# Bell experiment would somehow prove non-locality and information FTL?

#### heusdens

The famous Bell experiment would somehow proof non-locality and/or traveling of information faster then light.

A very simple explenation of the experiment is this: there is a subatomic event that creates a particle pair going opposite directions. The subatomic event determines the possible outcomes, as for example if one particle has spin up, the other must have spin down (conservation law).
But in the quantum mechanical sense, we don't know which particle has spin up and which has spin down.

So if we examine (observe) one particle and find it has spin down, this the determines the other observation, that the other particle has spin up.
But QM says both particles are in undefined states before observing.

Somehow then the act of observing one particle and indentifying it's spin causes the other particle to behave as determined by the other observation.
The two particles, before detection, can be at very long distance from each other at which no interaction could take place between the two observations, considering the speed of light.

This then somehow gets interpretated as non-locality or faster-then-light travel of information.

But there is a more simple explenation. The state of both particles are already determined when they get created in the experiment and from the physical laws we know one has spin up and one has spin down.
Just that we can't identify which particle has spin up and which has spin down. So, identifying one particle is in fact identifying both particles.
Nothing mysterious. It doesn't involve non-locality or faster-then-light travel of information.

(another way of looking it is this: instead of the unknown spin which gets detected, we could also say we already know which particle has spin up and which has spin down, the only thing we don't know if the spinup particele goes left or right, and likewise wether the spindown particle goes right or left, just that we know they go opposite directions. If we detect the spinup particle to go left, then we for sure we know the spindown partice went right.
In this way of interpreting this QM experiment, we see that there is nothing mysterious about it: no non-locality involved or faster-then-light travel of information.)

PS>
I don't know if the actual experiment involved measuring spin, it could also have been some other conserved quantity, like electric charge, for example the particle pair creation of electron and positron.

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#### jtbell

Mentor
But there is a more simple explenation. The state of both particles are already determined when they get created in the experiment
This is the assumption of "reality" of physical properties before they are measured. Bell's Theorem says that a theory cannot be both "local" and "realistic." You have to give up one or the other, if you accept the validity of Bell's Theorem.

#### heusdens

This is the assumption of "reality" of physical properties before they are measured. Bell's Theorem says that a theory cannot be both "local" and "realistic." You have to give up one or the other, if you accept the validity of Bell's Theorem.
No, it is not. I just changed the description of the unobserved property of the particle from being it's charge to it's direction if flight.
So instead of the two particles being in a superposition of a electron and a positron, it becomes now an electron and a positron in a superposition of two directions.

#### Crosson

It looks like you are discussing the EPR experiment, designed by Einstein as a refutation of QM. Bell's inequality showed that the quantum mechanical predictions of the results of the EPR experiment are incompatible with "local realism". Long after Einstein and Bell, the experiment has been performed and the results are in favor of QM, not local reality.

Here is a description of EPR:

Imagine that there is a pair of (literally) identical twin brothers who are interested in dating a pair of identical twin sisters. The brothers live together, but their dates live seperate lives on opposite sides of town.

Each brother has the same three evening suits, red, white and black. Thus, on any given date the only difference between the two brothers is their suit (possibly the same, as well).

Based on the color of his suit (and nothing else, since the brothers are otherwise identical and the sisters are identical), each brother gets either a slap or a smile from his date.

After many dates, the brothers compare notes:

1) If they wear the same suit, they get the same reaction.

2) Choosing suits at random, half the time the brothers share the same fate (both get slaps or both get smiles) and the other half of the time they recieve different fates.

(***this describes the basic EPR experiment with slap/smile corresponding to spin and the three suits corresponding to the three indepenent directions on which we analyze spin***)

Bell's theorem addresses the question: what selection shceme are the women using that produces the results above? The answers are grim for a local realist, either:

1) There is no sheme, its just a coincedence (unacceptable).

2) The women have non-local correlation i.e. telepathy, pheromones, etc.

Since the 1990s the experiments have been definitive; no physicist doubts the existence of nonlocality.

#### drphysica

Your idea doesn’t support the experiment; it also doesn't explain the collapse of the wave function between entangled particles when they measured. (Why does the wave function collapses when we know through what slit particle went, when other times it behaves as a wave.) There is no simpler explanation to this and your idea suggests the theory of hidden variables, which was disproved long time ago ( see Bell’s inequality). The non-locality is indeed exists but not the idea of FTL travel also there is no information being transferred between entangled states. It is clear that you don't have the background knowledge on quantum mechanics and experimental physics, before you try to explain what is what and how I suggest you do some research on the subject otherwise this kind of discussions are pointless. http://en.wikipedia.org/wiki/EPR_paradox :)

#### FunkyDwarf

I've often thought this way about QM.You have to realise that essentially, as boring and mundane as it sounds, nothing spooky is really happening. Just because you dont know or have not measured the spin or other undetermined property does NOT mean it exists in two at the same time and one determines the other. The particles have a precise spin when the event occurs and remain that way, nothing will change that. However given the 50/50 probability, the outcome is uncertain from a measurement and information point of few. This makes the line between what is 'actually true' aka reality, and what has been measured, rather fuzzy.

