Quantum Gravity in a Nutshell1 E-Book

Balungi Francis

• Herausgeber: Balungi Francis
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2020

Beschreibung

This math-free book is a good introduction to quantum gravity and has a lot of interesting history about the development of the theory since 1899. It's an informal introduction to a very difficult and doubtfully intelligible theory doubted even by its most ingenious contributors. The reader should expect that he/she will have to concentrate hard on what Balungi says but the rewards are significant. He is a talented physicist and a good writer. If you read it carefully and stop to think about the message as it unfolds then you will get a worthwhile if imperfect picture of what the theory is saying and how it was invented... It's buried treasure and you will have to do some digging. It is a really serious attempt to do all that can be done in an informal style. Balungi explains and re-defines Einstein's theory of general relativity, quantum mechanics, black holes, the complex architecture of the universe, elementary particles, gravity, and the nature of the mind. This wonderful and exciting book is optimal for physics graduate students and researchers. Not since Stephen W Hawking's celebrated best-seller Brief History of Time has physics been so vividly, intelligently and entertainingly revealed.

Leseprobe

QUANTUM GRAVITY IN A NUTSHELL1 

BALUNGI FRANCIS

PRAISE FOR QUANTUM GRAVITY IN A NUTSHELL1

––––––––

“Some physicists, mind you, not many of them, are physicist-poets. They see the world or, more adequately, physical reality, as a lyrical narrative written in some hidden code that the human mind can decipher. Balungi Francis, is one of them...Balungi's book is a gem. It's a pleasure to read, full of wonderful analogies and imagery and, last but not least, a celebration of the human spirit.”—GPS Astrophysics & Adventure

“If your desire to be awestruck by the universe we inhabit needs refreshing, theoretical physicist Balungi Francis...is up to the task.”—Jess

“[Quantum Gravity in a Nutshell1] is simultaneously aimed at the curious layperson while also useful to the modern scientist... Balungi lets us nibble or gorge ourselves, depending on our appetites, on several scrumptious equations. He doesn’t expect everyone to be a master of the equations or even possess much mathematical acumen, but the equations serve as appetizers for those inclined to get their fill, so to speak.”—Monitor News & The Observer

This book is a book of two halves. The first is a history of physics and in particular the twin pillars of modern physics: The General Theory of Relativity and Quantum Theory. The second is a journey through Quantum Gravity.Making sense of modern physics can be hard, very hard, for the non scientist. For many years I have read many books grappling with the subject, some good and some not so good.Balungi's book is a game changer.

The descriptions of Quantum theory and Quantum mechanics were wonderful. I experienced at least three genuine aha moments, moments when you close your eye, lay the book on your lap and breathe slowly with the shear joy of understanding.As well as the explanations there is also the joy of the writing. This book is a marvel. It is highly recommended. Proffessor  Basel

“With its warm, enthusiastic language and tone, [What is Real?] is also deeply humanistic in approach, using words like elegant and beauty about a subject...that can seem impenetrably dense and abstract...Quantum Gravity in a Nutshell1 takes much the same approach.”—Cosmos Magazine

“Balungi writes beautiful prose while walking the reader through the history and concept of 'reality' and what it all means for the yet to be discovered universe and thus our own lives.”—Casto Universe-News

“Balungi writes with elegance, clarity and charm. . . . A joy to read, as well as being an intellectual feast.”—East Africa News

“Balungi offers vast, complex ideas beyond most of our imagining—‘quanta,’ ‘grains of space,’ ‘time and the heat of black holes’—and condenses them into spare, beautiful words that render them newly explicable and moving.”—NACA Community

“Balungi’s lyrical language, clarity of thought, and passion for science and its history make the title a pleasure to read (albeit slowly), and his diagrams and footnotes will allow readers to understand the material better and tackle a more expert level of insight.”—Goodreads

“Balungi smoothly conveys the differences between belief and proof. . . his excitement is contagious and he delights in the possibilities of human understanding.”—Science Monthly

“Science buffs will admire Balungi's lucid writing...Cutting-edge theoretical physics for a popular audience that obeys the rules (little math, plenty of drawings), but it's not for the faint of heart.”—Physics Reviews

