THE PRINCIPLE OF EQUIVALENCE OF ENERGY SPENT ON PROCESS AND OF STEP OF TIME

It was formulated the physical principle of the equivalence of the energy expense during the process of the Universe spreading and of the step of time. It was also shown that physical time is a material quantity connected with expending our Universe at constant velocity. A parallel was carried out between the increase of the size of the drops and bubbles and the expending of the Universe. The above principle is in full agreement with SR and GTR. It was shown as well that physical time could quantize.

From the Galileo Free Fall String to the Principle of Equivalence

We consider the string with the length l, the left end and the right end of which is non relativistically accelerated by the constant acceleration a. We calculate the motion of such string and then the motion of the Galileo free fall string in gravity. The solutions are not identical. So, we distinguish between noninertial field and the gravity field and we discuss the principle of equivalence. In conclusion we suggest to drop charged objects from the very high tower Burj Khalifa in order to say crucial words on the principle of equivalence.

From classical theory to spin 2 gravity

We consider here the simple derivation of the Einstein equations by Fock. Then, we approach the way from the spin 1 fields to the spin 2 fields for massive and massless particles and we derive the gravity equations from this base. In conclusion, we discuss the principle of equivalence in classical Einstein theory and in the Schwinger spin 2 gravity

Quantum Theory of Massless Particles in Stationary Axially Symmetric Spacetimes

Quantum equations for massless particles of any spin are considered in stationary uncharged axially symmetric spacetimes. It is demonstrated that up to a normalization function, the angular wave function does not depend on the metric and practically is the same as in the Minkowskian case. The radial wave functions satisfy second order nonhomogeneous differential equations with three nonhomogeneous terms, which depend in a unique way on time and space curvatures. In agreement with the principle of equivalence, these terms vanish locally, and the radial equations reduce to the same homogeneous equations as in Minkowski spacetime.

Derivation of general relativistic gravitational potential energy using principle of equivalence and gravitational time dilation

Einstein’s theory of general relativity which has been experimentally proved to be true theory of gravity doesn’t need gravitational potential energy to predict trajectory of particles in space. This is because general relativity is a purely geometric theory. Objects move along the geodesics in the curved space-time. The energy-momentum tensor that warps the space-time as per Einstein’s field equations takes into account only the energy/momentum of matter and radiation. Thus, gravitational potential energy doesn’t come into picture in Einstein’s theory of gravity and its role is taken over by curvature of space-time. However, general relativistically correct expression for gravitational potential energy is required for energy conservation and some energy-based approaches in physics. Conventionally, correct form of gravitational potential energy is derived by using full mathematical formality of general relativity. In this paper, we describe an event by which we derive the same general relativistic expression for gravitational potential energy simply by using the principle of equivalence and gravitational time dilation.

Free Falling Szilard Engine, Entropic Forces and Landauer’s principle; Revisiting the Principle of Equivalence

Gedanken experiments illustrating exemplifications of the Landauer principle in the free falling Einstein elevator are treated. Double-well simplest information system embedded into the free falling elevator is addressed. Infinitesimal horizontal force applied to the particle m transfers it from position “0” to position “1”, emerging from the free falling double-well system confining mass m. When thermal noise is considered, the potential barrier of kBT should be surmounted for the erasing of one bit of information. Entropic forces arising in the free falling elevator are considered. The maximal change in the entropy of free-joint polymer chain attached to the free falling elevator is estimated as ΔSmax≅kB, and it is remarkably independent of the mass attached to the chain and the parameters of the chain itself. Free falling minimal Szilard engine is treated. The informational re-interpretation of the minimal Szilard process is shaped as follows: the energy kBTln2 necessary for erasing of 1 bit of information is spent for lifting up mass, whatever, is the value of this mass. Appropriate choice of frames enables elimination of gravity in the considered system; however elimination of the thermal noise (dissipation processes) by the same procedure is impossible.

General Covariance

The general theory of relativity is introduced based on the principle of equivalence. Gravity is shown to arise dues to spacetime curvature. Specific examples of curved spacetimes are presented from the approximate but more intuitive to the complex: Uniform gravitational field (Galilean metric), the Newtonian weak field metric, Schwarzschild’s exterior and interior solutions, black holes, and cosmological spacetimes. A brief discussion on distances, areas and volumes in curved spaces is also given.