Hope that makes sense
-G

#### heusdens

Your idea doesn’t support the experiment; it also doesn't explain the collapse of the wave function between entangled particles when they measured. (Why does the wave function collapses when we know through what slit particle went, when other times it behaves as a wave.) There is no simpler explanation to this and your idea suggests the theory of hidden variables, which was disproved long time ago ( see Bell’s inequality). The non-locality is indeed exists but not the idea of FTL travel also there is no information being transferred between entangled states. It is clear that you don't have the background knowledge on quantum mechanics and experimental physics, before you try to explain what is what and how I suggest you do some research on the subject otherwise this kind of discussions are pointless. http://en.wikipedia.org/wiki/EPR_paradox :)
The observation (measuring the state of the particle) alters the state, which is the same as saying that the wave function collapses.

The question wether - prior to observation - a particle is in a defined state, is something unknowable. Knowing the state of the particle requires an observation and this observation alters the state of the particle.

When we consider the experiment as explained http://en.wikipedia.org/wiki/Bell's_Theorem#Description_of_Bell.27s_theorem
it is obvious that the only factor of interest is not the respective angels of Alice and Bob, but only the difference between the angels is of relevance.
Further, the scores are somewhat illogical, because a series of scores like +1, -1, -1, +1 (which means: correlated scores and opposite correlated scores) add up the same as unrelated scores (0, 0, 0, 0).
From this one can already conclude that the angel which scores the most is at 45 and 135 degrees , since at angles of 0 and 180 degree the scores cancel each other and at 90 and 270 degrees the scores are also zero.

Although the set up looks like we have two measurements involved, which somehow miracelously (action-at-a-distance) influence each other, it can be asserted that this is in fact one measurement that takes place, although it involves two locations.
The only setting one can make is changing the angle between Alice and Bob. Alice and Bob could both change the angle at their location the same amount in the same direction, without this influencing the outcomes, simply because the difference of the angles stay the same.
And although the source emits the particles in random fashion, this does not contradict the fact that the particles are colerated. Same as I throw a dice, I don't know what side comes up, but I do know that the value summed with the opposite side of the dice always adds up to 7.

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#### heusdens

I've often thought this way about QM.You have to realise that essentially, as boring and mundane as it sounds, nothing spooky is really happening. Just because you dont know or have not measured the spin or other undetermined property does NOT mean it exists in two at the same time and one determines the other. The particles have a precise spin when the event occurs and remain that way, nothing will change that. However given the 50/50 probability, the outcome is uncertain from a measurement and information point of few. This makes the line between what is 'actually true' aka reality, and what has been measured, rather fuzzy.

Hope that makes sense
-G
I agree with that. But the jargon of QM somewhat obfuscates that, and makes things unnecessarily incomprehensible.
We have to understand what realy goes on, to predict the outcomes.
The fact is that on one hand it is totally random, but on the other hand it definately is not!
You need to make that subtle distinction here!

Suppose we design an experiment as follows: we have a dice throwing machine, and everytime we make an observation, the dice gets rolled. Now in this setup, two observers can chooce themselves which side they are going to inspect (let's name them: top, bottom, left, right, front and back). The two observers (A and B) on each observation can freely choose which side to inspect, they note the scores. Now miraculously, each time when A and B choose opposite sides, their scores total as 7. How does the dice know which side each observer chooses? And does the choice of the observers which side to inspect somehow influence the outcome?
In this case we know it is not.

We in fact do not have two random observations, but in fact only ONE observation (although we split the observation at two different points). The total scores of A and B together would otherwise not correlate when they choose opposites sides for inspection.

See, that is the same kind of correlations we have in quantum mechanics, just that it isn't miracalous at all upon further inspection. Like in the dice experiment above, the illusion is created that we do two seperate observations, which would somehow determine the outcome of the experiment, but we know in this case, the outcome was determined previously by the dice rolling machine. Only that in reality - on the qm level - we can not know how the dice rolled before we make the observation.

