scholarly journals Modified Newton's Law of Gravitation due to Minimal Length in Quantum Gravity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmed Farag Ali ◽  
A. Tawfik
Keyword(s):  
Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Recent Theory ◽  
Entropic Force ◽  
Doubly Special Relativity ◽  
Newton's Law ◽  
Newton’S Law ◽  
Area Law

A recent theory about the origin of the gravity suggests that the gravity is originally an entropic force. In this work, we discuss the effects of generalized uncertainty principle (GUP) which is proposed by some approaches to quantum gravity such as string theory, black hole physics, and doubly special relativity theories (DSR), on the area law of the entropy. This leads to aarea-type correction to the area law of entropy which implies that the number of bitsNis modified. Therefore, we obtain a modified Newton’s law of gravitation. Surprisingly, this modification agrees with different sign with the prediction of Randall-Sundrum II model which contains one uncompactified extra dimension. Furthermore, such modification may have observable consequences at length scales much larger than the Planck scale.

scholarly journals Planck-scale corrections to Friedmann equation

Open Physics ◽  
2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Adel Awad ◽  
Ahmed Ali
Keyword(s):  
Black Hole Physics ◽  
Planck Scale ◽  
Friedmann Equation ◽  
Uncertainty Principles ◽  
Entropic Force ◽  
Raychaudhuri Equation ◽  
Emergent Phenomenon ◽  
Doubly Special Relativity ◽  
Equation Solving ◽  
Friedmann Robertson Walker

AbstractRecently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde’s proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde’s proposal and two known models of GUPs, we obtain modifications to Newton’s law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the p = ωp equation of state.

scholarly journals BUILDING A CASE FOR A PLANCK-SCALE-DEFORMED BOOST ACTION: THE PLANCK-SCALE PARTICLE-LOCALIZATION LIMIT

2005 ◽  
Vol 14 (12) ◽  
pp. 2167-2180 ◽  
Author(s):  
GIOVANNI AMELINO-CAMELIA
Keyword(s):  
Quantum Gravity ◽  
Semiclassical Approximation ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Doubly Special Relativity ◽  
Logarithmic Corrections ◽  
Additional Challenge ◽  
Scale Particle ◽  
Particle Localization

"Doubly-special relativity" (DSR), the idea of a Planck-scale Minkowski limit that is still a relativistic theory, but with both the Planck scale and the speed-of-light scale as nontrivial relativistic invariants, was proposed as a physics intuition for several scenarios which may arise in the study of the quantum-gravity problem, but most DSR studies focused exclusively on the search of formalisms for the description of a specific example of such a Minkowski limit. A novel contribution to the DSR physics intuition came from a recent paper by Smolin suggesting that the emergence of the Planck scale as a second nontrivial relativistic invariant might be inevitable in quantum gravity, relying only on some rather robust expectations concerning the semiclassical approximation of quantum gravity. Here, we attempt to strengthen Smolin's argument by observing that an analysis of some independently-proposed Planck-scale particle-localization limits, such as the "Generalized Uncertainty Principle" often attributed to string theory in the literature, also suggests that the emergence of a DSR Minkowski limit might be inevitable. We discuss a possible link between this observation and recent results on logarithmic corrections to the entropy-area black-hole formula, and observe that both the analysis reported here and Smolin's analysis appear to suggest that the examples of DSR Minkowski limits for which a formalism has been sought in the literature might not be sufficiently general. We also stress that, as we now contemplate the hypothesis of a DSR Minkowski limit, there is an additional challenge for those in the quantum-gravity community attributing to the Planck length the role of "fundamental length scale."

scholarly journals EFFECT OF THE GENERALIZED UNCERTAINTY PRINCIPLE ON COMPACT STARS

2013 ◽  
Vol 22 (05) ◽  
pp. 1350020 ◽  
Author(s):  
AHMED FARAG ALI ◽  
ABDEL NASSER TAWFIK
Keyword(s):  
String Theory ◽  
Thermodynamic Properties ◽  
Quantum Gravity ◽  
Special Relativity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Compact Stars ◽  
Doubly Special Relativity ◽  
Heisenberg Principle

Based on the generalized uncertainty principle (GUP), proposed by some approaches to quantum gravity such as string theory and doubly special relativity theories, we investigate the effect of GUP on the thermodynamic properties of compact stars with two different components. We note that the existence of quantum gravity correction tends to resist the collapse of stars if the GUP parameter α is taking values between Planck scale and electroweak scale. Comparing with approaches, it is found that the radii of compact stars become smaller relative to the cases utilizing standard Heisenberg principle. Increasing energy almost exponentially decreases the radii of compact stars.

