Basic question about entanglement

[WendyE]

I'm only just beginning to really learn about entanglement, and I just have some questions about what entanglement actually means.

Let's say we have one electron and put it in a magnet field. We find out what it's spin was along one axis based on whether a photon is emitted. But now we know with 100% certainty that the electron is now spin up along that axis. That is, if we turn the mag field off and back on without reorienting the field, no photon will be emitted.

Now let's say we have a pair of entangled electrons, meaning their spins are completely opposite along all axis'. Now we separate them. If we put one electron in a magnetic field, and it gives off a photon, then we know we have changed it's state. We know that before the magnetic field was applied, the electron was spin down, and the other electron was spin up along that same axis. But here's my question:

After the measurement, have both electrons flipped over, or just the one we measurered? Did the act of measurement screw up the entanglement?

 

[QuantumBend]

I'm only just beginning to really learn about entanglement, and I just have some questions about what entanglement actually means.

Let's say we have one electron and put it in a magnet field. We find out what it's spin was along one axis based on whether a photon is emitted. But now we know with 100% certainty that the electron is now spin up along that axis. That is, if we turn the mag field off and back on without reorienting the field, no photon will be emitted.

Now let's say we have a pair of entangled electrons, meaning their spins are completely opposite along all axis'. Now we separate them. If we put one electron in a magnetic field, and it gives off a photon, then we know we have changed it's state. We know that before the magnetic field was applied, the electron was spin down, and the other electron was spin up along that same axis. But here's my question:

After the measurement, have both electrons flipped over, or just the one we measurered? Did the act of measurement screw up the entanglement?

Yes, measurings stopped the entangling. They now have 100% probables of spins NEVER NEVER real spins.

 

[WendyE]

"... 100% probabilities of spins, NEVER real spins."
-- point taken

I know I'm missing something, because I don't see what is so weird about entanglement yet. When two electrons are put together, they automatically align themselves so that their spins are opposite. Why is it weird that each individual electron maintains their respective states when they are separated? It would be weird if you could influence the distant electron by something you do to the nearby one, but that doesn't seem to be the case. Am I wrong about that?

 

[QuantumBend]

"... 100% probabilities of spins, NEVER real spins."
-- point taken

I know I'm missing something, because I don't see what is so weird about entanglement yet. When two electrons are put together, they automatically align themselves so that their spins are opposite. Why is it weird that each individual electron maintains their respective states when they are separated? It would be weird if you could influence the distant electron by something you do to the nearby one, but that doesn't seem to be the case. Am I wrong about that?

No you not wrong about that. You not understand SUPERPOSITION - this your problem = I know this.

 

[Ilja]

"... 100% probabilities of spins, NEVER real spins."
-- point taken

I know I'm missing something, because I don't see what is so weird about entanglement yet. When two electrons are put together, they automatically align themselves so that their spins are opposite. Why is it weird that each individual electron maintains their respective states when they are separated? It would be weird if you could influence the distant electron by something you do to the nearby one, but that doesn't seem to be the case. Am I wrong about that?

If you don't see what is so weird, you have to look at Bell's inequalities. Think about how one can manage to win in the http://ilja-schmelzer.de/realism/game.php" .

 

[DrChinese]

I know I'm missing something, because I don't see what is so weird about entanglement yet. When two electrons are put together, they automatically align themselves so that their spins are opposite. Why is it weird that each individual electron maintains their respective states when they are separated? It would be weird if you could influence the distant electron by something you do to the nearby one, but that doesn't seem to be the case. Am I wrong about that?

It is not weird that they are aligned when measured at the same angle settings. Bell noted that this led to inconsistencies at OTHER angle settings. Typically, for photons you look at settings like 60 or 120 degrees (which yield the same results) or other variations. These lead to so-called Bell Inqualities (including CHSH), which cannot be explained by local hidden variable theories.

