guest1202 wrote:Theorem: There is no probability distribution p(i,j,k,m) which
yields the above hypothetical marginals pAB , pA'B , pAB' , pA'B'
as true marginals.
The theorem is a special case of Bell's theorem.
Despite the simplicity of its statement and proof,
it is considered one of the most important scientific
advances of the past centuries. If it is false or even if there is
any mistake in any of its accepted proofs, that will be huge news,
shaking the scientific establishment to its roots.
guest1202 wrote:Theorem: There is no probability distribution p(i,j,k,m) which
yields the above hypothetical marginals pAB , pA'B , pAB' , pA'B'
as true marginals.
The theorem is a special case of Bell's theorem.
Despite the simplicity of its statement and proof,
it is considered one of the most important scientific
advances of the past centuries. If it is false or even if there is
any mistake in any of its accepted proofs, that will be huge news,
shaking the scientific establishment to its roots.
guest1202 wrote:An explicit presentation would only require specifying 16 probabilities
from which one could easily check by hand that they do indeed yield the
hypothetical marginals as true marginals. Taking into account the Alice-Bob
symmetry of the underlying quantum state and the fact that all the probabilities
must sum to 1, actually only 7 probabilities need be specified.
guest1202 wrote:guest1202 wrote:An explicit presentation would only require specifying 16 probabilities
from which one could easily check by hand that they do indeed yield the
hypothetical marginals as true marginals. Taking into account the Alice-Bob
symmetry of the underlying quantum state and the fact that all the probabilities
must sum to 1, actually only 7 probabilities need be specified.
The reduction to 7 probabilities isn't correct. Although the underlying quantum
state is Alice-Bob symmetric, encoded into the hypothetical marginals
are measurement angles (as given in Peres' book) which are not, and the marginals
themselves are not. So, one needs to specify all 16 probabilities p(i,j,k,m), or only
15 taking into account that they must sum to 1.
Also, I misspoke when I said that I expected the linear system for the probabilities to
be inconsistent. The linear system might be consistent, with no solutions for which all
the probabilities are non-negative. I meant that the linear system augmented with the
condition that all probabilities be non-negative must be inconsistent. (Unless, of course,
Bell's theorem is wrong ! )
I wonder if the moderators would tolerate me calling other posters "stupid".
The insults don't particularly bother me, but the inconsistency in enforcing
decorum does seem telling. In one of my initial posts back in December, a moderator
chastised me just for saying that I found papers of one of the posters "hard to read".
He characterized that as a "flame".
guest1202 wrote:I wonder if the moderators would tolerate me calling other posters "stupid".
guest1202 wrote:
I've seen some regulars make puzzling statements on the order of
"a mathematical inequality can NEVER be violated,
Mathematical inequalities generally make some assumptions which
are necessary for their validity.
Dirkman wrote:guest1202 wrote:
I've seen some regulars make puzzling statements on the order of
"a mathematical inequality can NEVER be violated,
Mathematical inequalities generally make some assumptions which
are necessary for their validity.
Well wikipedia says a math inequality is something like 1< 2, and a math inequation is something like x<2, and I dont see how the mathematical inequality 1< 2 could be violated. I dont know...just saying, I dont know much math or physics.
FrediFizzx wrote: Given the CHSH string of expectation terms that can range from -1 to +1 do you think the following as a result for CHSH is possible?
+1 -(-1) + 1 +1 = 4
luca valeri wrote:Hi Joy,
Did I understand you right, that you accept the first line with the C's in the Wikipedia Derivation of the CHSH inequality but not the equality with the second line below?
But if you accept the first line - and it can be questioned, whether this should be true in local realistic theories - the following lines follow from simple mathematical manipulations, that are true independent of the physical meaning. Isn't it?
Best regards
Luca
luca valeri wrote:And Fred,
you saidFrediFizzx wrote: Given the CHSH string of expectation terms that can range from -1 to +1 do you think the following as a result for CHSH is possible?
+1 -(-1) + 1 +1 = 4
if A,A',B and B' can take only the values 1 or -1 (depending on the hidden variable lambda).
Do you think AB + AB' + A'B - A'B' <= 2 is wrong?
luca valeri wrote:if A,A',B and B' can take only the values 1 or -1 (depending on the hidden variable lambda).
Do you think AB + AB' + A'B - A'B' <= 2 is wrong?
Joy Christian wrote:luca valeri wrote:if A,A',B and B' can take only the values 1 or -1 (depending on the hidden variable lambda).
Do you think AB + AB' + A'B - A'B' <= 2 is wrong?