“A fascinating adventure into the outer limits of space and into the smallest atom...Balungi manages to break down complex, proven ideas into smaller, easily assimilated concepts so those with little to no scientific background can understand the fundamental ideas...Balungi's infectious enthusiasm and excitement for his subject help carry readers over the more difficult aspects, allowing one to let the imagination soar...An exciting description of the evolution of physics takes readers to the edge of human knowledge of the universe.”—Universal Awareness

“Balungi draws deep physics into the light with rather greater success... He wears a broad erudition lightly, casually and clearly explaining.”—Break through Nominations

Quantum Gravity in a Nutshell1

Copyright © Balungi Francis 2018

Copyright ©Visionary School of Quantum Gravity 2018

Copyright ©SUSP Science Foundation 2019

Copyright © Barungi Francis 2019

Copyright © Bill Stone Services 2020

First published 2018

Balungi Francis asserts the moral right to be identified as the author of this work.

All rights reserved. Apart from any fair dealing for the purposes of research or private study or critism or review, no part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, or by any information storage and retrieval system without the prior written permission of the publisher.

Revised Edition: 2020

Cover by: znamide.

TABLE OF CONTENTS

DEDICATION

PREFACE

1. Solving Quantum Gravity

2. Mass Ain’t What It Used To Be

3. A Brief Account on the Implications of Quantum Gravity

4. Hidden in plain sight1: A simple link between Quantum mechanics and General relativity

5. Quantum Gravity in a Nutshell

6. Hidden in plain sight2: From white dwarfs to Black Holes

7. Murder of Germans Sacred Cow: Experimental Test of General Relativity

8. What is Special about the Energy Density?

9. How to Calculate a Mysterious Repulsive Force Pulling Galaxies Apart

10. A Simple Link between MONDian Dynamics and the Dark Universe

11.  Derivation of the Temperature and Entropy of Black Holes

12. Particle Creation by Black Holes: Is it Hawking’s Approach or My Approach?

13. Is There A Limit To How Small Black Holes Can Become?

14. On the Quantum Electrodynamics and Quantum Gravity Magnetic Field Limits.

15. Emergent Gravity

16. A New Alternative to Entropic Gravity

17. A new Approach to the Modification of Newtonian Dynamics (MOND)

18. Reinventing Gravity “The Fifth Force”

19. Resolving the Proton Radius Puzzle

20. The Bekenstein Hawking Area-Entropy Law

21. New Physics: Regularization and Physics beyond the Standard Model

22. A Grand Unification

23. A Unified Bohr and Quantum Gravity Theory

24. Everything

25. The Theory of Light

26. Making Sense with Semi-Classical Gravity

27. The Art of Reductionism

28. Construction of a Consistent Physical Theory of Nature

29. Is It Possible That There Is A Universe In Every Particle?

30. Newton’s Biggest Blunder: Re-defining Gravity

Additional Readings

Space-time Singularity or Quantum Black Holes?

What is real? Is it Volume or Area Entropy Law of Black Holes?

Is it Dark Matter, MOND or Quantum Black Holes?

What is real? General Relativity or Quantum Gravity

Appendix 1

Derivation of the Energy density stored in the Electric field and Gravitational Field

Appendix 2

Emergence of Gravity

Appendix 3

Determining the length scale at which the force of Gravity is strong between any two electrons

Appendix 4

Revised Gravitation Theory for the Modified Newtonian Dynamics (MOND) Paradigm and Beyond

Epilogue

Glossary

Bibliography

Acknowledgments

About the Author

DEDICATION

To my wife Wanyana Ritah,

My sons Odhran & Leander ,

and lastly to Carlo Rovelli

PREFACE

There is a need for a book on a Quantum Theory of Gravity that is not directed at specialists but, rather, sets out the concepts underlying this subject for a broader scientific audience and conveys joy in their beauty. The author has written with this goal in mind, and has succeeded admirably. This wonderful and exciting book is optimal for physics graduate students and researchers. The physical explanations are exceedingly well written and integrated with formulas. Quantum Gravity is the next big thing and this book will help the reader understand and use the theory.

