B Layman question about faster than light communication

[mataku]

Okay, first of all so I'm in no way educated in the concepts and especially the notation of quantum physics; my knowledge is confined to a very simple superficial understanding.

However, if someone could educate me about why faster than light communication is impossible in the scenario I'm about to present, I would be very thankful.

My current understanding is that given a quantum entangled pair, 'forcing' a particular spin of a particle breaks entanglement, however, merely measuring the spin of a particle preserves entanglement (or the consequence of entanglement), and its twin can be measured to have the exact opposite spin.

I've also read that entanglement is possible with 3 particles at a time as opposed to only 2. From my understanding, if particle [1] is 'forcefully' given a spin, its entanglement between particles [2] and [3] is broken, so likewise I assume that the entanglement between [2] and [3] is also broken.

Given that assumption, it seems possible to determine if particle [1] has been 'forced' into a particular spin, or has been left undisturbed, by testing entanglement between particles [2] and [3].

In a communication situation, an ordered collection of groups of [1] particles would be sent light years away, and then an instrument would incrementally check, groups of corresponding [2] and [3] particles to see if they have been 'forcefully' disturbed or not. If a group of particles is found to have been disturbed (with a reasonable error margin), a 1 bit of data is generated, if not, a 0 bit of data is generated. Much like polling in computer science.

However, I'm well aware that faster than light communication is impossible in physics, so please tell me where I've gone wrong.

 

[bhobba]

Yes - you can break entanglement at your end and know the state at that time. But the trouble is knowing the state at the other end. To do that you have to measure it - breaking entanglement so no information can be sent. And no, there is no way of knowing the state before the measurement.

The best way of looking at EPR type stuff is simply as a correlation. Like red and green pieces of paper in separate envelopes. You can send each of them to the other other side of the universe if you like. As soon as you open one envelope you know instantly what the other one is - no problem - but there is no way to use it to send information. EPR type stuff is exactly the same as that except it has some statistical properties different to ordinary probability theory. What Bell discovered is if you want it to have the same kind of properties as ordinary probability you need an interpretation with some kind of FTL signalling.

Best to read Bells actual paper:
https://hal.archives-ouvertes.fr/jpa-00220688/document

Personally I am a bit of maverick in that I believe correlations should be excluded from questions of locality ie the existence of FTL signalling. In our most powerful theories - Quantum Field Theories - the idea of locality is replaced by the so called cluster decomposition property that to really make sense excludes correlations:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/

Thanks
Bill

 

[Nugatory]

so likewise I assume that the entanglement between [2] and [3] is also broken.

Even if [2] and [3] are no longer entangled, the statistics you get measuring [2] and [3] are the same whether a previous measurement of [1] has been made or not. So... no message is being sent.

 

[StevieTNZ]

You can't force an observable into one of the possible states it can take on (e.g. spin up over spin down). The result is random. That's the essence of the question, at least to me.

 

[DrChinese]

I've also read that entanglement is possible with 3 particles at a time as opposed to only 2. From my understanding, if particle [1] is 'forcefully' given a spin, its entanglement between particles [2] and [3] is broken, so likewise I assume that the entanglement between [2] and [3] is also broken.

Given that assumption, it seems possible to determine if particle [1] has been 'forced' into a particular spin, or has been left undisturbed, by testing entanglement between particles [2] and [3].

The [time] sequence of measuring entangled particles 1, 2 and 3 has no observable effect on the outcomes. This is a prediction of QM. There are many ways to create entangled systems of 3 or more particles, and there are any number of experiments that have verified the predictions.

That should tell you everything you need to know: because you cannot state that your hypothetical message is going from point A to point B rather than from B to A. Also, as already pointed out above by StevieTNZ and others, you cannot "force" an entangled particle into a specific state. The outcome will be random.

 

[timmdeeg]

The best way of looking at EPR type stuff is simply as a correlation. Like red and green pieces of paper in separate envelopes. You can send each of them to the other other side of the universe if you like. As soon as you open one envelope you know instantly what the other one is - no problem - but there is no way to use it to send information.

