How do particles become entangled?

[TheDonk]

How do particles become entangled? I've heard that it's when two particles bump into each other. How is this "bump" defined? What does it mean for 2 particles to bump? Is it based on distance apart, or something else?

 

[marlon]

https://www.physicsforums.com/showthread.php?t=42368&highlight=entanglement

The second post in this thread gives the answer to your question...

regards

marlon

 

[TheDonk]

I don't think it does...

"Well let's say that Alice and Bob both deliver a particle (A and B) and that we get an entangled state."

This is the part I'm asking about. How does this happen?

 

[jvangael]

I know for example in one of the first experiments performed to test the Bell inequalities, Alain Aspect used a phenomenon which is called Atomic Radiative Cascades to create entangled photons. The basic idea was to excite a certain atom (Calcium?) to an excited state. Most atoms fall back in a lower state sending out one photon, but once in a while the atom makes a "pitstop" at an intermediate level and thus sends out 2 photons. Using some angular momentum conservation you can show that these two photons are entangled. I don't know the exact details but this is what I recall.

Hope it helps,

Jurgen

 

[caribou]

I'm not sure of what the "bump" is either, only that it's an interaction and entanglement is extremely common in nature from all the interactions going on.

 

[NanoTech]

Marlon's analogy is good,but I am a little confused about how the density matrix would determine that there is no measurement that particle A can perform in order to distinguish the two ensembles, maybe I need to look at it from a relativistic stand-point of each particle. Dave

 

[blip]

My brain is still trying to wrap itself around exactly what happens during entranglement but let me ask two questions and see if someone (like Marlon or otherwise) can help me.

Question 1

Let´s assume Bob and Alice are holding each of the respective entangled photons and Bob goes zooming off into space.
At this point neither of them know what orientation the photons are in right? (Or does that depend on the source of their creation, like a calcite crystal?). Anyhow, when Bob measures his I understand that there is no way for Alice to know the measurement with more than 50% accuracy. But can she know whether he's made any measurement at all? Making the 1 bit NO MEASUREMENT, and the 0 state MEASUREMENT.

Questions 2

After the initial measurement between a pair of entangled photons the wave function has collasped and any further measurements won't influence the other, right?

 

[jvangael]

Hi Blip,

So when Bob performs a measurement Alice does not gain any information on her state nor can she tell whether Bob made his measurement. TBut, Bob can conclude in which state Alice's qubit will be in when she measures.

After Alice and Bob's measurements are performed on their entangled pair, the wave function indeed collapses. Because Bob knows which state his qubit is in for sure and Alice knows which state her qubit is in for sure, the state of their qubits is a product state or 2 unrelated physical systems or qubits.

Hope it helps.

Jurgen

 

[blip]

Thanks jvangael for the response, it does help.

 

[alexepascual]

TheDonk must be frustrated by now. None of the replies really answers his question. I was going to post exactly the same question when I found your post. I'll re-formulate the question to see if this helps and I hope it agrees with the original question's intent.
I would assume we know what entanglement means in a context such as EPR, quantum teleportation, etc. So, this is not the problem. Most descriptions of entanglement describe features of two particles that show that they are indeed entangled, and the more quatitative analyses may describe the degree of entanglement by using the density matrix, but this is not the question we are seeking an answer for either.
Let's say we have a hydrogen molecule. We know from Pauli's exclusion principle that the electrons will have opposite spin. If we separate the atoms, their spins will be entangled. So far so good. But the question is: How did the electrons become entangled when the molecule was created? By what mechanism did the states where both spins are "down" or both are "up" dissapear?.
A similar example could be given in terms of a collision. We heard that every time that two particles interact they become entangled. So if two particles bump into each other, then they must become entangled to a certain degree. Probably the case of a collison is more complex that the one I discussed before (the hydrogen molecule) because in the case of the collision there are more variables involved such as momentum, position, etc.
But in either case, there are combinations of the original tensor product of the separate Hilbert spaces that dissapear. How does this happen? Does entropy for the interacting particles change? How? is there a need to assume some dissipative effect?
I realize a discussion of this phenomenom may become very involved. If anybody here has seen an article on the web where this subject is explained, I would appreciate your pointing us in the right direction. Just remember, we already know what entanglement is, what we want to know is how two particles can become entangled in the first place. We want all the details about what happens when we bring them together. I think an understanding of this is crucial to tackle things such as environment-induced decoherence, the measurement problem, etc.
Once again, If you are knoledgeable about these topics I'll appreciate your guidance.
-ALex Pascual-

 

[TheDonk]

alexepascual is right. The answers haven't been exactly what I was asking for. The #4 post, by jvangael was getting closer, but it is more of the way people can do it instead of the general way it happens.

I'm hoping for an answer like:
When two fundamental particles are within x nanometers away.

I know it probably won't involve distance but there must be a single property that two particles can have that will entangle them.

 

[masudr]

Two particles must have interacted. If they have, then two measurements represented by operators A and B must behave like [A, B] = ih and then we have entanglement.

 

[blip]

So when Bob performs a measurement Alice does not gain any information on her state nor can she tell whether Bob made his measurement. TBut, Bob can conclude in which state Alice's qubit will be in when she measures.

What if they each perform a measurement simultaneously, say one vertical and the other horizontal? Afterwords they send their photon through a wave plate of the type corresponding to the measurement they each made.

Would they pass through their respective plates?

 

[TheDonk]

Two particles must have interacted. If they have, then two measurements represented by operators A and B must behave like [A, B] = ih and then we have entanglement.

"Two particlees must have interacted."
Can you give me an example of how two particles could interact to become entangled? A simple (if possible) step by step process where two particles start off not entangled and become entangled.

I'm not familiar with this equation and I don't know what i and h are. Can you explain what it means without the equation?