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#### Tomsk

But what if Alice and Bob agree before the experiment that Alice will measure the number on the top of the dice (or the spin in the z-direction) and Bob measure the left-most number on the dice (spin in the x-direction). At a quantum level we can't do this (I think the spin operators for different directions don't commute)! If this dice has 1 on top and 6 on the bottom, it could have 2 (or 5) OR 3 (or 4) as the left most number. If 2 (or 5) is the left most number, then the top most could be 3 (or 4) OR 1 (or 6), but we can't know as we can only look at one side at a time!! (I think... I haven't actually studied spin at all... ) And yet they must both have definite answers, seeing as both Alice and Bob have measured them.....

Here is a very interesting (in my opinion...) paper on it: http://fr.arxiv.org/PS_cache/quant-ph/pdf/0604/0604064.pdf but what do I know. I haven't studied this stuff properly, so I wouldn't be surprised if there's something I haven't understood. It seems that one has to choose between Einstein's view of realism and locality though.... :uhh:

#### JesseM

Suppose we design an experiment as follows: we have a dice throwing machine, and everytime we make an observation, the dice gets rolled. Now in this setup, two observers can chooce themselves which side they are going to inspect (let's name them: top, bottom, left, right, front and back). The two observers (A and B) on each observation can freely choose which side to inspect, they note the scores. Now miraculously, each time when A and B choose opposite sides, their scores total as 7. How does the dice know which side each observer chooses? And does the choice of the observers which side to inspect somehow influence the outcome?
In this case we know it is not.
How is this machine supposed to work? If it's a classical machine, which just always throws the dice in such a way that the opposite sides add up to 7 (regardless of whether the observers choose the opposite sides or not), then this is not analogous to the situation in QM, there would be nothing "spooky" about this correlation and nothing to contradict local realism.

Here's a closer analogy. 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.

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#### DrChinese

Gold Member
Here is a very interesting (in my opinion...) paper on it: http://fr.arxiv.org/PS_cache/quant-ph/pdf/0604/0604064.pdf but what do I know. I haven't studied this stuff properly, so I wouldn't be surprised if there's something I haven't understood. It seems that one has to choose between Einstein's view of realism and locality though.... :uhh:
True, you cannot logically stay with both realism and locality after Bell and Aspect.

#### DrChinese

Gold Member
See, that is the same kind of correlations we have in quantum mechanics, just that it isn't miracalous at all upon further inspection. Like in the dice experiment above, the illusion is created that we do two seperate observations, which would somehow determine the outcome of the experiment, but we know in this case, the outcome was determined previously by the dice rolling machine. Only that in reality - on the qm level - we can not know how the dice rolled before we make the observation.
Not miraculous?

The idea that the dice have locally predetermined values does not hold water. If it did, Bell's Theorem would be of no interest. Remember, experiments show the following:

1. When Alice & Bob are measured at the same angle, the results are perfectly correlated. This gives the illusion that the values are predetermined, true enough. This points you towards realism, and follows the reasoning of EPR.

2. But when Alice & Bob are measured at the different angles, the results are obey the cos^2 function. This, however, gives the "illusion" that locality is violated because the spin statistics don't follow the realistic assumption of 1. This follows the reasoning of Bell.

If you only look at 1. and not at 2., then of course it seems pretty simple. But that isn't the whole story.

#### jtbell

Mentor
Here's a closer analogy. 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.
Oh good! Another example to "compete" with Mermin's machine from his famous article:

http://qt.tn.tudelft.nl/~lieven/qip/extra/mermin_moon.pdf [Broken]

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#### heusdens

But what if Alice and Bob agree before the experiment that Alice will measure the number on the top of the dice (or the spin in the z-direction) and Bob measure the left-most number on the dice (spin in the x-direction). At a quantum level we can't do this (I think the spin operators for different directions don't commute)! If this dice has 1 on top and 6 on the bottom, it could have 2 (or 5) OR 3 (or 4) as the left most number. If 2 (or 5) is the left most number, then the top most could be 3 (or 4) OR 1 (or 6), but we can't know as we can only look at one side at a time!! (I think... I haven't actually studied spin at all... ) And yet they must both have definite answers, seeing as both Alice and Bob have measured them.....

Here is a very interesting (in my opinion...) paper on it: http://fr.arxiv.org/PS_cache/quant-ph/pdf/0604/0604064.pdf but what do I know. I haven't studied this stuff properly, so I wouldn't be surprised if there's something I haven't understood. It seems that one has to choose between Einstein's view of realism and locality though.... :uhh:
My example experiment of throwing a dice and then look from two sides, is of course not a real quantum event, so you can't relate that exactly to a real quantum experiment. But is shows just that even when this dice rolling is a random process, it also has aspects which make some observations correlated.
Like for example: measuring from the same side, gives always the same outcome, measuring from opposite sides, always gives a sum total of 7.
And if we measure from two other sides (not same or opposite) means that the outcomes will be distinct and uncorrelated (don't add up to 7). In fact in that case the relative measurement position of A in respect to B then makes a difference. One way of looking at this is saying that this difference is "caused" by the measurement itself (the choice of what side to look at), but one also can explain it as that this is already "set" by the experiment (throwing the dice) itself, this two explenations (although they oppose each other) are not distinghuishable (we can't make any measurement which would show the right explenation). The cause of that is that both the throwing of the dice and the choice of what side to look at, are independend of each other.

