Discussion:
String theory and non-separability
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Mike
2005-06-20 09:37:47 UTC
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What does string theory have to say about,
1. The quantum postulate?
2. The denial of separability?
3. The Bell experiment results?

Einstein's problem with Bohr was that he saw Bohr as denying
spatio-temporal separability in the case of two previously interacting
systems. That is, two systems share the same state even if separated
by vast distances. Einstein couldn't accept this denial of
separability and worked with Podolsky and Rosen to design the EPR
Gedankenexperiment to make his objection explicit.

Bohr believed in what Schrödinger first called "entanglement" and what
we call the denial of separability. According to Folse, Bohr's
acceptance of the quantum postulate was the basis for Bohr's
disagreement with Einstein. The quantum postulate states that it is
impossible to provide a space-time description of the "discontinuous
change of state that an atomic system under goes in its interaction
with the radiative field".

Howard goes on to explain that Einstein's belief in separability was
based on Einstein's acceptance of field theory as the basis for
describing reality. Field theories are based on the ontology of a
mathematical manifold. Mathematical manifolds individuate points by
specifying a non-vanishing interval between points. Field theories
individuate systems and states by specifying a non-vanishing interval
between systems and states. For general relativity, the interval is
the 4-dimensional spatio-temporal , or metrical, interval. QM denies
that entangled systems have separate states.

--Mike Jr.


_______________________________________________________________________________
Web page of SPS: http://schwinger.harvard.edu/~sps/
Posted via: http://groups.google.com/groups?group=sci.physics.strings
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Mike
2005-06-27 07:25:18 UTC
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I have read Zwiebach's book. Strings have a finite length (self-dual
radius) thus String theory avoids the field-theoretic extreme by
admitting physical systems only of a finite magnitude. I understand
that in this way string theory neatly side-steps the problem of the
infinite self-energy of the electron.

I noticed that the String theories described by Zwiebach respect
locality (i.e. Einstein's first-signal principle). What I couldn't
find was a reference to Bell's theorem (Bell, 1964). If locality is
respected, then the experimental falsification of Bell's theorem
(Aspect, et al, 1981) implies a violation of separability. Since QM is
a local, non-separable theory this violation comes as no surprise.

But what does multi-dimensional string theory have to say about
non-separability? One option would be a backdoor connection through
higher dimensions that appear separate in four dimensions. One way to
picture such a connection would be to fold a sheet of paper in half (no
crease) and then use a needle and thread to connect the two ends of the
sheet. An ant traveling on the outside surface of the paper would see
a large distance between the two holes while the string length could be
quite small.

Or perhaps two particles become entangled and then move down separate
halves of the sheet. Over time, the distance around the paper can
become quite large.

Does string theory offer a hint at an explanation of quantum
non-separability? Can you point me to any papers that discuss string
theory and quantum non-separability? I was surprised to not see any
references to non-separability in Zwiebach's book and I figured that
I must have overlooked something.

--Thank you,
--Mike Jr.
Post by Mike
What does string theory have to say about,
1. The quantum postulate?
2. The denial of separability?
3. The Bell experiment results?
Einstein's problem with Bohr was that he saw Bohr as denying
spatio-temporal separability in the case of two previously interacting
systems. That is, two systems share the same state even if separated
by vast distances. Einstein couldn't accept this denial of
separability and worked with Podolsky and Rosen to design the EPR
Gedankenexperiment to make his objection explicit.
Bohr believed in what Schrödinger first called "entanglement" and what
we call the denial of separability. According to Folse, Bohr's
acceptance of the quantum postulate was the basis for Bohr's
disagreement with Einstein. The quantum postulate states that it is
impossible to provide a space-time description of the "discontinuous
change of state that an atomic system under goes in its interaction
with the radiative field".
Howard goes on to explain that Einstein's belief in separability was
based on Einstein's acceptance of field theory as the basis for
describing reality. Field theories are based on the ontology of a
mathematical manifold. Mathematical manifolds individuate points by
specifying a non-vanishing interval between points. Field theories
individuate systems and states by specifying a non-vanishing interval
between systems and states. For general relativity, the interval is
the 4-dimensional spatio-temporal , or metrical, interval. QM denies
that entangled systems have separate states.
--Mike Jr.
_______________________________________________________________________________
Web page of SPS: http://schwinger.harvard.edu/~sps/
Posted via: http://groups.google.com/groups?group=sci.physics.strings
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
_______________________________________________________________________________
Web page of SPS: http://schwinger.harvard.edu/~sps/
Posted via: http://groups.google.com/groups?group=sci.physics.strings
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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