B Layman question about faster than light communication

[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.

 

[rede96]

If the process was local, the outcomes - random as you mention - would be independent (factorizable) even if they were correlated.

I’m not sure I understand your point. What do you mean exactly by independent or factorizable? I think this is the part I never quite grasp.

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.

Just to reiterate, I’m not arguing against the physics. I just can’t for the life in me see how Bells theorem prohibits local variables and leads to the conclusion there must be instantaneous communication between the entangled pair.

EDIT: I can see why it prohibits pre existing states. But I don’t get why not having a pre existing state means nothing local going on.

 

[PeterDonis]

What do you mean exactly by independent or factorizable?

Have you read Bell's paper? You can find it here:

http://www.drchinese.com/David/Bell_Compact.pdf

Equation (2) in the paper describes a factorizable probability function.

I’m not arguing against the physics. I just can’t for the life in me see how Bells theorem prohibits local variables

This is a "B" level thread, and the question you are implicitly asking here really needs at least an "I" level discussion, if not "A" level. So you really need to start a separate thread. (I would strongly recommend reading the Bell paper first.)

and leads to the conclusion there must be instantaneous communication between the entangled pair.

It doesn't lead to that conclusion. It just says local hidden variable models can't reproduce the actual QM correlations. It doesn't make any claims about what other kind of model can reproduce the QM correlations, or whether such a model requires instantaneous (FTL) communication. Those are separate questions.

 

[DrChinese]

1. I’m not sure I understand your point. What do you mean exactly by independent or factorizable? I think this is the part I never quite grasp.

2. Just to reiterate, I’m not arguing against the physics. I just can’t for the life in me see how Bells theorem prohibits local variables and leads to the conclusion there must be instantaneous communication between the entangled pair.

1. Let's say that the action on each side is independent, no communication between them (which would need to be FTL, to match experiments in which the distance is too far to be c or less). Therefore if there is any random factor involved that is NOT like your scenario I ("pre-existing state"): there is a chance that the result on one side (which is random and independent) and the result on the other side (which is random and independent) will not match up.

2. This is NOT a conclusion or deduction from Bell. Bell excludes local realistic theories. It could be non-local or non-realistic (or both).

 

[rede96]

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.

Sorry, that wasn’t what I was trying to demonstrate. In my card example both the card and measurement angle were random. So the result wasn’t inevitable once the measurement angle was selected.

It’s just that there was something additional going on that meant the two paired cards were random in a similar way which led to correlations.

 

[rede96]

1. Let's say that the action on each side is independent, no communication between them (which would need to be FTL, to match experiments in which the distance is too far to be c or less). Therefore if there is any random factor involved that is NOT like your scenario I ("pre-existing state"): there is a chance that the result on one side (which is random and independent) and the result on the other side (which is random and independent) will not match up.

Ok, thanks for explaining that. Again maybe it’s my understanding of what a pre-existing state.

Lets say the action on each side is independent. So I produce and measure a number of entangled particles. For the sake of argument I measure them all at the same angle. I find each pair may give a different result each time, (e.g. one pair up down and the next down up etc) but each pair are always correlated.

So I assume this is because they are exact copies of each other, it makes sense that their results always match at the same angle. I also assume as each pair appear to be random, albeit correlated, they don’t have a pre-existing state in those circumstances.

But what I think you are saying is that for each pair to be independent, random and exactly correlated, they must have a pre-existing state. As their correlation can’t be explained any other way using local variables. Is that correct?

And what Bells theorem says is they can’t have a pre-existing state, so something non local must be going on.

Is that sort of the gist of it?

 

[DrChinese]

Ok, thanks for explaining that. Again maybe it’s my understanding of what a pre-existing state.

Lets say the action on each side is independent. So I produce and measure a number of entangled particles. For the sake of argument I measure them all at the same angle. I find each pair may give a different result each time, (e.g. one pair up down and the next down up etc) but each pair are always correlated.

So I assume this is because they are exact copies of each other, it makes sense that their results always match at the same angle. I also assume as each pair appear to be random, albeit correlated, they don’t have a pre-existing state in those circumstances.

But what I think you are saying is that for each pair to be independent, random and exactly correlated, they must have a pre-existing state. As their correlation can’t be explained any other way using local variables. Is that correct?

And what Bells theorem says is they can’t have a pre-existing state, so something non local must be going on.

Is that sort of the gist of it?

Yes, I was showing you that if there are to be the proper stats at the same angles, and they are random and independent (no FTL communication), there cannot be anything depending on anything OTHER than the initial state (i.e. the measurement system). And yes, Bell would rule that out (the initial state a la EPR) when you check other angle settings.

There could be FTL communication. There could be retrocausal communication. There are some other hypothetical mechanisms. But nothing Local Realistic.

 

[rede96]

Have you read Bell's paper? You can find it here:

This is a "B" level thread, and the question you are implicitly asking here really needs at least an "I" level discussion, if not "A" level. So you really need to start a separate thread. (I would strongly recommend reading the Bell paper first.)

Thanks for the link. I have read Bell's paper but unfortunately the math is beyond me. Hence why I am trying to take the logic approach. It's also why I stay around the B level.

But the posts here have helped (thanks to everyone) so I'll reflect and go through the paper again and start a new thread as recommended.

Thanks again.