 

[alexepascual]

TheDonk:
"i" is the square root of (-1) and "h" is Plank's constant. A and B are what is called "Hermitian Operators" which represent "observables".
If you have little knowledge of quantum mechanics, I suggest you look at some tutorials on the web. Depending on the level at which you want to understand it, the math may become a little intimidating though. In parallel to reading some non-mathematical articles, I suggest you read a book on linear algebra, which is needed for Quantum.
But let me tell you that I think the previous post does not answer your question or mine, and I don't see the conection between what he says and the interaction between two particles.
-Alex-

 

[Eye_in_the_Sky]

How do particles become entangled?

First of all let's explain the idea of quantum "entanglement".

Suppose that we have two particles, 1 and 2, with corresponding Hilbert spaces H₁ and H₂. Suppose that particle 1 is in the state |ψ> Є H₁, and that particle 2 is in the state |φ> Є H₂, and all of this is before the two particles interact. Then, prior to the interaction, the state of the joint system is simply

|ψ>|φ>.

Now, suppose that the interaction between these two particles is such that

|ψ>|φ> → Σ_k a_k|ψ_k>|φ_k> ,

where each a_k ≠ 0, and there are at least two distinct values for k (and, of course, the |ψ_k> (|φ_k>) are linearly independent).

Then, the state of the joint system after the interaction can no longer be written as a simple (tensor) product of one element from H₁ with one element from H₂ – it must be written as a linear combination of such products. The two particles are now said to be in an "entangled" state.

Next, you ask regarding the interaction itself, referring to it as a sort "bumping" between the two particles:

I've heard that it's when two particles bump into each other. How is this "bump" defined? What does it mean for 2 particles to bump? Is it based on distance apart, or something else?

It sounds like the type of interaction you have in mind is that of a "collision-like" scenario. So, let's use the example of an "elastic collision". Then, with regards to the "bump" itself, there is nothing really special about it. What is special here is that we are dealing with quantum states.

First let's conceptualize the situation classically. Think of two particles (which repel one another) on a collision course as viewed in their center-of-mass frame. If the particles are directed perfectly "head-on", each one will bounce back in exactly the opposite direction. On the other hand, if their lines of flight are slightly "off-center", each one will be deflected by some angle from its original line of flight, such that:

The smaller the distance between the two lines of flight, the greater the angle of deflection.[/color]

However, no matter what the distance between the two lines of flight happens to be, we know that:

The momentum of each particle must be equal and opposite to that of the other. [/color]

Clearly, the momenta of the two particles are "correlated" ... and this is due to conservation of momentum.

Classically, we have no difficulty conceptualizing the situation. But, quantum mechanically, we find a bit of a 'twist'.

Suppose that the initial wavefunction for each particle has a very sharp momentum, with particle 1 traveling (to a very good approximation) in the +z direction, and particle 2 traveling (to a very good approximation) in the -z direction. Then, in particular, the wavefunction for each particle's position will show a 'spread' in the xy-plane.

Next, after the particles have gone "bump" and have flown well apart, the wavefunction of the joint system will involve a superposition of the various angles of deflection resulting from each of the possible distances between the two lines of flight consistent with the spread of each particle's initial wavefunction in the xy-plane.

Heuristically, looking at a "reduced" wavefunction |θ>, with θ denoting the angle of the line of flight relative to the z-axis, the above interaction can be summarized as:

|0>|π> → ∫a(θ)|θ>|π+θ> dθ .

Thus, there is nothing really 'special' about the "bump" itself. What is 'special' in all of this is that objects which go "bump" are described by quantum states.

 

[alexepascual]

Eye:
Thanks for your detailed answer. I understood most of it, but I still have a lot of questions. My knowledge about the description of multiple-particle systems is kind of defficient. I have a rough grasp of it but there are a lot of things I don't know.
About the original question by TheDonk, he framed the question using the example of a collision between two elementary particles. It may be that he did so because he read some place that particles become entangled after they "bump" into each other. Your analysis of the collision is very detailed and clear. As a matter of fact in your explanation there is a mixture of mathematical expressions with a more intuitive description. I doubt that TheDonk has the mathematical knowledge needed to understand the mathematical description. (I have not asked him how much math or QM he knows), but I am sure he must have learned something from your non-mathematical description, (provided he understands superpositions).
I suspect though, that a collision of two particles may not be the simplest example to study how two particles can become entangled. Wouldn't spin entanglement be easier to understand?
Going back to my difficulties,
I understand that the description of two non-interacting particles that are not entangled whoud consist of a combination of pairs of base states from each separate Hilbert space, and that this is represented by the tensor product of both Hilbert spaces. Now, I have always thought of the tensor product in terms of the combination of base vectors, but I have never thought about what happens to the states of two particles when we describe them in the combined Hilbert space. Assuming non-interaction, what would happen with the complex coefficients? do we just multiply them together for each individual element of the tensor? If so, what about the time dependence?. As I am writing this, I am thinking that it would not make sense to multiply the coefficients because then you might get interferences where there are none. On the other hand, I can see that the probability of finding the composite system in any of the combinations is proportional to the product of the probabilities of each individual base state.
I think what I said a few lines above might be somewhat confising. I said "what happens to the states...". I understand that the states of the individual particles remain unperturbed. What I meant is that I don't understand how to use the coefficients form the individual base states to construct the compound state.
I am now asking you just these simple questions because I think it may be better to tackle one small point at a time.(If I don't understand the simple things I won't be able to undestand the more complex ones). I recall from previous threads that you were very patient with me and I am very grateful for that.

TheDonk:
Eye-in-the_Sky is a very knowledgeable guy and I think he can help us. If you tell us a little more about how much math and quantum mechanics you know, maybe we can give you explanations that not too elementary or too advanced for your level. I consider myself a beginner, but there may be things which I have already understood that I may be able to explain. About myself, although I got a bachellor's degree in physics, which involves two quarters of quantum mechanics and two quarters of classical mechanics, not to mention mathematical methods, I feel that what I studied for school was always in a rush and I never got to understand each of the topics completely. I continue to read books and articles so that I can learn what for one reason or another I didn't learn in school. And I have found this forum to be a great place to learn and to help others.
With respect to the topic of entanglement, I am very optimistic that Eye_in_the_Sky will be able to help us gain a better understanding.

