Narrow Results

The classical-quantum duality at the basis of quantum theory is here extended to the Planck scale domain. The classical/semiclassical gravity (G) domain is dual (in the precise sense of the classical-quantum duality) to the quantum (Q) elementary particle domain: $O_Q=o_P^2{O}_G^{-1}$, $o_P$ being the Planck scale. This duality is universal. From the gravity (G) and quantum (Q) variables $(O_G,O_Q)$, we define new quantum gravity (QG) variables $O_{\mathrm{\text{QG}}}=(1/2)(O_G+O_Q)$ which include all (classical, semiclassical and QG) domains passing through the Planck scale and the elementary particle domain. The QG variables are more complete than the usual ($O_Q$, $O_G$) ones which cover only one domain (Q or G). Two$O_G$ or $O_Q$ values $(\pm )$ are needed for each value of $O_{\mathrm{\text{QG}}}$ (reflecting the two dual ways of reaching the Planck scale). We perform the complete analytic extension of the QG variables through analytic (holomorphic) mappings which preserve the light-cone structure. This allows us to reveal the classical-quantum duality of the Schwarzschild–Kruskal spacetime: exterior regions are classical or semiclassical while the interior is totally quantum: its boundaries being the Planck scale. Exterior and interior lose their difference near the horizon: four Planck scale hyperbolae border the horizons as a quantum dressing or width: “l’horizon habillé”. QG variables are naturally invariant under $O_G\to O_Q$. Spacetime reflections, antipodal symmetry and PT or CPT symmetry are contained in the QG symmetry, which also shed insight on the global properties of the Kruskal manifold and its present renewed interest.

We propose a heuristic derivation of Casimir effect in the context of minimal length theories based on a Generalized Uncertainty Principle (GUP). By considering a GUP with only a quadratic term in the momentum, we compute corrections to the standard formula of Casimir energy for the parallel-plate geometry, the sphere and the cylindrical shell. For the first configuration, we show that our result is consistent with the one obtained via more rigorous calculations in Quantum Field Theory (QFT). Experimental developments are finally discussed.

The physical history of the Universe is completed by including the quantum Planckian and trans-Planckian phase before inflation in the Standard Model of the Universe in agreement with observations. In the absence of a complete quantum theory of gravity, we start from quantum physics and its foundational milestone. The universal classical-quantum (or wave-particle) duality, which we extend to gravity and the Planck domain. As a consequence, classical, quantum Planckian and super-Planckian regimes are covered, and the usual quantum domain as well. A new quantum precursor phase of the Universe appears beyond the Planck scale $(t_P)$: $10^{-61}{t}_P\le t\le t_P$; the known classical/semiclassical Universe being in the range: $t_P\le t\le 10^{+61}{t}_P$. We extend in this way the de Sitter Universe to the quantum domain: classical-quantum de Sitter duality. As a result: (i) The classical and quantum dual de Sitter temperatures and entropies are naturally included, and the different (classical, semiclassical, quantum Planckian and trans-Planckian) de Sitter regimes characterized in a precise and unifying way. (ii) We apply it to relevant cosmological examples as the CMB, inflation and dark energy. This allows us to find in a simple and consistent way. (iii) Full quantum inflationary spectra and their CMB observables, including in particular the classical known inflation spectra and the quantum corrections to them. (iv) A whole unifying picture for the Universe epochs and their quantum precursors emerges with the cosmological constant as the vacuum energy, entropy and temperature of the Universe, clarifying the so-called cosmological constant problem which once more in its rich history needed to be revised.

We study a family of noncommutative spacetimes constructed by one four-vector. The large set of coordinate commutation relations described in this way includes many cases that are widely studied in the literature. The Hopf-algebra symmetries of these noncommutative spacetimes, as well as the structures of star product and twist are introduced and considered at first order in the deformation, described by four parameters. We also study the deformations to relativistic kinematics implied by this framework, and calculate the most general expression for the momentum dependence of the Lorentz transformations on momenta, which is an effect that is required by consistency. At the end of the paper we analyse the phenomenological consequences of this large family of vectorlike deformations on particles propagation in spacetime. This leads to a set of characteristic phenomenological effects.

