Related papers: Dynamics and Hidden Variables
We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…
Under the spin-position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra, substitutes the vector-matrix spin model built on the Pauli spin operator. The standard quantum operator-state…
Coincidence experiments on EPR pairs show strong violations of Bell's Inequalities at certain filter settings which is widely believed to mean that local hidden variable models cannot explain these results. In this paper it is shown that…
Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the…
We show that the Hadamard and Unitary gates could be implemented by a unitary evolution together with a measurement for any unknown state chosen from a set $A = {{| {\Psi_i} > ,| {\bar {\Psi}_i} >}}({i = 1,2})$ if and only if $| {\Psi_1} >…
In the paper, the EPR paradox is explored by the approach of quantum supervaluationism that leads to a "gappy" semantics with the propositions giving rise to truth-value gaps. Within this approach, the statement, which asserts that in the…
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…
It is a well-known fact that all the statistical predictions of quantum mechanics on the state of any physical system represented by a two-dimensional Hilbert space can always be duplicated by a noncontextual hidden-variables model. In this…
We consider alternative models to quantum mechanics, that have been proposed in the recent years in order to explain the EPR correlations between two particles. These models allow in principle local hidden variables produced at the source,…
In this work we represent the $1/2$ Spin particles with complex quaternions using a transformation to 2x2 matrices in order to obtain the Pauli matrices. With this representation we determine the states, rotation operators and the total…
If the quantum mechanical description of reality is not complete and a hidden variable theory is possible, what arises is the problem to explain where the rates of the outcomes of statistical experiments come from, as already noticed by…
Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with an arbitrary axis of quantization. This axis acts as a…
Hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics. We start with a quantum-mechanical model and describe various properties that can be asked of a hidden-variable model. We present…
EPR correlations exist and can be observed independently of any a priori given frame of reference. We can even construct a frame of reference that is based on these correlations. This observation-based frame of reference is equivalent to…
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
A careful ab initio construction of the finite-mass (1/2,1/2) representation space of the Lorentz group reveals it to be a spin-parity multiplet. In general, it does not lend itself to a single-spin interpretation. We find that the…
Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Violation of Bell's Inequalities gives experimental evidence for the existence of a spin 1/2 which has two simultaneous axes of spin quantization rather than one. These couple to form a resonance state, called the spin fringe, and this…
Pairs of spin-1/2 particles are prepared in a Werner state (namely, a mixture of singlet and random components). If the random component is large enough, the statistical results of spin measurements that may be performed on each pair…