EPR-correlation

[Pete]

Does anyone know how to prove whether or not two particles in s spin-singlet state of a spin 1/2-system remain in a tangled state after a measurement of the spin of one of the particles is made?

 

Thanks

 

Pete

[swansont]

Measure them in a different basis and observe the correlation (or lack thereof)

[Pete]

Measure them in a different basis and observe the correlation (or lack thereof)

Thanks for chiming in swansont!

 

That's what I'm trying to determine, i.e. what does quantum mechanics predict when this is done?

 

Let me clarify - I'm asking how to use quantum theory to predict if the particles are still entangled after the first measurement is done. I don't exactly have a lab to do the experiments.

 

To be more precise - Consider a two particle system in a spin-singlet state. Suppose one measures the z-component of spin of particle 1 to be "up." Particle 1 would then be left in the state |(1):z;+> (The (1)" means is particle "1", the "z" means that the basis is the basis corresponding to spin measured relative to the z-axis and "+" denotes the spin up state). We know that a subsequent measurement of the z-component of spin of particle 2 will be "down." I.e. we would find particle 2 in the state |(2):z;->.

 

Suppose particle 1 is found in the state |(1):z;+>. Then quantum theory states that |(1):z;+> can be expressed as the superposition of the the base kets |(1):x;+> and |(1): x;->. If the x-component of the spin of particle 1 is measure and the result is "+" then particle 1 will be in the |(1):x;+> eigenstate. Here's the big question - Does does quantum theory predict that the result will be the particle 2 in the state |(2):x;-> when the x-component of spin of particle 2 is measured? If so/not then how can it be proven using quantum mechanics?

 

Pete

[Klaynos]

Once particle 1 has been measured, the entanglement has been broken.

 

So if both z and x spin components where entangled, and you measure z on 1, you've broken the entanglement so the x-component is no longer entangled.

 

To show this you need to apply the operator for measuring the spin z-component to the wavefunction.

[Pete]

Once particle 1 has been measured, the entanglement has been broken.

Its proof I'm looking for. Not assertions.

To show this you need to apply the operator for measuring the spin z-component to the wavefunction.

That's pretty vauge. I don't see how that will prove anything. Please be more specific.

 

Pete

[Klaynos]

Its proof I'm looking for. Not assertions.

 

That's part of entanglement it only lasts until the first interaction.

 

That's pretty vauge. I don't see how that will prove anything. Please be more specific.

 

Pete

 

Well it depends on the situation you're dealing with, you'd need to write out the wavefunctions for the particles.

 

And then work out the operator that is applied to them (the measurement).

 

And then apply that operator to the wavefunctions.

 

You can't really do it for general situations. But the operator will change the wavefunction, you can work out how much if you work out the commutator for the two operators, if it's 0 they can be measured independently of each other, which I don't think spin componants can be. This also depends on the wavefunctions though, it's easier to write out a "general" wavefunction to test the principle though. A good QM text will talk about this.

[swansont]

Let's use the example of two spin-1/2 particles, with zero total spin. Particles are entangled if measurement in any particular basis yields the answer of one particle being spin up and the other spin down. This is true for every measurement.

 

However, the measurement of a spin up particle in another basis will give spin up some fraction of the time and spin down the rest. The spin down particle will behave similarly , but finding one spin up and one spin down will happen 50% of the time. There's no provision in QM for how that particle was prepared in that state, only that the state is known.

 

And that's a basic difference between entangled states and non-entangled states. If the individual states are known, they cannot be entangled, because the above measurement applies. Only if the individual states aren't known can they be entangled.

[reilly]

As far as persistence is concerned, the measurement technique will determine the longevity of the entanglement. Generally photons are measured destructively, as in, for example, measurement by the photoelectric effect. Polarization measurements, however, do not have to be destructive, so one has a choice. One can set polarizer to pass a photon with spin +1, and block spin -1. So, a +1 particle will still be in a +1 state after measurement, and a spin -1 photon will be destroyed by absorption. It all depends on the details of the measurement process.

 

If a singlet photon state gives a +1 along any axis, then the other photon will have spin -1 along the same axis, as is required by conservation of angular momentum. If the axes are different, then a measurement of 1 photon implies a probability distribution for the other measurement. A +1 measurewment in the z direction says that the other particle will be +1 50% of the time, -1 otherwise, if measured alnong the x axis. Further, the same is true for Sz = -1. So, as is required by the fact that Sx and Sy do not commute, a measurement of Sz does not specify the measurement for, say, Sx whether or not the two photons are entangled.

