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## Cheating a faster than light signal.

A spin zero particle decays into a pair of spin 1/2 particles, each particle in a superposition state of up and down. The pair of particles head off in two opposite directions. One of them enters an apparatus that will collapse its wave function and decide the life and death of a cat based on the result. When the collapse occurs, the other particle immediately changes state from superposition state to eigenstate. I measure the state of the particle and place a bet with some chump about the condition of the cat. Sometime later, the verification of the cat's state arrives after having traveled at the speed of light, and I win the bet.

No real information has traveled faster than light, but that's small comfort to the chump.
 Recognitions: Gold Member Science Advisor Staff Emeritus You've almost re-discovered the EPR Bell paradox ! Almost. Because the start was good (with the singlet state and so on). But afterwards you don't use it. Consider this: Out of a bag containing white and black balls, one picks a ball and cut it in two halves. Each half is sent off in two different directions: one to you, and the other one to the cat. If half a black ball enters the device, the cat is killed. If it is half a white ball, not so. Upon receipt of your half of the ball, you know that when it is black, the cat is dead now, and if it is white, the cat lives.

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 Quote by vanesch You've almost re-discovered the EPR Bell paradox ! Almost. Because the start was good (with the singlet state and so on). But afterwards you don't use it. Consider this: Out of a bag containing white and black balls, one picks a ball and cut it in two halves. Each half is sent off in two different directions: one to you, and the other one to the cat. If half a black ball enters the device, the cat is killed. If it is half a white ball, not so. Upon receipt of your half of the ball, you know that when it is black, the cat is dead now, and if it is white, the cat lives.
But in your scenario, the chump will take my money. His confederate saw the balls when they took off and sent a light signal to him. He got the information before the half-a-ball arrived. In my scenario, his confederate didn't know what would happen to the cat when the spin zero particle decayed.

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## Cheating a faster than light signal.

 Quote by jimmysnyder But in your scenario, the chump will take my money. His confederate saw the balls when they took off and sent a light signal to him. He got the information before the half-a-ball arrived. In my scenario, his confederate didn't know what would happen to the cat when the particle decayed.
But why do you allow the confederate to see which ball was picked in the classical scenario, but forbid the confederate to see the result of your spin measurement in the quantum scenario? That seems a little arbitrary, you could just as well say that in the classical scenario the choice of which ball to cut in half was made in a sealed room by an impartial judge, while in the quantum scenario a confederate was secretly observing your spin measurement and passed that information on to the would-be chump using a light-signal. Basically it all just comes down to which macroscopic event you allow the confederate to see and which you keep secret from him.

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 Quote by jimmysnyder But in your scenario, the chump will take my money. His confederate saw the balls when they took off and sent a light signal to him. He got the information before the half-a-ball arrived. In my scenario, his confederate didn't know what would happen to the cat when the spin zero particle decayed.
Ok then

Consider this, in YOUR scenario: on the track of the particle that goes my way, the confederate has installed a Stern-Gerlach machine which measures the spin of that particle, and lets it continue my way. He sends the result of his measurement with a light signal to the chump.

 Mentor Blog Entries: 1 But you forgot that the chump was hip to your scam and had his confederate give the remote Stern-Gerlach magnet a spin, randomizing its orientation. Now you'll have to wait for the morning paper to find out what happened to that cat.

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 Quote by Doc Al But you forgot that the chump was hip to your scam and had his confederate give the remote Stern-Gerlach magnet a spin, randomizing its orientation. Now you'll have to wait for the morning paper to find out what happened to that cat.
That's good

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 Quote by JesseM But why do you allow the confederate to see which ball was picked in the classical scenario, but forbid the confederate to see the result of your spin measurement in the quantum scenario? That seems a little arbitrary, you could just as well say that in the classical scenario the choice of which ball to cut in half was made in a sealed room by an impartial judge, while in the quantum scenario a confederate was secretly observing your spin measurement and passed that information on to the would-be chump using a light-signal. Basically it all just comes down to which macroscopic event you allow the confederate to see and which you keep secret from him.
The confederate knows what color half-a-ball was sent the moment it was sent. He can send a light signal that goes faster than the half-a-ball does. The chump gets the money.

However, the only thing he knows when the zero-spin particle decayed and my particle was sent is that it is in a superposition state. He doesn't know what will happen when the measurement is taken some time later. The particles went in opposite directions, so the cat is farther away from the chump and I than the decay location. He can't send a meaningful signal until the particle is measured. At that time he will have to be located where the cat is, not where the decay occured. Now he can send a light signal, but he is too far away and the particle will arrive at my end before the light signal does. I get the money.

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 Quote by vanesch Ok then Consider this, in YOUR scenario: on the track of the particle that goes my way, the confederate has installed a Stern-Gerlach machine which measures the spin of that particle, and lets it continue my way. He sends the result of his measurement with a light signal to the chump.
Not only will he make a chump of me, but he will be in a position to make chumps of the people at his location. Either way, a faster than light signal got cheated.

By the way, in my scenario, I was measuring a particle in an eigenstate. It was in that state because when the particle at the cat end was measured, my particle went into an eigenstate immediately. Spooky action at a distance.

In your scenario, the confederate will be measuring a particle in a superposition state. He will know what is going to happen to the cat before it happens.

It's all a cheat because no one really knows what happened to the cat, only what very likely happened. It's subject to the reliability of the poison, etc.