I think it should be noted that while the colors are defined before measurement the quantum states e.g. spin up or spin down are not.

 

[David Byrden]

As timmdeeg said, it's not exactly like sending red and green bits of paper. It's similar but...weird.

With the papers, you may not know their colours, but they have colours. The information exists somewhere, just not in your brain.
With the entangled particles, the information does not exist until you measure one. But the fact of them being correlated does exist.

David

 

[rede96]

But the fact of them being correlated does exist.

So does that mean the correlations exist prior to be them being measured? Which would suggest the correlations are created when an entangled pair are created?

 

[PeroK]

So does that mean the correlations exist prior to be them being measured? Which would suggest the correlations are created when an entangled pair are created?

That the measurements are correlated is essentially what entanglement means.

 

[bobob]

In a communication situation, an ordered collection of groups of [1] particles would be sent light years away, and then an instrument would incrementally check, groups of corresponding [2] and [3] particles to see if they have been 'forcefully' disturbed or not. If a group of particles is found to have been disturbed (with a reasonable error margin), a 1 bit of data is generated, if not, a 0 bit of data is generated. Much like polling in computer science.

However, I'm well aware that faster than light communication is impossible in physics, so please tell me where I've gone wrong.

You've gone wrong in your understanding of relativity. When you refer to "light years away," that distance in light years is in your reference frame only. The distance between any two points on a lightlike ray is zero. Furthermore, two measurements, A and B, which are made at spacelike separations occur at exactly the same time in some frame. In another frame, A occurs before B and in yet another frame, B occurs before A. Spacelike events have no time ordering. Instead imagine that your measurements always occur at the same time, since they do in some frame and that has to be consistent with those measurements made in other frames.If you could send a message the way you describe, then in some frame, the message would be received before it was sent.

 

[rede96]

That the measurements are correlated is essentially what entanglement means.

I’m a little confused. There is a difference between measurements being correlated and entangled particles having a correlation before being measured. Which is what I understood from the statement that correlations exist prior to measuring.

 

[Nugatory]

I’m a little confused. There is a difference between measurements being correlated and entangled particles having a correlation before being measured. Which is what I understood from the statement that correlations exist prior to measuring.

There's nothing to correlate before the measurements, because there aren't any results to check for correlation.

 

[rede96]

There's nothing to correlate before the measurements, because there aren't any results to check for correlation.

So how should I understand this statement:

With the entangled particles, the information does not exist until you measure one. But the fact of them being correlated does exist.

 

[Nugatory]

So how should I understand this statement:

Write down the wave function of the entangled pair before measurement: something like $|\alpha_1\rangle|\beta_1\rangle+|\alpha_2\rangle|\beta_2\rangle$. It's not unreasonable to apply the English-language word "correlated" to this system, but the truth is in the math, not the words. When we say that the measurement results are "correlated" we're using the word in a more precise sense.

 

[David Byrden]

I find that relative-state many-worlds interpretations make sense to us humans. So, in that way of thinking, the particles' joint state is - relative to you - unknown because no information about it has reached you. But the particles themselves exist in two "worlds" and in each "world" they have a definite joint state. The equation written by Nugatory expresses this exactly.

So, how does that help? When you measure one particle, you enter one of the two "worlds", chosen randomly. Not because you are consciously aware of the result, but because it infests you and your environment via trillions of entanglement relations. You become, very subtly but definitely, tainted by that information.

Then, when you go to the other particle, you can find only the corresponding result there, regardless of when the measurement gets made. That's the only result that you and your environment "match up" to.

Nothing moves faster than light, in that way of looking at it.

 

[PeroK]

So how should I understand this statement:

You don't have to try to understand it. The correct term is "entangled".

 

[rede96]

I find that relative-state many-worlds interpretations make sense to us humans. So, in that way of thinking, the particles' joint state is - relative to you - unknown because no information about it has reached you. But the particles themselves exist in two "worlds" and in each "world" they have a definite joint state. The equation written by Nugatory expresses this exactly.

