Schrodingers Cat revisited

[Slinkey]

In the Schrodingers cat argument a phial of poison is triggered by a random atomic event. The argument in this case was would the cat be in a superposition of being alive and dead before we open the box to find out the fate of the cat.

 

Here is a new slant that may have been said already. Let's face it there are plenty of brainier people in this field than me!

 

We create a pair of entangled photons. They are directed along equal paths to the poison phial. In this case the trigger on the poison device is as follows:

should the detector find a photon is polarised in the vertical plane the device is completely de-activated. Should it, however, detect a photon is polarised in the horizontal plane it will trigger the device and kill the cat.

 

The experiment is set up such that the pair of entangled photons strike the detector simultaneously.

 

What happens?

[Mr Skeptic]

The cat observes whether or not the poison vial broke... Anyhow, quantum doesn't really work like that, when a quantum state gets too big it collapses.

[Slinkey]

The cat observes whether or not the poison vial broke... Anyhow, quantum doesn't really work like that, when a quantum state gets too big it collapses.

 

Indeed. Decoherence. But that doesn't answer my question. The device is triggered by quanta of light. I'm not interested in the old saw of the cat being in a superposition. What I am interested in is whether entangled photons can trigger the device or not.

[swansont]

I don't think the entanglement matters at all here, and neither does the superposition of the state of the cat. You're sending two conflicting signals to the device.

[Slinkey]

I don't think the entanglement matters at all here, and neither does the superposition of the state of the cat. You're sending two conflicting signals to the device.

 

Ah, but the photons are being asked to be in one of two states once they hit the device. QE says that once the polarization of the first photon is known we can deduce the polarization of the other. Here they are being asked the question simultaneously. How can they decide what state to be in?

[swansont]

You are detecting them simultaneously on the same detector. How can you tell the difference between the two? You haven't stated how you would do this detection.

[5614]

I think your method of detection here is of critical importance. I also think there are two relevant questions.

 

The first, of whether the cat will die, seems a simple one. You must have some sort of polarising filter (or some way to measure the polarisation), which will then result in a signal, say 1 or 0, being sent to the poision vial, thus killing or not killing the cat.

 

In this scenario, assuming both photons reach the polarisation detection circuit at the same instant, both a 1 and a 0 will be sent. The reason I said it were simple is because in a digital electronic system 1+0-->1... i.e. the signal which says "keep the cat alive" cannot undo the signal saying "kill the cat". As the signals come at exactly the same instant you cannot seperate or prioritise one signal or the other, both signals must be processed equally, a signal and a lack of a signal is simply a signal. However if, instead of 1 and 0, your polarisation detector results in a 1 or -1 signal, then the two signals will combine to form 0, i.e. no action will be taken.

 

It is a simple question of how the "kill" and "not-kill" signals merge, when both sent through the same circuit at the same instant.

 

As for how the entanglement collapsing works, if both photons are truly detected at the same instant, then they'll both go from a superposition to a definitive state in that instant. Remember with QE the wavefunction collapse is instantaneous. Everything happens in a instant, it's not so nice to think of that happening in reality, but this is a thought experiment and so I can't see a problem.

[swansont]

.

 

It is a simple question of how the "kill" and "not-kill" signals merge, when both sent through the same circuit at the same instant.

 

Exactly. And adding in entanglement is a separate issue that complicates the problem.

[Slinkey]

....As for how the entanglement collapsing works, if both photons are truly detected at the same instant, then they'll both go from a superposition to a definitive state in that instant. Remember with QE the wavefunction collapse is instantaneous. Everything happens in a instant, it's not so nice to think of that happening in reality, but this is a thought experiment and so I can't see a problem.

 

The trouble I am having with this is that according to the literature it is when we detect the photon that it collapses into one state or the other. A planck moment before detection the photon has no definite polarisation (and neither does its entangled twin). Whatever I do to photon a has an effect on photon b and if I do something to photon b it has an effect on photon a.

 

This sounds ok to me if you measure one photon and then the other photon. The collapse has already taken place before you measure the second photon. The wavefunction is being collapsed by the first event.

 

In my thought experiment, both photons are being measured at the same time and thus they collapse at the same time. The wavefunction is being collapsed by both events.

 

Intuition (not a good tool for science I know but this is a thought experiment after all) tells me that the photons could be in any state. They could be both horizontally polarised, or both vertically polarised, or have opposing polarisations.

 

To me, if it was any other way then there must be hidden variables.

[swansont]

Intuition is often a really bad predictor of how quantum mechanics will behave.

[Slinkey]

Intuition is often a really bad predictor of how quantum mechanics will behave.

 

I was waiting for someone to say that, and yes, I agree. However, what do you think of my question? I guess what I'm realy asking is what is the nature of the collapse of the wave function? If, as I state above, we measure one and a moment later measure the other we assume that the polarisation of the second photon was "set" by the polarisation we measured for the first photon thus evoking non-locality. Its like the first photon told the second photon what plane it was polarised and the other changed in accordance.