 

[WendyE]

Ok, I see what's weird now. When you measure the spin of one particle, the other automatically collapses into the corresponding negative spin. But this can't be explained by saying that both particles came out predisposed to behave that way. Bell's theorem proves otherwise. (I'm still trying to convince myself that there is no way that the particles could be preprogrammed to behave in a way that appears to violate Bell's theorem, but I don't have much sophistication, so I'll take your word for it).

My next question isn't so easy. What's the explanation for this? The thing that occurs to me without any mathematical rigor is that maybe electons move in time differently. Like, maybe they DON'T move in time. Quantum mechanics says that there is a probability that an electron can pop up anywhere in the universe. Even if it won't ever actually happen because the probability is too small, doesn't this concept violate relativity too? And according to quantum, the particle is in a state of being everywhere at once with probabilities defined by it's wavefunction. So is the act of moving it according to the space-time we're conscious of just changing it's wavefunction description with respect to the macroscopic world? It moves it in xyz, but somehow it doesn't leave the first particle. The first particle's wavefunction becomes part of the second particle's wavefunction description. So the second particle is both places at once. Are they suspended in time? Maybe they just don't exist in time, and that explains how they can be everywhere at once. But they can obviously react with time evolving systems, which gives them the appearance of evolving in time.

Is any of this supported? Or is it complete garbage?

 

[Phrak]

Ok, I see what's weird now. When you measure the spin of one particle, the other automatically collapses into the corresponding negative spin.

Maybe.

After the spin of one particle, prepared in a spin singlet, is observed, observation of the other particle along the same direction will yield the opposite spin.

The sublte distinction here is between 'what can be observed', or 'what is knownable' as opposed to the stronger, but unsubstanciated 'what is'.

 

[edguy99]

"... 100% probabilities of spins, NEVER real spins."
-- point taken

I know I'm missing something, because I don't see what is so weird about entanglement yet. When two electrons are put together, they automatically align themselves so that their spins are opposite. Why is it weird that each individual electron maintains their respective states when they are separated? It would be weird if you could influence the distant electron by something you do to the nearby one, but that doesn't seem to be the case. Am I wrong about that?

Same question for photons, if you generate 2 photons in such a way as they are entangled, why is it not expected that when measured they would both be the same? I miss what's weird about this?

 

[WendyE]

Same question for photons, if you generate 2 photons in such a way as they are entangled, why is it not expected that when measured they would both be the same? I miss what's weird about this?

I kind of understand the reasoning why entanglement is weird now. To explain, I'll start by assuming it's NOT weird, and explain what we expect to find in this scenario:

Say we've got a bucket load of entangled electrons (a bucket can hold quite a few). We separate the pairs and keep them isolated from the other electrons so the entanglement doesn't get screwed up. Now, let's assume (wrongly, it turns out) that each pair of entangled electrons is predisposed to behave in a certain way given a certain stimulus. That's what people mean when they suggest "hidden variables" in the system. This way of thinking suggests that the math of quantum mechanics while not wrong is not complete. Let's assume this. It certainly makes more sense to our monkey brains to assume this. Einstein assumed it, too, and went to great lengths to prove that the math of quantum mechanics is not complete.

But here's what Bell did with our entangled electrons. He said that if our entangled electrons were predisposed to act the same way under the same stimulus (one opposite the other, actually), then we could do a test to show this. Instead of always measuring the spin along the same axis for both electrons, we will randomly measure the spin about 1 of three axis for each electron. The spin is always either up or down, and it's 50/50 which it'll be as far as the math tells us. But if the electrons are predisposed, then it's predetermined how the spin will turn out if a certain axis measured. Let's say electron #1 is predisposed to have spins up, up, down along the axis' we measure, and so electron #2 is predisposed to have spins down, down, up along the same axis'. We can only measure one of these on each electron in the pair. Let's measure axis 1 on electron 1 and axis 2 on electron 2. We should get (up, down). Notice that the odds of getting an (up, down) or (down, up) pair is greater than the odds of getting (up, up) or (down, down). This will always be the case for our predisposed electrons, regardless of how they are predisposed (that is, electron 1 could be programmed for up, down, up and electron 2 would then be down, up, down). This means that if we do a whole lot of measurements, more than half the time we will get an (up, down) or (down, up) pair. IF the electrons are predisposed to act a certain way given a certain stimulus.

