On the Synergic Relationships between Special Relativity and Quantum Theories

The successful results of the relativistic form of a quantum field theory that is derived from aLagrangian density justify its general usage. The significance of the Euler-Lagrange equations of a quantum particle is analysed. Many advantages of this approach, like abiding by the conservation laws of energy, momentum, angular momentum, and charge are well known. The merits of this approach also include other properties that are still not well known. For example, it is shown that a quantum function of the form ψ(t, r) describes a pointlike particle. Furthermore, the Lagrangian density and the Hamiltonian density take a different relativistic form – the Lagrangian density is a Lorentz scalar, whereas the Hamiltonian density is the T00 component of the energy-momentum tensor. It is proved that inconsistencies in the electroweak theory stem from negligence of the latter point.

Getting deeper insight into stopping power problems in radiation physics using the Noether's theorem corollary

The theories that combine two different approaches in dealing with interacting objects, for instance, treating electromagnetic laser field classically, and the interacting atom as a quantum object, have some ambiguities and, as such, they should be labeled as ?mixed?. From the Noether's Theorem Corollary, which we proved earlier, about the conservation laws of energy, momentum and angular momentum in mixed theories, follows that the aforementioned theories do not support the law of angular momentum/spin conservation (to be precise, the obtained result does not imply that the law of conservation of angular momentum and spin is not valid generally, but rather that mixed theories can produce the results which might violate this law). In present paper, an additional explanation following our Corollary is given to why the calculation of the stopping power in the fully quantized theory gives better results than those that were obtained in mixed theories, which further confirms the predictions of our Corollary.

INFORMATION CONSERVATION IS FUNDAMENTAL: RECOVERING THE LOST INFORMATION IN HAWKING RADIATION

In both classical and quantum world, information cannot appear or disappear. This fundamental principle, however, is questioned for a black hole, by the acclaimed "information loss paradox." Based on the conservation laws of energy, charge, and angular momentum, we recently show the total information encoded in the correlations among Hawking radiations equals exactly to the same amount previously considered lost, assuming the nonthermal spectrum of Parikh and Wilczek. Thus the information loss paradox can be falsified through experiments by detecting correlations, for instance, through measuring the covariances of Hawking radiations from black holes, such as the manmade ones speculated to appear in LHC experiments. The affirmation of information conservation in Hawking radiation will shine new light on the unification of gravity with quantum mechanics.

Long-time shallow-water equations with a varying bottom

We present and discuss new shallow-water equations that model the long-time effects of slowly varying bottom topography and weak hydrostatic imbalance on the vertically averaged horizontal velocity of an incompressible fluid possessing a free surface and moving under the force of gravity. We consider the regime where the Froude number ε is much smaller than the aspect ratio δ of the shallow domain. The new equations are obtained from the ε→0 limit of the Euler equations (the rigid-lid approximation) at the first order of an asymptotic expansion in δ2. These equations possess local conservation laws of energy and vorticity which reflect exact layer mean conservation laws of the three-dimensional Euler equations. In addition, they convect potential vorticity and have a Hamilton's principle formulation. We contrast them with the Green–Naghdi equations.