We argue that the quantum nature of matter and gravity should lead to a discretization of the allowed states of the matter confined in the interior of black holes. To support and illustrate this idea, we consider a quadratic extension of general relativity (GR) formulated à la Palatini and show that nonrotating, electrically charged black holes develop a compact core at the Planck density which is nonsingular if the mass spectrum satisfies a certain discreteness condition. We also find that the area of the core is proportional to the number of charges times the Planck area.

The first step to complete physical theories is to contemplate on the axiomatic character of the principles. This principle of relativity was formulated by Galileo and used by Newton to derive the laws of motion, and later was placed by Einstein at the center of the Special Theory and the General Relativity. This work considers the general principle of relativity as an expression of the inherent characteristic of the most important quantity in physics - the energy - that states that the energy is constant and is independent of the type or speed of movement of an object. The energy of an object is expressed as one entity that equals the sum of two energy expressions with different character. One of these two terms is denoted as the exposed energy with a kinetic character and represents the magnitude of the field of an object. This new definition of the energy offers several perspectives that are valid for both the classical and relativistic physics and provides insights beyond these two as: i) it leads to a coherent and complete model that relates the energy with the momentum and the force, ii) enables to construct the lagrangian that can be used to derive the equations of motion without artifices, iii) offers an original viewpoint on the dark matter and dark energy that is coherent with recent developments. Einstein was the first to deny the separate existence of gravitation and electromagnetism and has implied that the goal of a unified theory would be to explain the existence and to calculate the properties of matter. He revolutionized the use of the principles of symmetry in deriving the physical laws. It is known that the classical and quantum domain do not overlap and one would not expect the same governing symmetry principles in both domains. To calculate the properties of matter we employ spatial parameters that are related with the energy state of an object and the force that it exhibits. The mechanism assumes the common origin of different forces at the highest energy level. These spacetime parameters can be used to derive the electric and gravitational forces through a single mechanism that respects the LT dimensional analysis using neither the electrical charge nor the gravitational constant.

If one is willing to consider the current cosmic microwave back ground temperature as a quantum gravitational effect of the evolving primordial cosmic black hole (universe that constitutes dynamic space-time and exhibits quantum behavior) automatically general theory of relativity and quantum mechanics can be combined into a ‘scale independent’ true unified model of quantum gravity. By considering the ‘Planck mass’ as the initial mass of the baby Hubble volume, past and current physical and thermal parameters of the cosmic black hole can be understood. Current rate of cosmic black hole expansion is being stopped by the microscopic quantum mechanical lengths. In this new direction authors observed 5 important quantum mechanical methods for understanding the current cosmic deceleration. To understand the ground reality of current cosmic rate of expansion, sensitivity and accuracy of current methods of estimating the magnitudes of current CMBR temperature and current Hubble constant must be improved and alternative methods must be developed. If it is true that galaxy constitutes so many stars, each star constitutes so many hydrogen atoms and light is coming from the excited electron of galactic hydrogen atom, then considering redshift as an index of ‘whole galaxy’ receding may not be reasonable. During cosmic evolution, at any time in the past, in hydrogen atom emitted photon energy was always inversely proportional to the CMBR temperature. Thus past light emitted from older galaxy's excited hydrogen atom will show redshift with reference to the current laboratory data. As cosmic time passes, in future, the absolute rate of cosmic expansion can be understood by observing the rate of increase in the magnitude of photon energy emitted from laboratory hydrogen atom. Aged super novae dimming may be due to the effect of high cosmic back ground temperature. Need of new mathematical methods & techniques, computer simulations, advanced engineering skills seem to be essential in this direction.