143 research outputs found
Two-particle interference in standard and Bohmian quantum mechanics
The compatibility of standard and Bohmian quantum mechanics has recently been
challenged in the context of two-particle interference, both from a theoretical
and an experimental point of view. We analyze different setups proposed and
derive corresponding exact forms for Bohmian equations of motion. The equations
are then solved numerically, and shown to reproduce standard quantum-mechanical
results.Comment: Minor corrections, 2 references added, version to appear in J. Phys.
Lie symmetries of Einstein's vacuum equations in N dimensions
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions,
with a cosmological term. For this purpose, we first write down the second
prolongation of the symmetry generating vector fields, and compute its action
on Einstein's equations. Instead of setting to zero the coefficients of all
independent partial derivatives (which involves a very complicated substitution
of Einstein's equations), we set to zero the coefficients of derivatives that
do not appear in Einstein's equations. This considerably constrains the
coefficients of symmetry generating vector fields. Using the Lie algebra
property of generators of symmetries and the fact that general coordinate
transformations are symmetries of Einstein's equations, we are then able to
obtain all the Lie symmetries. The method we have used can likely be applied to
other types of equations
On relativistic elements of reality
Several arguments have been proposed some years ago, attempting to prove the
impossibility of defining Lorentz-invariant elements of reality. I find that a
sufficient condition for the existence of elements of reality, introduced in
these proofs, seems to be used also as a necessary condition. I argue that
Lorentz-invariant elements of reality can be defined but, as Vaidman pointed
out, they won't satisfy the so-called product rule. In so doing I obtain
algebraic constraints on elements of reality associated with a maximal set of
commuting Hermitian operators.Comment: Clarifications, reference added; published versio
Finite-Dimensional Bicomplex Hilbert Spaces
This paper is a detailed study of finite-dimensional modules defined on
bicomplex numbers. A number of results are proved on bicomplex square matrices,
linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces,
including the spectral decomposition theorem. Applications to concepts relevant
to quantum mechanics, like the evolution operator, are pointed out.Comment: 21 page
The bicomplex quantum Coulomb potential problem
Generalizations of the complex number system underlying the mathematical
formulation of quantum mechanics have been known for some time, but the use of
the commutative ring of bicomplex numbers for that purpose is relatively new.
This paper provides an analytical solution of the quantum Coulomb potential
problem formulated in terms of bicomplex numbers. We define the problem by
introducing a bicomplex hamiltonian operator and extending the canonical
commutation relations to the form [X_i,P_k] = i_1 hbar xi delta_{ik}, where xi
is a bicomplex number. Following Pauli's algebraic method, we find the
eigenvalues of the bicomplex hamiltonian. These eigenvalues are also obtained,
along with appropriate eigenfunctions, by solving the extension of
Schrodinger's time-independent differential equation. Examples of solutions are
displayed. There is an orthonormal system of solutions that belongs to a
bicomplex Hilbert space.Comment: Clarifications; some figures removed; version to appear in Can. J.
Phy
Can Everett be Interpreted Without Extravaganza?
Everett's relative states interpretation of quantum mechanics has met with
problems related to probability, the preferred basis, and multiplicity. The
third theme, I argue, is the most important one. It has led to developments of
the original approach into many-worlds, many-minds, and decoherence-based
approaches. The latter especially have been advocated in recent years, in an
effort to understand multiplicity without resorting to what is often perceived
as extravagant constructions. Drawing from and adding to arguments of others, I
show that proponents of decoherence-based approaches have not yet succeeded in
making their ontology clear.Comment: Succinct analysis forthcoming in Found. Phy
A first experimental test of de Broglie-Bohm theory against standard quantum mechanics
De Broglie - Bohm (dBB) theory is a deterministic theory, built for
reproducing almost all Quantum Mechanics (QM) predictions, where position plays
the role of a hidden variable. It was recently shown that different coincidence
patterns are predicted by QM and dBB when a double slit experiment is realised
under specific conditions and, therefore, an experiment can test the two
theories. In this letter we present the first realisation of such a double slit
experiment by using correlated photons produced in type I Parametric Down
Conversion. Our results confirm QM contradicting dBB predictions
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