 

[TheDonk]

Thanks to both Eye_In_The_Sky and to alexepascual. I have a relatively good understanding of math and bad in QM. I've taken a course on linear algebra, and I understand at least the basics of vector calculus. That's about the extent of my math knowledge. As for QM I've only heard the hype. I've seen the "possibilities" on tv and I've read some stuff. Unfortunately I don't know what superposition or tensors are but I'm going to relook into them because I tried to understand them a couple years ago.

Eye_in_the_Sky, your explanation helped, tho I'm still confused.

I suspect though, that a collision of two particles may not be the simplest example to study how two particles can become entangled. Wouldn't spin entanglement be easier to understand?

So certain properties of two particles become entangled? To properly explain 2 entangled particles, it isn't enough to just say they are entangled but you would need to say which properties are entangled. Is this right? What are all the properties that can be entangled? Is there anything else needed to explain how to particles are entangled? I guess these questions are off topic...
Maybe someone should explain how the entanglement of the spin of two particles would happen unless it's very similar to the collision explanation. What properties are entangled from the collision entanglement?

 

[alexepascual]

I think it would be correct to say that some property (observable) of the particle is entangled with that same property or another of the other particle, but maybe Eye can correct me.
In the case of the collision, position and momentum become entangled. In Eye's example, if you find one particle to have certain momentum, the momentum of the other particle has to be per force the opposite. You could also draw conclusions about the other particle's position.
In the case of spins, if you have two hydrogen atoms, each has only one electron, and when you put them in a magnetic field, the spin will take an orientation up or down (with respect to the vertical magnetic field).To be more precise, the spin of each atom will be both up and down at the same time (which is one of the main characteristics of quantum systems). This is called a superposition of states.
If you bring both atoms together, they'll form a molecule. But for those alternatives in which both spins are up or both spins are down, it will be impossible to form a molecule because of Pauli's exclusion principle. So, I guess if you were shooting these atoms towards each other, some would "stick" and some would bounce . About the ones that bounce you can say that their spin is mostly pointing in the same direction while you can be sure that those that stuck to form a molecule have their spins pointing in opposite directions. This relationship between the spins is what entanglement is. Now, you can pull the atoms apart and that relationship (if one is up the other is down) will persist, even if the atoms are taken appart a long distance. When I say "one is up, the other one is down" don't take me wrong. Actually they are both in a superposition of "up" and "down". It is just that when you measure spin on one, at that point you collapse the wave function and one of the two states "up" or "down" becomes reality. If you find one atom to be "up" the other one will be down. In all this discussion we are considering only the spin of the electron in each atom. There are other kinds of spin for the atom but they can be ignored. (at least for a simple treatment?). The nice thing about spin states is that they have only two values (up or down). Momentum and position though are continuous variables, which makes the analysis much more complicated.
I said that a particle can be in different states at the same time which are "superposed". That superposition is represented in a vector space where each dimension represents each of the "base states" that make up the superposition. This vector space is called a Hilbert space. The compuond state is represented by a vector in Hilbert state, and how much of each base state goes into the superposition is represented by the magnitude of the "components" of the vector. (the projection of the vector on each of the base vectors). A Hilbert space can have infinite dimmensions, which is always the case for continuous variables.
I suggest again that you look (maybe google?) for some tutorials on quantum mechanics. You need to learn these things if you want to understand entanglement in some depth. The concept of Hilbert space (also called "state space" is easier to understand when considering spin, because for one electron or proton, it is just a two-dimensional space.
As you are working with vectors, you use matrices to manipulate these vectors, and that's where you need to use linear algebra. You should also try to learn the "Dirac notation". It is not too hard and it is fun. You may be able to find some tutorial on it. Oh! now that I remember, "Wikipedia" has a lot of info on quantum mechanics. Do a search in google for Quantum + Wikipedia and I think you'll find it.

 

[Mike2]

If you bring both atoms together, they'll form a molecule. But for those alternatives in which both spins are up or both spins are down, it will be impossible to form a molecule because of Pauli's exclusion principle. So, I guess if you were shooting these atoms towards each other, some would "stick" and some would bounce . About the ones that bounce you can say that their spin is mostly pointing in the same direction while you can be sure that those that stuck to form a molecule have their spins pointing in opposite directions. This relationship between the spins is what entanglement is. Now, you can pull the atoms apart and that relationship (if one is up the other is down) will persist, even if the atoms are taken appart a long distance. When I say "one is up, the other one is down" don't take me wrong. Actually they are both in a superposition of "up" and "down". It is just that when you measure spin on one, at that point you collapse the wave function and one of the two states "up" or "down" becomes reality. If you find one atom to be "up" the other one will be down.

Once they are entangled, can you force the spin of one electron to be up so that the distant electron's spin must be down? That would create instant communication, right?

 

[Eye_in_the_Sky]

Concerning my earlier post (#16), two points of clarification are warranted.

First, regarding what I wrote:

... after the particles have gone "bump" and have flown well apart, the wavefunction of the joint system will involve a superposition of the various angles of deflection resulting from each of the possible distances between the two lines of flight consistent with the spread of each particle's initial wavefunction in the xy-plane.

This is definitely an oversimplification. In particular, from this simplification, it may appear that the resulting quantum state is merely given by a quantum superposition of the possible classical trajectories. But this is surely not the case! [... However, it is worth noting that for an inverse-square law of force between the two particles, the differential scattering cross section, dσ/dΩ, calculated classically happens to coincide precisely with the quantum-mechanical one (e.g. Rutherford scattering).]