 

In the experiment I propose we have a simulataneous collapse situation - both photons are asked to be polarised in one plane or the other at the same time (and I concede it is right here that I am most probably in need of correction). Which photon does the telling?

 

Please don't be too harsh with me if I am making a complete ass of myself here!

[5614]

If a photon did the "telling"... well, that is basically hidden variable theory. Neither photon does the "telling". Instead think of it as a single wavefunction that collapses.

 

Remember the the wavefunction collapse is instantenous. I don't especially like the idea of everything happening at the same time and instantenously, but that is what your thought experiment is. My dislike is based far more on the fact you are observing two photons at the same instant, than the fact that on top of this they're entangled. Despite our dislike, this is the nature of thought experiments!

 

Rereading your post, Slinkey, I think if you think more of a single wavefunction collapse, and not one photon determining the other's polarisation, it may help. This won't help you visualise the situation in your head, but I think getting past the "one photon's property determines the other's" way of thinking may help.

[swansont]

I think you'll never be in a position to have this actually be an issue. You will be limited by several factors, including the Heisenberg Uncertainty Principle.

[Slinkey]

.....Rereading your post, Slinkey, I think if you think more of a single wavefunction collapse, and not one photon determining the other's polarisation, it may help. This won't help you visualise the situation in your head, but I think getting past the "one photon's property determines the other's" way of thinking may help.

 

Would it be better to think of the entangled photons as a single system in that case?

 

Remember the the wavefunction collapse is instantenous. I don't especially like the idea of everything happening at the same time and instantenously

 

What intestests me in your reply is that the wave function collapses in no time because what keeps jumping into my mind is that the reason entangled photons behave like this is because what appears as two different events to us - the photons leaving the source and reaching the detectors - is in the reference frame of the photons a singular event ie. the photons leaving the source and reaching their destinations happens in no time in the RF of the photons. Thus is some sense you could argue that their polarisations are set at source in accordance with the demand of their destination.

 

Does that make sense?

 

The act of measurement is very intriguing. Do the photons choose their polarisation or does the detector force them to be one or the other? Which way does the jazz flow... so to speak.

 

I think you'll never be in a position to have this actually be an issue. You will be limited by several factors, including the Heisenberg Uncertainty Principle.

 

I guess that probably is correct and the thought experiment is void on that alone.

 

I wonder about the Uncertainty Principle because as I understand it is says that we cannot make a measurement to this kind of accuracy, however, could it not be argued that although we cannot measure with the required accuracy (and I do understand this is not a limitation of our equipment - it is a fact of nature) it does not mean it cannot happen. I guess I am asking what is the probability of two entangled photons being detcted at the same time on top of what would happen.

[5614]

Would it be better to think of the entangled photons as a single system in that case?

Yes.

 

What intestests me in your reply is that the wave function collapses in no time because what keeps jumping into my mind is that the reason entangled photons behave like this is because what appears as two different events to us - the photons leaving the source and reaching the detectors - is in the reference frame of the photons a singular event ie. the photons leaving the source and reaching their destinations happens in no time in the RF of the photons. Thus is some sense you could argue that their polarisations are set at source in accordance with the demand of their destination.

 

Does that make sense?

In the photon's referrence frame, now you're just trying to make it complicated ! It's a hard one, as you say the photon does not experience time, so maybe we could argue that the photon does know what its polarisation is, because after the detection, and before the detection, it's all the same to a photon. Big maybe!

 

The act of measurement is very intriguing. Do the photons choose their polarisation or does the detector force them to be one or the other? Which way does the jazz flow... so to speak.

Regardless of what the photon may think, in our frame, the photon is in a superposition. The detector collapses this superposition and forces the photon to chose a state.

 

When a photon in a superposition is observed, and the superposition collapses into a definitive state, is that a truly random? If you have an entangled photon, which is either polarised up or down, when you observe it, is it truly 50/50 whether it is up or down?

 

I wonder about the Uncertainty Principle because as I understand it is says that we cannot make a measurement to this kind of accuracy, however, could it not be argued that although we cannot measure with the required accuracy (and I do understand this is not a limitation of our equipment - it is a fact of nature) it does not mean it cannot happen. I guess I am asking what is the probability of two entangled photons being detcted at the same time on top of what would happen.

It could happen, however I don't think we could ever claim it did happen, due to the uncertainity principle. More to the point, as said before, the superposition collapse is instant, so is there really any problem?

 

 

This is kinda random, but you may find this: http://math.ucr.edu/home/baez/physics/Quantum/bells_inequality.html which talks about the EPR paradox and Bell's Inequality interesting. It's a long read, take it slowly!