Fermions tunneling from apparent horizon of FRW universe

In the paper [R.-G. Cai, L.-M. Cao, Y.-P. Hu, arXiv: 0809.1554], the scalar particles' Hawking radiation from the apparent horizon of Friedmann–Robertson–Walker (FRW) universe was investigated by using the tunneling formalism. They obtained the Hawking temperature associated with the apparent horizon, which was extensively applied in investigating the relationship between the first law of thermodynamics and Friedmann equations. In this Letter, we calculate fermions' Hawking radiation from the apparent horizon of FRW universe via tunneling formalism. Applying WKB approximation to the general covariant Dirac equation in FRW spacetime background, the radiation spectrum and Hawking temperature of apparent horizon are correctly recovered, which supports the arguments presented in the paper [R.-G. Cai, L.-M. Cao, Y.-P. Hu, arXiv: 0809.1554].     

Mach's principle. Part 1. Initial state of the universe the universe

The integral formulation of equations of general relativity proposed earlier as a mathematical tool for Mach's principle forbids the conventional singular cosmologies but is compatible with the de Sitter initial space.     

The opacity of the universe and the strong equivalence principle

A possible explanation of why the advanced (i.e. acausal) solutions of Maxwell's equations are not observed in nature is by way of absorption by an opaque universe. As Davies has shown, the ever expanding, general relativistic cosmological models fail to provide the needed absorption. This is perhaps not surprising. In fact, the absorption mechanism calling for an interplay between local physics and cosmology, is usually developed adopting the strong equivalence principle, SEP, which precludes such interplay. We show that complete absorption of electromagnetic radiation by ionized intergalactic plasma is obtained provided a violation of the SEP, of the order of the Hubble's constant, is allowed to occur. The same degree of violation was previously found to be compatible with a large body of observational data.     

Gravitational anomaly and Hawking radiation of apparent horizon in FRW universe

Motivated by the successful applications of the anomaly cancellation method to derive Hawking radiation from various types of black hole spacetimes, we further extend the gravitational anomaly method to investigate the Hawking radiation from the apparent horizon of a FRW universe by assuming that the gravitational anomaly also exists near the apparent horizon of the FRW universe. The result shows that the radiation flux from the apparent horizon of the FRW universe measured by a Kodama observer is just the pure thermal flux. The result presented here will further confirm the thermal properties of the apparent horizon in a FRW universe.     

Evidence for the quantum birth of our universe

We present evidence for a nonsingular origin of the Universe with intial conditions determined by quantum physics and relativistic gravity. In particular, we establish that the present temperature of the microwave background and the present density of the Universe agree well with our predictions from these intial conditions, after evolution to the present age using the Einstein-Friedmann equation. Remarkably, the quantum origin for the Universe naturally allows its evolution at exactly the critical density. We also discuss the consequences of these results to some fundamental aspects of quantum physics in the early Universe.     

On principle of inertia in closed universe

If our universe is asymptotic to a de Sitter space, it should be closed with curvature in O(Λ)$O(\Lambda )$ in view of dS special relativity. Conversely, its evolution can fix on Beltrami systems of inertia in the ds-space without Einstein's ‘argument in a circle’. Gravity should be local ds-invariant based on localization of the principle of inertia.     

Interacting three fluid system and thermodynamics of the universe bounded by the event horizon

The work deals with the thermodynamics of the universe bounded by the event horizon. The matter in the universe has three constituents namely dark energy, dark matter and radiation in nature and interaction between then is assumed. The variation of entropy of the surface of the horizon is obtained from unified first law while matter entropy variation is calculated from the Gibbss’ law. Finally, validity of the generalized second law of thermodynamics is examined and conclusions are written point wise.     

Uncertainty principle and uncertainty relations

It is generally believed that the uncertainty relation q p1/2, where q and p are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path of a particle in an interference experiment (such as the double-slit experiment).The failure of the uncertainty relation to produce these results is not a question of the interpretation of the formalism; it is a mathematical fact which follows from general considerations about the widths of wave functions.To express the uncertainty principle, one must distinguish two aspects of the spread of a wave function: its extent and its fine structure. We define the overall widthW and the mean peak width w of a general wave function and show that the productW w is bounded from below if is the Fourier transform of . It is shown that this relation expresses the uncertainty principle as it is used in the single- and double-slit experiments.     