Author’s Note

Our search for ultimate understanding—the Quantum Theory of Gravity—has long been the quest of such great scientists as Aristotle, Newton, Einstein, Hawking and many others, and is expected to transform science, providing clarity and understanding that is unknown today, ideally via one single overlooked principle in nature. So far, this quest has produced theories such as Special Relativity, General Relativity and Quantum Mechanics, and such recent proposals as "Dark Matter" and "Dark Energy" in cosmology. Yet these all suffer serious internal problems and compatibility issues with each other, introducing even more questions, mysteries and paradoxes—and often even violations of our laws of physics upon closer examination. As a result, the Quantum Theory of Gravity continues to elude us, leaving a fractured and divided scientific community with no clear direction forward. This has also resulted in the mathematisation of physics which has resulted in the reduction of the cosmos to a mathematical entity, which has not only confused physicists but accounts for their worst and most distracting assertions. This book makes a first case for the latter, with clear discussions exposing the flaws in the above concepts and more, while stepping back to take a good look at the scientific legacy we have inherited.

We are probably asking the wrong questions at the moment, nevertheless it is impossible to resist the temptation to try. After all, the other fundamental forces – except gravity – fit very neatly with quantum mechanics.

Balungi Francis 2018

1. Solving Quantum Gravity

To the intra-atomic movement of electrons, atoms would have to radiate not only electromagnetic but also gravitational energy if only in tiny amounts. As this is hardly true in nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics, but also the new theory of gravitation.

Albert Einstein

The development of a quantum theory of gravity began in 1899 with Max Planck’s formulation of “Planck scales” of mass, time, and length. During this period, the theories of quantum mechanics, quantum field theory and general relativity had not yet been developed. This means that Planck himself had no idea about what he had just developed-behind the Black board. Planck was not aware of quantum gravity and what it would mean for physicists. But he had just coined in formula one of the starting point for the holy grail of physics.

After P.Bridgman’s disapproval of Planck’s units in 1922, Albert Einstein having published the General Relativity theory, a few months after its publication he noted that “to the intra-atomic movement of electrons, atoms would have to radiate not only electromagnetic but also gravitational energy if only in tiny amounts, as this is hardly true in nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics, but also the new theory of gravitation”. This showed Einstein’s interest in the unification of Planck’s quantum theory with his newly developed theory of Gravitation.

Then in 1933 came Bronstein’s cGh-plan as we know it today. In his plan he argued a need for Quantum Gravity. In his own words he stated: “After the relativistic quantum theory is created, the task will be to develop the next part of our scheme that is, to unify quantum theory (h), special relativity (c) and the theory of gravitation (G) into a single theory”. Thus the theory of quantum gravity is expected to be able to provide a satisfactory description of the microstructure of space time at the so called Planck scales, at which all fundamental constants of the ingredient theories, c (speed of light), h ( Planck constant) and G ( Newton’s constant), come together to form units of mass, length and time.

Therefore the need for the theory of quantum gravity is crucial in understanding nature, from the smallest to the biggest particle ever known in the universe. For example, “we can describe the behavior of flowing water with the long- known classical theory of hydrodynamics, but if we advance to smaller and smaller scales and eventually come across individual atoms, it no longer applies. Then we need quantum physics just as a liquid consists of atoms” Daniel Oriti in this case imagines space to be made up of tiny cells or atoms of space and a new theory of quantum gravity is required to describe them fully.

The aim of this book is to develop a theory capable of explaining the quantum behavior of the gravitational fields and thereafter explain the problems involving a combination of very high energy and very small dimensions of space such as, the behavior of Black holes and the study of the properties of the early universe.

For us to solve quantum gravity (QG), we need to address, understand and resolve in detail the problems brought about by the failure of the general theory of relativity (GR). Below I outline briefly where GR breaks down and later I resolve each of these problems with applications.

(1) General relativity fails to explain details near or beyond space-time singularities. That is, for high or infinite densities where matter is enclosed in a very small volume of space.  Abhay Ashtekar says that; when you reach the singularity in general relativity, physics just stops, the equations break down

(2)General relativity fails to account for dark matter.

