Uncertainty relation in a third-quantized universe.

SchrÖdinger Wave Functional in Quantum Yang–Mills Theory from Precanonical Quantization

Science sets itself apart from other paths to truth by recognizing that even its greate practitioners sometimes err.

Inspired by string theory, Heisenberg's uncertainty principle can be generalized to include the photon-electron gravitational interaction, which leads to the Generalized Uncertainty Principle (GUP). Although GUP considers gravitational uncertainty at the minimum fundamental length scale in physics, it does not consider the effects of spacetime curvature on quantum mechanical uncertainty relations. The Extended Uncertainty Principle (EUP) is a generalization of Heisenberg's Uncertainty Principle that, unlike the GUP, applies to large length scales. GEUP is also a linear combination of EUP and GUP that creates minimal uncertainty on large length scales. The Einstein-Gauss-Bonnet theory (EGB) can be considered as one of the most promising candidates for modified gravity. In this paper, by using GUP, EUP, and GEUP, we intend to obtain the Hawking temperature of a four-dimensional EGB black hole in the asymptotically flat and (Anti)-de Sitter spacetime. We show that coupling constant, cosmological constant, mass, and radius significantly affect Hawking temperature and decrease or increase Hawking temperature depending on the chosen horizons.

We address the issue of the relation between the canonical functional Schr\"odinger representation in quantum field theory and the approach of precanonical field quantization proposed by the author, which requires neither a distinguished time variable nor infinite-dimensional spaces of field configurations. We argue that the standard functional derivative Schr\"odinger equation can be derived from the precanonical Dirac-like covariant generalization of the Schr\"odinger equation under the formal limiting transition $\gamma^0\varkappa\rightarrow\delta(\mathbf{0})$, where the constant $\varkappa$ naturally appears within the precanonical quantization as the inverse of a small "elementary volume" of space. We obtain a formal explicit expression of the Schr\"odinger wave functional as a continuous product of the Dirac algebra valued precanonical wave functions, which are defined on the finite-dimensional covariant configuration space of the field variables and space-time variables.

We present a theoretical analysis of the statistical fluctuations in the coherent spontaneous harmonic radiation (CSHR) generated by a free electron laser (FEL) under the conditions applicable in a previously published experiment [1] where sub-Poisson optical fluctuations were observed. The numerical analyses presented here document the conclusion that the emission of CSHR can serve as a useful test bed for analyses of the nonclassical aspects of electron beam formation and radiation. Two possible explanations for the observed fluctuations in the CSHR are investigated as limiting physical mechanisms: the fluctuations in the number density of the radiating electrons, the so-called and the quantum fluctuations in the radiation field. When the uncertainties in the radiation field are considered as the only noise source as in the analysis, the statistical fluctuations in the CSHR would result in Poisson statistics. On the other hand, when the electron shot noise is regarded as the only noise contribution as assumed by the shot-noise model, we find numerically and analytically that the fluctuations, as characterized by the Fano factor, would be much smaller than those due to the quantum uncertainties in the radiation field in the analysis. The experimentally observed fluctuations are larger than those due to shot noise, but smaller than those due to quantum fluctuations in the field. Hence, neither the classical shot-noise model nor the quasi-classical analysis can explain the experimental results. Given the results presented in this report, it is clear that attention must be given to the other phenomena-including the quantum fluctuations in the electromagnetic field and the nonclassical electron correlation, which contributed to the observed laser fluctuations.

Based on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On the other hand, this suggests modified dispersion relations (MDRs) enabling an estimation for the difference between the group velocity of gravitons and that of photons. Utilizing features of the UV/IR correspondence and the obvious similarities between GUP (including non‐gravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant (apparently manifesting gravitational influences on the vacuum energy density), we suggest a possible solution for the cosmological constant problem.

