New four coordinates are introduced which are related to the usual space-time coordinates. For these coordinates, the Euclidean four-dimensional length squared is equal to the interval squared of the Minkowski space. The Lorentz transformation, for the new coordinates, becomes an SO(4) rotation. New scalars (invariants) are derived. A second approach to the Lorentz transformation is presented. A mixed space is generated by interchanging the notion of time and proper time in inertial frames. Within this approach the Lorentz transformation is a (...) 4-dimensional rotation in an Euclidean space, leading to new possibilities and applications. (shrink)

The Maxwell equations are shown to be the one-photon spin-one quantum equations. All Maxwell equations (without sources) are derived simultaneously from first principles, similar to those which have been used to derive the Dirac relativistic electron equation. The wavefunction is a linear combination of the electric and magnetic fields. The procedure is not unique, there are ambiguities of adding a scalar field. A quaternionic representation of the Maxwell equations (with sources) is constructed, a covariant reformulation of which is presented. Whittaker (...) potentials are analysed. Conservation laws are derived using a method of “pseudo-Lagrangians.”. (shrink)

For quantum systems, whose energy ratios En/E0 are integers, and |E0| is the smallest energy, the time dependent wavefunctions and expectation values of time independent operators have time periodicitiy with a time period T equal to T = h/|E0|, where h is the Planck constant. This periodicity is imposed on the wavefunctions due to undersampling in energy, but following a similarity with aliasing in signal analysis, it may allow to probe future and past events under the condition that our world (...) is in reality a true four-dimensional, “static” space–time. We suggest an experiment to test that possibility. A positive result will indicate that we live in a four-dimensional space–time. A negative result (not getting signals from the future) will indicate that four-dimensional space–time is not physical one and that we live in a three-dimensional space with a time. (shrink)

We deal with Lagrangians which are not the standard scalar ones. We present a short review of tensor Lagrangians, which generate massless free fields and the Dirac field, as well as vector and pseudovector Lagrangians for the electric and magnetic fields of Maxwell’s equations with sources. We introduce and analyse Lagrangians which are equivalent to the Hamilton-Jacobi equation and recast them to relativistic equations.