Notice also that we (implictly) assumed the dice would always line up with facces in the exact measurement direction. So we use a somewhat abstract dice, that would never deviate from those positions, which is also different then a macro world experiment, in which the faces could in principle line up in any direction.

With experiments and observations you have to ask:
- Are the observations independend of each other?
- Does the act of observation disturb the outcome?

Translated to the quantum world, this means, what quantity or property is being measured, and how "fixed" is that quantity.
Measuring electron mass or charge would not alter that property, but measuing it's speed or spin status, would disturb the outcome, I guess.

#### heusdens

Not miraculous?

The idea that the dice have locally predetermined values does not hold water. If it did, Bell's Theorem would be of no interest. Remember, experiments show the following:

1. When Alice & Bob are measured at the same angle, the results are perfectly correlated. This gives the illusion that the values are predetermined, true enough. This points you towards realism, and follows the reasoning of EPR.

2. But when Alice & Bob are measured at the different angles, the results are obey the cos^2 function. This, however, gives the "illusion" that locality is violated because the spin statistics don't follow the realistic assumption of 1. This follows the reasoning of Bell.

If you only look at 1. and not at 2., then of course it seems pretty simple. But that isn't the whole story.

Yes, but look a bit deeper. Alice and Bob can each pick an angle, but please discern that in fact only one angle is of interest, the difference between angle of Alice and Bob.
Further note that correlated scores (+1 , -1) add up to zero AS WELL as uncorrelated scores (0, 0).
This explains why angles of 0 / 180 and 90 / 270 degrees have minimum values, and because of symmetry, the maximum values are exactly in between.
Which already shows why that angle is 45 or 135 degrees.

And for measuring the outcomes, you take the sum total of squares for each angle, which add up to (1)^2 and (-1)^2, and then you take the square of that, which gives 1/2 sqrt(2) which is 0.71..

#### heusdens

How is this machine supposed to work? If it's a classical machine, which just always throws the dice in such a way that the opposite sides add up to 7
Wrong! The fact that opposite sides have an outcome that add up to 7 is INDEPENDEND of how we throw the dice!!!!
It's a shame you don't see that!!

(and btw. I have nothing revealed of the nature of the "machine" perhaps the "dice rolling" is an event based on some underlying quantum event).

(regardless of whether the observers choose the opposite sides or not), then this is not analogous to the situation in QM, there would be nothing "spooky" about this correlation and nothing to contradict local realism.
The "local realism" aspect of this experiment is that observers can choose which side to inspect, which act is independend on of the "dice rolling" experiment.

Here's a closer analogy. 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.
First of all, I constructed this "experiment" that resembles some aspects of quantum nature. And of course, when throwing normal dices, this isn't an exact analogy of real quantum events, neither did I claim that!

Furter: I did't state that measuring a spin status is equivalent to my roling dice experiment, of course not.

A spin status is not a fixed observable, since I guess that in some cases we disturb that status. And possible in other cases, this quantity does not get disturbed.

So the error in your logic is to assume that either the spin status is something fixed, or it is not fixed (independend of the measurement).
While a real world anology can already show that such an assumption is not always true, but depends on the set up of the experiment.

But still there is the anology. If A and B choose to observe the dice from the same position or opposite position, they get somehow correlated results (the result is either the same or adds up to 7), but in other cases not!!!

It's same remarkable, I think!
Now please explain me, when A looks from the top, but B chooses neither the top, nor the bottom, he gets uncorrelated results (in fact in this case, the outcomes can be a selection of 4 distinct values, for each side).
But what determines the outcome of the result that B observes?
a. The experiment itself, rolling the dice, or
b. The choice of which side to observe

If we just assume that we don't know anything about the dice (as analogous to the quantum experiment) before we make these independend measurements, it is not determinable what causes this outcome. Was the number on the side that B chooses already fixed before B observes it, or does B somehow influence the outcome, just by the choise of the side to observe?
We can never know that, if the dice was realy a quantum experiment.

Only of course that in the macro world example, we can already know how the dice was lined up before the "measurements" take place, and in the quantum world, this is not possible.