So, how does that help? When you measure one particle, you enter one of the two "worlds", chosen randomly. Not because you are consciously aware of the result, but because it infests you and your environment via trillions of entanglement relations. You become, very subtly but definitely, tainted by that information.

Then, when you go to the other particle, you can find only the corresponding result there, regardless of when the measurement gets made. That's the only result that you and your environment "match up" to.

Nothing moves faster than light, in that way of looking at it.

To be honest I’m just an interested layman and probably never going to understand all this as much as I’d like.

But from what I do understand so far is that on one hand we have the math (Bell) that says there can’t be any predetermined property of the particles which is responsible for the correlation we measure. And on the other hand the physics tell us the correlations can’t be through any sort of communication between the particles, as nothing can communicate faster than light.

For me the simplest interpretation is, one of those is wrong.

 

[bobob]

But from what I do understand so far is that on one hand we have the math (Bell) that says there can’t be any predetermined property of the particles which is responsible for the correlation we measure. And on the other hand the physics tell us the correlations can’t be through any sort of communication between the particles, as nothing can communicate faster than light.

For me the simplest interpretation is, one of those is wrong.

Why is that? Correlation does not imply causation. No causation means no need to communicate nor does there need to be any predetermined property.

 

[David Byrden]

Bells' theorem doesn't say exactly what you wrote.

It says that the correlation between the measured properties is slightly greater than you would expect if the particles were both initially given fully correlated properties, which they kept secret inside themselves until measured.

It rules out THAT rather obvious explanation. But it doesn't say that the particles bear no relation to each other at all. The equation that Nugatory wrote could also be called a "property of the particles".

David

 

[rede96]

Why is that? Correlation does not imply causation. No causation means no need to communicate nor does there need to be any predetermined property.

Not in the sense I think you are referring to. But there is something that causes the correlations. You don't get a 100% correlation by chance. So what causes the correlations?

Bells' theorem doesn't say exactly what you wrote.

It says that the correlation between the measured properties is slightly greater than you would expect if the particles were both initially given fully correlated properties, which they kept secret inside themselves until measured.

David

I guess this is the part I am having difficulty in understanding. Just what the statistics do actually tell us about the cause of the correlations.

For example, and forgive the elementary analogy, but I can imagine a ball, which is painted with a sort of two tone paint. Depending on what angle you look at the ball it will show a different colour. Look at it from the front (0 degrees) and you see green. Look at it from the side (90 degrees) and you see red. (Each ball has a black spot to indicate direction.) I make another ball but with the opposite effect. E.g. look at it from the front and you see red not green.

Neither ball can be said to have a particular colour. As it depends on what angle you view the ball. But there is always a 100% negative correlation when the balls are viewed at the same angle.

Now I make a lot of pairs, where the angle you see red or green is totally random and could be any combination of angles. But each pair are made so they will always be 100% correlated when viewed from the same angle. However due to the randomness I introduced, if Bob and Alice take measurements at the typical 0, 120 and 240 degree angles, I may not get the expected probabilities that are based on the balls just having two properties, e,g, red or green.

That is kind of how I view entanglement.

So what I was trying to get my head around is if I could model that example would I be able to replicate the results from experiments on entangled particles.

I'm pretty sure the answer is going to be no. But I just don't understand the Math enough to figure out why.

 

[DrChinese]

... I can imagine a ball, which is painted with a sort of two tone paint. Depending on what angle you look at the ball it will show a different colour. Look at it from the front (0 degrees) and you see green. Look at it from the side (90 degrees) and you see red. (Each ball has a black spot to indicate direction.) I make another ball but with the opposite effect. E.g. look at it from the front and you see red not green.

Neither ball can be said to have a particular colour. As it depends on what angle you view the ball. But there is always a 100% negative correlation when the balls are viewed at the same angle.

Now I make a lot of pairs, where the angle you see red or green is totally random and could be any combination of angles. But each pair are made so they will always be 100% correlated when viewed from the same angle. However due to the randomness I introduced, if Bob and Alice take measurements at the typical 0, 120 and 240 degree angles, I may not get the expected probabilities that are based on the balls just having two properties, e,g, red or green.

