Planck Length Scale Research Articles

GUP with minimal length and maximal momentum on the thermodynamics of relativistic fermi gas

This work attempts to investigate the influence of the linear and quadratic generalized uncertainty principle (LQGUP) on the thermodynamical characteristics of relativistic Fermi gas. The general thermodynamical characteristics of relativistic Fermi gas, such as mean energy, pressure, entropy, and specific heat, are obtained. According to the modified function of temperature for mean energy and specific heat of relativistic Fermi gas, we find that at high temperature limit, the value of deformation parameter in the framework of LQGUP has an important effect on thermodynamic characteristics. It appears that the deformation parameter’s value is rising at higher energy levels of science, resulting in the minimal measurable length reaching close to the Planck length scale.

℘ -adic quantum mechanics, the Dirac equation, and the violation of Einstein causality

This article studies the breaking of the Lorentz symmetry at the Planck length in quantum mechanics. We use three-dimensional ℘ -adic vectors as position variables, while the time remains a real number. In this setting, the Planck length is 1/℘ , where ℘ is a prime number, and the Lorentz symmetry is naturally broken. In the framework of the Dirac-von Neumann formalism for quantum mechanics, we introduce a new ℘ -adic Dirac equation that predicts the existence of particles and antiparticles and charge conjugation like the standard one. The discreteness of the ℘ -adic space imposes substantial restrictions on the solutions of the new equation. This equation admits localized solutions, which is impossible in the standard case. We show that an isolated quantum system whose evolution is controlled by the ℘ -adic Dirac equation does not satisfy the Einstein causality, which means that the speed of light is not the upper limit for the speed at which conventional matter or energy can travel through space. The new ℘ -adic Dirac equation is not intended to replace the standard one; it should be understood as a new version (or a limit) of the classical equation at the Planck length scale.

Quantum gravity constraints on fine structure constant from GUP in braneworlds

The Generalized Uncertainty Principle (GUP) has been discussed in the thick braneworld scenario. By considering Rydberg atoms in this background, we show that the spacetime geometry affects Maxwell equations inducing an effective dielectric constant on the space. In its turn, the corrected Coulomb potential by the gravitational interaction yields a deviation on the 3-dimensional Bohr radius. Then, we compute the corrections on the fine structure constant owing to the GUP in higher-dimensional spacetime. We also found constraints for the deformation parameter beta and D-dimensional Planck length l_{D} by comparing the predicted deviations with the recent empirical data of the fine structure constant. We compute the intermediate length scale, which in principle may be larger than the Planck length scale. It is conjectured that below such scale Quantum Gravity effects should take place.

Dimensionless Physics: Planck Constant as an Element of the Minkowski Metric

Diakonov theory of quantum gravity, in which tetrads emerge as the bilinear combinations of the fermionic fields, suggests that in general relativity the metric may have dimension 2; i.e., [{{g}_{{mu nu }}}] = 1{text{/}}{{[L]}^{2}}. Several other approaches to quantum gravity, including the model of superplastic vacuum and BF-theories of gravity support this suggestion. The important consequence of such metric dimension is that all the diffeomorphism invariant quantities are dimensionless for any dimension of spacetime. These include the action S, interval s, cosmological constant Λ, scalar curvature R, scalar field Φ, etc. Here we are trying to further exploit the Diakonov idea, and consider the dimension of the Planck constant. The application of the Diakonov theory suggests that the Planck constant hbar is the parameter of the Minkowski metric. The Minkowski parameter hbar is invariant only under Lorentz transformations, and is not diffeomorphism invariant. As a result, the Planck constant hbar has the dimension of length. Whether this Planck constant length is related to the Planck length scale, is an open question. In principle there can be different Minkowski vacua with their own values of the parameter hbar . Then in the thermal contact between the two vacua their temperatures obey the analog of the Tolman law: {{hbar }_{1}}{text{/}}{{T}_{1}} = {{hbar }_{2}}{text{/}}{{T}_{2}}.