(3) General relativity also fails to be quantized.

Singularity Resolution in Quantum Gravity

The demand for consistency between a quantum description of matter and a geometric description of spacetime, as well as the appearance of singularities (where curvature length scales become microscopic), indicate the need for a full theory of quantum gravity. For example; for a full description of the interior of black holes, and of the very early universe, a theory is required in which gravity and the associated geometry of space-time are described in the language of quantum physics. Despite major efforts, no complete and consistent theory of quantum gravity is currently known, even though a number of promising candidates exist.

The first step towards the development of a quantum theory of gravity lies in studying the kind of physics behind black holes which are born when normal stars die or which were formed in regions of high energy density in the early universe. Black holes on the other hand, are completely collapsed stars that is, stars that could not find any means to hold back the inward pull of gravity and therefore collapse to a singularity.

This section is aimed at answering questions like; i) Do objects continually collapse to a singularity or there is a limiting distance below which the very notions of space and length cease to exist?

Theorem:- A star more than three times the size of our Sun collapses in this way; the gravitational forces of the entire mass of a star overcomes the electromagnetic forces of individual atoms and so collapse inwards. If a star is massive enough it will continue to collapse creating a Black hole, where the whopping of space time is so great that nothing can escape not even light, it gets smaller and smaller. The star in fact gets denser as atoms even subatomic particles literally get crashed into smaller and smaller space, and its ending point is of course a space time singularity.

––––––––

The appearance of singularities in any physical theory is an indication that either something is wrong or we need to reformulate the theory itself. Singularities are like dividing something by zero. One such theory plagued by singularities is the General theory of relativity (GR) and the problems in GR arise from trying to deal with a universe that is zero in size (infinite densities). However, quantum mechanics suggests that there may be no such thing in nature as a point in space-time, implying that space-time is always smeared out, occupying some minimum region. The minimum smeared-out volume of space-time is a profound property in any quantized theory of gravity and such an outcome lies in a widespread expectation that singularities will be resolved in a quantum theory of gravity. This implies that the study of singularities acts as a testing ground for quantum gravity.

Loop quantum gravity (LQG) suggests that singularities may not exist. LQG states that due to quantum gravity effects, there must be a minimum distance beyond which the force of gravity no longer continues to increase as the distance between the masses become shorter or alternatively that interpenetrating particle waves mask gravitational effects that would be felt at a distance. It must also be true that under the assumption of a corrected dynamical equation of LQ cosmology and brane world model, for the gravitational collapse of a perfect fluid sphere in the commoving frame, the sphere does not collapse to a singularity but instead pulsates between a maximum and minimum size, avoiding the singularity.

Additionally, the information loss paradox is also a hot topic of theoretical modeling right now because it suggests that either our theory of quantum physics or our model of black holes is flawed or at least incomplete. and perhaps most importantly, it is also recognized with some prescience that resolving the information paradox will hold the key to a holistic description of quantum gravity, and therefore be a major advance towards a unified field theory of physics.

The paradox, as formulated, arises from considerations of the ultimate fate of the information that falls into a black hole: does it disappear as it falls into the black hole singularity? As well, what happens to the information of a black hole when it evaporates to nothing due to Hawking radiation? If a black hole loses all of its energy, then all of the information about all of the particles that fell in it would be lost as well. Of course the disappearance of information would be a violation of conservation laws of energy, which states that no energy or information can be destroyed.

Planck stars

To resolve the black hole singularities and the information paradox. We consider the possibility that the energy of a collapsing star and any additional energy falling into the hole could condense into a highly compressed core with density of the order of the Planck density. If this is the case, the gravitational collapse of a star does not lead to a singularity but to one additional phase in the life of a star: a quantum gravitational phase where the  gravitational attraction is balanced by a quantum pressure.