And secondly, the following point must also be clarified:

... with regards to the "bump" itself, there is nothing really special about it.

... there is nothing really 'special' about the "bump" itself.

These statements are made only with respect to the phenomenon of "entanglement". On the other hand (as indicated above), the interaction itself is, of course, quantum mechanical – and in that respect, there is certainly something 'special' about the "bump".

 

[alexepascual]

Mike:
The spins are entangled as far as what you are going to find if you measure them on both ends. Once you force one spin into another direction, you lost your correlations. As far as I know, no communication is possible using entanglement.

 

[Mike2]

Mike:
The spins are entangled as far as what you are going to find if you measure them on both ends. Once you force one spin into another direction, you lost your correlations. As far as I know, no communication is possible using entanglement.

Are you saying that forcing the spin into a particular state is the same as measuring that state? Or is there just a greater probability of being in a state with an applied force as opposed to knowing for certain after measuring the spin?

 

[alexepascual]

As far as I know, measurement is supposed to tell you something about the state of the particle before you influence it by applying any force which might change the state. If you change the state, then you don't know what it was before. If you are going to measure spin, you make the particle go through a Stern-Gerlach apparatus. The Stern-Gerlach apparatus does apply a force to the particle but this force does not change the spin. It is just that those particles with spin "up" go thorugh one channel and those with spin "down" go thorugh the other channel. Typically, you know that the particle went through a certain channel by having it strike some kind of detector. When the particle hits the detector, the state is destroyed. But at least you know what it was just before detection,(or during detection?) which is what you where looking for.
I think what I have just said makes a little more clear the issue of applying a force to the state to change it. (you don't want to do that). But on the other hand I have to accept that it is a very imprecise description. For instance, when you measure, you don't find what the state really was before measurement, but in reality you collapse the wave function and find the particle to be in one of the possible states in the superposition.
I think it was believed years ago that when you make a measurement of a quantum state you usually get a result that is kind of random because the "observer" is influencing the thing he is measuring. But I think today it is believed that it is not because any kind of influence that you get a random result. There is some built-in randomness in the process of measurement.
I would also like to mention that there is something called "the measurement problem", which in the view of many, has not been satisfactorily solved. So, some of the questions you may ask may not have a definitive answer yet.
I understand this may sound confusing and probably I have not explained it clearly. But I hope it helps a little.

 

[Mike2]

As far as I know, measurement is supposed to tell you something about the state of the particle before you influence it by applying any force which might change the state. If you change the state, then you don't know what it was before. If you are going to measure spin, you make the particle go through a Stern-Gerlach apparatus. The Stern-Gerlach apparatus does apply a force to the particle but this force does not change the spin. It is just that those particles with spin "up" go thorugh one channel and those with spin "down" go thorugh the other channel. Typically, you know that the particle went through a certain channel by having it strike some kind of detector. When the particle hits the detector, the state is destroyed. But at least you know what it was just before detection,(or during detection?) which is what you where looking for.

Yes, all honest conversation helps.

I quess what I was getting at is not to actually measure the spin, but only to influence the probabilities with a force - a force not so strong as to make certain the spin after the force is applied, but only strong enough to influence the probability of finding it in a desired state if a measurement were to be done. The communication would be for us to apply a force proportional to the message (e.g. an audio signal) and the other side would actually do the measuring. Is this possible? Or does any interaction at all on our side, whether measured or not, destroy the entanglement? IIRC entangled atoms must be held in isolation in order to be reliable. Entanglement is destroyed when one side interacts with the environment. Is this because the environment is random? Does this still hold if the "environment" is a subtle known force?

 

[selfAdjoint]

I don't know what a force strong enough to affect the probability of a spin but too weak to change the spin would be in QM. Spin (around a given axis) only comes in a discrete set of states, so you either leave it in the state it is, that is, you don't interact with it, or less you influence it and then you are operating on the spin state with some operator and the state goes into some set of discrete eigenvalues. It looks to me to be all or nothing.

And therefore yes, if you truly interact with either entangled particle, you collapse the entangled state. Anything that finds out what the spin state of one particle is, disentangles the other particle, if it is still entangled. What you don't know is whether your measured spin of this particle was determined by a prior measurement of the other or not.

 

[CharlesP]

Experiment

I am primarily an experimentalist, and although I have been through the formal courses and mathematics of quantum mechanics it sometimes seems more like a ceremony than any aid to conceptualizing. I found the pauli spin matrices most frustrating. To satisfy my conceptualizing one must describe the experiment in great detail. The literature is generally highly abbreviated.
When a hydrogen molecule is formed did a previous wave function collapse to form the paired electrons?
In a laser beam are the photons entangled?
In the Bell experiment he chose angles that were not 0 or 90 degrees thus confusing me beyond help. Isn't there a simpler experiment out now with simpler equations?
I have a real problem with these Alice and Bob experiments because none of the instruments in my lab are named Alice or Bob.
I have found it very hard to corner an expert and ask questions.

 

[Mike2]

I don't know what a force strong enough to affect the probability of a spin but too weak to change the spin would be in QM. Spin (around a given axis) only comes in a discrete set of states, so you either leave it in the state it is, that is, you don't interact with it, or less you influence it and then you are operating on the spin state with some operator and the state goes into some set of discrete eigenvalues. It looks to me to be all or nothing.

And therefore yes, if you truly interact with either entangled particle, you collapse the entangled state. Anything that finds out what the spin state of one particle is, disentangles the other particle, if it is still entangled. What you don't know is whether your measured spin of this particle was determined by a prior measurement of the other or not.

The electromagnetic force is governed by interaction with the photon. For a weak enough magnetic field, some electrons will interact with the photons of the magnetic field, and some will not. And for a series of entangles pairs, we would never know on our end which electron spins were effected by the magnetic field photons and which were not. We would only know that on the average more of them are affected with a stronger magnetic field than with a weaker magnetic field. However, if the pairs remain dependent on the electron spins on our side because they are entangle, then a measurement on their side would reveal and average affected by the magnetic field on our side, right?