Wavelet field decomposition and UV \u2018opaqueness\u2019

A large body of work over several decades indicates that, in the presence of gravitational interactions, there is loss of localization resolution within a fundamental (∼ Planck) length scale ℓ. We develop a general formalism based on wavelet decomposition of fields that takes this UV ‘opaqueness’ into account in a natural and mathematically well-defined manner. This is done by requiring fields in a local Lagrangian to be expandable in only the scaling parts of a (complete or, in a more general version, partial) wavelet Multi-Resolution Analysis. This delocalizes the interactions, now mediated through the opaque regions, inside which they are rapidly decaying. The opaque regions themselves are capable of discrete excitations of ∼ 1/ℓ spacing. The resulting effective Feynman rules, which give UV regulated and (perturbatively) unitary physical amplitudes, resemble those of string field theory.

Pre-inflation and trans-Planckian censorship

We investigate the implication of Trans-Planckian Censorship Conjecture (TCC) for the initial state of primordial perturbations. It is possible to set the state of perturbation modes in the infinite past as the Minkowski vacuum, only if the pre-inflationary era is past-complete. We calculate the evolution of the perturbation modes in such a pre-inflationary era and show that at the beginning of inflation the perturbation modes with wavelengths much shorter than the Hubble scale (but still larger than the Planck length scale) will behave as they are in the Bunch-Davis state. Therefore, a past-complete pre-inflationary evolution may automatically prepare the initial state required for the inflationary perturbations at the CMB window while obeying the TCC.

Dark energy as a large scale quantum gravitational phenomenon

In our recently proposed quantum theory of gravity, the universe is made of ‘atoms‘” of space-time-matter (STM). Planck scale foam is composed of STM atoms with Planck length as their associated Compton wave-length. The quantum dispersion and accompanying spontaneous localization of these STM atoms amounts to a cancellation of the enormous curvature on the Planck length scale. However, an effective dark energy term arises in Einstein equations, of the order required by current observations on cosmological scales. This happens if we propose an extremely light particle having a mass of about [Formula: see text], forty-two orders of magnitude lighter than the proton. The holographic principle suggests there are about [Formula: see text] such particles in the observed universe. Their net effect on space-time geometry is equivalent to dark energy, this being a low energy quantum gravitational phenomenon. In this sense, the observed dark energy constitutes evidence for quantum gravity. We then invoke Dirac’s large number hypothesis to also propose a dark matter candidate having a mass halfway (on the logarithmic scale) between the proton and the dark energy particle, i.e. about [Formula: see text].

Effect of non-commutativity of space-time on thermodynamics of photon gas

Doubly special relativity(DSR) introduce a minimal length scale i.e. the Planck length scale, which is independent length scale in addition to the speed of light in the normal special theory of relativity(STR). Doubly special relativity leads to study the $\kappa$-Minkowski space-time. In this paper, we present the result of our investigation on the thermodynamics of photon gas in the $\kappa$-Minkowski space-time. For studying this, we start with the $\kappa$-deformed dispersion relation and keep terms upto first order in the deformation parameter $a$ and we study that how does $\kappa$-deformed dispersion relation affect the thermodynamics of photon gas. In the limit, deformation parameter $a \rightarrow 0$, we get back all the results in the special theory of relativity(STR)\cite{partition}.

Commutative or noncommutative spacetime? Two length scales of noncommutativity

Noncommutativity of the spacetime coordinates has been explored in several contexts, mostly associated to phenomena at the Planck length scale. However, approaching this question through deformation theory and the principle of stability of physical theories, one concludes that the scales of noncommutativity of the coordinates and noncommutativity of the generators of translations are independent. This suggests that the scale of the spacetime coordinates noncommutativity could be larger than the Planck length. This paper attempts to explore the experimental perspectives to settle this question, either on the lab or by measurements of phenomena of cosmological origin.

A Consistency Check for the Free Scalar Field Theory Realization of the Doubly Spacial Relativity**Supported by Research Institute for Astronomy and Astrophysics of Maragha (RIAAM) under Research Project No. 1/6025-73

We study a free scalar field theory in the framework of the Magueijo-Smolin model of the “Doubly Special Relativity” (DSR) which is a non-linear realization of the action of the Lorentz group on momentum space admitting an invariant energy cutoff. We show that unlike the standard quantum field theory, the Klein-Gordon equation obtained via Euler-Lagrange field equation and Heisenberg picture equation of motion of the field are not equivalent in this framework, at least up to the first order of the Planck length scale.