Gravitational pressure,apparent horizon and thermodynamics of FLRW universe in the teleparallel gravity

In the context of the teleparallel equivalent of general relativity the concept of gravitational pressure and gravitational energy-momentum arisen in a natural way. In the case of a Friedmann–Lemaitre–Robertson–Walker space FLRW we obtain the total energy contained inside the apparent horizon and the radial pressure over the apparent horizon area. We use these definitions to written a thermodynamics relation \(T_{A}dS_{A} = dE_{A}+P_{A}dV_{A}\) at the apparent horizon, where \(E_{A}\) is the total energy inside the apparent horizon, \(V_{A}\) is the areal volume of the apparent horizon, \(P_{A}\) is the radial pressure over the apparent horizon area, \(S_{A}\) is the entropy which can be assumed as one quarter of the apparent horizon area only for a non stationary apparent horizon. We identify \(T_{A}\) as the temperature at the surface of the apparent horizon. We shown that for all expanding accelerated FLRW model of universe the radial pressure is positive.     

Uncertainty principle for generalized diffusions

It is shown that with any generalized diffusion a complementary variable, theprobabilistic group velocity (PGV), can be associated, such that the uncertainties in the position (diffusion) and its complementary PGV (like momentum) satisfy a Heisenberg-type uncertainty relation. It is shown that the bound is achieved in the linear Gaussian case. In the statistical steady state, the PGV vanishes identically. The uncertainty in the PGV is an achievable upper bound to the rate of the RMS value of the diffusion. The PGV is further related to the entropy rate of the diffusion process.     

Uncertainty principle in larmor clock

It is well known that the spin operators of a quantum particle must obey uncertainty relations. We use the uncertainty principle to study the Larmor clock. To avoid breaking the uncertainty principle, Larmor time can be defined as the ratio of the phase difference between a spin-up particle and a spin-down particle to the corresponding Larmor frequency. The connection between the dwell time and the Larmor time has also been confirmed. Moreover, the results show that the behavior of the Larmor time depends on the height and width of the barrier.     

Uncertainty principle limits on the cosmological constant

The identification of the cosmological constant term with the energy density of the vacuum enables lower and upper limits to be placed on its value. The upper limit arises from the constraint that the total zero-point energy, which also gravitates, should not dominate cosmological dynamics, while the lower limit can result from the operational requirement that the vacuum-energy shifts over atomic or nuclear scales be at least measurable over Hubble time scales.     

Generalized uncertainty principle, modified dispersion relations and the early universe thermodynamics

In this paper, we study the effects of Generalized Uncertainty Principle (GUP) and Modified Dispersion Relations (MDRs) on the thermodynamics of ultra-relativistic particles in early universe. We show that limitations imposed by GUP and particle horizon on the measurement processes, lead to certain modifications of early universe thermodynamics.     

Uncertainty principle and minimal energy dissipation in the computer

Reversible computation is briefly reviewed, utilizing a refined version of the Bennett-Fredkin-Turing machine, invoked in an earlier paper. A dissipationless classical version of this machine, which has no internal frietion, and where the computational velocity is determined by the initial kinetic energy, is also described. Such a machine requires perfect parts and also requires the unrealisstic assumption that the many extraneous degrees of freedom, which contribute to the physical structure, do not couple to the information-bearing degrees of freedom, and thus cause no friction Quantum mechanical computation is discussed at two levels. First of all we deplore the assertion. repcatedly found in the literature, that the uncertainty principle. Eth, with t equated to a switching time, yields any information about energydissipation. Similarly we point out that computation is not an iterated transmission and receiving process, and that considerations, which avoid the uncertainty principle, and instead use quantum mechanical channel capacity considerations, are equally unfounded. At a more constructive level we ask whether there is a quantum mechanical version of the dissipationless computer. Benioff has proposed one possible answer Quantum mechanical versions of dissipationless computers may suffer from the problems found in electron transport in disordered one-dimensional periodic potentials. The buildup of internal reflections may give a transmission coefficient. through the whole computation, which decreases exponentially with the length of the computation.     

Hawking radiation as tunneling and the unified first law of thermodynamics at the apparent horizon of the FRW universe

Relations between the tunneling rate FRW universe are investigated. The namics in such a dynamical system. first law of thermodynamics through and the unified first law of thermodynamics at the apparent horizon of the tunneling rate arises as a consequence of the unified first law of thermodyAnalysis shows how the tunneling is intimately connected with the unified the principle of conservation of energy.