Narrow Results

We have extended a recent approach to Deformed Special Relativity based on deformed dispersion laws, entailing modified Lorentz transformations and, at the same time, noncommutative geometry and intrinsically discrete space–time. In so doing we have obtained the explicit form of the modified Lorentz transformations for a special class of modified momentum-energy relations often found in literature and arising from quantum gravity and elementary particle physics. Actually, our theory looks as a very simple and natural extension of special relativity to include a momentum cutoff at the Planck scale. In particular, the new Lorentz transformations do imply that for high boost speed $(V\sim c)$ the deformed Lorentz factor does not diverge as in ordinary relativity, but results to be upper bounded by a large finite value of the order of the ratio between the Planck mass and the particle mass. We have also predicted that a generic boost leaves unchanged Planck energy and momentum, which result invariant with respect to any reference frame. Finally, through matrix deformation functions, we have extended our theory to more general cases with dispersion laws containing momentum-energy mixed terms.

We are considering a possibility for detecting nonperturbative effect in process of top pair production in association with a high $p_T$ photon. Starting from previous results on two solutions for a spontaneous generation of an effective interaction of a top pair with a pair of electroweak bosons, we show that a solution with effective cutoff $\mathrm{\Lambda }\simeq 10^2\mathrm{\text{TeV}}$ is already contradicting to the existing data, while the other one with $\mathrm{\Lambda }\simeq 10^{16}\mathrm{\text{TeV}}$ (just the Planck scale) could be reconciled with data and give predictions for process $p+p\to \bar{t}t\gamma +X$, which could be effectively checked at the LHC with $\sqrt{s}=13\mathrm{\text{TeV}}$. The confirmation of the predictions would mean a strong support for the existence of nonperturbative effects in the electroweak interaction.

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.

It is argued that the "problem of time" in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a (4+2n)-dimensional pseudo-Euclidean line element, with the extra 2n being the number of internal phase space dimensions of the observed system. In the refined structure, the inverse of the Planck time takes over the role of observer-independent conversion factor usually played by the speed of light, which now emerges as an invariant but derivative quantity. In the relativistic theory based on the refined structure, energies and momenta turn out to be invariantly bounded from above, and lengths and durations similarly bounded from below, by their respective Planck scale values. Along the external timelike world-lines, the theory naturally captures the "flow of time" as a genuinely structural attribute of the world. The theory also predicts expected deviations — suppressed quadratically by the Planck energy — from the dispersion relations for free fields in the vacuum. The deviations from the special relativistic Doppler shifts predicted by the theory are also suppressed quadratically by the Planck energy. Nonetheless, in order to estimate the precision required to distinguish the theory from special relativity, an experiment with a binary pulsar emitting TeV range γ-rays is considered in the context of the predicted deviations from the second-order shifts.

The existence of extra dimensions and a minimal length scale are modifications of our spacetime which are suggested by string theory. In models with additional dimensions, the Planck scale can be lowered to values accessible by future colliders and in ultra high energetic cosmic rays. Effective theories which extend beyond the standard-model by including extra dimensions and a minimal length allow the computation of observables and can be used to make testable predictions. Expected effects that arise within these models are the production of gravitons and black holes. Furthermore, the Planck length is a lower bound to the possible resolution of spacetime which might be reached soon.

Lorentz invariance plays a pivotal role in the derivation of the Hawking effect, which crucially requires an integration in arbitrarily small distances or, equivalently, in unbounded energies. New physics at the Planck scale could, therefore, potentially modify the emission spectrum. We argue, however, that the kinematic invariance can be deformed in such a way that the thermal spectrum remains insensitive to trans-Planckian physics.

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.

In the framework of the most-studied doubly special relativity models the use of the naive formula v = dE/dp has been argued to lead to inconsistencies connected to different rules of transformation, under boosts, of particles with the same energy but with different masses. In this paper, we show that, at least in 1 + 1 dimensions, doubly special relativity can be formulated in such a way that the formula v = dE/dp is fully consistent with the invariance of the relative rest, easily fitting to the relativity principle. It is also argued that, always in 1 + 1 dimensions, is not necessary to renounce to the usual (commutative) Minkowski spacetime endowed with energy-independent boost transformations. The compatibility of the approach with superluminal propagation, with linear addition rule for energy, and possible extensions to 3 + 1 dimensions are also discussed.

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.

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.

Considering the expected thermal equilibrium characterizing the physics at the Planck scale, it is here stated, for the first time, that, as a system, the space-time at the Planck scale must be considered as subject to the Kubo-Martin-Schwinger (KMS) condition. Consequently, in the interior of the KMS strip, i.e. from the scale ℬ = 0 to the scale ℬ = ℓ_planck, the fourth coordinate g₄₄ must be considered as complex, the two real poles being ℬ = 0 and ℬ = ℓ_planck. This means that within the limits of the KMS strip, the Lorentzian and the Euclidean metric are in a "quantum superposition state" (or coupled), this entailing a "unification" (or coupling) between the topological (Euclidean) and the physical (Lorentzian) states of space-time.

In this study, a radical hypothesis concerning the wave-particle duality exhibited by extremely small objects in nature is explored by developing a Planck lattice model of space–time that grapples with the uncertain dynamic quantum structure of space–time at the Planck scale. Upon applying the Planck lattice model to two notable experiments that most clearly demonstrate the essence of wave-particle duality, one immediately finds that it successfully shows in a relatively straightforward and physically consistent manner how parcels of matter and energy, i.e., electrons and photons, respectively, can behave like waves. The heuristic concepts regarding the underlying structure of space–time contained herein are intended to show the classical particle description of matter and energy as fundamental, while at the same time doing away with the widely held notion of a continuous space–time.

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.

It is shown that the problem of the cosmological constant is connected with the problem of emergence of quantum mechanics. Both of them are principal aspects of physics at the Planck scale. Probability amplitudes describe evolution of the harmonic oscillator non-equilibrium distributions in a thermal bath. The Planck constant ħ, the Fock space and the Schrödinger equation appear in the natural way. For massless fields it leads, in particular, to appearance of masses, and, consequently, of the cosmological constant in the gravitational equations. The path integral for the relativistic particle propagator is presented.

A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated to a minimal uncertainty in position measurements, which is encoded in deformed commutation relations. Once applied in the Heisenberg dynamics, they give effects potentially detectable in low energy experiments. For instance, an isolated harmonic oscillator becomes intrinsically nonlinear and its dynamics shows a dependence of the oscillation frequency on the amplitude, as well as the appearance of higher harmonics. Here we analyze the free decay of micro and nano-oscillators, spanning a wide range of masses, and we place upper limits to the parameters quantifying the commutator deformation.

The four-fermion gravitational interaction is induced by torsion. It gets dominating below the Planck scale. The regular, axial-axial part of this interaction by itself does not stop the gravitational compression. However, the anomalous, vector-vector interaction results in a natural way both in big bounce and in inflation.

Questions to discuss:

• If the SM with elementary Higgs field is completely confirmed with the discovery of a heavy scalar boson at LHC and Tevatron?
• Does the Higgs mass value of 126 GeV point to the need of new physics below the Planck scale?
• Do we need the next Higgs factory to solve problems with its identification?
• How can we distinguish extended Higgs sector from the standard one as well as from the composite Higgs?

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.