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#### ZapperZ

Staff Emeritus
2018 Award
I think you do not see the difference between:

1. A classical particle having an initial spin (say 0) angular momentum, and then at a later time split into two and move in opposite direction. You measure the spin angular momentum of one particle and immediately know the spin of the other one simply by invoking a conservaton of angular momentum.

2. The EPR-type experiment.

There IS a difference here and that is what Bell-type analysis is detecting. You missed an important factor that separates the classical (example 1) and the quantum (example 2) cases - SUPERPOSITION. The classical example has a definite angular momentum for each particle before they are measured. The quantum example does not. The superposition of all spin states is what makes the quantum scenario different. It is the very reason why you change the angle of polarization in those experiments - you are trying to detect the non-commuting component of that observable that isn't collapsed upon measurement.

The superposition aspect is what makes the EPR-type experiment different than a simple classical conservation-law measurement. One has to understand what superposition is, and how it is detected and how it makes itself known in our measurements.

Zz.

#### heusdens

Not miraculous?

The idea that the dice have locally predetermined values does not hold water. If it did, Bell's Theorem would be of no interest. Remember, experiments show the following:

1. When Alice & Bob are measured at the same angle, the results are perfectly correlated. This gives the illusion that the values are predetermined, true enough. This points you towards realism, and follows the reasoning of EPR.

2. But when Alice & Bob are measured at the different angles, the results are obey the cos^2 function. This, however, gives the "illusion" that locality is violated because the spin statistics don't follow the realistic assumption of 1. This follows the reasoning of Bell.

If you only look at 1. and not at 2., then of course it seems pretty simple. But that isn't the whole story.

The error in logic is to assume that either the observable is a "fixed" property, or it is not. As I show in my "real world" example of the dice throwing example, and obsering it from two sides by two different observers, this assumption can already be shown to not hold water in all cases.

#### heusdens

I think you do not see the difference between:

1. A classical particle having an initial spin (say 0) angular momentum, and then at a later time split into two and move in opposite direction. You measure the spin angular momentum of one particle and immediately know the spin of the other one simply by invoking a conservaton of angular momentum.

2. The EPR-type experiment.

There IS a difference here and that is what Bell-type analysis is detecting. You missed an important factor that separates the classical (example 1) and the quantum (example 2) cases - SUPERPOSITION. The classical example has a definite angular momentum for each particle before they are measured. The quantum example does not. The superposition of all spin states is what makes the quantum scenario different. It is the very reason why you change the angle of polarization in those experiments - you are trying to detect the non-commuting component of that observable that isn't collapsed upon measurement.

The superposition aspect is what makes the EPR-type experiment different than a simple classical conservation-law measurement. One has to understand what superposition is, and how it is detected and how it makes itself known in our measurements.

Zz.

See my "dice rolling" experiment with two independend observers that observe the event from a selected side.

Also that "experiment" shows that in some cases the results are correlated, and in other cases, they do not.

#### ZapperZ

Staff Emeritus
2018 Award
See my "dice rolling" experiment with two independend observers that observe the event from a selected side.

Also that "experiment" shows that in some cases the results are correlated, and in other cases, they do not.
I did. I still don't see how this illustrates ANY degree of superposition, which is a necessary ingredient for any EPR-type experiment.

Zz.

#### CarlB

Homework Helper
Only of course that in the macro world example, we can already know how the dice was lined up before the "measurements" take place, and in the quantum world, this is not possible.
The problem in understanding here is that there's some difficult to understand machinery going on that is a bit subtle in the usual EPR case.

Rather than waste time on this case, where the mystery requires a difficult analysis of a continuous probability distribution, you will see that your explanation is hopeless more quickly if you try to explain the discrete versions of this paradox.

I'm snowed in, in Seattle, and bored, so I'll go look on the web for a decent introduction.

Mermin is famous for explaining things clearly:
http://people.ccmr.cornell.edu/~mermin/homepage/talk.pdf

Let me look around, there may be something else out there. .... .... ..... Nah, the above is about as clear and short as it gets.

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#### heusdens

I did. I still don't see how this illustrates ANY degree of superposition, which is a necessary ingredient for any EPR-type experiment.

Zz.
I can't make a "classical" set up behave like a "quantum" experiment set up, that is the limit of the analogy.

Neither did I claim that this "dice rolling" experiment with two independend obserbations would be a 'real' quantum mechanical experiment, because it is not.
I was just showing that even in this classical behaviour, you have to take care about how you interpret it. For instance, we already know (because we can take a peek before we do the actual measurement) how the dice is lined up (and please take note that the dice does not have just 6 states, that is only true for one side of the dice, but the side adjacent to the side we inspect has also 4 different states) which we could not do in a "real" quantum experiment.

