Measurable Maximal Energy and Minimal Time Interval

The possibility of finding the measurable maximal energy and the minimal time interval is discussed in different quantum aspects. It is found that the linear generalized uncertainty principle (GUP) approach gives a non-physical result. Based on large scale Schwarzshild solution, the quadratic GUP approach is utilized. The calculations are performed at the shortest distance, at which the general relativity is assumed to be a good approximation for the quantum gravity and at larger distances, as well. It is found that both maximal energy and minimal time have the order of the Planck time. Then, the uncertainties in both quantities are accordingly bounded. Some physical insights are addressed. Also, the implications on the physics of early Universe and on quantized mass are outlined. The results are related to the existence of finite cosmological constant and minimum mass (mass quanta).

Impacts of Generalized Uncertainty Principle on Black Hole Thermodynamics and Salecker-Wigner Inequalities

We investigate the impacts of Generalized Uncertainty Principle (GUP) proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity on black hole thermodynamics and Salecker-Wigner inequalities. Utilizing Heisenberg uncertainty principle, the Hawking temperature, Bekenstein entropy, specific heat, emission rate and decay time are calculated. As the evaporation entirely eats up the black hole mass, the specific heat vanishes and the temperature approaches infinity with an infinite radiation rate. It is found that the GUP approach prevents the black hole from the entire evaporation. It implies the existence of remnants at which the specific heat vanishes. The same role is played by the Heisenberg uncertainty principle in constructing the hydrogen atom. We discuss how the linear GUP approach solves the entire-evaporation-problem. Furthermore, the black hole lifetime can be estimated using another approach; the Salecker-Wigner inequalities. Assuming that the quantum position uncertainty is limited to the minimum wavelength of measuring signal, Wigner second inequality can be obtained. If the spread of quantum clock is limited to some minimum value, then the modified black hole lifetime can be deduced. Based on linear GUP approach, the resulting lifetime difference depends on black hole relative mass and the difference between black hole mass with and without GUP is not negligible.

Chemical Freeze-Out and Higher Order Multiplicity Moments

We calculate the non-normalized moments of the particle multiplicity within the framework of the hadron resonance gas (HRG) model. At finite chemical potential $mu$, a non-monotonic behavior is observed in the thermal evolution of third order moment (skewness $S$) and the higher order ones as well. Among others, this observation likely reflects dynamical fluctuations and strong correlations. The signatures of non-monotonicity in the normalized fourth order moment (kurtosis $kappa$) and its products get very clear. Based on these findings, we introduce a novel condition characterizing the universal freeze-out curve. The chemical freeze-out parameters $T$ and $mu$ are described by vanishing $kappa, sigma^2$ or equivalently $m_4=3,chi^2$, where $sigma$, $chi$ and $m_4$ are the standard deviation, susceptibility and fourth order moment, respectively. The fact that the HRG model is not able to release information about criticality related to the confinement and chiral dynamics should not veil the observations related to the chemical freeze-out. Recent lattice QCD studies strongly advocate the main conclusion of the present paper.