That is kind of how I view entanglement.

So what I was trying to get my head around is if I could model that example would I be able to replicate the results from experiments on entangled particles.

I'm pretty sure the answer is going to be no.

Yes, the answer is no.

Use the example you provided of the 0, 120 and 240 degrees. You would need the following to hold true:

1. If the balls are measured at the same angle, you ALWAYS get the expected result (0% matches for Type II PDC, 100% matches for Type I PDC).
2. If you measure at any other pair of different angles (0 & 120, 0 & 240, etc.) you get the quantum prediction (75% matches for Type II PDC, 25% matches for Type I PDC).

I refer to this as the DrChinese challenge. Because you cannot hand pick a data set that that will obey this. That's the problem you face.

Try it for permutations that seem favorable. The only way it works out is if you know which 2 angles you are going to pick in advance, which allows you to skew the results (i.e. it's a cheat). After all, the objective is to have a model that works when the experimenter chooses the angle settings, not you.

 

[David Byrden]

I guess this is the part I am having difficulty in understanding. Just what the statistics do actually tell us about the cause of the correlations.

The statistics support a many-worlds model.
They suggest that when you measure the first particle, it takes on the angle that you measured at, i.e. it adopts one of your measurement bases. And the other particle now has the identical angle - that's why the correlation is a cosine rather than a sawtooth.
So, we can imagine that before the measurement, the two particles existed in a continuum of "many worlds" where they always had matching angles and there was a "world" for each possible angle.
I'm not suggesting millions of alternate universes! The "worlds" are local even if they do exist. But really they are a mental model that behaves according to QM rules.

David

 

[PeterDonis]

The statistics support a many-worlds model.

They also support every other interpretation of QM, since all interpretations make the same predictions for the results of experiments. Please be careful when making such statements.

 

[zonde]

So what I was trying to get my head around is if I could model that example would I be able to replicate the results from experiments on entangled particles.

I'm pretty sure the answer is going to be no. But I just don't understand the Math enough to figure out why.

Your example has certain symmetry - the change in coincidence rate is always proportional to change in relative angle.
But that means that as relative angle goes from 0 to 90 degrees coincidence rate should change from 0 to 1 by 90 identical steps i.e. coincidence rate should change by 1/90 for every degree. But QM predicts that coincidence rate changes as $\sin^2$ of relative angle. And that's quite different change rate - it lacks the symmetry that your example has i.e. for angles close to 0, 90, 180 ... degrees coincidence rate changes less, but for angles close to 45, 135, 225 ... degrees coincidence rate changes more. In other words relative angle and coincidence rate does not change the same way in QM.

 

[rede96]

1. If the balls are measured at the same angle, you ALWAYS get the expected result (0% matches for Type II PDC, 100% matches for Type I PDC).
2. If you measure at any other pair of different angles (0 & 120, 0 & 240, etc.) you get the quantum prediction (75% matches for Type II PDC, 25% matches for Type I PDC).

I refer to this as the DrChinese challenge. Because you cannot hand pick a data set that that will obey this. That's the problem you face.

Actually there may be a data set I can hand pick that would give this result. (I think!) It would only work for that combination of angles of course. But it does demonstrate that there is a way to have pre-determined properties that will give the same results as QM. At least for an isolated case like this.

EDIT: Scratch that! I got the Type I and Type II the wrong way around.

 

[rede96]

But that means that as relative angle goes from 0 to 90 degrees coincidence rate should change from 0 to 1 by 90 identical steps i.e. coincidence rate should change by 1/90 for every degree

Not necessarily, although I take your point. But there is no reason why we couldn't manufacture the balls in my example to be skewed so they didn't follow that symmetry.

But QM predicts that coincidence rate changes as sin2sin2\sin^2 of relative angle.

This is probably a stupid question but doesn't that mean all nature needs to do is produce entangled pairs that follow that rule?

 

[DrChinese]

Actually there may be a data set I can hand pick that would give this result. (I think!) It would only work for that combination of angles of course. But it does demonstrate that there is a way to have pre-determined properties that will give the same results as QM. At least for an isolated case like this.