But you might think of the "superposition" of states as those two independend chances (the chance for the 1 out of 6 numbers facing up, and the 1 out of 4 chances for the numbers facing front, that is if we exclude possibility of the dice angle of rotation) in this experiment.

But please note: the chances for getting one number on top and another number at the front, are correlated too, since if we have 1 on top, the front can not display 1 or 6, etc., still the chance for any of the remaining numbers for the front side is 1 out of 4 for each remaining number.
And also note that even when the outcomes are determined after rollling the dice, and before we make the actual measurements, we know (from our "non quantum" position in which we can take measurements any time) that the choice of both observers do influence the outcomes.
Suppose 1 is on top. But which number A sees depends on his choice of side to observe. So it "looks like" he can alter the outcome by chosing which side to observe (and this is for one observer exactly equal to rolling the dice once more, and take the observation from the top always, while ignoring the previous result).
Stil (in the experiment and how we decided to perform it) the dice itself remains in it's "same state" (but which is unknown). That is the dice itself does not change one bit just by choosing a side and looking at it. But what state the dice is in, we don't know only until after we choose a side and look at it (and each observer is of course to look only once at the dice), since the state we observe is not only determined by the "real" position the dice is in, but also determined by the side we choose to observe.

If we adopt the "rules" of this experiment (in which it is absolutely forbidden to take measurements in any other way as described), we would however not be in the position of knowing that fact. Wether or not the choice of the observer influences the outcome is something (under the rules) undeterminable.

If we interpret this experiment in the way QM would do, how about "realism" and / or "locality"?

"Realism" would say that the outcome of the observation is independend of the choice of the sides. However, as we can show, that is not the case.

Only thing we know there are hidden parameters. That is of course because the dice itself has definite choices for which number appears on which side. The rule is just that opposites sides have a sum of 7.

This is an anology for a QM experiment, which reveals some conservation number. Like conservation of charge, mass/energy, momentum or any such quantum number.

But as it shows up, to "reveal" that opposite sides sum up to 7, it depends of course what side A and B choose, only if they choose opposite sides, this feature is revealed.

Note:
To make the "experiment" more "look like" a quantum experiment, let is abstain from calling it a dice, and let us have two obsers A and B sufficiently apart, that only have a display.
The display has a control light. If it flashes green they can make the observation.
The observation is done by pressing a butting numbered 1 to 6, and the display then shows the outcome, which is a number from 1 to 6.
After they have done the observation they can press a RESET button which switches the green light off, to allow the next observation to be made. Etc.
Afterwards both observers compare notes, which show which button each pressed for each experiment, and what outcome they had.

Please note also that although it seems A and B make two independend choices (6 choices for A and indepently 6 choices for B), this can be reduced to one of the observers always choose a fixed number (say 1) and only the other make a choice between 1 to 6.
Because the choice which A makes, would rather contribute to have the dice rolling once again, and ignore the previous result, so that reduces to throwing the dice only once and always observe it from the top (for instance).
The choise B makes, is of course in this set up relevant.

(and for symetrical reasons the same reasoning applies if we switch positions of A and B).

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#### heusdens

The problem in understanding here is that there's some difficult to understand machinery going on that is a bit subtle in the usual EPR case.

Rather than waste time on this case, where the mystery requires a difficult analysis of a continuous probability distribution, you will see that your explanation is hopeless more quickly if you try to explain the discrete versions of this paradox.

I'm snowed in, in Seattle, and bored, so I'll go look on the web for a decent introduction.

Mermin is famous for explaining things clearly:
http://people.ccmr.cornell.edu/~mermin/homepage/talk.pdf

Let me look around, there may be something else out there. .... .... ..... Nah, the above is about as clear and short as it gets.

Oh boy, well we have here just storms and some rain, that is in Groningen, Netherlands.....

Hope you can manage to survive a couple of days when snowed in....

#### heusdens

Mermin is famous for explaining things clearly:
http://people.ccmr.cornell.edu/~mermin/homepage/talk.pdf

Let me look around, there may be something else out there. .... .... ..... Nah, the above is about as clear and short as it gets.
What we can see from the result (in the document above) is that the outcome is CORRELATED when either A or B or both choose a detector setting of "1".
And they get RANDOM results when A and B choose a detecor setting of "2".

Further, if A or B choose a 1 but NOT BOTH, the result is NEVER BOTH G, and if BOTH choose 1 the result is NEVER BOTH R.

I don't think the "dice rolling" experiment can simulate that results, but I will see if I can come with a similar example which shows those kind of results.