Since the energy density or pressure is expressed as force per unit surface area of a star we have,

Therefore nature appears to enter the quantum gravity regime when the energy density of matter reaches the Planck scale. The point is that this may happen well before relevant lengths become planckian. For instance, a collapsing spatially compact universe bounces back into an expanding one. The bounce is due to a quantum-gravitational repulsion which originates from the modified Heisenberg uncertainty, and is akin to the force that keeps an electron from falling into the nucleus. The above given statement is based on the following facts:

The resolution of classical singularities under the assumption of a maximal acceleration has been studied using canonical methods for Rindler, Schwarzschild, Reissner-Nordstrom, Kerr-Newman and Friedman-Lemaitre metrics.

To reconcile quanum mechanics with general relativity, we develop a quantum geometry in relativistic phase space (Rindler space) in which the maximal (proper) acceleration of a particle is modified to read,

Where, c is the constant speed of light, r is the linear dimension of a particle , α is the coupling constant (or size of the extra dimensions), n is a positive number (or the extra dimension number and is the flux in the extra dimension

This acceleration is based on an assumption, that particles are extended objects, never to be identified with mathematical points in ordinary space. This acceleration is important because it cures strong singularities that plague general relativity. This acceleration is also a straight forward consequence of our modified uncertainty relation given as,

,

Where r represents the size of a star, in this case-horizon radius, p is the momentum of a particle approaching or falling into the hole of a star, α is the coupling constant and n is positive. From the above given uncertainty principle, we derive the planck length. such that when the momentum , the gravitational coupling constant for gravitational interactions is and finally n=1/2. We get the planck length as the minimum length of space-time as

––––––––

Therefore from the uncertainity principle, the repulsion force is given by,

Therefore bounce does not happen when the universe is of planckian size, as was previously expected; it happens when the matter energy density reaches the Planck density in this way,

Let the surface area of a star be,  then the matter energy density will be given as,

For a Schwarzschild black hole with radius  and . We have a maximum energy density value wnen n=1 given as,

At this energy density, a Planck star is formed. The key feature of this theoretical object is that this repulsion arises from the energy density, not the Planck length, and starts taking effect far earlier than might be expected. This repulsive 'force' is strong enough to stop the collapse of the star well before a singularity is formed, and indeed, well before the Planck scale for distance. Since a Planck star is calculated to be considerably larger than the Planck scale for distance, this means there is adequate room for all the information captured inside of a black hole to be encoded in the star, thus avoiding information loss.

The analogy between quantum gravitational effects on

Where is the Planck length. Taking  we have the size of a star as,

Singularity Resolution under the Assumption of Maximal Acceleration and Minimal length for both the Schwarzschild and Reissner- Nordstrom Black Hole

Under the assumption of  ( where is the coupling constant), in the Caianeillo maximum acceleration model ( ) , we derive the minimum radius to which a gravitating body can collapse in the commoving frame for both the Schwarzschild and Reissner-Nordstrom Black hole.

In the context of a geometrical unification of quantum mechanics and general relativity in phase space, Caianiello was the first person to propose the existence of a maximal proper acceleration for massive particles. Caianiello was able to derive the value for the maximum acceleration of a particle of rest mass m from the time-energy uncertainty relation. Caianiello model was based on two assumptions; and  for (3).

Applications of Caianiello’s model include cosmology, the dynamics of accelerated strings, neutrino oscillations and the determination of a lower neutrino mass bound. There is also evidence for maximal acceleration and singularity resolution in covariant loop quantum gravity found by Rovelli and Vidotto.

In this book we propose an adhoc assumption of  where is the coupling constant. This differs from Caianiello's model assumption of . Therefore the maximum acceleration(3) will be given by,

(4)

Where, r is the smallest possible distance between any two masses. In this book r takes values for the Schwarzschild and Reissner-Nordstrom radius.

Equation (4) given above reduces to the value that was earlier derived by Caianiello under two conditions;

(i) When   and for a Schwarzschild Black hole of mass M. Where is the gravitational coupling constant .

(ii) When and for a Reissner-Nordstrom Black hole. Where   is the electromagnetic coupling constant .