 

Klaynos and I pretty much agree.

 

Regards,

Reilly Atkinson

[Pete]

That's part of entanglement it only lasts until the first interaction.

Once again all you have done is to make an assertion with no derivation to demonstrate that what you say is true. You didn't provide a derivation which proved that what you claim is true is really the case. When I start a thread whose sole purpose is to find a proof of something then its of absolutely no use to me to simply sau that "It can be shown." Claiming it can be shown does not help me when I'm actually looking for the step by step derivation. And it cannot be deduced from anything posted in this thread so far.

 

In any case I spend most of my day at the university where I'll be starting graduate school again. I start taking classes next week. Yay!!!

 

I met and spoke with one of the professors who teaches quantum mechanics and I told him about my interest in this subject. What a coincidence!! It turned out that he has a strong interest in EPR-correlations. This very subject is one of his areas of interest. The professor explained this to me that (if he's correct that is) there is no such derivation, i.e. it can't be proven. It is something which given as a postulate. This may turn out to be wrong but at least I found a kindred spirit who is also interested in superluminal communication.

 

Klaynos - Your outline does not provide a route to any sort of derivation that I can see. And "Good" QM texts don't address this exact situation, i.e. series of measurements. Texts almost always talk exclusively about single measurements.

Well it depends on the situation you're dealing with' date=' you'd need to write out the wavefunctions for the particles.

[/quote']

I see no need to write out the wave function. All one needs here is the spin degree of freedom.

And then work out the operator that is applied to them (the measurement).

What operator are you referring to? The situation here is not to take one measurement. In this case one is taking a series of measurements. In what sense are you speaking about "Work out the operator"?

And then apply that operator to the wavefunctions.

Do you mean apply the operator to the spinor since the wave function is of no use in this problem.

You can't really do it for general situations.

Ummmmm ... nobody mentioned "general situations". I know that I sure I didn't. I stated something very specific' date=' i.e. a [i']spin-singlet state of a spin 1/2-system[/i]. That is something very specific.

 

I appreciate your efforts.

 

swansont - Glad to see you posting on this topic. Much appreciated.

This is true for every measurement.

What do you mean "for every measurement"? Which measurements are you refering to? Are you referring to the first measurement of the spin of each pair of particles?

Only if the individual states aren't known can they be entangled.

I was hoping that I'd be clear by now that I don't accept statements like this on faith. Either this is something that is derived or it is something postulated. Which are you saying it is?

Edited August 27, 2008 by Pete

[Klaynos]

The drivations are quite long, and I've not had enough sleep over the last few days due to 18hour days doing volunteer work.

 

Any advanced undergraduate level text book should explain how to do what I described, and doing so will show you that my first statement is true. My personal preference for text book is Quantum Mechanics my Alastair I M Rae, Institute of Physics, London, 2002 (4th edition). But I don't know whether that's easily avaliable in the US.

 

I apologise that I've not gone into the derivations but I know you're not stupid, and I'm really tired so I'd rather point you in the right direction.

 

Oh and spin-singlet state of a spin 1/2-system is still quite general, how was the state created, how was the entanglement created, are the particles in any kind of potential, how are the measurements preformed...

[Pete]

The drivations are quite long, and I've not had enough sleep over the last few days due to 18hour days doing volunteer work.

I'm going to a university tommorrow so if you can quote a source then I can merely look it up in their library.

Any advanced undergraduate level text book should explain how to do what I described, and doing so will show you that my first statement is true.

I have two graduate level texts and an advanced undergraduate text and none of them even touch this topic.

My personal preference for text book is Quantum Mechanics my Alastair I M Rae, Institute of Physics, London, 2002 (4th edition). But I don't know whether that's easily avaliable in the US.

I just checked the university online catalog and see that they have it. I can make a copy of the derivation myself when I go there tommorrow. Can you tell me where in the book I need to start copying?

I apologise that I've not gone into the derivations but I know you're not stupid, and I'm really tired so I'd rather point you in the right direction.

No probelmo my good man. I understand perfectly. I was merely looking for a reference anyway since I know I can hit a library and look it up

Oh and spin-singlet state of a spin 1/2-system is still quite general, how was the state created, how was the entanglement created, are the particles in any kind of potential, how are the measurements preformed...

What difference does it make how it was created since the math should be the same? The state vectors should be identical. If it matters how the measurements are performed then thats a problem since quantum mechanics does not make such a distinguishment. If the particle was in a potential then I would have stated it since that's another problem all together. In fact the paper I have on EPR-correlations and superluminal signals describes juust what I've described to you. There was nothing in the paper about how the spin is measured etc.

