I can't promise you will all be changed, in the twinkling of an eye or otherwise. Some of you might be.
All I'm going to do this week is present the problem, and give you time to make a prediction based on some simple statistics that can be observed in nature.
This is prediction is a refined, simplified, toy-model version of Bell's Theorem, which was published over sixty years ago. Experimental tests of Bell's Theorem were realized beautifully in 1980's by Alain Aspect and collaborators in France. Since that time many other such experiments have been performed, and all of them find that quantum mechanics describes reality.
And I want to be clear about this: there is exactly nothing "weird" about quantum mechanics, and any problems or paradoxes we might encounter here have nothing to do with quantum mechanics.
Quantum mechanics does nothing but describe reality.
So it is reality--not quantum mechanics-- that is weird.
Reality is weird specifically in a way that philosophers from Aristotle to Ayer have said either cannot be (Aristotle), or can be but cannot be known about (Kant), or cannot even be meaningfully talked about (Ayre): "For one cannot conceive of an observation which would enable one to determine..." the truth or falsity of a metaphysical statement about the nature of “transcendental reality”.
That statement by Ayre--a British positivist who was considered one of the great minds of mid-20th century philosophy--is something I like to keep very much in mind, because reality does not care what Ayer or I or anyone else can conceive of.
"But I don't understand how you could measure that" is not a criticism of any proposition, it is a statement of my own limitations. Sometimes I don't understand how a thing can be plausible or testable because it isn't. Other times I don't understand how a thing can be plausible or testable because I'm not too bright. Figuring out which is the case is work, but it's work that has to be done if I'm to distinguish the two situations. Just finding something inconceivable is not an argument against it. If it was, it would be an argument against reality, as I will eventually demonstrate, because reality is inconceivable, and thanks to Bell’s genius we can know that.
So here is a metaphorical version of Bell's argument, which is something Ayre--a philosopher with no training in physics--couldn't imagine. Rather than photons or electrons I'm going to talk about repeatedly flipping a pair of very peculiar coins under varying circumstances, which allows me to draw an even stronger conclusion than Bell and others have, and which shows the structure of the argument in a way that many people should be able to intuitively grasp. I hope.
Imagine a room that looks like this:
It's a long rectangle with three daises at each end, painted red (top), blue (middle), and green (bottom). I’ve added the colours just to make the image prettier. I've also given them some stripes to make them more visually distinct and to suggest the polarizer angles that are set in real experiments of this kind.
In the centre of the room is a plinth with two coins on it, shown here as white circles resting on the black top of the plinth.
Two experimenters enter the room and repeatedly go through the following procedure:
They each pick up a coin, turn their backs to each other standing with their butts against the plinth.
They then both walk to one of the daises they are facing, chosen at random and independently of one another. So one third of the time they go to the top, one third to the middle, one third to the bottom, and what one of them does is completely independent of what the other does.
Arriving at the dais of their choice they stand on it and flip their coin. They write down the result--heads or tails--on a board hung on the wall adjacent to each dais, so they know what the result was and which dais they were standing on. They also note the trial number--which is just the number of times they've repeated the procedure--beside each result.
Then they return the coins to the plinth start over again.
After doing this a bunch of times they have a look at the data and see the following.
First, being good scientists, they look at the overall statistics. They notice that each coin appears fair: the same number of heads and tails come up at each end of the room. Digging a little deeper, they notice that it doesn't matter what dais the coin is being flipped on: they are fair regardless. This is all unremarkable and what you would expect if the coins are just classical hunks of stamped and milled metal.
Things start to look odd when they start looking at the outcome of each pair of flips, thought. They start by looking at cases where they have both happened by random chance to have stood on the same colour dais.
In these cases the coins always come out identically.
Top/top flips, middle/middle flips, bottom/bottom flips: in each of these cases if one coin lands heads so does the other one, and if one coin lands tails, the other one does too. The total number of heads and tails for each coin is still identical, though, so the paired coins are fair even though they have this perfect correlation between them.
Finally, they look at cases where one person stood on a top dais and the other stood on a bottom one.
In these cases, the coins always come out differently.
If one is heads the other is tails, and vice versa.
Again, though, they are still fair: equal number of heads and tails, just perfectly anti-correlated.
Now here is the question:
Given these results, we can make a prediction about what we'll see if we compare top/middle or bottom/middle outcomes.
What is that prediction and why?
In doing this analysis it is useful to imagine that the coins are somehow programmed by the plinth each time they are set down on it that specify the outcome for each dais (top/middle/bottom), and that these programs are identical in each case, so if one coin has H/T/T then the other has H/T/T as well. The second thing we can infer about the programming is that the ends have to be different, so we can never have T/H/T or H/H/H, because that would violate the observation that the top and bottom dais results are always opposite each other.
The thing that allows us to set up the analysis in this way is the law of local causality, which says simply: What a thing is now causes what it does now.
This is not mysterious or controversial, although it's not often stated in this explicit form. It is in fact the absolute bedrock of knowledge creation: we look at how things behave (what they do) and infer from that how they may be (what they are) based on the idea "if they are like X they would behave like Y." The dialectic of science goes precisely like this, everywhere, all the time: observe an object with a behaviour, form a few ideas about how the object would have to be to cause that behaviour, consider cases where those various ways of being would lead to different behaviours from one another, and make observations in those cases to see which idea is more likely. Round and round this goes until you've got one idea that is the clear winner... at least for now.
So we can always infer "being" from "doing". We may not want to bother in any given case, but we can never claim it can't be done. This has surprisingly far-reaching consequences.
When we see two objects behaving with such strongly correlated behaviour as this imaginary experiment produces we are fully justified in considering the possibility that there is something about the objects in question that causes their behaviour, and that thing is shared between them. The idea that they have a top/middle/bottom result “programmed into them” at the start of each trial is a very general hypothesis that captures a whole family of possibilities: in particular, any cause where the outcome of the flip of one coin can't influence the outcome of the flip of the other.
The actual physical cause could be magnetic fields or gravitational anomalies or little mechanical whirligigs inside the coins: it doesn’t matter. Whatever the details are, the general situation is that the coins are somehow “preset” by the plinth in a way that determines the outcome when they are flipped on any given dais, and both coins are programmed the same way, and the programs are constrained to be ones where the result for the top and bottom dais are opposite each other, and nothing changes after they are programmed.
So this analysis based on programs is very general and powerful. It is a valid description of any non-communication-based mechanism that would cause the coins to behave in the observed manner, with same-dais flips the same, top/bottom dais flips the opposite, and all flips having a 50/50 chance of coming out heads or tails.
Write down the allowed programs given these constraints and see what you can say about the top/middle or middle/bottom results, where one coin is flipped on a middle dais and one is on a top or bottom dais. Feel free to share in the comments, but don't look in the comments before you've tried it yourself!
Next week I'll set out what the prediction is, and talk about what actually happens when an experiment of this kind is performed with entangled photons.
And in doing so, I will show you a mystery.
I read this several times. I'm not really sure what you want us to do. Your description of causation seems OK. It seems to fit what I think of causation in social data. I'm just not sure what's really going in the post.