So, this test has been done. And the number of (up, down) or (down, up) pairs is NOT greater than 50%. The electrons are NOT predisposed to act a certain way. That means that before you measure electron #1 along a certain axis, electron #2 had a 50/50 chance of being spin up. After you measure electron #1 though, electron #2 has a 100% chance of being observed with spin opposite that found for electron 1. So, measuring electron #1 appears to have instantly changed something about electron #2. That's what's weird!

 

[DrChinese]

Same question for photons, if you generate 2 photons in such a way as they are entangled, why is it not expected that when measured they would both be the same? I miss what's weird about this?

This WOULD actually be expected if the result is predetermined (i.e. if there were hidden variables. So clearly, that is not the weird part.

The weird part is that at OTHER angles, the results are not as you might expect. A decision on how to measure Alice appears to affect the results at Bob - at least once you correlate them. The outcomes clearly defy normal logic. So that is the issue.

 

[edguy99]

...Instead of always measuring the spin along the same axis for both electrons, we will randomly measure the spin about 1 of three axis for each electron. ...

Thanks, that was a big help. It appears that it is expected that the spin when measured from 3 different axis is expected to be the same on the same electron. I assume it is correct that an electron could be spinning such that it is spinning up on one axis, but down when measured from another axis?

When you say randomly measure the spin, do you mean the 2 people agree that one will measure on x and the 2nd on y, or do they simply pick a direction and risk perhaps both measuring the same axis?

Thanks

 

[DrChinese]

We can only measure one of these on each electron in the pair. Let's measure axis 1 on electron 1 and axis 2 on electron 2. We should get (up, down). Notice that the odds of getting an (up, down) or (down, up) pair is greater than the odds of getting (up, up) or (down, down). This will always be the case for our predisposed electrons, regardless of how they are predisposed (that is, electron 1 could be programmed for up, down, up and electron 2 would then be down, up, down). This means that if we do a whole lot of measurements, more than half the time we will get an (up, down) or (down, up) pair. IF the electrons are predisposed to act a certain way given a certain stimulus.

I do not believe this is accurate as you have described it.

If you look at the x-axis of Alice's electron, the y-axis of Bob's electron can be anything. These are not directly related in any way. However, you CAN measure Bob's electron at other angles than x or y (which are 90 degrees apart). For instance, you can measure at 30 degrees or 60 degrees. Now you have something of a mixture of x and y. It is here, at angles where there is a mixture, that the issues relating to Bell's Theorem arise.

 

[JesseM]

I'll repost an analogy I came up with a while ago to show why the statistics seen in entanglement are "weird", and how Bell's theorem shows they can't be explained by local hidden variables:

Suppose we have a machine that generates pairs of scratch lotto cards, each of which has three boxes that, when scratched, can reveal either a cherry or a lemon. We give one card to Alice and one to Bob, and each scratches only one of the three boxes. When we repeat this many times, we find that whenever they both pick the same box to scratch, they always get opposite results--if Bob scratches box A and finds a cherry, and Alice scratches box A on her card, she's guaranteed to find a lemon.

Classically, we might explain this by supposing that there is definitely either a cherry or a lemon in each box, even though we don't reveal it until we scratch it, and that the machine prints pairs of cards in such a way that the "hidden" fruit in a given box of one card is always the opposite of the hidden fruit in the same box of the other card. If we represent cherries as + and lemons as -, so that a B+ card would represent one where box B's hidden fruit is a cherry, then the classical assumption is that each card's +'s and -'s are the opposite of the other--if the first card was created with hidden fruits A+,B+,C-, then the other card must have been created with the hidden fruits A-,B-,C+.