 

I'm cuious as to why you think that the results of a measurement depend on how the measurement takes place.

[Klaynos]

The result does not change depending on the measurement, but particle after the measurement will change depending on the measurement method used, an example of this is given above with the polarisation example.

 

The creation method will change what about the two particles is entangled.

[Pete]

The result does not change depending on the measurement, but particle after the measurement will change depending on the measurement method used, an example of this is given above with the polarisation example.

 

The creation method will change what about the two particles is entangled.

Do you know the page number in Alastair I M Rae's text? I'm at the library now and need the page numbers so I can copy them. I'm hoping it will be easy to find but if not please post the page numbers,,

 

Too late: I've been on campus all morning and have to leave now so I can't wait anymore for your reply.

 

Klaynos - In the future can you do me a favor? In the future, if you choose to respond to a post/question of mine, such as the one I asked last night, i.e.

I can make a copy of the derivation myself when I go there tommorrow. Can you tell me where in the book I need to start copying?

Please read it carefully and then, if I ask for a page number, then please either you say that you don't know where in the text you are referring to or post the page numbers of the derivation that you intented to point me to. Now I have to go home empty handed.

 

But don't worry about it though, I'll get over it .

 

I'll be back here next wednesday anyway for my first class. I can try to get it then. In the meantime please post exactly where in the text you claim that this derivation is. I ooked inside the text and saw nothing resembling what you were saying is in there.

 

Thank you

 

Pete

Edited August 27, 2008 by Pete

[swansont]

What do you mean "for every measurement"? Which measurements are you refering to? Are you referring to the first measurement of the spin of each pair of particles?

 

Every entangled pair. If you you measure one to be spin up, the other one must be spin down.

 

 

I was hoping that I'd be clear by now that I don't accept statements like this on faith. Either this is something that is derived or it is something postulated. Which are you saying it is?

 

I thought this was the obvious conclusion.

 

If you have a basis of |1> and |2>, and a particle in state |1> (and another in |2>), but you measure each in some other basis, the state will be Z = a|A> + b|B>

 

a and b will tell you the probability of finding the particles in each state. There is no interaction between the particles. Let's say the probabilities are each 50%. If we measure both, the chances of getting |A>+|B> or |B>+|A> is also 50%

 

They can't be entangled if that result is correct. But this situation arises only when you already know the states of the particles.

[Pete]

Welcome Reilly! I'm very happy to see that you're posting here!

 

Let's use the example of two spin-1/2 particles, with zero total spin. Particles are entangled if measurement in any particular basis yields the answer of one particle being spin up and the other spin down. This is true for every measurement.

That is certainly sufficient, but it isn't necessary. Two particles are said to be in an entangled state if and only if there is an EPR-correlation between them. There is more than one way to do this. One way is to use the example I provided, i.e. to do just as you said. This is Bohm's method of getting two particles to be EPR correlated. Another way is to do what Einstein, Podolsky and Rosen used did, i.e. use measurements of x and p_x. One could do that using particles with no spin.

 

In Sakurai's QM text the author refers to the following decay process as a source of particles in entangled states. The following decay process creates two particles which are born in a spin-singlet state

 

[math]\eta \rightarrow \mu^{-} + \mu^{+}[/math]

 

The initial value of the total spin of the system is zero. Choose coordinates such that the total orbital angular momentum is zero, i.e. L = 0. Therefore the total angular momentum will equal the total spin angular momentum, i.e. J = S which is zero. When [math]\eta[/math] decays into [math]\mu^{-}[/math] and [math]\mu^{+}[/math]. This means that the spins must add up to zero, i.e. the spins of each of the two particles mut be equal and opposite. The particles are then in an entangled state.

 

I will assume that Klaynos and Reilly are correct and the particles will not be entangled after the first measurement. But I'm also assuming that this is not a postulate (I misunderstood that professor I met yesterday regarding this) . and as such it can be derived. It is that derivation that I'm seeking. Klaynos mentioned above The drivations are quite long,.. . To me that tells me that he knows of a place where teh derivation can be found because Klaynos told me that its in Rae's text. I'm now waiting for Klaynos to tell me what pages the derivation is located on. Calling Klaynos!!!

 

Let me get something straight folks. I am not saying that Klaynos and Reilly are wrong. I never did in fact. I don't understand why you seem to keep assuming that is the case. Please stop making that assumption? Please go back and read the question I asked more closely, okay? Here. I'll make it easy for you. I asked

Does anyone know how to prove whether or not ....