I guess the question is whether you can have more than two particles involved with entanglement. If the two hydrogen atoms are entangeled, can our electron become entangled with a magnetic field photon (simple because it interacted) without destroying the previous entanglement? How then are many particles entangled if not all at once? I'm assuming entanglement=interaction.

Or is it that we simply cannot change the random nature of the electron spins on the other side? Is it that we can only know what their spin is by examining ours?

 

[Eye_in_the_Sky]

some responses

I suspect though, that a collision of two particles may not be the simplest example to study how two particles can become entangled. Wouldn't spin entanglement be easier to understand?

I don't know if the spin perspective makes it any easier to understand "how" the particles become entangled; but the spin perspective certainly presents some conceptual advantages. It was Bohm, in 1951, who recast the EPR scenario in just such terms. Then, in 1964, with the Bohmian version in mind, Bell discovered his famous inequality.

So, think of two spin-1/2 particles flying off in opposite directions such that the spin state of the joint system is given by

|ψ_sing> = (1/√2)(|+>|-> – |->|+>) .

Notice that I haven't written the axis with respect to which the spin components |±> are specified. That's because it doesn't matter! It comes out the same no matter what. Go ahead check it out:

|+>_z|->_z – |->_z|+>_z = |+>_x|->_x – |->_x|+>_x
= |+>_y|->_y – |->_y|+>_y .

That's the beauty of the so-called "singlet" state, |ψ_sing>.

You can immediately see what this means in terms of a spin measurement of just one of the particles relative to any given axis n. Let's say we measure the spin of the first particle, so that the observable for the joint system is

S_n x 1 ,

where "x" denotes "tensor product".

Then, the eigenprojectors corresponding to each of the two possible outcomes are:

P₁^n,+ = (|+><+|)_n x 1 ,

P₁^n,- = (|-><-|)_n x 1 .

Now, project |ψ_sing> (and then normalize) to get the resulting state of the joint system for each of the two possible results in this measurement of particle 1:

particle 1 is "+" → 'new' joint state is: |+>_n|->_n ,

particle 1 is "-" → 'new' joint state is: |->_n|+>_n .

Again, this holds for a spin-component measurement along any given axis n.
______________

Once they are entangled, can you force the spin of one electron to be up so that the distant electron's spin must be down? That would create instant communication, right?

Note that in a spin measurement of the above kind, what we have in mind is a Stern-Gerlach device (or the equivalent). For such a physical arrangement, there is no "forcing" of spin to be in any particular direction. However, there is "forcing" of the particle to move either "up" or "down" spatially in relation to the axis n in a manner which correlates with spin. Thus, by detecting the presence of the particle – say particle 1 – in either of these "up" or "down" tracks, a measurement corresponding to the projector P₁^n,+ or P₁^n,- (respectively) has been performed.

Note, furthermore, that the interaction of particle 1 with a Stern-Gerlach device has no effect on particle 2. Although particle 1 is deflected from its original line flight, particle 2 will not show any such deflection. Nevertheless, if particle 1 is detected in the upper track, then its state is |+>_n, and particle 2 is then necessarily in the state |->_n. Similarly, if particle 1 is detected in the lower track, then its state is |->_n, and particle 2 is then necessarily in the state |+>_n.

Now, let's get to your first question, Mike2.

Once they are entangled, can you force the spin of one electron to be up so that the distant electron's spin must be down?

By "forcing", it appears to me that you mean some kind of apparatus which will, for example, leave the |+> as it is, but cause the |-> to become a |+>. Can we do this? Sure! ... why not?

So, let's do this to particle 1, while it is jointly with particle 2 in the |ψ_sing> state. We then get

(1/√2)(|+>|-> – |->|+>) → (1/√2)|+>(|-> – |+>) .

Do you see what's going on? Here, we are acting directly upon the "spin" of particle 1 to modify it. This is similar to what happens in the Stern-Gerlach scenario, except there we were acting directly upon the "position" of particle 1. In both cases, the property which we 'modify' with regard to particle 1 has no effect whatsoever on the corresponding property of particle 2. To think otherwise is to misconstrue the phenomenon of "entanglement".

Now, you can see this quite clearly by considering the form of the Hamiltonian for the joint system in such a process:

H_total = (H₁ + H_mod) x H₂ ,

where H_k is the 'free' Hamiltonian for particle k, and H_mod is the Hamiltonian for the interaction which modifies the status of particle 1. As you can see, the time evolution for the two particles is completely decoupled.

And now, let's get to your second question:

That would create instant communication, right?

Indeed, if the "entanglement" phenomenon were such that a direct 'manipulation' of some property particle 1 would induce an (immediate) corresponding change in some property of particle 2, then yes that would be a means for superluminal communication. However, in the above example, we saw that the change "forced" upon particle 1 had no effect upon particle 2.

Nevertheless, one may still wish to contend that somehow, by some as yet unidentified quantum-mechanical effect, perhaps superluminal signaling could be achieved. But no! ... In the late 1970's Eberhard proved that "Quantum nonlocality" does not permit superluminal signaling.
______________

Eye_in_the_Sky, your explanation helped, tho I'm still confused.

So certain properties of two particles become entangled? To properly explain 2 entangled particles, it isn't enough to just say they are entangled but you would need to say which properties are entangled. Is this right? What are all the properties that can be entangled? Is there anything else needed to explain how to particles are entangled?

Yes, certain properties (and in general, any dynamical properties) of two particles can become entangled. In a complete description of the entanglement, we must not only specify which properties have become entangled, but also in what manner. If we can write down the quantum state for the joint system, then the description is complete (... least from the quantum-mechanical perspective).