Type I is a lot easier to work with - that's the one where both particles will have the SAME polarization at the same measurement angle. And the quantum prediction is 25% match rate when the measurement angles are 120 degrees apart.

The challenge: you supply the predetermined values for 0, 120 and 240 degrees. I pick the 2 angles to measure at. Good luck!

 

[zonde]

But there is no reason why we couldn't manufacture the balls in my example to be skewed so they didn't follow that symmetry.

If you randomize directions of angles in your set of balls then for large set of balls they will approach that symmetry. Any asymmetry of individual balls will be masked by that randomization.

This is probably a stupid question but doesn't that mean all nature needs to do is produce entangled pairs that follow that rule?

Well, the problem is that relative angle is non-local variable. Measurement settings on the other hand are described by local variables (polarizer rotation angle). So the challenge is to come up with the rule in such a way that we can take as a parameters two local variables instead of one non-local variable.

 

[rede96]

The challenge: you supply the predetermined values for 0, 120 and 240 degrees. I pick the 2 angles to measure at. Good luck!

:) I think we both know I'm not going to be able to do that. It is possible to derive properties that will give the QM results but it requires a built in random factor that is only present when measuring at different angles. Which obviously means the particles would need to know the measurement angles. So that doesn't work either.

The only other thing I thought of was that there is some unknown interaction between the spin state of a particle and the electric field (or polarizer) that introduces an error factor that causes some particles not to orientate as expected. It's just that when the two measurement angles are the same or 180 degrees apart the errors cancel and we always see perfect correlations for those cases.

If I was to make that assumption then I could build in a property that adjusts the spin states depending on the difference in angle. Not because I'd need to know the angles up front, but because it is the actual angles that produce the errors. Like the particles are expecting a universal 'North' If that makes sense? And any deviation of the measurement angle to that universal North produces an error sometimes. The further away from North or South the bigger the error. Maximum being 90 degrees. Or something like that :)

 

[rede96]

If you randomize directions of angles in your set of balls then for large set of balls they will approach that symmetry. Any asymmetry of individual balls will be masked by that randomization.

Well, the problem is that relative angle is non-local variable. Measurement settings on the other hand are described by local variables (polarizer rotation angle). So the challenge is to come up with the rule in such a way that we can take as a parameters two local variables instead of one non-local variable.

Sorry to ask, but I don't think I've ever really understood properly by local and non local. I did look it up on google but it just confused me. Would you be able to clarify for me please?

 

[David Byrden]

I don't think that the red/green ball example captured the spirit of entanglement in a clear way. I will give a pizza based example.

So: suppose you are a pizza delivery person. Your employer, "24 hour pizzas", makes delicious pizzas, half covered in tomato, half in cheese. And I mean literally exact halves, with a perfect straight boundary running through the centre.

You never see an entire pizza. You are given each pizza in a box with a large clock drawn on its lid. And your responsibilities include punching a small ventilation hole in the lid.

You habitually punch the hole in the "6" digit of the clock face. Through the hole you see a tiny spot on the pizza. Over many deliveries you notice that this spot is either tomato or cheese, with 50% probability. Having seen the pizza machine, you know that it drops the pizzas into the boxes with random orientation so this is expected.

 

[David Byrden]

One day your employer institutes an offer; buy two pizzas and the second one is half price! You find yourself delivering pairs of boxes, manufactured together. And you notice something odd; the toppings that you see through the two holes in the two boxes always match.

You conclude that the pizza machine, although it orients pizzas at random , will orient two pizzas the same way if they are manufactured together.

And then you get playful.

Instead of making the two holes at "6", you make one hole at "6" and the other at "3". What do you expect to see? You expect zero correlation. Even though you don't know the angle at which the pizza pair is oriented, you expect the holes to show matching toppings exactly 50% of the time. Think about it.

And then you try another test. You make the holes at "6" and "4:30".

Now, you expect 75% match, 25% mismatch. Again, it's worth thinking about this until you see why.

But you get a higher match rate.