scholarly journals COHERENT STATES IN GRAVITATIONAL QUANTUM MECHANICS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350004 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Quantum Gravity ◽  
Coherent States ◽  
Scale Effects ◽  
Black Hole Physics ◽  
Probability Distributions ◽  
Planck Scale ◽  
Experimental Tests ◽  
Heisenberg Algebra ◽  
Adjoint Representation ◽  
Weight Functions

We present the coherent states of the harmonic oscillator in the framework of the generalized (gravitational) uncertainty principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity and black-hole physics and implies a minimal measurable length. Using a recently proposed formally self-adjoint representation, we find the GUP-corrected Hamiltonian as a generator of the generalized Heisenberg algebra. Then following Klauder's approach, we construct exact coherent states and obtain the corresponding normalization coefficients, weight functions and probability distributions. We find the entropy of the system and show that it decreases in the presence of the minimal length. These results could shed light on possible detectable Planck-scale effects within recent experimental tests.

scholarly journals A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS

2010 ◽  
Vol 19 (12) ◽  
pp. 2003-2009 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Uncertainty Principle ◽  
Deformed Algebra ◽  
Heisenberg Uncertainty

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

scholarly journals QUANTUM CORRECTIONS TO NEWTON'S LAW

2002 ◽  
Vol 17 (36) ◽  
pp. 2371-2381 ◽  
Author(s):  
B. F. L. WARD
Keyword(s):  
Scalar Field ◽  
Quantum Gravity ◽  
Quantum Corrections ◽  
New Approach ◽  
Newton's Law ◽  
Newton’S Law

We present a new approach to quantum gravity starting from Feynman's formulation for the simplest example, that of a scalar field as the representative matter. We show that we extend his treatment to a calculable framework using resummation techniques already well-tested in other problems. Phenomenological consequences for Newton's law are described.

GUP-corrected thermodynamics of accelerating and rotating black holes

2017 ◽  
Vol 26 (05) ◽  
pp. 1741018 ◽  
Author(s):  
Muhammad Rizwan ◽  
K. Saifullah
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Hawking Temperature ◽  
Rotating Black Holes ◽  
Gravity Effects ◽  
Klein Gordon ◽  
Black Hole Remnant

When quantum gravity effects, that are based on generalized uncertainty principle with a minimal measurable length, are incorporated into black hole physics the Klein–Gordon and Dirac equations get modified. Using these modified equations we investigate tunneling of scalar particles and fermions from event and acceleration horizons of accelerating and rotating black holes and obtain the modified Hawking temperature with quantum gravity effects. We see that Hawking temperature depends on black hole parameters as well as the quantum numbers of emitted fermions. The quantum corrections slow down black hole evaporation and leave a black hole remnant. This contradicts complete evaporation of a black hole which is presaged by the standard temperature formula for black holes. The modified Hawking temperatures presented here, in appropriate limits, are consistent with the previous results in the literature.

The holographic principle, the equipartition of energy and Newton’s gravity

2017 ◽  
Vol 32 (39) ◽  
pp. 1771003
Author(s):  
M. Sadiq
Keyword(s):  
Quantum Gravity ◽  
Free Parameter ◽  
Loop Quantum Gravity ◽  
Planck Scale ◽  
Scale Factor ◽  
Holographic Principle ◽  
Entropic Force ◽  
Classical Gravity ◽  
Equipartition Of Energy

Assuming the equipartition of energy to hold on a holographic sphere, Erik Verlinde demonstrated that Newton’s gravity follows as an entropic force. Some comments are in place about Verlinde’s assumptions in his derivation. It is pointed out that the holographic principle allows for freedom up to a free scale factor in the choice of Planck scale area while leading to classical gravity. Similarity of this free parameter with the Immirzi parameter of loop quantum gravity is discussed. We point out that the equipartition of energy is inbuilt into the holographic principle and, therefore, need not be assumed from the outset.

scholarly journals QUANTUM CORRECTIONS TO NEWTON'S LAW IN RESUMMED QUANTUM GRAVITY

2005 ◽  
Vol 20 (15) ◽  
pp. 3502-3505 ◽  
Author(s):  
B. F. L. WARD
Keyword(s):  
Scalar Field ◽  
Quantum Gravity ◽  
Quantum Correction ◽  
Quantum Corrections ◽  
New Approach ◽  
Newton's Law ◽  
Newton’S Law

We present the elements of resummed quantum gravity, a new approach to QG based on the work of Feynman using the simplest example of a scalar field as the representative matter. We show that we get a UV finite quantum correction to Newton's law.

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