 

[alexepascual]

Eye_in_the_sky:
Thanks a lot for your detailed post. I just printed it out and it'll take me a few days to go over it. (I have final exams soon and not much time for this)
As soon as I have read and understood (or failed to understand) everything you write I'll respond to your post. Thanks again.
Mike:
I understand what you want to do is to communicate using entanglement. As far as I know, this has been proven not to be possible. The correlations present in entangled particles are "set" at the time the particles are interacting with each other, before they separate. Once they separate, those correlations persist and they reflect their past condition when they were together. If you make any changes to one, that will not affect the other. Not only that, but you will loose your correlations. If you think that the mere act of destroying the correlations can be used to communicate, I think it could be easily proven that that is not the case. With respect to instantaneous communication, remember that according to special relativity, simultaneity (did I spell it wrong?) is not something that can be defined. Events will look simultaneous in one frame of reference while they will appear at different times in another frame. Not only that, their order in time, if they are space-related, could be reversed depending on the frame of refference.
So I think a causality argument could also be used against the possibility of "instantaneous communication"
About changing the state on one side: let me give you a simple classical example: If we have a set of two cards, one has a 1 written on it and the other one has a 0, and we give them to two different peaple that go to different cities (without knowing what their cards are). We know that when they look at their cards, if the first one has a 0 on it, the other one will have a 1 for sure. That is if nobody changed them. If you have someone changing the zero into a one, then the original correlations don't hold, and, what is more important, the other card didn't magically change to keep the correlation. I know this example is not totally appropriate because is classical (superposition is missing) but except for that, I still think it illustrates this issue very well and the argument can still be used for a quantum system.

 

[TheDonk]

alexepascual, I agree with everything you said accept this line.

...I think a causality argument could also be used against the possibility of "instantaneous communication"

Wouldn't instantaneous communication prove that one object isn't causing the other to change at all? Wouldn't it mean that they ARE the same object? It would be like looking at two sides of the same coin. One object (or what we thought was it's own object) is in a different location than the other, but we would now have shown that location has nothing to do with identity.

 

[alexepascual]

TheDonk:
I like the fact that you try to see things from a diffetrent angle. I am the same way. But I have some difficulty with your idea.
If we were only talking about two entangled particles of the same type, then your idea might make some sense and it would deserve being explored further. On the other hand, remember that what is entangled is not the particles themselves but properties of the particles. Also consider the things that have entangled properties do not have to be of the same type. How would you apply your reasoning in that case?
On the other hand, about my comment on a causality argument, someone could reject it on the grounds that there is no reason to exclude the possibility of a violation of causality. But it happens that on a macroscopic scale we have a definite direction in which time "runs" (that direction in which entropy increases). So maybe a violation of causality in a macroscopic scale is not possible.
Think of this: You invent this cute machine that allows you to send instantaneous messages. You send your partner experimentalist to a star a good distance from earth. Then you send a message, which in your frame of reference is received "instantaneously". I another person's frame of reference (someone on a spaceship moving at a great speed in a certain direction) the reception of the message happens before it was sent.
Does this violate causality? Well, thinking again about it maybe not, because if the events are "space related" none of them can be considered to be a cause of the other.
Changing the subject: did you have a chance to look at wikipedia?

 

[Eye_in_the_Sky]

whoops!

There is a problem with some of the things I wrote in an earlier post of this thread.

Back in post #29, I wrote:

By "forcing", it appears to me that you mean some kind of apparatus which will, for example, leave the |+> as it is, but cause the |-> to become a |+>. Can we do this? Sure! ... why not?

The said process, as seen from within the Hilbert space of that particle, is clearly non-unitary. Nevertheless, there must be some physical arrangement which can bring it about ... but I am not precisely sure what it is, nor how to represent it mathematically.

Furthermore, the claim I made that in such a process we would get

(1/√2)(|+>|-> – |->|+>) → (1/√2)|+>(|-> – |+>)

... is definitely wrong! (... because the final state shows a preferred direction which can be identified on the "particle-2 end".)

Moreover, to say that such process is describable by a Hamiltonian such as

H_total = (H₁ + H_mod) x H₂ ,

where H_k is the 'free' Hamiltonian for particle k, and H_mod is the Hamiltonian for the interaction which modifies the status of particle 1.

... is also wrong! (... because such a Hamiltonian implies that the said process, as seen from within the Hilbert space of particle 1, is unitary.)

Nonetheless, the 'spirit' of my answer still stands. It is just as alexepascual puts it at the end of post #30 (note, I have inserted boldface for emphasis):

About changing the state on one side: let me give you a simple classical example: If we have a set of two cards, one has a 1 written on it and the other one has a 0, and we give them to two different peaple that go to different cities (without knowing what their cards are). We know that when they look at their cards, if the first one has a 0 on it, the other one will have a 1 for sure. That is if nobody changed them. If you have someone changing the zero into a one, then the original correlations don't hold, and, what is more important, the other card didn't magically change to keep the correlation. I know this example is not totally appropriate because is classical (superposition is missing) but except for that, I still think it illustrates this issue very well and the argument can still be used for a quantum system.

 

[TheDonk]

If we were only talking about two entangled particles of the same type, then your idea might make some sense and it would deserve being explored further. On the other hand, remember that what is entangled is not the particles themselves but properties of the particles. Also consider the things that have entangled properties do not have to be of the same type. How would you apply your reasoning in that case?

I agree that this reasoning would point towards the entangled objects not being the same object but who's to say that the properties are not objects of some type? I think it could still work either way... maybe not tho, because of the next thing you said:

Think of this: You invent this cute machine that allows you to send instantaneous messages. You send your partner experimentalist to a star a good distance from earth. Then you send a message, which in your frame of reference is received "instantaneously". I another person's frame of reference (someone on a spaceship moving at a great speed in a certain direction) the reception of the message happens before it was sent.
Does this violate causality? Well, thinking again about it maybe not, because if the events are "space related" none of them can be considered to be a cause of the other.