Remark: the description of the run 2 2 is a bit vague, it just states SOMETIMES BOTH G. Does that mean that BOTH R also can occur sometimes, and G R and R G? Is it realy random?

And one further note: the experiment is symetric in respect to observers. If A and B switch their position, we get the same outcome.
The detector settings however clearly are not. Else a detector setting of 1 1 and 2 2 would have identical results, which they have not.

So, the only mystery is why the detector settings ain't symetric.

And then another remark. I don't completely understand the set up.
If the setup for such experiments prescribes that the two detectors get their "observable" from one source, and that observations taking place at each detector don't interfere with each other, then there is some mystery.

However, as I see the experiment setup as explained in the document, such interference does take place (see page 4). So, that is not like setting up a source that emits it's "observable" to the two detectors, since somehow I suspect that what is seen at one dectector infleunces what is seen at the other detector.
Am I right?

If you understand the setup, can you please explain it to me?

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#### vanesch

Staff Emeritus
Gold Member
it is obvious that the only factor of interest is not the respective angels of Alice and Bob, but only the difference between the angels is of relevance.
Hi there !

You are confused about the EPR setup and Bell's theorem, but you're not the first one, and not the last one. Many people first think of the Bell situation like you do - hey, even Bell himself did so ! However, Bell wasn't such a naive person as to confuse initial state correlations with causal influences, and he explains that very well in a rather nice article: "Professor Bertlmann's socks", in his book "Speakable and unspeakable in quantum mechanics" (which you should get your hands on if you're interested in these issues). Bell analysed what were the CONDITIONS on a SET OF CORRELATIONS that result from them being simply a result of initial-state correlations, and one of his results is Bell's inequality.

Now, take the quantum predictions, but forget about how they came about (in other words, forget about the formalism of quantum theory that gave rise to these predictions). Simply look at the correlations predicted by QM, for the different angle settings of Alice and Bob. It turns out that the SET of correlations by this relationship, violates the Bell inequality. It means that they cannot be the result of "initial-state" correlations.

But notice that Bell never said that any kind of correlation cannot follow from initial-state correlations! He went on looking what conditions such a set of correlations must satisfy, so he clearly recognized that observational correlations could be simply due to initial state correlations - otherwise he'd have been quite an idiot !

Although the set up looks like we have two measurements involved, which somehow miracelously (action-at-a-distance) influence each other, it can be asserted that this is in fact one measurement that takes place, although it involves two locations.
Nope. That's exactly the Bell kind of condition.

The only setting one can make is changing the angle between Alice and Bob. Alice and Bob could both change the angle at their location the same amount in the same direction, without this influencing the outcomes, simply because the difference of the angles stay the same.
Yes, that's true. But the point is that we have to find initial conditions which determine INDEPENDENTLY, given ONLY BOB'S ANGLE, whether to click or not at Bob's. Because, if there's no action at a distance, once the particle in Bob's direction is set off, it cannot "know" what will be Alice's setting, so its reaction to Bob's setup shouldn't depend on whether or not Alice is rotating her angle.

And although the source emits the particles in random fashion, this does not contradict the fact that the particles are correlated. Same as I throw a dice, I don't know what side comes up, but I do know that the value summed with the opposite side of the dice always adds up to 7.
Sure. But things are not as simple as that. Of course for certain correlations, such explanations are possible, but not for the entire set. This follows from the fact that, given a "particle state" (which contains the "correlation information") and given an angle b at Bob's, we need to be able to calculate, only from these two data, whether the detector at Bob will click or not. This can - I hope you agree with me - not depend on the setting of the detector angle at Alice.

In the case of your dice machine, we have to imagine in fact that two dice, in identical positions, are sent off to Alice and Bob, who are allowed to look at one specific side. The correlation variable is of course the position of the dice, which takes on the values by 3 parameters (actually, only 2 are independent if there are no "mirror dice", but let us suppose that there are): top face, right face, and forward face. However, in order to limit the amount of possibilities, let us take it that the result of a measurement is only:
+: outcome 4, 5 or 6
-: outcome 1, 2 or 3

We will also limit ourselves to the case where Bob can only see the top/right/forward face, and alice only the bottom/left/backward face.

You can do the finer details if you want to.

Now, as you say, indeed, such a system can explain the perfect anti-correlations: whenever Alice looks at the bottom and Bob looks at the top, they find +/- or -/+, never ++ or --.

Let us consider all cases:

Top - right - forward
a = ( + + +)
b = ( + + -)
c = (+ - +)
d = (+ - -)
e = ( - + +)
f = ( - + -)
g = (- - +)
h = (- - -)

Let us consider that the machine generates Na times the first kind of dice throw, Nb times the second kind of dice throw, etc...