I.e. all I asked was how to prove what the final state of entanglement was. Are we now clear on that? So merely repeating that the particles are no longer entangled is of no interest to me in this thread.

 

Pete

[Dr. Jekyll]

I.e. all I asked was how to prove what the final state of entanglement was. Are we now clear on that? So merely repeating that the particles are no longer entangled is of no interest to me in this thread.

Hello Pete!

 

Can't one just re-measure the particles? I mean, then you should get the same result as the previous. If the results are the same, the particles are no longer entangled, or they never were entangled.

[Pete]

Can't one just re-measure the particles? I mean, then you should get the same result as the previous. If the results are the same, the particles are no longer entangled, or they never were entangled.

Of course you can measure the results. But being entangled means that there is a relationship between the two which exists even when the quantum state is not in a particular eigenstate. Just because two particles have opposite spin doesn't mean that they are entangled. One could create such a system quite easily but that doesn't mean that the particles would be entangled.

 

I have the feeling that the particles aren't entangled after the first measurement but am unsure. One of the physics professors who has an interest in this subject confirmed this for me but I'm not happy until I see it proven. In the present case I'm trying to figure out how to show that after the second measurement (i.e. a subsequent measurement of the z-component of spin) the state would have the following representation

 

|Psi> = a|+,-> + b|-,+> + c|+,+> + d|-,->

 

where [math]|a|^2 = |b|^2 = |c|^2 = |d|^2[/math]. If the particles were still entangled after this second measurement then the state would have the following superposition

 

|Psi> = a|+,-> + b|-,+>

 

If this is the case then the particles would still be entangled. This is a measureable result. If they are still entangled then it would be possible to send information FTL, i.e. it could be used to send information faster than the speed of light.

 

Pete

[foodchain]

Of course you can measure the results. But being entangled means that there is a relationship between the two which exists even when the quantum state is not in a particular eigenstate. Just because two particles have opposite spin doesn't mean that they are entangled. One could create such a system quite easily but that doesn't mean that the particles would be entangled.

 

I have the feeling that the particles aren't entangled after the first measurement but am unsure. One of the physics professors who has an interest in this subject confirmed this for me but I'm not happy until I see it proven. In the present case I'm trying to figure out how to show that after the second measurement (i.e. a subsequent measurement of the z-component of spin) the state would have the following representation

 

|Psi> = a|+,-> + b|-,+> + c|+,+> + d|-,->

 

where [math]|a|^2 = |b|^2 = |c|^2 = |d|^2[/math]. If the particles were still entangled after this second measurement then the state would have the following superposition

 

|Psi> = a|+,-> + b|-,+>

 

If this is the case then the particles would still be entangled. This is a measureable result. If they are still entangled then it would be possible to send information FTL, i.e. it could be used to send information faster than the speed of light.

 

Pete

 

 

Would solving that have to show for how the information is transferred? Trying to avoid a word trap, entangled states are responsible for the spooky action at a distance stuff, so I would think to show how this information “traveled” would then mean that particle has that much information in it? Such as using FTL to send a perfect message from controlled point A to controlled point B?

 

As a possible rewording or example, if say a subatomic particle had to occupy space in an atomic shell, would the movement or field or whatever the electron of such then be somewhat like FTL? THis would still have to resemble time in some fashion though right? Else if this was a natural phenomena I don’t again see how QM could produce the classical physics stuff.

 

Not trying to block your way to an answer, I honesty don’t have it:D

[Pete]

Would solving that have to show for how the information is transferred?

I don't understand this question. Can you rephrase it for me please? Thanks.

Trying to avoid a word trap, entangled states are responsible for the spooky action at a distance stuff, so I would think to show how this information “traveled” would then mean that particle has that much information in it? Such as using FTL to send a perfect message from controlled point A to controlled point B?

I don't know if entangled states can be used to transmit information FTL if the states are not entangled during a series of measurements. I have the feeling they aren't. But I'm looking into all of this during this fall. Right now I'm waiting for Klaynos to answer my question so I can see the derivation that he's speaking about for myself. Perhaps this weekend I'll create a web page to illustrate what I'm talking about.

As a possible rewording or example, if say a subatomic particle had to occupy space in an atomic shell, would the movement or field or whatever the electron of such then be somewhat like FTL?

No. Because one cannot follow the particle during that kind of motion. In quantum mechanics there are no classical trajectories and the position of a particle cannot be given as a function of time. No information could ever be transmitted this way.