The cosmological constant (CC) term in Einstein's equations, Λ, was first associated to the idea of vacuum energy density. Notwithstanding, it is well-known that there is a huge, in fact appalling, discrepancy between the theoretical prediction and the observed value picked from the modern cosmological data. This is the famous, and extremely difficult, "CC problem". Paradoxically, the recent observation at the CERN Large Hadron Collider of a Higgs-like particle, should actually be considered ambivalent: on the one hand it appears as a likely great triumph of particle physics, but on the other hand it wide opens Pandora's box of the cosmological uproar, for it may provide (alas!) the experimental certification of the existence of the electroweak (EW) vacuum energy, and thus of the intriguing reality of the CC problem. Even if only counting on this contribution to the inventory of vacuum energies in the universe, the discrepancy with the cosmologically observed value is already of 55 orders of magnitude. This is the (hitherto) "real" magnitude of the CC problem, rather than the (too often) brandished 123 ones from the upper (but fully unexplored!) ultrahigh energy scales. Such is the baffling situation after 96 years of introducing the Λ-term by Einstein. In the following I will briefly (and hopefully pedagogically) fly over some of the old and new ideas on the CC problem. Since, however, the Higgs boson just knocked our door and recalled us that the vacuum energy may be a fully tangible concept in real phenomenology, I will exclusively address the CC problem from the original notion of vacuum energy, and its possible "running" with the expansion of the universe, rather than venturing into the numberless attempts to replace the CC by the multifarious concept of dark energy.

Starting from a generalization of the quantum trajectory theory (based on the stochastic Schr\"odinger equation - SSE), non-Markovian models of quantum dynamics are derived. In order to describe non-Markovian effects, the approach used in this article is based on the introduction of random coefficients in the usual linear SSE. A major interest is that this allows to develop a consistent theory of quantum measurement in continuous time for these non-Markovian quantum trajectory models. In this context, the notions of instrument, a priori and a posteriori states are rigorously described. The key point is that by starting from a stochastic equation on the Hilbert space of the system, we are able to respect the complete positivity of the mean dynamics for the statistical operator and the requirements of the axioms of quantum measurement theory. The flexibility of the theory is next illustrated by a concrete physical model of a noisy oscillator where non Markovian effects come from random environment, coloured noises, randomness in the stimulating light, delay effects. The statistics of the emitted photons and the heterodyne and homodyne spectra are studied and we show how these quantities are sensible to the non-Markovian features of the system dynamics, so that, in principle, the observation and analysis of the fluorescence light could reveal the presence of non-Markovian effects and allow for a measure of the spectra of the noises affecting the system dynamics.

Quantum fluctuations of a real massless scalar field are studied in the context of the Generalized Uncertainty Principle (GUP). The dynamical finite vacuum energy is found in spatially flat Friedmann-Robertson- Walker (FRW) spacetime which can be identified as dark energy to explain late time cosmic speed-up. The results show that a tiny deviation from the standard uncertainty principle is necessary on cosmological ground. By using the observational data we have constraint the GUP parameter even more stronger than ever.

We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). This is a direct result of the fourth equation of our manuscript which unconventionally compares the action integral of General relativity with the second derived action integral, which then permits Equation (5), which is a bound on the Cosmological constant. What we have done is to replace the Hamber Quantum gravity reference-based action integral with a result from John Klauder’s “Enhanced Quantization”. In doing so, with Padamabhan’s treatment of the inflaton, we then initiate an explicit bound upon the cosmological constant. The other approximation is to use the inflaton results and conflate them with John Klauder’s Action principle for a way, if we have the idea of a potential well, generalized by Klauder, with a wall of space time in the Pre Planckian-regime to ask what bounds the Cosmological constant prior to inflation, and to get an upper bound on the mass of a graviton. We conclude with a redo of a multiverse version of the Penrose cyclic conformal cosmology. Our objective is to show how a value of the rest mass of the heavy graviton is invariant from cycle to cycle. All this is possible due to Equation (4). And we compare all these with results of Reference [1] in the conclusion, while showing its relevance to early universe production of black holes, and the volume of space producing 100 black holes of value about 10^2 times Planck Mass. Initially evaluated in a space-time of about 10^3 Planck length, in spherical length, we assume a starting entropy of about 1000 initially.