Thinking that the machine isn't random as you assumed, you make the pairs of holes elsewhere, but always 1.5 hours apart on the clock face. The results are the same.

Bell's Theorem says that no normal pizza can do this.

 

[David Byrden]

Now you're really curious. You decide to investigate the single pizza boxes by making more holes. And you use statistics to figure out what's going on.

The results are insane.

No matter how many holes you punch around that clock diagram, there is always a guaranteed correlation between two consecutive holes but not over any longer time. The pizza must be moving in response to your hole punching!

For two consecutive holes, with an angle A between them, the correlation is cosine-squared(A). That has a simple explanation: each time you make a hole, and see cheese or tomato, the pizza swings around so that your latest hole is in the middle of the cheese or tomato half.

And what about the pairs of pizzas, when you make one hole in each box? Exactly the same correlation! Cosine squared!

OK , so you make one hole in one pizza box and both pizzas rotate the same way! It's like they're connected! But this works only for the first two holes, if you make one in each box. On all subsequent holes, the pizzas act independently.

 

[zonde]

Sorry to ask, but I don't think I've ever really understood properly by local and non local. I did look it up on google but it just confused me. Would you be able to clarify for me please?

In context of Bell inequalities two events are non-local to each other if they are space-like separated i.e. they are out of each others past light cones.

 

[mfb]

From my understanding, if particle [1] is 'forcefully' given a spin, its entanglement between particles [2] and [3] is broken

The relation between (2) and (3) doesn't change if you measure (1). If that is an entangled state or not depends on what exactly you entangle how.

 

[rede96]

I don't think that the red/green ball example captured the spirit of entanglement in a clear way. I will give a pizza based example.

Thanks for the Pizza analogy, interesting way of looking at it. But for me the issue is the same. The pizza has a pre-determined state prior to measurement, which of course can't be the case. All the measurement is doing is showing what already exists though the hole. From what I understand the spin state of a particle isn't like that. To continue with your analogy it would only be when the hole is punched that somehow the punching of the hole interacts with the pizza and either a tomato or cheese state will be visible. Not because the pizza is turning in the box but through some other unknown process. E.g. the angle the light entered the box will some how cause either a tomato or cheese state to come into existence. Before the light enters the box there is no cheese or tomato state.

Where I get confused about Bell is, if there is some interaction between the way spin state is measured and the particle itself, why does that lead to there having to be some non local variable explanation (i.e. instantaneous communication between the two particles) or other interpretations?

Or in other words, as particles don't have a pre-determined spin state then I can't see how Bell's theorem applies to them. So why can't it be that there is just some unknown process that happens when a particle interacts with the magnetic field or in the case of photos, a polarizer?

 

[David Byrden]

I wrote the "pizza" example to represent the mathematics of entanglement in a way that's easily comprehensible.

Of course a quantum particle doesn't have a solid, fixed existence like a pizza, but my point is that we can explain the observations of the pizza with a simple model (the pizza turning when you make a hole). We don't know if that's really happening. In quantum mechanics, it's not appropriate to even ask "what's really happening". But it's useful to have a mental model that will give the same results as the real thing.

 

[David Byrden]

Where I get confused about Bell is, if there is some interaction between the way spin state is measured and the particle itself, why does that lead to there having to be some non local variable explanation (i.e. instantaneous communication between the two particles) or other interpretations?

Or in other words, as particles don't have a pre-determined spin state then I can't see how Bell's theorem applies to them. So why can't it be that there is just some unknown process that happens when a particle interacts with the magnetic field or in the case of photos, a polarizer?

The "pizza" example represents exactly the way that entangled particles have correlated measurements. So you should be able to see that it cries out for an explanation. Something links those two pizzas.

It's very telling that the correlation graph for two entangled particles is the same as for two consecutive measurements on a single particle.

The mental model adopted by the pizza delivery person is, both pizzas swing around simultaneously to the same angle. That's not possible if you consider speed-of-light issues and the plain fact that the pizzas are not connected. But the model gives the correct predictions in his context. Surely that's a step towards understanding?