If anyone can describe a physical experiment that can measure each quantity
AB + AB' + A'B - A'B'
within the standard EPR-Bohm setup, and then evaluate the average
< AB + AB' + A'B - A'B' >
without cheating (and without statistical obfuscations designed to cheat),
then I will withdraw my claim that Bell and his followers have been cheating the physics community for the past fifty years.
So here is my challenge to the followers of Bell:
Describe an experiment that can measure each quantity
AB + AB' + A'B - A'B'
within the standard EPR-Bohm setup, and convince us that it can actually be done (at least by the deterministic God of Spinoza).
FrediFizzx wrote:Joy Christian wrote:luca valeri wrote:if A,A',B and B' can take only the values 1 or -1 (depending on the hidden variable lambda).
Do you think AB + AB' + A'B - A'B' <= 2 is wrong?
If anyone can describe a physical experiment that can measure each quantity
AB + AB' + A'B - A'B'
within the standard EPR-Bohm setup, and then evaluate the average
< AB + AB' + A'B - A'B' >
without cheating (and without statistical obfuscations designed to cheat),
then I will withdraw my claim that Bell and his followers have been cheating the physics community for the past fifty years.
So here is my challenge to the followers of Bell:
Describe an experiment that can measure each quantity
AB + AB' + A'B - A'B'
within the standard EPR-Bohm setup, and convince us that it can actually be done (at least by the deterministic God of Spinoza).
Hmmm... Did guest1202 rub off on you? Now you are proposing an impossible task.
Joy Christian wrote:luca valeri wrote:if A,A',B and B' can take only the values 1 or -1 (depending on the hidden variable lambda).
Do you think AB + AB' + A'B - A'B' <= 2 is wrong?
If anyone can describe a physical experiment that can measure each quantity
AB + AB' + A'B - A'B'
within the standard EPR-Bohm setup, and then evaluate the average
< AB + AB' + A'B - A'B' >
without cheating (and without statistical obfuscations designed to cheat),
then I will withdraw my claim that Bell and his followers have been cheating the physics community for the past fifty years.
So here is my challenge to the followers of Bell:
Describe an experiment that can measure each quantity
AB + AB' + A'B - A'B'
within the standard EPR-Bohm setup, and convince us that it can actually be done (at least by the deterministic God of Spinoza).
***
guest1202 wrote: I don't expect to convince Dr. Christian and his followers, but maybe they will prove me wrong.
I'm writing this for the benefit of readers not familiar with Bell's theorem.
guest1202 wrote:A source sends a "hidden variable" which I shall call t to widely separated Alice and Bob. Think of it as a slip
of paper with some writing on it. The writing specifies what each will measure. In Dr. Christian's notation,
if Alice will obtain result +1 when she measures a quantity "A", then the slip t says "A(t) = +1"; otherwise it
says "A(t) = -1". Besides specifying the result of measuring quantity A it also specifies what happens if she
measures a different quantity A' . Written on the slip along with the result A(t) is A'(t) = +1 or A'(t) = -1.
However, Alice cannot read both the result A(t) and A'(t) at the same time. That it how quantum mechanics
is set up, so if we want to reproduce quantum mechanics, we cannot assume the Alice can measure both.
However, we can imagine that some more informed entity Gideon (aka God) can read the entire slip, in particular the result that will occur if Alice measures A and also what will occur when she measures A'.
Similarly for Bob, of course; his possible results are written on the slip an called B(t) and B' (t).
(Think of Alice and Bob as receiving identical slips, but Alice doesn't have resources to read what Bob's result will be,
and vice versa.)
The question of whether quantum mechanics can be reproduced by this classical theory comes down to whether
it is possible to specify the statistics of the contents (slips) of the urn so that classical probability theory
predicts exactly what quantum mechanics predicts. What quantum mechanics predicts are the
four "hypothetical marginals" denoted , and of my previous posts. The "statistics of the urn" are defined by the probability function denoted p = p(i,j,k,m) in those posts.
Joy Christian wrote:
If anyone can describe a physical experiment that can measure each quantity
AB + AB' + A'B - A'B'
within the standard EPR-Bohm setup, and then evaluate the average
< AB + AB' + A'B - A'B' >
without cheating (and without statistical obfuscations designed to cheat),
then I will withdraw my claim that Bell and his followers have been cheating the physics community for the past fifty years.
So here is my challenge to the followers of Bell:
Describe an experiment that can measure each quantity
AB + AB' + A'B - A'B'
within the standard EPR-Bohm setup, and convince us that it can actually be done (at least by the deterministic God of Spinoza).
***
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