We constrain the Friedmann-Robertson-Walker (FRW) model with a “radiation-like” contribution to the Friedmann equation against the astronomical data. We analyze the observational bounds on a (1 + z)4 term from type Ia supernovae (SNIa) data, Fanaroff-Riley type IIb (FRIIb) radio galaxy (RG) data, baryon oscillation peak and cosmic microwave background radiation (CMBR) observations. We argue that it is not possible to determine the energy densities of individual components scaling like radiation from a kinematic astronomical test. The bounds for the density parameter of the total radiation-like term can be obtained. We find different interpretations of the presence of a scaling-like radiation term: the FRW universe filled with a massless scalar field in a quantum regime (the Casimir effect), the FRW model in a semiclassical approximation of loop quantum gravity, the FRW model in the Randall-Sundrum scenario with dark radiation or a cosmological model with global rotation. In this paper, we mainly concentrate on the Casimir effect arising from quantum effects of a scalar field. This contribution can describe a decaying part of the cosmological constant. We discuss the back-reaction of gravity on the Casimir-type force which is a manifestation of the vacuum fluctuations of the quantum scalar field at low temperature. It is shown that, while the Casimir energy gives rise to the accelerating Universe, the cosmological constant term is still required. We argue that a small negative contribution of a radiation-like term can reconcile the tension between the observed primordial 4He and D abundances. Moreover, the presence of such a contribution can also remove the disagreement between the Hubble parameter H0 values obtained from the SNIa and Wilkinson Microwave Anisotropy Probe (WMAP) satellite data.

The observation that type Ia supernovae (SNe Ia) are fainter than expected given their redshifts has led to the conclusion that the expansion of the universe is accelerating. The widely accepted hypothesis is that this acceleration is caused by a cosmological constant or some dark energy field that pervades the universe. We explore what the supernovae data tell us about this hypothesis by answering the question: Can these data be explained with a model in which the strength of gravity varies on a cosmic timescale? We conclude that they can and find that the supernovae data alone are insufficient to distinguish between a model with a cosmological constant and one in which G varies. However, the varying-G models are not viable when other data are taken into account. The topic is an ideal one for undergraduate physics majors.

We explore an extension of the ΛCDM model in which the pressure p of the dark energy (DE) fluid evolves with the expansion of the Universe, expressed as a function of the scale factor a. The corresponding energy density ρ is derived from the continuity equation, resulting in a dynamical equation-of-state parameter w ≡ p/ρ during the late-time expansion of the Universe. The pressure is modeled using a Taylor expansion around the present epoch (a = 1), introducing deviations from a cosmological constant within the dynamical dark energy (DDE) framework. At first order, a single new parameter Ω1 captures linear deviations, while a second-order parameter, Ω2, accounts for quadratic evolution in the pressure. We constrain the first- and second-order DDE models using multiple observational datasets and compare their performance against ΛCDM and the CPL parameterization. A joint analysis of Planck CMB, DESI, and DESY5 data yields the strongest evidence for DDE, with a 2.7σ deviation in the first-order model and over 4σ in the second-order model — providing strong statistical support for a departure from a cosmological constant. The reconstructed DE evolution in the second-order case reveals a distinctive non-monotonic behavior in both energy density and w DE(a), including clear phantom-crossing phenomena. Notably, the late-time evolution of w DE(a) remains consistent across datasets and shows strong agreement with the CPL parameterization, underscoring the robustness of the pressure-based approach.

This paper presents a novel approach to the cosmological constant problem by the use of the Clifford algebras of space Cl3,0 and anti-space Cl0,3 with a particular focus on the paravector representation, emphasizing the fact that both algebras have a center represented just by two coordinates. Since the paravector representation allows assigning the scalar element of grade 0 to the time coordinate, we consider the relativity in such two-dimensional spacetime for a uniformly accelerated frame with the constant acceleration 3H0c. Using the Rindler coordinate transformations in two-dimensional spacetime and then applying it to Minkowski coordinates, we obtain the FLRW metric, which in the case of the Clifford algebra of space Cl3,0 corresponds to the anti-de Sitter (AdS) flat (k=0) case, the negative cosmological term and an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra Cl0,3 leads to the de Sitter model with the positive cosmological term and the exact form of the scale factor used in modern cosmology.

We describe the measurement process for a model system whose Schr\"odinger equation yields to explicit solution. Any device for an effectively irreversible measurement must not just be a ``meter'' with a single degree of freedom; it must also contain a ``heat bath'' with many degrees of freedom. Such a bath may cause an effectively instantaneous decay of quantum coherences between macroscopically distinct meter readings, i.e., impart practically classical behavior to the meter. In turn, such a meter can be read without thereby suffering back reactions. We establish the limits in which a meter reading is uniquely related, with reasonable certainty, to a definite eigenvalue of the measured observable.