 

[rede96]

The mental model adopted by the pizza delivery person is, both pizzas swing around simultaneously to the same angle. That's not possible if you consider speed-of-light issues and the plain fact that the pizzas are not connected. But the model gives the correct predictions in his context. Surely that's a step towards understanding?

Yes and no. Your example helps to understand that with reference to spin, particles can’t have a pre-existing state. But it doesn’t explain why non local variables (faster than light communication or other interpretations) are needed to account for the correlations measured.

For me there is a difference between

a) something that has a pre-existing state which is guaranteed to show up when measured.

And

b) something that has no pre-existing state and it’s state is a random result of the interaction of the thing itself and the measurement.

So as I understand it all Bell tells us is that the spin correlations we measure in entangled particles can’t be due to a)

Of course the correlations would still need to be explained but as I see it there is nothing weird about measuring a property of two exact duplicates of something (as in entangled particles) and getting the same result. Albeit a negative correlation in some cases.

 

[David Byrden]

I find it hard to understand your mental model here. You say that the particles have no pre existing state, you are aware that the measurement result is therefore random, but you're not surprised by the correlation between entangled particles?

If they were truly random there would be no correlation. It wouldn't matter that they were exact duplicates. That's what "random" means.

When a casino buys a lot of dice from a manufacturer, they expect high quality identical dice, but they don't want all those dice to throw the same sequence of numbers. It wouldn't be random.

Conversely, if the particles were obliged to yield the same result because they had been manufactured as exact duplicates, then the memory of their manufacture would be a "pre existing state" within them. Which you already ruled out.

 

[rede96]

I find it hard to understand your mental model here. You say that the particles have no pre existing state, you are aware that the measurement result is therefore random, but you're not surprised by the correlation between entangled particles?

If they were truly random there would be no correlation. It wouldn't matter that they were exact duplicates. That's what "random" means.

When a casino buys a lot of dice from a manufacturer, they expect high quality identical dice, but they don't want all those dice to throw the same sequence of numbers. It wouldn't be random.

Conversely, if the particles were obliged to yield the same result because they had been manufactured as exact duplicates, then the memory of their manufacture would be a "pre existing state" within them. Which you already ruled out.

It might just be my interpretation of the meaning of terms like “pre-existing state” or even the proper meaning of “random” so let me try and explain.

Scenario 1

If I have two playing cards, say the ace of spades and the ace of hearts, it doesn’t matter how I measure these cards, I know I’ll always measure the ace of spades as the ace of spades and the ace of hearts as the ace of hearts. They have a pre-existing state. I can say their properties were always the ace of spades and ace of hearts, even before I measure them.

This, as I understand it, is the situation bells theorem rules out.

Scenario 2

Let’s say the value of the cards could be either the ace of spades or the ace of hearts. But the value purely depends on how I measure it (E.g. what angle I view it at) and the property of the card. Sometimes I get the ace of hearts, sometimes I get the ace of spades. I can say the results are random. They don’t have a pre-existing state. I can’t say anything about the value of either card prior to it being measured as the result is a combination of the properties of the card and the properties of how I measure it. In other words when the card comes into existence, it doesn’t know how it will be measured. So it can’t have a value.

As I understand it, the math from Bells theorem doesn’t apply the above scenario.

So...

I notice in the second case there is a 100% correlation between the two cards. And when I do some measurements at different angles (120, 240 and 0) I get a 25% match rate and not the 33% match rate I get with the scenario 1, All Bells theorem tells us is that those values can’t be pre-existing. E.g. scenario 1 can’t apply.

It doesn’t rule out anything from scenario 2 (as I currently understand it)

So I may not know what is causing the correlation but I can’t rule out local variables.

Moreover, for me, it makes sense that if the results are not time dependent, then if I can replicate the exact set of conditions that led to result I can replicate the result. That might be almost impossible at the macro level but at the particle level there aren’t that many variables. Hence it also makes sense to me that entanglement is just replicating a set of properties for the pair of particles. So I shouldn’t be surprised when I get correlated results.

(EDIT: Just correcting some typos!)

