Can grandpa understand the Bell's Theorem?

[DrChinese]

SpectraCat,

According to you, in the gedanken experiment #2 we will not get a simple cos^2 correlation coefficient because their photons are non-entangled. According to my prediction the gedanken experiment #2 does produce the cos^2 correlation coefficient, because in my interpretation this result is nothing to do with entanglement (influence over distance). This is why this experiment questions a role (and probably the existence) of the influence over distance that is the most important conclusion of the Bell theorem. This what I mean by saying that the gedanken experiment #2 can falsify the Bell's theorem.

Basically, you are making an incorrect prediction for an experiment that has already been performed and yielded different results. Also, yours is NOT the classical prediction. It is just something you made up out of thin air with not the slightest justification or mathematical derivation. You may as well claim that your prediction is .758401 and state that performing the experiment will falsify Bell. Which it wouldn't. It would "only" falsify QM.

 

[miosim]

http://plato.stanford.edu/entries/qt-epr/#1.3 (Einstein's versions of the EPR argument):
“… The central point of EPR was to argue that in interpreting the quantum state functions the real states of spatially separate objects are independent of each other …”

Yes, that was their incorrect argument.

Can you collaborate about disprove of EPR argument?

Basically, you are making an incorrect prediction for an experiment that has already been performed and yielded different results…

Can you please describe this experiment?

… Also, yours is NOT the classical prediction.
What does classical prediction mean? …

It is just something you made up out of thin air with not the slightest justification or mathematical derivation.

My prediction is based on the same mathematical derivation as prediction for Aspect's experiment, but on the different interpretation of events; in my interpretation the cos^2 correlation coefficient is nothing to do with non-local interactions.

Can you demonstrate that this mathematical derivation is based on non-local interactions?

 

[DrChinese]

Can you collaborate about disprove of EPR argument?Can you please describe this experiment?

This has already been done many times in this circular thread. After 400 posts, if you don't know that Bell's Theorem is a disproof of EPR, I really don't know what to tell you. As to the experiment, I have told you previously that I don't have a reference and don't know any reason there would be one. Maybe you will be the first to write up this null result.

 

[JDoolin]

\Psi=(|H_A>\otimes|V_B> + |V_A>\otimes|H_B>)

Is there anywhere online where I could get an introductiton to that notation? (or if not online, a good introductory text?) I had one professor that called it "bra" "ket" notation, and usually <A|, the "bra" represented an operator, and |B> represented a "ket" which was some numerical value or vector or matrix.

But I can't find anything under "bra ket notation," so I guess that terminology isn't in common usage.

Anyway, when I last posted to this thread, I was wondering whether somehow the |H_A&gt; , |H_B&gt; notation referred somehow to matrices, for instance

|H_A>=\begin{pmatrix}
cos(\theta_A )\\
sin(\theta_A)
\end{pmatrix}?

But with the multiplication |H_A&gt; |H_B&gt; of course, matrices can't be multiplied that way, but you introduced a new operator here: \otimes which might resolve it?

 

[SpectraCat]

Is there anywhere online where I could get an introductiton to that notation? (or if not online, a good introductory text?) I had one professor that called it "bra" "ket" notation, and usually <A|, the "bra" represented an operator, and |B> represented a "ket" which was some numerical value or vector or matrix.

But I can't find anything under "bra ket notation," so I guess that terminology isn't in common usage.

Anyway, when I last posted to this thread, I was wondering whether somehow the |H_A&gt; , |H_B&gt; notation referred somehow to matrices, for instance

|H_A>=\begin{pmatrix}
cos(\theta_A )\\
sin(\theta_A)
\end{pmatrix}?

But with the multiplication |H_A&gt; |H_B&gt; of course, matrices can't be multiplied that way, but you introduced a new operator here: \otimes which might resolve it?

It is called Dirac notation, or bra-ket notation. The wikipedia page is a decent place to start for an intro. The \otimes is just used to indicate that the state is composed of two "kets" (i.e. vectors) from different vector spaces. For example, if you treat a molecule in the Born-Oppenheimer approximation, you could write it's total wavefunction as a composition of the electronic and vibrational wavefunctions (there are other contributions which might also be important), which are solved independently.

It does not make sense to write the product of two kets from the same vector space (i.e. |m>|n> is non-sensical), so the \otimes is useful to make explicit that the two states come from different vector spaces. Note that the notation for the dot product of a bra and a ket vector (<m|n>) does NOT combine vectors from the same space. The space of bra vectors is "dual" to the space of "ket" vectors, but is not identically the same. For example, you might write the position space representation of some ket |n> as the wavefunction \psi_n(x) ... in that case, the position space representation of the bra <n| that is dual to |n> would be the complex conjugate of the same wavefunction ... i.e. \psi_n^*(x).

Hope this helps.