595 research outputs found
Failure of Bell's Theorem and the Local Causality of the Entangled Photons
A counterexample to Bell's theorem is presented which uses a pair of photons
instead of spin-1/2 particles used in our previous counterexamples. A locally
causal protocol is provided for Alice and Bob, which allows them to simulate
observing photon polarizations at various angles, and record their results as
A=+/-1 in S^3 and B=+/-1 in S^3, respectively. When these results are compared,
the correlations are seen to be exactly those predicted by quantum mechanics;
namely cos 2(alpha - beta), where alpha and beta are the angles of polarizers.
The key ingredient in our counterexample is the topology of 3-sphere, which
remains closed under multiplication, thus preserving the locality condition of
Bell.Comment: 4 pages; Further elaborations may be found in arXiv:0904.4259,
arXiv:quant-ph/0703179, arXiv:0707.1333, arXiv:0806.3078, and
arXiv:quant-ph/070324
Whither All the Scope and Generality of Bell's Theorem?
In a recent paper James Owen Weatherall has attempted a simple local-deterministic model for the EPR-Bohm correlation and speculated about why his model fails when my counterexample to Bell's theorem succeeds. Here I bring out the physical, mathematical, and conceptual reasons why his model fails. In particular, I demonstrate why no model based on a tensor representation of the rotation group SU(2) can reproduce the EPR-Bohm correlation. I demonstrate this by calculating the correlation explicitly between measurement results A = +1 or -1 and B = +1 or -1 in a local and deterministic model respecting the spinor representation of SU(2). I conclude by showing how Weatherall's reading of my model is misguided, and bring out a number of misconceptions and unwarranted assumptions in his imitation of my model as it relates to the Bell-CHSH inequalities
Disproof of Bell's Theorem: Further Consolidations
The failure of Bell's theorem for Clifford algebra valued local variables is
further consolidated by proving that the conditions of remote parameter
independence and remote outcome independence are duly respected within the
recently constructed exact, local realistic model for the EPR-Bohm
correlations. Since the conjunction of these two conditions is equivalent to
the locality condition of Bell, this provides an independent geometric proof of
the local causality of the model, at the level of microstates. In addition to
local causality, the model respects at least seven other conceptual and
operational requirements, arising either from the predictions of quantum
mechanics or the premises of Bell's theorem, including the Malus's law for
sequential spin measurements. Since the agreement between the predictions of
the model and those of quantum mechanics is quantitatively precise in all
respects, the ensemble interpretation of the entangled singlet state becomes
amenable.Comment: 11 pages; This is a followup to arXiv:quant-ph/0703179; see also
arXiv:quant-ph/070324
Why the Quantum Must Yield to Gravity
After providing an extensive overview of the conceptual elements -- such as
Einstein's `hole argument' -- that underpin Penrose's proposal for
gravitationally induced quantum state reduction, the proposal is constructively
criticised. Penrose has suggested a mechanism for objective reduction of
quantum states with postulated collapse time T = h/E, where E is an
ill-definedness in the gravitational self-energy stemming from the profound
conflict between the principles of superposition and general covariance. Here
it is argued that, even if Penrose's overall conceptual scheme for the
breakdown of quantum mechanics is unreservedly accepted, his formula for the
collapse time of superpositions reduces to T --> oo (E --> 0) in the strictly
Newtonian regime, which is the domain of his proposed experiment to corroborate
the effect. A suggestion is made to rectify this situation. In particular,
recognising the cogency of Penrose's reasoning in the domain of full `quantum
gravity', it is demonstrated that an appropriate experiment which could in
principle corroborate his argued `macroscopic' breakdown of superpositions is
not the one involving non-rotating mass distributions as he has suggested, but
a Leggett-type SQUID or BEC experiment involving superposed mass distributions
in relative rotation. The demonstration thereby brings out one of the
distinctive characteristics of Penrose's scheme, rendering it empirically
distinguishable from other state reduction theories involving gravity. As an
aside, a new geometrical measure of gravity-induced deviation from quantum
mechanics in the manner of Penrose is proposed, but now for the canonical
commutation relations [Q, P] = ih.Comment: 33 pages (TeX, uses mtexsis) plus 3 figures (epsf). To appear in
``Physics Meets Philosophy at the Planck Scale'' (Cambridge University
Press). Two footnotes adde
Bell's Theorem Versus Local Realism in a Quaternionic Model of Physical Space
In the context of EPR-Bohm type experiments and spin detections confined to spacelike hypersurfaces, a local, deterministic and realistic model within a Friedmann-Robertson-Walker spacetime with a constant spatial curvature (S^3 ) is presented that describes simultaneous measurements of the spins of two fermions emerging in a singlet state from the decay of a spinless boson. Exact agreement with the probabilistic predictions of quantum theory is achieved in the model without data rejection, remote contextuality, superdeterminism or backward causation. A singularity-free Clifford-algebraic representation of S^3 with vanishing spatial curvature and non-vanishing torsion is then employed to transform the model in a more elegant form. Several event-by-event numerical simulations of the model are presented, which confirm our analytical results with the accuracy of 4 parts in 10^4 . Possible implications of our results for practical applications such as quantum security protocols and quantum computing are briefly discussed
Disproof of Bell's Theorem
We illustrate an explicit counterexample to Bell's theorem by constructing a
pair of spin variables in S^3 that exactly reproduces the EPR-Bohm correlation
in a manifestly local-realistic manner.Comment: 1 page; Substantively improved and simplified versio
What Really Sets the Upper Bound on Quantum Correlations?
The discipline of parallelization in the manifold of all possible measurement
results is shown to be responsible for the existence of all quantum
correlations, with the upper bound on their strength stemming from the maximum
of possible torsion within all norm-composing parallelizable manifolds. A
profound interplay is thus uncovered between the existence and strength of
quantum correlations and the parallelizability of the spheres S^0, S^1, S^3,
and S^7 necessitated by the four real division algebras. In particular,
parallelization within a unit 3-sphere is shown to be responsible for the
existence of EPR and Hardy type correlations, whereas that within a unit
7-sphere is shown to be responsible for the existence of all GHZ type
correlations. Moreover, parallelizability in general is shown to be equivalent
to the completeness criterion of EPR, in addition to necessitating the locality
condition of Bell. It is therefore shown to predetermine both the local
outcomes as well as the quantum correlations among the remote outcomes,
dictated by the infinite factorizability of points within the spheres S^3 and
S^7. The twin illusions of quantum entanglement and non-locality are thus shown
to stem from the topologically incomplete accountings of the measurement
results.Comment: 23 pages; Forthcoming in a FQXi sponsored book on Bell's Theorem and
Quantum Entanglement (2011); Provides foundations to the examples worked out
in arXiv:0904.4259, arXiv:quant-ph/0703179, and arXiv:1005.493
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