Let's say we "connect" two objects for instantaneous communication. Then one person flies really fast away towards another star. Unless the people come back to the same frame of reference, there is no agreement on who is older than who. I may be wrong but each person would be able to say they are older than the other person. So if one person starts communicating when will the other person get the info? I don't think they could decide on what instantaneous is, could they? I think we need someone who knows special relativity well to answer this. But if I'm right, this will only enforce the point I quoted you on above.

Back to the topic of what causes entanglement. I've seen some explanations but am having big problems learning a few things that I need to. What is the bare minimum concepts I need to know to understand an explanation of the cause of entanglement? Superposition? Wave functions? Do I need to understand the quantum operators? Better understand Hilbert space? All of these I only have a vague idea in. I thought I knew everything to know about Hilbert space, but now I'm not sure.

Thanks for the info so far.

 

[alexepascual]

The Donk:
You definitely need to understand about superposition of states. Also look into the EPR experiment but in the version where they use the spin of particles (not position and momentum).
It may also help to learn a little more about the special theory of relativity. The twin paradox is not related to the topic of our discussion. But you may want to look into instanteneity and get a good understanding of the Lorentz transformations. Different frames of reference refer to observers moving at different velocities.
Again: take a look at Wikipedia
-Alex-

Eye:
Your posts require a lot more thinking. I'll reply in about three weeks. (after classes are over). Thanks again.

 

[Eye_in_the_Sky]

What is the bare minimum concepts I need to know to understand ... entanglement? Superposition? Wave functions? Do I need to understand the quantum operators?

As a bare minimum for a good understanding of "entanglement", I think you will need the following:

1) a "2-dimension vector space" with "inner product";

2) an "orthonormal basis" on that space;

3) a "tensor product" of two such spaces;

4) the "singlet state" in the resulting tensor-product space;

5) "linear operators" on the resulting tensor-product space;

6) the "Projection Postulate" of Quantum Mechanics.

 

[Eye_in_the_Sky]

When a hydrogen molecule is formed did a previous wave function collapse to form the paired electrons?

If we imagine looking at the Schrödinger time-evolution for a pair of hydrogen atoms coming together, we would find that the resulting state shows a superposition of two general scenarios:

(i) the two atoms 'bounced off one another' and no molecule was formed;

(ii) the two atoms 'joined together' and formed an H₂-molecule.

A subsequent "measurement" of some kind is then required to establish which scenario prevails, and (in an established terminology) that measurement then 'collapses' the wavefunction.

This is analogous to what takes place when a particle is incident upon a step potential. In general, an incident wave packet will split up into two wave packets, one corresponding to reflection and another to transmission. A subsequent measurement is then required to 'decide' which scenario prevails.
______________

In a laser beam are the photons entangled?

Here, it sounds like you are alluding to the property of "coherence", which in this context means an extremely large number of photons can (to a very good approximation) be described collectively by the same (single-particle) quantum state.

 

[yanniru]

Well, after reading all these posts, I conclude that no one understands entanglement.

I have read elsewhere of two explanations that make some sense. Particles in superfluids are entangled because their wavefunctions overlap and are in quantum coherence, like photons in a laser beam. Essentially they act like a single particle.

And the second is like unto it: the EPR paradox is explained by overlapping wavefunctions with the conceptual addition of the extra dimensions of string theory.
The entangled particles were made in ten dimensions at a point in space and time. Six of these dimensions compactify and continue to keep the two particles in contact as they separate in space by a thread of the compactified dimension. That is, their wave functions overlap in the compactified dimensions.

Of course I am not sure if any of that is true. What I do understand is that when physicists cannot explain some phenomenon, they give it a name and go on with life. So far entanglement is one of the things that they still cannot explain. Thay can predict, but they cannot explain.

Richard

 

[TheDonk]

I thought wave functions had no cut-off value at a certain distance and spanned the whole universe... If so, when are they combined? Unless there is degrees of entanglement and everything is slightly entangled. I'm quite sure that isn't the case.
Maybe I'm wrong about wave functions... if not, could you explain?

 

[alexepascual]

Richard:
Your version of entanglement using the compactified dimensions of string theory is interesting. Could you give us your source?
I hope this is something someone has worked out to the point of making the idea feaseable.
Thanks,
-Alex-

 

[yanniru]

Sorry. I am the source. Although when I posted it once before on this forum, someone replied that he had also thought of the same thing.

I am not trained to make the idea feasible. Perhaps you are. I take that explanation as evidence that the extra dimensions exist. Not sure why no bono fide string theorist has pursued it.

 

[Louis Cypher]

Qm Entanglement



--------------------------------------------------------------------------------

Posted this on another forum and they just deleted it and wouldn't respond to my questions so I'm assuming it's nonsense, what I wanted too know though is why it's nonsense, to help me learn a bit more about qm; after reading an article on qbits and how they can use entanglement to check parity in a different way so that q information doesn't become lost by observation I had the thought if we entangle a photon and then observe the two photons entangled state a computer could take this information via observing another entangle photon, and do it computationally to check the quantum or just use error bit from then on any information that computer and the other chose to send quantumly would instantaneously be transfereed wireless without broadband information exchange at insatantaneous speed; the applications of the idea are endles, why is this wrong, please answer?!? I'm dying to know.

thanks

--------------------------------------------------------------------------------
Last edited by Louis Cypher : Today at 03:45 PM.

 

[Louis Cypher]

finding a way to keep the photon hanging around might be a little tricky but then, you could send off for a new photon every once in a wile which could equally be sent by being entangled with the original; obviously a feed back loop from quantum to computer would need to recode information to be transmitted to re entangle the photon after this, but qbit parity check would maintain integrity? Any responses appreciated, even if you do tell me I'm an idiot?