Exploring the unification of quantum theory and general relativity with a Bose–Einstein condensate

Despite almost a century’s worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as ‘quantizing gravity’, resulting in a theory of ‘quantum gravity’. The opposite approach is ‘gravitizing QT’ where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using a Bose–Einstein condensate (BEC) to search for clues. In particular, we study how a single BEC in a superposition of two locations could test a gravitizing QT proposal where wavefunction collapse emerges from a unified theory as an objective process, resolving the measurement problem of QT. Such a modification to QT due to general relativistic principles is testable near the Planck mass scale, which is much closer to experiments than the Planck length scale where quantum, general relativistic effects are traditionally anticipated in quantum gravity theories. Furthermore, experimental tests of this proposal should be simpler to perform than recently suggested experiments that would test the quantizing gravity approach in the Newtonian gravity limit by searching for entanglement between two massive systems that are both in a superposition of two locations.

Regimes of mini black hole abandoned to accretion

Being inspired by the Eddington’s idea, along with other auxiliary arguments, it is unveiled that there exist regimes of a black hole that would prohibit accretion of ordinary energy. In explicit words, there exists a lower bound to black hole mass below which matter accretion process does not run for black holes. Not merely the baryonic matter, but, in regimes, also the massless photons could get prohibited from rushing into a black hole. However, unlike the baryon accretion abandoned black hole regime, the mass-regime of a black hole prohibiting accretion of radiation could vary along with its ambient temperature. For example, we discuss that earlier to [Formula: see text] s after the big-bang, as the cosmological temperature of the Universe grew above [Formula: see text] K, the mass range of black hole designating the radiation accretion abandoned regime, had to be in varying state being connected with the instantaneous age of the evolving Universe by an “one half” power law. It happens to be a fact that a black hole holding regimes prohibiting accretion of energy is gigantic by its size in comparison to the Planck length-scale. Hence the emergence of these regimes demands mini black holes for not being viable as profound suckers of energy. Consideration of accretion abandoned regimes could be crucial for constraining or judging the evolution of primordial black holes over the age of the Universe.

Universal property of quantum gravity implied by uniqueness theorem of Bekenstein-Hawking entropy

We have searched for a universal property of quantum gravity, where "universal" means to be independent of any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on). To do so, we have investigated carefully the basis of black hole thermodynamics. The uniqueness of Bekenstein-Hawking entropy lets us extract a reasonable universal property of quantum gravity from the conditions justifying Boltzmann formula. The universal property indicates a repulsive gravity at Planck length scale, otherwise stationary black holes can not be regarded as thermal equilibrium states of gravity.

Universal Property of Quantum Gravity implied by Bekenstein-Hawking Entropy and Boltzmann formula

We search for a universal property of quantum gravity. By "universal", we mean the independence from any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on). To do so, we try to put the basis of our discussion on theories established by some experiments. Thus, we focus our attention on thermodynamical and statistical-mechanical basis of the black hole thermodynamics: Let us assume that the Bekenstein-Hawking entropy is given by the Boltzmann formula applied to the underlying theory of quantum gravity. Under this assumption, the conditions justifying Boltzmann formula together with uniqueness of Bekenstein-Hawking entropy imply a reasonable universal property of quantum gravity. The universal property indicates a repulsive gravity at Planck length scale, otherwise stationary black holes can not be regarded as thermal equilibrium states of gravity. Further, in semi-classical level, we discuss a possible correction of Einstein equation which generates repulsive gravity at Planck length scale.

Spectral triplets, emergent geometry and entropy in Moyal plane

It was shown by Doplicher et.al. that the measurement of spacetime intervals of the order of Planck length scale is operationally impossible, as the process of measurement invariably gives rise to a black hole formation. This can be avoided by postulating non-vanishing commutation relations between the coordinates, which are now promoted to the level of operators. Formulation of quantum mechanics in these kinds of spaces through the introduction of Hilbert spaces of Hilbert-Schmidt operators is then shown to allow the construction of spectral triplets a la Connes naturally. The computation of spectral distance between pure and mixed states is then shown to exhibit a deep connection between entropy and geometry.

Is a tabletop search for Planck scale signals feasible?