The problem is that if this were true, it would force you to the conclusion that on those trials where Alice and Bob picked different boxes to scratch, they should find opposite fruits on at least 1/3 of the trials. For example, if we imagine Bob's card has the hidden fruits A+,B-,C+ and Alice's card has the hidden fruits A-,B+,C-, then we can look at each possible way that Alice and Bob can randomly choose different boxes to scratch, and what the results would be:

Bob picks A, Alice picks B: same result (Bob gets a cherry, Alice gets a cherry)

Bob picks A, Alice picks C: opposite results (Bob gets a cherry, Alice gets a lemon)

Bob picks B, Alice picks A: same result (Bob gets a lemon, Alice gets a lemon)

Bob picks B, Alice picks C: same result (Bob gets a lemon, Alice gets a lemon)

Bob picks C, Alice picks A: opposite results (Bob gets a cherry, Alice gets a lemon)

Bob picks C, Alice picks picks B: same result (Bob gets a cherry, Alice gets a cherry)

In this case, you can see that in 1/3 of trials where they pick different boxes, they should get opposite results. You'd get the same answer if you assumed any other preexisting state where there are two fruits of one type and one of the other, like A+,B+,C-/A-,B-,C+ or A+,B-,C-/A-,B+,C+. On the other hand, if you assume a state where each card has the same fruit behind all three boxes, like A+,B+,C+/A-,B-,C-, then of course even if Alice and Bob pick different boxes to scratch they're guaranteed to get opposite fruits with probability 1. So if you imagine that when multiple pairs of cards are generated by the machine, some fraction of pairs are created in inhomogoneous preexisting states like A+,B-,C-/A-,B+,C+ while other pairs are created in homogoneous preexisting states like A+,B+,C+/A-,B-,C-, then the probability of getting opposite fruits when you scratch different boxes should be somewhere between 1/3 and 1. 1/3 is the lower bound, though--even if 100% of all the pairs were created in inhomogoneous preexisting states, it wouldn't make sense for you to get opposite answers in less than 1/3 of trials where you scratch different boxes, provided you assume that each card has such a preexisting state with "hidden fruits" in each box.

But now suppose Alice and Bob look at all the trials where they picked different boxes, and found that they only got opposite fruits 1/4 of the time! That would be the violation of Bell's inequality, and something equivalent actually can happen when you measure the spin of entangled photons along one of three different possible axes. So in this example, it seems we can't resolve the mystery by just assuming the machine creates two cards with definite "hidden fruits" behind each box, such that the two cards always have opposite fruits in a given box.

...and you can modify this example to show some different Bell inequalities, see post #8 of this thread if you're interested.

 

[DrChinese]

I'll repost an analogy I came up with a while ago to show why the statistics seen in entanglement are "weird", and how Bell's theorem shows they can't be explained by local hidden variables: ...

JesseM's anaolgy is good. A quick comment: this applies to certain specific measurement angle settings. These angles vary according to whether you are observing entnagled electrons or entangled photons. He didn't label the settings in his example, but typcially would be for photonsL A=0 degrees, B=120 degrees, C=240 degrees. Note that A, B and C are 120 degrees apart; that is the key. There are a variety of settings that yield similar type results, but not angles do.

 

[WendyE]

I do not believe this is accurate as you have described it.

If you look at the x-axis of Alice's electron, the y-axis of Bob's electron can be anything. These are not directly related in any way. However, you CAN measure Bob's electron at other angles than x or y (which are 90 degrees apart). For instance, you can measure at 30 degrees or 60 degrees. Now you have something of a mixture of x and y. It is here, at angles where there is a mixture, that the issues relating to Bell's Theorem arise.

My description isn't very accurate, I know. I'm still working on figuring out the specifics. I think I have the right general idea. My description doesn't seem all that different than JesseM's, except I actually said some wrong things by putting it in terms of actual spins.