Clearly, in case, say, g: if Bob measures the top face, he'll have a - outcome, if he looks at the right face, he'll have a - outcome, and if he'll measure the forward face, he'll have a + outcome. In the same case g, Alice will have a + outcome for the bottom face, she will have a + outcome for the left face, and she'll have a - outcome for the backward face. In case Bob and Alice measure opposite faces, they find perfect anti correlation. No problem.
Perfect anti-correlation can be explained without a problem in such a setup.

Let us assume that the machine generating the dice is "stationary", meaning, the Na, Nb, Nc... numbers are about constant for a big (say, 10^6) number of trials (Na + Nb + ... Nh = 10^6), and that if we re-start the machine, it will generate them in about the same quantities (but not in the same order of course!) This is simply the assumption that the correlations we measure at a certain time, are also the same when we measure them in a later trial.

Right.

Clearly, we have that Nc + Nd < Nc + Nd + Nb + Ng, because we add a few positive numbers.

Now, Nc + Nd is the number of cases in which we have on Bob's side, a + for the top side, and a - for the right side. In other words, if we do the run, with Bob looking (for all events) to the top, and Alice looks (for all events) to the left side, Nc + Nd is the number of outcomes where Bob has + and Alice has + outcomes.

So (Nc + Nd) is the number for the + + simultaneous outcomes with Bob in the "top" state, and Alice in the "left" state. If we divide it by 10^6, we say that the simultaneous probability for ++ in the (bob=top,alice=left) state, equals:

P(bob=top,alice=left) = (Nc + Nd)/10^6

In a similar way, (Nb+Nd) is the number for the + + simultaneous outcomes with Bob in the "top" state and Alice in the "backward" state.

P(bob=top,alice=back) = (Nb + Nd)/10^6

Finally, we also have (Nc + Ng) is the number for the ++ simultaneous outcomes with Bob in the "forward" state and alice in the "left" state:

P(bob=forward,alice=left) = (Nc + Ng)/10^6

From our initial inequality (which was trivial) follows:

P(bob=top,alice=left) < P(bob=top,alice=back) + P(bob=forward,alice=left)

You can think of any kind of similar experiment, the outcome will be always the same: if you have 3 possible kinds of measurements at Alice and Bob, which can give a + or - answer, and we know that there is a perfect (anti)correlation for the outcomes when the settings are pairwise associated (here {top-bottom ; right-left ; forward-backward}), then the OTHER correlations need to satisfy the above inequality.

This is the inequality that is violated by the QM predictions, if we choose 3 specific directions as our 3 kinds of measurements.

It is not the perfect anti-correlation which poses a problem. It is not an individual correlation between certain settings. It is the total set of correlations, namely {P(a,c),P(b,c),P(a,c)} which is incompatible with the above inequality.

Indeed, for spin-1 particles, we have that P(a,b) = 1/2 cos^2(th_alice - th_bob). This is the quantum-mechanical prediction, but we do not need to care about how this was established. It could just as well have been empirically established - assuming the quantum predictions are correct, without any reference to quantum mechanics. Indeed, let us, for sake of argument, do the following gedanken experiment:
1) Quantum theory is correct in our gedanken world
2) Newton had perfect photodetectors with 100% efficiency and a perfect EPR setup - but has never heard of quantum theory.

Our hypothetical Newton in our hypothetical world would then have empirically established some kind of Malus' law:
If Alice sets her analyser to the angle th_alice, and bob to the angle th_bob, then the simultaneous probability to have both of them click, is given by:
1/2 sin^2(th_alice - th_bob).

Now, let us pick 3 specific angles: 0, 45 degrees and 22.5 degrees, which we call a, b and c. We will write the simultaneous probability for alice and bob to click, by P(a,b) etc... Clearly, P(a,a) = 0. There is perfect anti-correlation. In the same way, P(b,b) and P(c,c) = 0.

Up to now, no problem, we can do that too with the dice machine.

But Newton also measured: P(a,b) = 1/2 sin^2(45 degrees) = 0.25.
Also P(b,c) = P(c,b) = 1/2 cos^2(22.5 degrees) = 0.0732.
Finally, P(a,c) = 1/2 cos^2(22.5 degrees) = 0.0732

We should have, according to the above reasoning:
P(a,b) < P(a,c) + P(c,b)

But if we fill in the numbers, we find:

0.25 <? 0.0732 + 0.0732

Which is obviously not satisfied. No talk about superposition, quantum state or whatever involved. In our imaginary world, Newton simply MEASURED the simultaneous probability of clicking, and found it to be equal to the 1/2 sin^2 law. There's no "dice machine" that can generate the same total set of correlations.

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