Exploring the Implications of the Deformation Parameter and Minimal Length in the Generalized Uncertainty Principle

The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are approximately equal to the Planck length. In this context, we have introduced a model that utilizes a combination of Schwarzschild’s radius and Compton length to quantify the gravitational length of an object. This model has provided a novel perspective in generalizing the uncertainty principle. Furthermore, it has elucidated the significance of the deforming linear parameter β and its range of variation from unity to its maximum value.

Critical Analysis of the Origins of Heisenberg's Uncertainty Principle

Analysis of the initial stages of the logical process followed by Louis de Broglie in establishing the electron phase wave equation in his 1924 thesis, which triggered the development of Wave Mechanics when Erwin Schrödinger formalized this concept with his vectorial wave equation. This development was soon followed by Quantum Mechanics, when Schrödinger proved that the Matrix Mechanics independently developed by Werner Heisenberg was equivalent to Wave Mechanics, with both theories leaving room for some degree of uncertainty as to the physical localization of the moving electron. This is what led Heisenberg to also formalize the Uncertainty Principle to take this situation into account. This principle was soon regarded as a fundamental axiomatic principle that seemed to make further exploration of the subatomic level of magnitude appear impossible to most researchers. We will analyze in this article the reason why the phase-wave velocity established by de Broglie generated this uncertainty in the localization of the moving electron in light of the current state of knowledge on the behavior of the electron in motion, in view of establishing the relevance of maintaining the Uncertainty Principle in the study of the subatomic level of magnitude.

Generalized uncertainty principle from long-range kernel effects:The case of the Hawking black hole temperature

We prove the existence of an analogy between spatial long-range interactions,which are of the convolution-type introduced in non-relativistic quantum mechanics,and the generalized uncertainty principle predicted from quantum gravity theories.As an illustration,black hole temperature effects are discussed.It is observed that for specific choices of the moment's kernels,cold black holes may emerge in the theory.

Squaring the Circle Is Possible When Taking into Consideration the Heisenberg Uncertainty Principle

Squaring the circle is one of the oldest challenges in mathematical geometry. In 1882, it was proven that π was transcendental, and the task of squaring the circle was considered impossible. Demonstrating that squaring the circle was not possible took place before discovering quantum mechanics. The purpose of this paper is to show that it is actually possible to square the circle when taking into account the Heisenberg uncertainty principle. The conclusion is clear: it is possible to square the circle when taking into account the Heisenberg uncertainty principle.

Uncertainty Principle for the Quaternion Linear Canonical Transform in Terms of Covariance

An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.

Generalized Uncertainty Principle and Thermodynamic Quantities of SAdS_5 Black Hole

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein- Hawking black hole entropy. The different correction leading terms are obtained by the different methods. In this paper, we calculate the correction to SAdS5 black hole thermodynamic quantity due to the generalized uncertainty principle. Furthermore we derive that the black hole entropy obeys Bekenstein Hawking area theorem. The entropy has infinite correction terms. And every term is finite and calculable. The corrected Cardy-Vedinde formula is derived. In our calculation, Bekenstein Hawking area theorem still holds after considering the generalized uncertainty principle. We have not introduced any hypothesis. The calculation is simple. Physics meaning is clear. We note that our results are quite general. It is not only valid for four-dimensional spacetime but also for higher-dimensional SAdS spacetime.

Generalized uncertainty principle and tunneling radiation of the SAdS_5 black hole

After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a fivedimensional Sehwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the Bekenstein-- Hawking entropy are derived. In a five-dimensional black hole the one order correction term in the Bekenstein-Hawking entropy correction term is proportional to the third power of the area, and the logarithmic correction term is a twoorder small quantity. The correction term is related to the dimension constant introduced in the generalized uncertainty principle. Because the black hole entropy is not divergent, the lowest value of the five-dimensional Schwarzschild anti de Sitter black hole horizon radius is obtained. After considering the generalized uncertainty principle, the radiation spectrum is still consistent with normalization theory.

Generating Real Random Numbers with Uncertainty Principle

The real random number generation is a critical problem in computer science.The current generation methods are either too dangerous or too expensive,such as using decays of some radioactive elements.They are also hard to control.By the declaration of uncertainty principles in quantum mechanics,real probabilistic events can be substituted by easier and safer processes,such as electron diffraction,photon diffraction and qubits.The key to solve the problem of Schr?dinger’s cat is to identify that the atom stays in different states after and before the decay,and the result of the decay is probabilistic according to the wave packet co llapse hypothesis.Same matter is able to possess different kinds of properties such as wave-particle duality due to that it can stay in various states,and which state will the matter stay is determined by the chosen set of physical quantities(or mechanical quantities).One eigenstate of a set of physical quantities can be a superpos ition of other eigenstates of different sets of physical quantities,and the collapse from a superposition to an eigenstate it contains is really random.Using this randomness,real random number can be generated more easily.

Addition to the Article with Stepan Moskaliuk on the Inter Relationship of General Relativity and (Quantum) Geometrodynamics, via Use of Metric Uncertainty Principle

We take note of the material offered in [1] as to Geometrodynamics as a way to quantify an inter relationship between a quantum style Heisenberg uncertainty principle for a metric tensor and conditions postulated as to a barotropic fluid, i.e. dust for early universe conditions. By looking at the onset of processes at/shorter than a Planck Length, in terms of initial expansion of the universe, we use inputs from the metric tensor as a starting point for the variables used in Geometrodynamics.

