Explaining Bell's Theorem: Proving We're All Connected

[cangus]

Please Explain This...

I was referenced to this article in order to prove that we all are somehow "connected" to each other. Can someone please explain Bell's Theorem in simple terms and how it proves that we are indeed all "connected ."
here's the article:

http://www.ncsu.edu/felder-public/kenny/papers/bell.html

 

[DrChinese]

I was referenced to this article in order to prove that we all are somehow "connected" to each other. Can someone please explain Bell's Theorem in simple terms and how it proves that we are indeed all "connected ."
here's the article:

http://www.ncsu.edu/felder-public/kenny/papers/bell.html

The referenced article says nothing about universal connection. You are no more connected to everything else in a non-local universe than you are in a local universe.

 

[cangus]

ok, let me start from the beginning... i was reading this webpage:
http://www.gnostic-jesus.com/
about 5 paragraphs into the article, it goes into everyone being "connected," and introduces Bell's Theorem. Maybe I am reading things wrong but I didnt understand the referenced article about Bell's Theorem. So, DrChinese, you're basically saying that this website is a hoax and that quantum physics in no way proves that we are "universally connected?"

 

[JesseM]

Here's a quickie explanation of the meaning of Bell's Theorem I wrote up on another forum (I don't agree it proves that 'we are all connected', BTW). First, check out this analogy from the book Time's Arrow and Archimedes' Point:

By modern standards the criminal code of Ypiaria [pronounced, of course, "E-P-aria"] allowed its police force excessive powers of arrest and interrogation. Random detention and questioning were accepted weapons in the fight against serious crime. This is not to say the police had an entirely free hand, however. On the contrary, there were strict constraints on the questions the police could address to anyone detained in this way. One question only could be asked, to be chosen at random from a list of three: (1) Are you a murderer? (2) Are you a thief? (3) Have you committed adultery? Detainees who answered "yes" to the chosen question were punished accordingly, while those who answered "no" were immediately released. (Lying seems to have been frowned on, but no doubt was not unknown.)

To ensure that these guidelines were strictly adhered to, records were required to be kept of every such interrogation. Some of these records have survived, and therein lies our present concern. The records came to be analyzed by the psychologist Alexander Graham Doppelganger, known for his work on long distance communication. Doppelganger realized that among the many millions of cases in the surviving records there were likely to be some in which the Ypiarian police had interrogated both members of a pir of twins. He was interested in whether in such cases any correlation could be observed between the answers given by each twin.

As we now know, Doppelganger's interest was richly rewarded. He uncovered the two striking and seemingly incompatible correlations now known collectively as Doppelganger's Twin Paradox. He found that

(8.1) When each member of a pair of twins was asked the same question, both always gave the same answer;

and that

(8.2) When each member of a pair of twins was asked a different question, they gave the same answer on close to 25 percent of such occasions.

It may not be immediately apparent that these results are in any way incompatible. But Doppelganger reasoned as follows: 8.1 means that whatever it is that disposes Ypiarians to answer Y or N to each of the three possible questions 1, 2, and 3, it is a disposition that twins always have in common. For example, if YYN signifies the property of being disposed to answer Y to questions 1 and 2 and N to question 3, then correlation 8.1 implies that if one twin is YYN then so is his or her sibling. Similarly for the seven other possible such states: in all, for the eight possible permutations of two possible answers to three possible questions. (The possibilities are the two homogeneous states YYY and NNN, and the six inhomogeneous states YYN, YNY, NYY, YNN, NYN, and NNY.)

Turning now to 8.2, Doppelganger saw that there were six ways to pose a different question to each pair of twins: the possibilities we may represent by 1:2, 2:1, 1:3, 3:1, 2:3, and 3:2. (1:3 signifies that the first twin is asked question 1 and the second twin question 3, for example.) How many of these possibilities would produce the same answer from both twins? Clearly it depends on the twins' shared dispositions. If both twins are YYN, for example, then 1:2 and 2:1 will produce the same response (in this case, Y) and the other four possibilities will produce different responses. So if YYN twins were questioned at random, we should expect the same response from each in about 33 percent of all cases. And for homogeneous states, of course, all six posible question pairs produce the same result: YYY twins will always answer Y and NNN twins will always answer N.

