Unification of classic and quantum mechanics

With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the three other known fundamental interactions, the physicist of the XXIst century has inherited an unfinished symphony: the unification of the quantum and the continuum. As an invitation to tomorrow's quantum geometers who must design the new rul...

The dynamics of a massive, relativistic spinning particle could be described either by the Dirac equation or by the Kerr solution of Einstein equations. However, one does not know a priori as to which of the two systems of equations should be used in a given situation, and the choice is dictated by experiments. It is expected that the Dirac equation holds for microscopic masses, and the Kerr solution for macroscopic masses. This suggests that Einstein gravity and the Dirac th...

It is shown that certain structures in classical General Relativity can give rise to non-classical logic, normally associated with Quantum Mechanics. A 4-geon model of an elementary particle is proposed which is asymptotically flat, particle-like and has a non-trivial causal structure. The usual Cauchy data are no longer sufficient to determine a unique evolution. The measurement apparatus itself can impose non-redundant boundary conditions. Measurements of such an object wou...

In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum space, which should be seen as complementary to the more spread algebraic one. In this frame we are able to rederive well-known algebraic expressions, as well as to treat yet unresolved issues, to wit, the explicit relation between both equ...

Solitary-particle quantum mechanics' inherent compatibility with special relativity is implicit in Schroedinger's postulated wave-function rule for the operator quantization of the particle's canonical three-momentum, taken together with his famed time-dependent wave-function equation that analogously treats the operator quantization of its Hamiltonian. The resulting formally four-vector equation system assures proper relativistic covariance for any solitary-particle Hamilton...

This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and connection have a fundamental role in the main action establishment. In the last section, as a result of an approximation for the main formulation, we obtain the relativistic Klein-Gordon equation.

In this paper, we shall present a new equation of motion with Quantum effect in spacetime. To do so, we propose a classical-quantum duality. We also generalize the Schordinger equation to the spacetime and obtain a relativistic wave equation. This will lead a generalization of Einstein's formula $E=m_0c^2$ in the spacetime. In general, we have $E=m_0c^2 + \frac{\hbar^2}{12m_0}R$ in a spacetime.

Quantum Electrodynamics (QED) has been so successful a theory that it is taken as a model for the production of further quantum theories. However, when the prescription for quantising electromagnetic interactions that so successfully resulted in QED is applied to General Relativity the theory obtained is not renormalizable. We derive a different method of quantising classical electromagnetism which also results in QED. We call the method the versatile method. We then apply th...

A reconciliation of gravitation and electromagnetism has eluded physics for neearly a century. It is argued here that this is because both quantum physics and classical physics are set in differentiable space time manifolds with point particles. Once we consider extended particles as in Quantum Superstring theory, and the consequential underlying Non-Commutative geometry, then a reconciliation is possible.

In 5D, I take the metric in canonical form and define causality by null-paths. Then spacetime is modulated by a factor equivalent to the wave function, and the 5D geodesic equation gives the 4D Klein-Gordon equation. These results effectively show how general relativity and quantum mechanics may be unified in 5D.