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 Quote by jimmysnyder He can't send a meaningful signal until the particle is measured.
That's the point. He can measure HIMSELF one of the particles, where ever he likes. (in the same way as he could get a glimpse of the color of the balls).

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 Quote by jimmysnyder In your scenario, the confederate will be measuring a particle in a superposition state. He will know what is going to happen to the cat before it happens.
But that is exactly the same as when he got a glimpse of the color of the ball!
 Recognitions: Gold Member Science Advisor Staff Emeritus If I may add something: The reason why one can always come up with an equivalent classical scenario in the case you mentioned (except for Doc Al's smart remark, which contains the essence in fact), is that as long as we are going to measure spins along one single axis (on the cat side, and at my side, or in between, by some spy), there is no observational difference between a true singlet state: |+>|-> - |->|+> and a statistical mixture of 50% |->|+> and 50% |+>|->, and the last situation can always be replaced by classical equivalences, because we have product states (each individual particle has a well-defined state, no entanglement). It is only when you start to look at measurements along different axes that there will occur funny correlations in the true singlet state, and not so in the mixture case.
 Blog Entries: 1 Recognitions: Gold Member My word, is it possible to send a signal faster than light after all? As I (half-? mis-?) understand it, particles that are in a superposition state have different measurement statistics than particles that are in eigenstates. I thought the import of the Bell experiment was to tell whether the daughter particles entered the eigenstate at the time of the decay or the time of the measurement. They proved it was at the time of the measurement. Have I erred in my understanding? Designate a sending station and a receiving station. From the midpoint of the two locations, send a stream of particles to both stations, all particles in superposition state. For each fixed interval of time at the sending station either do, or do not collapse the states of the particles. At the receiving station, for each fixed interval of time, gather from the measurement statistics whether the sender measured or didn't measure. You could send a Mozart symphony that way. This is pretty simple stuff, someone surely has already considered and rejected this idea. What's wrong.

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 Quote by jimmysnyder Designate a sending station and a receiving station. From the midpoint of the two locations, send a stream of particles to both stations, all particles in superposition state. For each fixed interval of time at the sending station either do, or do not collapse the states of the particles. At the receiving station, for each fixed interval of time, gather from the measurement statistics whether the sender measured or didn't measure. You could send a Mozart symphony that way. This is pretty simple stuff, someone surely has already considered and rejected this idea. What's wrong.
Nothing you do (or don't do) at remote location A can be detected simply by examining the data collected at remote location B. Only by comparing the two sets of measurement results do you deduce that the outcomes are correlated. (Which is not to say that something interesting isn't happening, but it's subtler than you think.)

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 Quote by jimmysnyder My word, is it possible to send a signal faster than light after all?
No, according to QM, this is not possible, be reassured.

 As I (half-? mis-?) understand it, particles that are in a superposition state have different measurement statistics than particles that are in eigenstates.
That depends ! If they come in statistical mixtures of eigenstates in the right proportion, then you cannot make the difference. What I mean is the following:

if the superposition is a |+> + b |->, then you cannot distinguish this, when measuring + or -, from a mixture of eigenstates, randomly presented, with a fraction |a|^2 of the time, the eigenstate |+> and the fraction |b|^2 of the time, the eigenstate |->.

And this is exactly what happens in such an EPR-Bell situation. So, locally, you will never know whether you still have a superposition, or whether you get eigenstates (but different ones, according to the statistical outcomes on the other side). In other words, what concerns local statistical distributions, EPR situations have nothing particular.

However, the *correlations* between the outcomes are peculiar.

 Designate a sending station and a receiving station. From the midpoint of the two locations, send a stream of particles to both stations, all particles in superposition state. For each fixed interval of time at the sending station either do, or do not collapse the states of the particles. At the receiving station, for each fixed interval of time, gather from the measurement statistics whether the sender measured or didn't measure.

That's what doesn't work, exactly because of the reason I said above. You can consider that you receive OR a superposition, OR a mixture of eigenstates, but *locally* they will always give you the same statistics, no matter what you measure.

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 Quote by vanesch That's what doesn't work, exactly because of the reason I said above. You can consider that you receive OR a superposition, OR a mixture of eigenstates, but *locally* they will always give you the same statistics, no matter what you measure.
Thanks. Actually, it's reasuring to know that I'm not going to get a Nobel prize for half-baked musings. This thread started as very light hearted, but has ended up quite educational. Let me summarize my new (half-? mis-?) understanding:

If I do a statistical study of the measurements of a bunch of particles, I can't tell whether my counterpart measured his or not, even though his measurement has put my particles into eigenstates.

The reason is that I can't distinguish between the following two scenarios:

A bunch of particles all in superposition states of a certain proportion of up and down.
A bunch of particles all in eigenstates, some up others down, and mixed in such proportion as to mimic the constitution of the superposition states.

Can Bell's experiment be explained to me in this kind of simple-minded language?
 Blog Entries: 1 Recognitions: Gold Member This is quite a coincidence. I have been reading the book Photons and Atoms by Claude Cohen-Tannoudji et.al. and had stopped in the middle of page 215. Now I picked it up for today's reading and get to the following near the bottom of the page (slightly edited): For example, a single-photon state which is a statistical mixture of eigenstates |1_1, 0_2> and |0_1, 1_2> with the weights |a|^2 and |b|^2 does not give fringes in w_1 (single counting rate) whereas these are observable with the superposition state a|1_1, 0_2> +b|0_1, 1_2> Can we look for interference fringes in the wave-like properties of the incoming particles?