[Note--I think Price actually gets the probability wrong here. If both twins are YYN, for example, then if they are questioned at random, the probability both will give the same answer would be P(first twin answers Y)*P(second twin answers Y) + P(first twin answers N)*P(second twin answers N) = (2/3)*(2/3) + (1/3)*(1/3) = 5/9, not 1/3 as Price claims. But this doesn't change the overall argument.]

Hence, Doppelganger realized, we should expect a certain minimum correlation in these different question cases. We cannot tell how many pairs of Ypiarian twins were in each of the eight possible states, but we can say that whatever their distribution, confessions should correlate with confessions and denials with denials in at least 33 percent of the different question interrogations. For the figure should be 33 percent if all the twins are in inhomogeneous states, and higher if some are in homogeneous states. And yet, as 8.2 describes, the records show a much lower figure.

Doppelganger initially suspected that this difference might be a mere statistical fluctuation. As newly examined cases continued to confirm the same pattern, however, he realized that the chances of such a variation were infinitesimal. His next thought was therefore that the Ypiarian twins must generally have known what question the other was being asked, and determined their answer partly on this basis. He saw that it would be easy to explain 8.2 if the nature of one's twin?'s question could influence one's own answer. Indeed, it would be easy to make a total anticorrelation in the different question cases be compatible with 8.1--with total correlation in the same question cases.

Doppelganger investigated this possibility with some care. He found, however, that twins were always interrogated separately and in isolation. As required, their chosen questions were selected at random, and only after they had been separated from one another. There therefore seemed no way in which twins could conspire to produce the results described in 8.1 and 8.2. Moreover, there seemed a compelling physical reason to discount the view that the question asked of one twin might influence the answers given by another. This was that the separation of such interrogations was usually spacelike in the sense of special relativity; in other words, neither interrogation occurred in either the past or the future light cone of the other. (It is not that the Ypiarian police force was given to space travel, but that light traveled more slowly in those days. The speed of a modern carrier pigeon is the best current estimate.) Hence according to the principle of the relativity of simultaneity, there was no determinate sense in which one interrogation took place before the other.

The situation in one version of the EPR experiment is almost exactly like the situation with these imaginary Ypiarian twins, except that instead of interrogators having a choice of 3 crimes to ask the twins about, experimenters can measure the "spin" of two separated electrons along one of three axes, which we can label a, b, and c (this is not the only type of EPR experiment--the one that is usually tested experimentally is one involving photons called the http://roxanne.roxanne.org/epr/eprS.html explains:

a b c a b c freq
+ + + - - - N1
+ + - - - + N2
+ - + - + - N3
+ - - - + + N4
- + + + - - N5
- + - + - + N6
- - + + + - N7
- - - + + + N8

Each row describes one type of electron pair, with their respective hidden variable values and their probabilites N. Suppose Alice measures the spin in the a direction and Bob measures it in the b direction. Denote the probability that Alice obtains +1/2 and Bob obtains +1/2 by


P(a+,b+) = N3 + N4

Similarly, if Alice measures spin in a direction and Bob measures in c direction, the probability that both obtain +1/2 is


P(a+,c+) = N2 + N4

Finally, if Alice measures spin in c direction and Bob measures in b direction, the probability that both obtain the value +1/2 is


P(c+,b+) = N3 + N7

The probabilities N are always non-negative, and therefore:


N3 + N4 <= N3 + N4 + N2 + N7
This gives

P(a+,b+) <= P(a+,c+) + P(c+,b+)

which is known as a Bell inequality. It must be satisfied by any hidden variable theory obeying our very broad locality assumptions.

But in reality, the Bell inequalities are consistently violated in the EPR experiment--you get results like P(a+, b+) > P(a+,c+) + P(c+,b+). Again, this shows that you can't just assume each pair of electrons had well-defined opposite spins on each axis before you measured them, despite the fact that whenever the two experimenters choose to measure along the same axis, they always find the two electrons have opposite spins on that axis. There are some ways to save the idea that the particle has a well-defined state before measurement, but only at the cost of bringing in ideas like faster-than-light communication between the electrons or the choice of measurements retroactively influencing the states of the two particles when they were created.