Is the Cosmological Constant, a “Vacuum” Field? We Explore This by Squeezing Early Universe “Coherent-Semi Classical States”, and Compare This to Energy from the Early Universe Heisenberg Uncertainty Principle

Our question delves into the nature of early universe vacuum fields, and if this initial vacuum field corresponds to a configuration of early universe space-time at the start of inflation. The answer as to this came out due to wanting to know if a cosmological constant, as given in the Einstein field equations is commensurate with the byproduct of squeezed states. We compare our answer, with the influx of energy as given by a modified Heinsenberg uncertainty principle, at the start of the inflationary era. The so called influx of energy is tied into the squeezed state phenomena as written up in the onset of this article. The impetus to writing this document came from Dr. Karim, in an e mail which the author relates to, in the introduction. Our claim is that the smallness of is what is driving the existence of the squeezed states.

Generalized Uncertainty Principle and Black Hole Entropy of Higher-Dimensional de Sitter Spacetime

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-- Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coetticient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty prlnciple and obtain the correction term caused by the generalized uncertainty principle. Because in our calculation we think that the Bekenstein-Hawking area theorem is still valid after considering the generalized uncertainty principle, we derive that the coefficient of the logarithmic term of the black hole entropy correction term is positive. This result is different from the known result at present. Our method is valid not only for four-dimensional spacetimes but also for higher-dimensional spacetimes. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the entropy correction of the complicated spacetime.

On the role of the uncertainty principle in superconductivity and superfluidity

We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because of the robustness of many-body quantum states with respect to the external environment, which is directly related to the uncertainty principle as applied to coordinates and momenta of the carriers. In the case of superconductors, this implies relationships between macroscopic quantities such as critical temperature and critical magnetic field, and microscopic quantities such as the amount of spatial squeezing of a Cooper pair and its correlation time. In the case of ultracold atomic Fermi gases, this should be paralleled by a connection between the critical temperature for the onset of superfluidity and the corresponding critical velocity. Tests of this conjecture are finally sketched with particular regard to the understanding of the behaviour of superconductors under external pressures or mesoscopic superconductors, and the possibility to mimic these effects in ultracold atomic Fermi gases using Feshbach resonances and atomic squeezed states.

Thermodynamic properties of massless Dirac–Weyl fermions under the generalized uncertainty principle

The Dirac–Weyl equation characterized quasi-particles in the T3 lattice are studied under external magnetic field using the generalized uncertainty principle(GUP). The energy spectrum of the quasi-particles is found by the Nikiforov–Uvarov method. Based on the energy spectrum obtained, the thermodynamic properties are given, and the influence of the GUP on the statistical properties of systems is discussed. The results show that the energy and thermodynamic functions of massless Dirac–Weyl fermions in the T3 lattice depend on the variation of the GUP parameter.

HEAT KERNELS AND HARDY'S UNCERTAINTY PRINCIPLE ON H-TYPE GROUPS

This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.

Thermodynamic effects of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle

The thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter is investigated.We calculate the analytical expresses of corresponding thermodynamic variables,e.g.,the Hawking temperature,entropy of the black hole.In addition,we derive the heat capacity to analyze the thermal stability of the black hole.We also compute the rate of emission in terms of photons through tunneling.By numerical method,an obvious phase transition behavior is found.Furthermore,according to the general uncertainty principle,we study the quantum corrections to these thermodynamic quantities and obtain the quantum-corrected entropy containing the logarithmic term.Lastly,we investigate the effects of the magnetic charge g,the dark matter parameter k and the generalized uncertainty principle parameterαon the thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle.

（Anti-）de Sitter Black Hole Entropy and Generalized Uncertainty Principle

We generalize the method that is used to study corrections to Cardy-Verlinde formula due to generalized uncertainty principle and discuss corrections to Cardy-Verlinde formula due to generalized uncertainty principle in （anti）- de Sitter space. Because in de Sitter black hole spacetime the radiation temperature of the black hole horizon is different from the one of the cosmological horizon, this spacetime is a thermodynamical non-equilibrium spacetime.

Uncertainty Principles for the Generalized Fourier Transform Associated with Spherical Mean Operator

The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.

Relationship between the Fundamental Constants of Physics Obtained from the Uncertainty Principle for Energy and Time

An attempt is done to calculate the value of the elementary electron charge from its relation to the Planck constant and the speed of light. This relation is obtained, in the first step, from the Pauli analysis of the strength of the electric field associated with an elementary emission process of energy. In the next step, the uncertainty principle is applied to both the emission time and energy. The theoretical result for e is roughly close to the experimental value of the electron charge.

Heisenberg Uncertainty Principle for n-Dimen-sional Linear Canonical Transforms

The uncertainty principle proposed by German physicist Heisenberg in 1927 is a basic principle of quantum mechanics and signal processing.Since linear canonical transformation has been widely used in various fields of signal processing recently and Heisenberg uncertainty principle has been endowed with new expressive meaning in linear canonical transforms domain,in this manuscript,an improved Heisenberg uncertainty principle is obtained in linear canonical trans-forms domain.

A NOTE ON UNCERTAINTY PRINCIPLE

weighted form of uncertainty principle is proved.