Harmonic oscillator is significantly important in quantum gravity for its dynamical properties. Dynamics of the harmonic oscillator can be modified by inserting a modified uncertainty relation considered in quantum cosmology models such as string theory and quantum loop gravity theory. In this paper, the equation of damped quantum harmonic oscillator has been solved with respect to the modified uncertainty relation and the effects of this modification have been probed in the case of the damped oscillating system.

In this study, The statistical consequences of minimal length supposition are investigated for a canonical ensemble of ideal gas. These effects are encoded in the socalled Generalized Uncertainty Principle (GUP) of the second order. In the framework of the considered GUP scenario, a unique partition function is obtained by using two different methods of quantum and classical approaches. It should be noticed that here we consider the magnitude of the momentum in the deformed Hamiltonian of the model. In this way, the model is different from the already existing model which does not have any significant result in the quantum approach. In particular, the corrections to the thermodynamical characteristics such as the mean energy, the entropy and the density of states are achieved. The induced improvements manifest themselves at very high-temperature limits. However, it is shown that, if one applies the predicted observational bound on the GUP deformation parameter, the modifications become more observable even at intermediate temperatures. The deformation parameter of the considered GUP model is also estimated for nowadays precision of measurements of the heat capacity of an ensemble of hydrogen atoms.

The challenge in developing a theory of quantum gravity stems from the fundamentally different ways the two theories describe physical systems. Quantum mechanics operates on discrete, probabilistic principles, while general relativity is a continuous, deterministic theory. The generalized uncertainty principle is a modified version of Heisenberg's uncertainty principle that applies quantum gravitational corrections to systems with strong gravity. As a clear example of these systems, white dwarfs can be mentioned. In white dwarfs, the gravitational pressure provides the necessary support against gravitational collapse, however, the generalized uncertainty principle has been shown to negate the Chandrasekhar limit in the presence of a minimum length, allowing white dwarfs to grow to any size, even infinitely large, which is in contradiction with physical astrophysical observations. This paper modifies the relationship between degeneracy pressure and density in white dwarfs using an alternative form of the uncertainty principle that incorporates a maximum length. We demonstrate that this new formalism recovers the Chandrasekhar limit and resolves the discrepancy between theory and observation.

The Werner Heisenberg's uncertainty principle, with the approach of governing probability rule in the world, provides important philosophical and theological questions, including: The first, what is the relationship between the uncertainty principle and causation? Second, what association is there between the uncertainty and theological questions like existence of God and freewill? Can such principle proves the theological questions or is it able to reject them? the paper comes to the conclusion that the Heisenberg's principle rejects causation. Also having a humble approach to the scientific interpretations, it mentions that without necessity of the creature's existence, it is not logical to trust the scientific theories in order to find any justification for their actions or behaviors. In addition, Heisenberg considers God as a Creator and Dominator of non-determinacy, and based on his idea, the uncertainty principle has a correlation with freewill. Finally, in favor of causality, the paper criticizes the principle and shows that it cannot be against believing to God or freewill.

While a great number of researches have focused on identifying the factors affecting carbon emissions, the role of economic policy uncertainty (EPU) on environmental quality has been less studied in the energy-environment literature. In this regard, the purpose of this study is to investigate how economic policy uncertainty affects CO2 emission in the group of developing countries with the highest levels of pollution. In addition, the moderating effect of economic policy uncertainty on CO2 emissions from renewable and non-renewable energy channels has been studied.  The results show that there is bidirectional causality between economic policy uncertainty and CO2 emissions. Then, a panel data model by the Generalized Method of Moments (GMM) is estimated to address the endogeneity problem. We find that increase in economic policy uncertainty has led to higher CO2 emissions. Furthermore, our findings underscore that 1 percent increase in the consumption of renewable energy has led to decrease CO2 emissions by 0.026 percent. In contrast, the consumption of nonrenewable energy has led to increase in CO2 emissions by 0.98 percent. Also, the results show that increase in economic policy uncertainty has led to a reduction in non-renewable energy consumption and thus a reduction in CO2 emissions during the period 2004 to 2020.

Considering the importance of the precautionary principle for development of international environmental law and taking into account that the "scientific uncertainty", is a problematic of the precautionary principle, this article tries to analyze the scientific uncertainties in the international environmental law’s context. In fact, one of the problems of implementing of the precautionary principle in the international environmental law the ambiguity on the issue of "scientific uncertainty" mentioned in many legal texts, both binding and non-binding. The purpose of this study is to describe the position and the role of scientific uncertainty in the realization of precautionary principle.This study explains the nature of legal gaps in the implementation of the precautionary principle in international environmental law. There are several legal methods and administrative procedures to dealing with the "scientific uncertainty", such as framework-protocol approach, scientific advisory boards, management approaches, prior informed consent, assessment and monitoring of environmental effects, temporary measures and so on. We can considerer these legal approaches and techniques in many environmental treaties, especially after the Rio Declaration 1992. Moreover, in the case study, the legal instruments dealing for scientific uncertainty in precautionary principle from the perspective of International Environment in the Convention on Climate Change in 1992 is analyzed.In this research, after studying the methods and techniques for dealing with scientific uncertainty, the suitable method to implement the precautionary principle in international environmental law has been analyzed. Due to legal problems for the implementation of the precautionary principle in international environmental law, still there is no consensus and common procedure for implementing these methods. However, this study suggests some solutions such as the practice of Governments, implementing the national system and development of environmental treaties based on the implementation of the precautionary principle.