Quantum gravity theory is untested experimentally. Could it be tested with tabletop experiments? While the common feeling is pessimistic, a detailed inquiry shows it possible to sidestep the onerous requirement of localization of a probe on Planck length scale. I suggest a tabletop experiment which, given state of the art ultrahigh vacuum and cryogenic technology, could already be sensitive enough to detect Planck scale signals. The experiment combines a single photon's degree of freedom with one of a macroscopic probe to test Wheeler's conception of "quantum foam", the assertion that on length scales of the order Planck's, spacetime is no longer a smooth manifold. The scheme makes few assumptions beyond energy and momentum conservations, and is not based on a specific quantum gravity scheme.

A laboratory scale fundamental time?

The existence of a fundamental time (or fundamental length) has been conjectured in many contexts. However, the “stability of physical theories principle” seems to be the one that provides, through the tools of algebraic deformation theory, an unambiguous derivation of the stable structures that Nature might have chosen for its algebraic framework. It is well-known that c and ħ are the deformation parameters that stabilize the Galilean and the Poisson algebra. When the stability principle is applied to the Poincare–Heisenberg algebra, two deformation parameters emerge which define two time (or length) scales. In addition there are, for each of them, a plus or minus sign possibility in the relevant commutators. One of the deformation length scales, related to non-commutativity of momenta, is probably related to the Planck length scale but the other might be much larger and already detectable in laboratory experiments. In this paper, this is used as a working hypothesis to look for physical effects that might settle this question. Phase-space modifications, resonances, interference, electron spin resonance and non-commutative QED are considered.

Particle Mass from Planck-Scale Fluctuations

In this article we present a theory of particle mass formation. The theory is conceptually based on the ideas that space time fluctuations of very high Planck-scale energy form mass if they exceed a certain threshold value that is a characteristic of the universe. The fluctuations at the length scales that are orders of magnitude smaller than what is currently accessible by direct or indirect experimental methods and of a quantum phenomenonological nature, much inference has to be made of the Planck length scale dynamics that form the observed created particles and their mechanics. Therefore a minimalistic theory should be the starting point, and it is what is proposed here in this rapid communication. Fluctuations of coupled space and time occur, are described statistically and in phase space and therefore are as conjugate variables related by an uncertainty principle the relativistic analogue of the Heisenberg uncertainty principle familiar in low energy quantum mechanics. An information-entropy argument is made for the derivation of the statistical distributions of the fluctuations, that are parametrized by the inverse temperature in order to conveniently connect to thermodynamics. In analogy with 3D 1p time or thermodynamical parameterized condensed matter Schroedinger - like quantum mechanical systems where fluctuations of the system obtain self-energy additional terms to the dispersion relation that describe stable and metastable excitations with mass - like or effective mass, the resulting minimally coupled 4D 1p or 4D-1p equations describing the observed worm-hole mouths obtain self-energy terms to the dispersion relation that derive massive Klein-Gordon - like equations.

SPIN-SURFING THE SPACE–TIME FOAM

We present the quantum spin as a novel test tool for probing directly the Planck scale space–time foam of quantum gravity. Quantum fluctuations of spatial support for the electric vector associated with the spin-one photon affect its polarization sufficiently to allow us to gain deep insights and unprecedented constraints on the most important and fundamental aspect of quantum gravity — the fluctuating structure of space–time with a Planck scale three-dimensional web. We show that the survival of strong polarization of X-rays and gamma rays from the Crab Nebula rejects the conventional space–time foam at Planck length scale and constrains the microscopic scale of quantum gravitational fluctuations to below 2 × 10-8l P .

Determining the minimal length scale of the generalized uncertainty principle from the entropy-area relationship

We derive the formula of the black hole entropy with a minimal length of the Planck size by counting quantum modes of scalar fields in the vicinity of the black hole horizon, taking into account the generalized uncertainty principle (GUP). This formula is applied to some intriguing examples of black holes - the Schwarzschild black hole, the Reissner-Nordstrom black hole, and the magnetically charged dilatonic black hole. As a result, it is shown that the GUP parameter can be determined by imposing the black hole entropy-area relationship, which has a Planck length scale and a universal form within the near-horizon expansion.