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Re: bell inequalities

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  • Eric Dennis
    ... I don t know if any of Bell s papers are on the web, other than maybe at the site for Phys Rev. ... Yes. ... I can t find any quant-ph/001210. That must be
    Message 1 of 47 , Nov 2, 2001
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      > Unfortunately I have not access to original Bell's paper. I have
      > possibility to order them but it would be too long. I just have a
      > couple of review articles on this subject but none of Bell's papers.
      > Where can I download them in e-form? I can imagine that the physical

      I don't know if any of Bell's papers are on the web, other than maybe at
      the site for Phys Rev.

      > result could be obtained in different ways. But it is vital to
      > understand the minimal premises needed to derive it. Moreover as a

      Yes.

      > of "necessary and sufficient conditions". Besides take a look at
      > quant-ph/001210 I just give a little extract (math symbols in LaTex,

      I can't find any quant-ph/001210. That must be the wrong ref number.

      > "
      > Consider a pair of spin one-half particles formed in the singlet spin
      > state and
      > moving freely in opposite directions. If one neglects the space part
      > of the
      > wave function then the quantum mechanical correlation of two spins in
      > the
      > singlet state spin is
      >
      > $E_{spin}(a; b) = <\psi_{spin}|a\cdot \sigma \otimes b\cdot \sigma
      > |\psi_{spin}> =
      > -a \cdot b$
      >
      > Here $a$ and $b$ are two unit vectors in three-dimensional space and
      > $\sigma =
      > (\sigma_{1}; \sigma_{2}; \sigma_{3})$ are the Pauli matrices.
      >
      > Bell's theorem states that the function
      >
      > $E_{spin}(a; b)$ can not be represented in the form
      >
      > $P(a,b)=\int A(a,\lambda)B(b,\lambda)d\rho(\lambda)$

      Right. So what can be represented in that form? Anything that is
      explainable *locally*. I don't know exactly what you mean by the above
      showing how qm probabilities are "nonKolmogorovian". All probabilities
      satisfy Kolmogorov's axioms. If they didn't--what would that mean?--they
      would be useless to us.

      Trying to understand the results of EPR-Bell experiments by denying basic
      mathematical truths (like the Kolmogorov axioms) is like trying to
      understand why balloons fly by denying that they are material objects.
      It's just throwing words at the problem without really facing up to it.

      > > I don't deny FTL influences. I think BIs prove the existence of FTL.
      > > That's all I mean by "non-locality"
      >
      > What about causality?

      BIs show that there is an apparent conflict between relativistic causality
      and qm. Now this may only be an apparent conflict (see
      http://www.objectivescience.com/articles/ed_tachy.htm), or it may be a
      real one. But, again, we must fact up to it.


      >
      > > That's a different issue. I'm talking about the fact that in a
      > measurement
      > >
      > > A --> P A P
      > >
      > > where P is a projector depending on the measurement result. Since
      > neither
      > > A nor P are local objects, this generally involves a non-local
      > change in
      > > the system.
      >
      > Sorry but it's mere a formal scheme (in operator approach). Do you
      > mean that the measurement
      > is taken instanteneously? But it only seems so because of
      > nonrelativistic approximation.

      No. The fact that they can perform the measurements fast enough to
      actually verify the qm violation of BIs in the lab means that this
      formalism is sufficient. And it is not merely a formal scheme. If you want
      to use Heisenberg operators, that is fine. But then you have to specify
      what happens to them after one makes a measurement. And what happens to
      them is exactly A-->PAP.

      > But it is impossible. Do you know some (obviously pure speculative)
      > papers on entanglement of tachyons? Since SRT does not forbid their
      > existence it would be interesting to analyse the possibility of their
      > entanglement along with probable effects.

      Whether or not SR forbids tachyons in general it certainly forbids them
      from interacting with normal particles (or else one gets causal
      paradoxes). It may be different in GR, though (see above link).

      > So if we knew the configuration of an apparatus we would foresee the
      > result of the measurement for sure like in classical mechanics? But in

      Yes.

      > QM it's impossible not (only) because of enormous amount of
      > information (like in class statistical mech) but because of \hbar=/=0
      > which prohibits the determination of state of the ssystem in such
      > CM-dynamic deterministic way. That is why I asked at the beginning
      > about the status of Plank's constant in dBB. It appears that dBB treat
      > it as phenomenological (intermediate) quantity.

      If that is what you mean by calling it phenomenological, then yes.
      However, I don't think the term "phenomenological" properly refers to
      "anything which doesn't put fundamental restrictions on our knowledge".
    • millipede8@yahoo.com
      ... The Casimir force = -dE/dx, where x is the separation between the metal plates and E is the ground state energy of the vacuum between the plates. By the
      Message 47 of 47 , Nov 8, 2001
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        > As far as I remember it always appears due to subtraction of one
        > infinity from another.

        The Casimir force = -dE/dx, where x is the separation between the
        metal plates and E is the ground state energy of the vacuum between
        the plates.

        By the way, Kasimir is an incorrect spelling. He signed his papers H.
        B. G. Casimir which stands for Hendrik Brugt Gerhard Casimir. He
        worked for Phillips corporation in Netherlands.

        > I hope that in correct theory no such tricks will be used.
        >It seems to me that the situation is close to that in claculus at 17-
        >18 centuries when such things as
        > 1-1+1-1+1...=0=1+(-1+1)+(-1+1)...=1=-1+(-1+1)+...=-1
        > and semiempirical results with infinitesimals and infinities were
        > widely discussed with heat.

        I also hope that a fully correct theory will be developed in my
        lifetime. I imagine all sorts of great physics will come from it.
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