The Secrets of Quantum Physics BBC4

[clive heath]

....I think it is because the equation
p(a,b) +p(a,b') +p(a',b) -p(a',b') <2*
contains a term that has to be subtracted ( the last one) and it just so happened that the experiment run by our presenter gave a negative number for that particular term so that it is added, a double negative as Gordon has detailed. Why there has to be a negative term is probably (!) because it wouldn't make statistical sense otherwise. It is as though the debit 3 in my previous trivial example has been cancelled (negated) and so the balance is now 10.

* in the original the p's are greek rhos and the inequality should be "equal to or less than" which I can't find on my special Alt characters

[Serial_Apologist]

For one who struggled with O Level Maths, it's a relief to find these issues boiled down to such elementary considerations!

[ferneyhoughgeliebte]

But why does a term "have to be subtracted", Clive? Where does the subtraction element enter into a "sum" (which means, I thought, "adding up")?

[ferneyhoughgeliebte]

As Gordon said - "the four terms have to add up to less than 2".

[french frank]

....I think it is because the equation
p(a,b) +p(a,b') +p(a',b) -p(a',b') <2*
contains a term that has to be subtracted

That does seem to be the key. That it was a special factor relating to the equation. I don't ask how Bell arrived at his equation

[Gordon]

In other words, where has this extra minus sign suddenly come from? Why isn't it a plus sign like all the others?

The "extra" - [your red one] is defined to be negative in the Inequality which comes from the Bell et al theory, you HAVE to subtract the 3rd term from the others. The confusion has arisen because in the example shown by JaK - his particular set of 4 experimental runs - that 3rd term's correlation from the instruments was a negative number. This strange result of the negative number from the experimental instruments [see the diagram in the Wiki article link below] - where does that come from, why is it negative not positive like the others? A simple explanation is that for that particular set up of the instruments the detectors measure a strongish disagreement in the particle states as they are accumulated from many photon pairs. It is possible that the settings of the instruments could produced correlations that were all positive but the theory says that even the negative value in the 3rd term would never cause the sum to be less than 2. For Einstein et al to be right that sum must always be LESS than or equal to 2.

Where it comes from in the theory I don't know because I don't fully understand that theory yet. Try looking at the Wiki Article on Bell's Inequality, it's all there; two of the references to that article - 2 and 5 - might also be helpful, they are both worth reading especially 5 as it has more background in plain English! Note that the 4 term equation used by JaK is not Bell's, his has only 3 terms 2 of which are negative, it's a development of it by the American Hippies [CHSH are their surname initial letters - John Clauser, Michael Horne, Abner Shimony and R. A. Holt]!!

http://en.wikipedia.org/wiki/Bell%27s_theorem

PS re 58, 63 and 64: "Adding up" a set of numbers includes the possibility that some of those numbers are not positive. I think your confusion is assuming that "adding" must ONLY refer to positive numbers. The result of an addition - the "Sum" - is the net result as Clive has noted in his bank balance analogy.

[ferneyhoughgeliebte]

Many thanks, Gordon - not least for your patience!

[clive heath]

I'm not so worried about there being a negative term in a sum of a set of probabilities as by a probability being negative unless it a deviation from a probability that you might expect on the basis of randomness and if that was explained then I didn't pick it up.

....this post-posted Gordon's and adds little, sorry.

[french frank]

Where it comes from in the theory I don't know because I don't fully understand that theory yet.

Et tu, Brute! (I've checked the Wiki article, thank you very much ).

[Flay]

p(a,b) +p(a,b') +p(a',b) -p(a',b') <2*

Gosh. I thought this related to a certain message boarder residing in the Philippines!

I started reading this page and developed vertigo.

I'll try again in the morning...

[Serial_Apologist]

Gosh. I thought this related to a certain message boarder residing in the Philippines!

I started reading this page and developed vertigo.

I'll try again in the morning...

[Pabmusic]

[ferneyhoughgeliebte]

Ah! So when it says that his location is "Chandler's Ford and Cadiz" ...

[Pabmusic]

Ah! So when it says that his location is "Chandler's Ford and Cadiz" ...

Capiz (as in Capiz shell - mother-of-pearl).

I can't recall two slits at the same time. Maybe about 1971-2 when I was first at college (but I still don't remember any of it).

[Oh dear. Wash my mouth out. Sorry, Mum. ]

[french frank]

Anyway. Now that we've sorted out Quantum Mechanics (keep up, Flay!), what's the next problem for the forum?