kaonyx
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Ahhhh! You see these inference rules of which thou spake are entirely a classical vanity! Allow me to illustrate.
I would like to discuss a specific example please, involving random numbers, because that is the challenge set to me by KenG. I will base this (very loosely) on the work done by The Irish physicist John Bell who famously demonstrated that Einstein's concern about the seriousness of the problem for physics, was fully justified.
If you have access to an Excel spreadsheet , type in this formula that should generate a random R or G, to represent a result of an experiment that is randomly green or red. (The F9 key forces a recalculate).
=IF(INT(RAND()*2)=0,"R","G"). I simply include this formula to illustrate the kind of data we are dealing with.
Ok now imagine we have a particle source located between two labs. An event in the source emits a two particles in opposite directions, into a detector located in each lab.
This particle causes two lights on each detector to light up randomly, much as our spreadsheet formula operates. (Two formulas for each detector).
Over lunch the physicists compare results. They get data sets like this:
R G<---*--->G R
G R<---*--->R R
R R<---*--->G G
R G<---*--->R G
G G<---*--->G R etc.
From the point of view of each lab, the results are random.
Here is a simple question for you.
Suppose that only after comparing these data sets side by side, over lunch, the physicists discover that there seems to be a rule operating between the labs.
It doesn't actually matter what the rule is, but let's make one up...
Suppose that the combination GG<---*--->RR is never observed.
And of course it is the same from each side, RR<---*--->GG is never observed.
What kind of theory can explain such a result?
The idea of the particle or the detectors passing signals between each other is ruled out because the experiment gives the same result when one of the detectors is on the moon and the other is on earth.
Maybe there is some kind of rule or formula or property that can be carried by the particle, that is like a computer program that can make a decision? But this idea falls flat, because it turns out that it doesn't matter which lab measures the properties first.
Now suppose that they also discover that not only is there no rule that can sent from the source, there is no POSSIBLE rule that can be sent from the source to account for the behaviour of the lights. This is very unsettling. (Some of the scientists go slightly insane and produce wacky theories about faster than light travel or telepathic alien jellyfish.) But the results withstand scrunity.
And now to make things worse, they conclude that the actions of the experimenters who detected properties in the lab, must pre-determine the lights in the lab that has not yet made the measurement. All of this done without any information or possible information transferred.
Quantum theory even goes a step further and says that the properties themselves are not "real" (ie clearly green or clearly red) until actually measured in the interaction with the detectors.
Finally now we can see how the role of the observer is implicated. Do you think that it is "mystical" and relies on the human mind? Or is this how things interact with each other, regardless of humans? Or does the reality we understand ultimately link to these spooky "entanglements" because of the "causal net" of "historical reality"?
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