 

[DrChinese]

Scenario 2

Let’s say the value of the cards could be either the ace of spades or the ace of hearts. But the value purely depends on how I measure it (E.g. what angle I view it at) and the property of the card. Sometimes I get the ace of hearts, sometimes I get the ace of spades. I can say the results are random. They don’t have a pre-existing state. I can’t say anything about the value of either card prior to it being measured as the result is a combination of the properties of the card and the properties of how I measure it. In other words when the card comes into existence, it doesn’t know how it will be measured. So it can’t have a value.

As I understand it, the math from Bells theorem doesn’t apply the above scenario.

This scenario is not an explanation that does the trick, because it cannot be used to explain the correlations. You cannot just say "suppose it did" because that's the whole purpose of Bell - to show that these type scenarios won't work.

If you have a nonlocal mechanism, one usually says that there is some FTL communication that occurs when a measurement is performed. That communication would then contain the measurement angle and the value of the result provided. The other particle, far away in terms of c, would then know to give an answer consistent with the first.

So no, Scenario 2 as you have cannot be local.

 

[David Byrden]

I'm afraid your model doesn't match reality.

You say that replicating the conditions will replicate the result. That's called "determinism".
In QM it's not like that. Replicating the exact conditions that sent out a particle, can yield a random result. Entanglement experiments are set up to do this.

You say that the state of your card is unknown because you don't yet know how you will measure it, but once you choose a measurement angle, the result is inevitable. QM is not like that. Even when we know the measurement angle for a polarity measurement, the result can be random.

 

[PeroK]

Scenario 2

Let’s say the value of the cards could be either the ace of spades or the ace of hearts. But the value purely depends on how I measure it (E.g. what angle I view it at) and the property of the card. Sometimes I get the ace of hearts, sometimes I get the ace of spades. I can say the results are random. They don’t have a pre-existing state. I can’t say anything about the value of either card prior to it being measured as the result is a combination of the properties of the card and the properties of how I measure it. In other words when the card comes into existence, it doesn’t know how it will be measured. So it can’t have a value.

As I understand it, the math from Bells theorem doesn’t apply the above scenario.

An important point about Bell's theorem is that it experimentally highlights a difference between pre-existing local variables that obey the laws of probability and quantum states that obey the laws of probability amplitudes. This creates a quantitative difference in the probablity of getting, for example, up or down at a particular measurement angle. Classical probability theory (pre-existing local variables) will give you one numerical answer and QM (probability amplitudes) will give you a different numerical answer.

It's not just a question of "randomness". It's a question of the numerical value of the probabilities that emerge from a repeated experiment.

 

[rede96]

An important point about Bell's theorem is that it experimentally highlights a difference between pre-existing local variables that obey the laws of probability and quantum states that obey the laws of probability amplitudes.

Ok I see. But aren’t they linked? Isn't the probability the probability amplitude squared? (Can’t remember if that’s right but thought they were linked somehow.)

 

[PeroK]

Ok I see. But aren’t they linked? Is the probability the probability amplitude squares? (Can’t remember if that’s right but thought they were linked somehow)

What do you mean by linked? The numerical values are given by different formulas, giving different results in certain cases. That gives the basis of an experiment to distinguish between the two cases. Namely, Bell's inequality.

 

[rede96]

What do you mean by linked?

Is the probability the probability amplitude squared?

 

[zonde]

Is the probability the probability amplitude squared?

Yes. But the problem is that there are no "coincidence amplitudes".

 

[PeroK]

Is the probability the probability amplitude squared?

It is for QM. Or, at least, the modulus squared of the complex probablity amplitide.

For hidden variables, it's simply a probablity that has a different numerical value.

 

[DrChinese]

But aren’t they linked? Isn't the probability the probability amplitude squared? (Can’t remember if that’s right but thought they were linked somehow.)

If the process was local, the outcomes - random as you mention - would be independent (factorizable) even if they were correlated. How would you get perfect correlations if the outcomes are both random and independent? And also follow the theta formula when measurement settings are different?

You can't use the EPR program for that, basically that's what we learned from Bell. Which is what you are trying to do, regardless of what you call it.