Question about Mulder and Scully experiment in The Fabric of the Cosmos

[Catquas]

In the fabric of the Cosmos by Brian Greene there is an experiment using the example of Mulder and Scully and boxes. It is an analogy to Bell's experiment determining whether articles have definite spin before you measure them. It shows that if they have definite spin before you measure them two entangled particles must have the same (or more precisely opposite) directions of spin more than 50% of the time. However it seems to me that you would get the exact same result either way. If you test three axes and each can be clockwise or counterclockwise, as a book shows there are nine possibilities. If the spin is randomly determined whenever you measure it and is always the same for both particles if you measure the same axis then it seems that in three out of the six possibilities the spins would be the same (or more precisely opposite). The other six spins would be the same 50% of the time. Therefore it seems than either case the spins would be the same more than 50%. Where am I going wrong here?

 

[Nugatory]

If the spin is randomly determined whenever you measure it and is always the same for both particles if you measure the same axis

You've caught the essence of the weirdness right there... How can the spin be always the same when you measure the same axis for both particles AND be randomly determined whenever you measure one particle? It's as if the random determination algorithm is "First, see if we're measuring the other particle on the same axis, and if so, return the same answer for both; otherwise determine the result for this particle randomly" - and that's pretty damned weird.

 

[Ken G]

Descriptions of the weirdness of entanglement often oversimplify the situation, which tends to make entanglement sound just like a pair of socks (a famous example)-- if you have a left sock and a right sock, and reach into your drawer and pick one in the dark, you know you will get a random result, and you know the other sock will be the opposite one. That sounds like what you are asking, but that isn't the weirdness of entanglement, so it shouldn't seem weird yet.

Remember, it was hard work for Bell to quantify the weirdness of entanglement, it had not really been appreciated prior to his result, even though great geniuses worked on quantum mechanics. So you shouldn't think it's super easy to see what is so weird about it! In fact, you never see the weirdness if you measure both spins around the same axis, all you get is the "socks," and it's also never weird if the axes are perpendicular, because then you get no correlation at all and have nothing to explain. You have to correlate the two spins when they are measured around axes that are neither parallel nor perpendicular to get the weirdness. I'm sure the Wiki on Bell's theorem gives a nice explanation, as do many other sites that people on here often refer to. There are a lot of threads on this-- you are not alone!

 

[Catquas]

Thanks for your responses.

My basic problem was that as Greene layed out the experiment, it seemed you would get agreement 2/3 of the time if either hypothesis was true (the deterministic hypothesis or the random but correlated hypothesis).

Ken G, I think your answer addresses this. If you only took into account measurements which were around unrelated axes (neither the same axis nor a perpendicular axis), I could seee how the deterministic hypothesis would require more than 50% correlation, but the random but correlated hypothesis (that is, the hypothesis which Bell's experiment supported) would require close to 50% correlation. In terms of the Mulder and Scully example, you wouldn't take into account cases where the same door was opened when calculating the percent agreement. Is that getting at how the exeperiment worked and showed it's result?

 

[Ken G]

In terms of the Mulder and Scully example, you wouldn't take into account cases where the same door was opened when calculating the percent agreement. Is that getting at how the exeperiment worked and showed it's result?

I think so, yes-- the surprising result is subtle and only appears when you open doors that are correlated but not completely correlated, that's where the surprising nature of the details of the correlations predicted by quantum entanglement appear. These correlations are in evidence in experiments, so it's clear that quantum mechanics gets it right, but there remains multiple ways to interpret this outcome that go well beyond the naive local realism it seems to overthrow.