So, let me see if I can understand what is actually going on a little better. Bell's inequality is not always violated when measuring entangled electron spins. It depends on what axis you choose to measure. If you only measure the x, y, and z axis, each separated by 90 degrees, you don't get any funny business. It has to do with the probability of measuring spin up at an angle 90 degrees to the original measurement, given you've already performed the first measurement, I think. Is that right?? So, measuring along 90 degree axis doesn't tell you anything, because it won't violate Bell's inequality by quantum math or by assumption of "hidden variables". I'm going to stop there, and wait to see if this is right before I continue trying to figure this out! Thanks for your comments!

 

[DrChinese]

So, let me see if I can understand what is actually going on a little better. Bell's inequality is not always violated when measuring entangled electron spins. It depends on what axis you choose to measure. If you only measure the x, y, and z axis, each separated by 90 degrees, you don't get any funny business. It has to do with the probability of measuring spin up at an angle 90 degrees to the original measurement, given you've already performed the first measurement, I think. Is that right?? So, measuring along 90 degree axis doesn't tell you anything, because it won't violate Bell's inequality by quantum math or by assumption of "hidden variables". I'm going to stop there, and wait to see if this is right before I continue trying to figure this out! Thanks for your comments!

Exactly! If it had been violated at 90 degrees, that would have been noticed immediately because the math would have jumped right out. As it is, you need to pick specific angles which are inconsistent with the so called "realistic" assumption... also know as hidden variables.

So, the choice of where the x-axis points is arbitrary. There is no absolute UP or LEFT or etc. So we pick an X. We can rotate that X through 360 degrees, a circle of course. Then according to the hidden variable assumption, there was an "answer" at every possible choice of X. (Actually, there would be an infinite number, but for our purposes we can just choose a few angles.) There needs to be a predetermined "answer" at each possible angle so that both entangled particles - when measured at the SAME angle setting - provides the appropriate matching result.

But Bell noticed something funny when he buried deeper into that assumption: the values would not be internally consistent. There would be settings in which 3 values could never match, although 2 alone would. As it happened, QM only postulates the 2 - and not the 3. If there are 3 or more, there is inconsistency. For electrons, you can see the problem if you look at angles like 0, 45 and 90 degrees. The correlation function for electron spin is cos^2(theta/2) so for orientations 90 degrees apart is .5 (which is the same as flipping coins, i.e. none). On the other hand, the correlation for 45 degrees apart is .8536. So the one "in the middle" is too closely correlated to the "outer" ones, which are not correlated at all. That makes no sense, and that is what Bell discovered.

 

[Ilja]

... But this can't be explained by saying that both particles came out predisposed to behave that way. Bell's theorem proves otherwise. ...

My next question isn't so easy. What's the explanation for this? ...The first particle's wavefunction becomes part of the second particle's wavefunction description...
Is any of this supported? Or is it complete garbage?

In entangled states, there is no "first particles wave function" or "second particles wave function". There is only a common wave function psi(q_1,q_2). Thus, this part is garbage.

The only possible explanation (of course, in a certain sense of "explanation", but this sense can be explained) is one which includes some causal FTL influence.

An example (and IMHO the most reasonable one) is given by the pilot wave interpretation.

 

[WendyE]

In entangled states, there is no "first particles wave function" or "second particles wave function". There is only a common wave function psi(q_1,q_2). Thus, this part is garbage.

The only possible explanation (of course, in a certain sense of "explanation", but this sense can be explained) is one which includes some causal FTL influence.

An example (and IMHO the most reasonable one) is given by the pilot wave interpretation.

Oh, right, of course. The entangled state shares a wavefunction. The pilot wave interpretation, ok. I have no idea what that is, but thanks for the lead!

I'm watching a great video series of lectures from iTunesU that introduces entanglement very well. It's from Standford, and is taught by Leonard Suskind. It's really good. He goes slow, and the math is really very easy. It's a great introduction to this topic. It's called "Modern Theoretical Physics - Fall 2006", for anyone who needs to start at the very beginning.