 

[alexepascual]

Sorry. I am the source. Although when I posted it once before on this forum, someone replied that he had also thought of the same thing.
I am not trained to make the idea feasible. Perhaps you are. I take that explanation as evidence that the extra dimensions exist. Not sure why no bono fide string theorist has pursued it.

Richard:
So far I have found the "many worlds" interpretation of quantum mechanics as the most acceptable and when I think about quantum phenomena I think in terms of this interpretation. I have only read popularization articles and books about string theory. Since I read these articles, I have wondered if there is any connection between the extra dimmensions of string theory and the branches of the many worlds interpretation.
I thought you had read some article explaining entanglement in terms of the string theory. I think if you believe your scheme might work, the best for you is to continue learning about QM and string theory until you can prove yourself how these extra dimmensions account for entanglement or that they don't.

instantaneously be transfereed wireless without broadband information exchange at insatantaneous speed; the applications of the idea are endles, why is this wrong, please answer?!? I'm dying to know.

Louis:
Most physicists agree that it is not possible to send information "instantaneously" using entanglement. Of course the applications would be many if you could do this. But it appears you can't. If you think most physicists are wrong, then, I think you should study the subject deep enough so that you can put your ideas in mathematical form.
If you just want to know why your idea is wrong, you can do a Google search for: entanglement + causality or "teleportation".
Other place where you can search about these topics is in Wikipedia. You can actually learn a lot about QM there.
If you wonder why someone can't just give you a detailed explanation. I think it is because the effort it woud take to explain it to you is much, much, greater than the effort you put in formulating your hypothesis in the first place.

Eye_in_the_sky:
I'll be reading your posts in the comming days (done with finals now) . I promise I'll give you a response soon.

TheDonk:
Where are you?

 

[Louis Cypher]

would apreciate a reply before end of week

Any ideas guys?
see previous post

 

[Kea]

entanglement

Elsewhere I posted this:

A categorical semantics of quantum protocols
S. Abramsky and B.Coecke
http://users.ox.ac.uk/~mert1596/QUOXIC/talks/samson.pdf

Y. is no doubt correct in saying that no one understands it, but
this is a pretty good start.

 

[TheDonk]

I looked into superposition and the EPR experiment and now understand what both of them are. (I already had an idea what they were)

But back to my original thread topic question. How do particles become entangled? Let's use spin for the example. When do two electrons that aren't entangled go together and become entangled? What needs to happen for the electrons to enangle? Shouldn't this be easy to answer? It seems like it would be simple to answer this in laymens terms and without math, tho any answer would be appreciated.

Could it be that almost everything entangles particles? Maybe most measurements entangle the particle and the particle measuring it? Can two different particle types (ie electron and photon) be entangled?

Could every single particle be entangled with a pair and the only way to untangle it is to entangle it with something else? But what would happen to the original? Maybe it entangles with the other left over particle. I obviously just made this up and have no evidence at all but it sounds cool. Would this be hard to disprove?

Louis Cypher:
Your idea makes sense, I think, but only if you can send info instantaneously, which we don't know how to do. What you're talking about is a little bit off topic. (tho I'm bad for going off topic too)

 

[Mike2]

I looked into superposition and the EPR experiment and now understand what both of them are. (I already had an idea what they were)

But back to my original thread topic question. How do particles become entangled? Let's use spin for the example. When do two electrons that aren't entangled go together and become entangled? What needs to happen for the electrons to enangle? Shouldn't this be easy to answer? It seems like it would be simple to answer this in laymens terms and without math, tho any answer would be appreciated.

Could it be that almost everything entangles particles? Maybe most measurements entangle the particle and the particle measuring it? Can two different particle types (ie electron and photon) be entangled?

Could every single particle be entangled with a pair and the only way to untangle it is to entangle it with something else? But what would happen to the original? Maybe it entangles with the other left over particle. I obviously just made this up and have no evidence at all but it sounds cool. Would this be hard to disprove?

Obviously if particles were not entangled and then become entangled, then they become entangled when they start to effect one another. This means that at the point that a photon goes from one to the other, then information from one goes to the other so that electron spins must line up accordingly. I suppose that even the most distant particles would eventually transfer a photon between them and become entangled. But distant atoms could also remain hidden from one another for a long time.

 

[TheDonk]

Obviously if particles were not entangled and then become entangled, then they become entangled when they start to effect one another. This means that at the point that a photon goes from one to the other, then information from one goes to the other so that electron spins must line up accordingly. I suppose that even the most distant particles would eventually transfer a photon between them and become entangled. But distant atoms could also remain hidden from one another for a long time.

Thanks for the response Mike. I'm not too familiar with QM yet so I still don't know some of these obvious things. You said they get entangled when they effect each other. In what ways can this happen. Is sending a photon the only way? Does sending a photon always entangle the electron that absorbs it? Can you give me an example of how a different property other than spin can become entangled?

In every atom that has an even amount of electrons, are all the electron pairs entangled? Id that what defines them as a pair in the first place?

 

[Louis Cypher]

reply

Thanks that's the sort of answer I was looking for, the have used photon entanglement to exchange info though haven't they or am I mistaken?

Quantum encription bob and alice thingy, I'm not talking about teleprtation there just firing the light along a wire or at another computer as in the Bob and Alice experiment.

Just starting a couple of A level style maths courses before I go on to the Degree, it's a pain it means I have to do eight years of study to go with the foundation year I've allready done, but then no one ever claimed physics was easy. look at my post as a reflection of quantum encryption not telportation then; ok if entanglement doesn't teleport it at least qould mean we could us light instead of electricity to transmit signals, and in turn a device could interpret this much like a modem and encode back to an electronic signal, dial up users would be chuffed, and we would no longer have need of dial up, everyone could use broadband and light is better than electricity for sending signals plus it would be very safe from hackers compared to the internet now.

Like I say just thinking

ideas are the cornerstone of science, thanks for replying, and for refraining from calling me an idiot