 

Klaynos - You still out there??

 

Pete

Edited August 31, 2008 by swansont
fix quote tag

[foodchain]

I don't understand this question. Can you rephrase it for me please? Thanks.

 

Just that the math would have to physically show each individual facet of how the information traveled if it did indeed travel. As such if it were occurring faster then light, I don’t know exactly what that math would look like.

 

No. Because one cannot follow the particle during that kind of motion. In quantum mechanics there are no classical trajectories and the position of a particle cannot be given as a function of time. No information could ever be transmitted this way.

 

I don’t mean in a highly linear sense of a line from point A to B or an obit in the sense of how a planet orbits. If Planck units are truly fundamental to quantum mechanics you can view the electron as a certain amount of energy right? As in it has to come in quanta, and that its movement in say an atomic shell is at least constrained by such right? My question then becomes somewhat I think in line with your topic if you can then replace the idea of observation itself with entanglement?

 

Such as is entanglement of the quanta in say a star stronger within the star then say any orbiting body? Would spooky action at a distance be constrained by any form of locality? I mean entanglement can be shown to occur between separated things in which the concept of FTL arises, such as measurement of spin on one particle can cause measurement of another particle to change or have some property in relation to observation of the first particle.

 

I always get confused with QM because its stated to explain aspects of how the physical world actually behaves. With that it is to be probabilistic and random in every sense. Yet a basic study of QM is the interaction of light with matter. I would tend to think this physical reality holds impact on say vision in an organism. Yet I can sit at my computer and do things that requires sight that produces some kind of coherent information. I would think giving the model picture of QM that reality should really look like static on the television, yet it does not appear that way. Would this even be remotely suggestive of anything at all? I mean could a possible question be how does the brain plug quantum behavior such as photons hitting the eyeball into conscious thought?

[Pete]

Wow. That's a lot and most of it I'm not sure is meaningful enough to answer or is readily answerable. But first things first;

Just that the math would have to physically show each individual facet of how the information traveled if it did indeed travel.

Sorry but I have no idea what that means. Can you give me an example by analogy from, say, communication using radio waves? Thanks.

 

Pete

[Norman Albers]

If we are detecting entangled measurements many kilometers' distance, I'd think the two distances of observers from common source are not precisely the same. Do they need to be? To what, a wavelength??? We could use a tight timing restriction relative to a tested interval, and thus know when to gate open our detection, but this would not depend on equal path lengths. May I invite comments on this letter of today: "Entangled 'particles' I've heard of as being commonly either electrons or photons, and obviously the latter over long distances. What is so is that they come from a common 4-point and then propagate either inside or on the light-cone. Yet their resolution exists irrespective of communication between observers. What balances this is that no single observer can yet know the results until a light-speed signal resolves this."

 

Just as you cannot sense photons going through one or another slit, once you measure entangled electrons you have changed the system. We must let go of the idea that we are simply determining what is there. We are part of the determination, not because of consciousness or any such anthropomorphism, but because measuring is process which disturbs or forces the original state.

Edited October 11, 2008 by Norman Albers
multiple post merged

[traveler]

I mean could a possible question be how does the brain plug quantum behavior such as photons hitting the eyeball into conscious thought?

 

The same way that information can be processed by ones brain which leads to changes made in the body that ultimately effects the offspring. Evolution in species is due to a brain reacting to its environment, which causes changes in the brain (ideas) which are passed along though the generations and mixed with other members of the generations.

 

A species can ultimately evolve by simply reacting to its environment.

 

If I'm always hot because I moved to a warmer climate, my body will acclimatize while I'm alive, and changes will be made to my offspring in the appropriate direction, such as less hair to be better adapted to the warmer climate.

[swansont]

The same way that information can be processed by ones brain which leads to changes made in the body that ultimately effects the offspring. Evolution in species is due to a brain reacting to its environment, which causes changes in the brain (ideas) which are passed along though the generations and mixed with other members of the generations.

 

A species can ultimately evolve by simply reacting to its environment.

 

If I'm always hot because I moved to a warmer climate, my body will acclimatize while I'm alive, and changes will be made to my offspring in the appropriate direction, such as less hair to be better adapted to the warmer climate.

 

Evolution does not work that way. Thoughts are not genetically encoded, and neither are adaptations (Lamarckism was falsified ages ago)

[Norman Albers]

What if the distances of the two observers are not at all the same? solidspin informs me that they sort of are equal, but what if one is close and the other later and farther? Does this change the results? How close is close?