, moriheru: We have a box which contains a radioactive source. If a particle is registered from radioactive decay, a contraption in the first box will swing two different hammers? One of these hammers cracks open a murderous agent that kills a cat within the first box and the second hammer will unshield the source of radioactive decay in a second box? And if, after the source in this second box is unshielded, and if a particle is detected in this second box, this box's own hammer will crack open a murderous agent that kills the cat in this box?

If this is your scenario, then if the radioactive source has a 50% chance of emitting a particle, you have a cat that is in a 50% dead state in the first box and a cat in a 25% dead state in the other one.

 

[David Carroll]

And if you had a third box, the 3rd cat would be in a 12.5% dead state. For each nth box, your nth cat is in a X%ⁿ dead state, where X denotes the percentage that a particle would be detected assuming the same radioactive source is in each box.

 

[David Carroll]

If you find the cat in the last box dead, you can assume all the other cats are dead too.

 

[Nugatory]

If this is your scenario, then if the radioactive source has a 50% chance of emitting a particle, you have a cat that is in a 50% dead state in the first box and a cat in a 25% dead state in the other one.

You have misunderstood the point of Schrodinger's thought experiment. There has never been any serious doubt that the cat is always either alive or dead (although we may not know which it is) with no funny 50% alive/50% dead states.

Schrodinger proposed the thought experiment to point out a problem with the 1920's vintage understanding of quantum mechanics - the formalism as it was then understood suggested that the cat could be in one of these funny states even though no one believed that.

The resolution came with the discovery of quantum decoherence some decades later. The half-dead/half-alive state very rapidly evolves into a state in which the cat is either alive or dead - we may not know which, but it is one or the other as surely as a tossed coin is heads or tails but not some funny mixture of the two.

 

[David Carroll]

Thanks for the clarification, Nugatory. Replace every statement containing the phrase "X% dead state" with "X% chance of being dead", then.

 

[Nugatory]

Thanks for the clarification, Nugatory. Replace every statement containing the phrase "X% dead state" with "X% chance of being dead", then.

And while we're adding clarifications... The comment above applies to macroscopic systems with many internal degrees of freedom such as cats, oysters, the needles and digital displays of our measuring instruments.

A microscopic system can be in one of these superimposed states (for example, half spin up and half spin down). Such systems are best described as being in neither state until they're measured, instead of being in both states at once.

 

[moriheru]

No I am not saying the isolators carry radioactive material and I said isolators becouse I didn't know any other word.
I am quite familiar with Schrodingerscat and it's implications, I was just wandering if the uncertantys of the state of Schrodingerscat would grow grow exponentially?! And what about the many world interpretation? Would one have four worlds?

 

[bhobba]

I was just wandering if the uncertantys of the state of Schrodingers cat would grow grow exponentially?! And what about the many world interpretation? Would one have four worlds?

The uncertainty's in QM occur at an observation. The observation is at the Geiger Counter - everything after that is common-sense classical.

Thanks
Bill

 

[David Carroll]

I think you'll have to be more specific about your experimental setup, moriheru. I had to sketch myself a picture to even visualize your set-up but since I'm getting several different interpretations (speaking of interpretations) of your set-up, I'm ending up with several different pictures. The hammer that is connected to the 2nd Schroedinger's cat box: which end is connected to it, the handle end or the ping end? And I'm assuming there are cats in both boxes?

 

[moriheru]

Here is the brilliant sketch

 

[moriheru]

Thanks David Carroll...You make a good discussion

 

[David Carroll]

In this case, either cat has a 50% chance of being dead, using the same radioactive source and probability as above. Both cats die or live together, with a 50% chance of both dying and a 50% of both living. One alive and the other dead wouldn't be possible.

 

[moriheru]

@David Carroll believe this is the equation for the state of SC so the equation would change for the 1/√2 to 1/√4!?

1/√2 l SC dead>+1/√2 lSC alive>

SC is Schrodingerscat

 

[Nugatory]

@David Carroll believe this is the equation for the state of SC so the equation would change for the 1/√2 to 1/√4!?

1/√2 l SC dead>+1/√2 lSC alive>

No. the sum of the squares of the two coefficients has to be one, which is equivalent to saying that the probability of finding the cat either alive or dead is 100%. You might want to google for "Born Rule".

 

[moriheru]

No. the sum of the squares of the two coefficients has to be one, which is equivalent to saying that the probability of finding the cat either alive or dead is 100%. You might want to google for "Born Rule".

Yes I understand it has to be normalized, that is afterall the point of the 1/2^1/2. Ah yes just noticed my equation is not renormalizable.