Maximal Acceleration in Quantum Gravity

Considering the event horizon of a Reissner-Nordstrom black hole of radius and gravitational coupling . Then substituting in (4), the growing acceleration approaching a classical singularity in the Reissner-Nordstrom metric is bounded by the existence of a maximal acceleration of;

(5)

Where e is charge on an electron, is the permittivity of free space and ћ is the reduced Planck constant.

Considering the event horizon of a Schwarzschild black hole of radius and gravitational coupling . Then substituting in (4), the growing acceleration approaching a classical singularity in the Schwarzschild metric is bounded by the existence of a maximal acceleration of;

(6)

Minimal Radius in Quantum Gravity

Because of the equivalence principle in the case of gravitational interaction, we propose to show here that the existence of a minimal length for both a Reissner and Schwarzschild Black hole is a straight forward consequence of our maximal acceleration value (4). In Newtonian law (center of mass system)

Where, R is the radius of a Black hole ( In this case the minimum radius to which a central mass will collapse), On arranging we have,

(7)

Where is the Schwarzschild radius .

Two results are thus deduced;

1) For the radius of the event horizon of a Reissner Black hole and , the minimum radius to which a gravitating body will collapse in a commoving frame of the Reissner-Nordstrom metric will have a value;

.  (8)

Where is the Planck length and  is the fine structure constant 1/137.

2) Similarly, for the radius of the event horizon of a Schwarzschild Black hole and , the minimum radius to which a gravitating body will collapse in a commoving frame of the Schwarzschild metric will have a value;

.  (9)

The above derivation clearly provides evidence for the existence of a maximal acceleration and minimal length which are both expected in the theory of quantum gravity to cure strong singularities such as, big bang, big crunch, black holes etc.

A Simple Derivation of the Minimum Radius of a Reissner -Nordstrom Black Hole: The Case of Accretion

Matter falling onto somebody is termed accretion. Suppose the matter is falling onto a star of mass M and radius R. Falling freely, it gains kinetic energy in exchange for gravitational potential energy . For a mass m falling from infinity to a distance r from the central mass M where relativistic quantum effects are taken into account, the matches the as

As the particle orbits closer and closer into a huge gravitational field its velocity increases up to a speed of light c, where the usual known kinetic energy formula does not apply. Instead we are forced to introduce a new formula that takes into account the gravitational coupling constant as

(10)

The self gravitation force of a star of radius R and mass M is known from Newton's gravitational force formula however the potential gravitational energy of a particle m falling from infinity to a distance r from a star will differ from the usual known potential formula as

(11)

Then surely,

On cancelling like terms we have,

(12)

Where,   is the Schwarzschild radius of a gravitating body and   is the gravitational coupling constant that determines the strength of the gravitational force and G is the gravitational constant.

The mass eventually hits the surface of the star and its Kinetic energy is released as heat, and appears in some form of radiation. The radius of a star can then be determined using the above formula as: For a particle at the event horizon of a Reissner-Nordstrom Black hole, . Where e is charge on an electron, is the permittivity of free space and is the reduced Planck constant. The radius of this star is;

=.

Then in terms of the Planck length we have,

Where is the Planck length .

Taking fourth powers on both sides of the equation we have,

.

Where   is the fine structure constant.

Therefore the above derivation implies that the radius of a Reissner-Nordstrom Black Hole is quantized in units of the Planck length and takes on only discrete units implying the quantized nature of space. In conclusion nature permits the existence of a minimum length beyond which the very notions of space and time cease to exist. I hope in my own view that this analysis will be useful for researchers involved in the field of quantum gravity and loop quantum cosmology.

Evidence for Minimal Length

General relativity predicts two kinds of singularities; the cosmological singularity at the beginning of our universe and the singularities at the centre of black holes. However, singularities signal the breakdown of general relativity and it is generally believed that they will be removed in a more fundamental theory of quantum gravity. The resolutions of singularities have been carried out directly in the frame work of Loop quantum gravity under the assumption of a maximal acceleration using canonical methods. However, in this example, singularities are resolved under the assumption of minimal length by creating a new cosmological model for the study of the gravitational collapse of a perfect fluid sphere. Two results are deduced;(i) a commoving observer accelerating with respect to his neighbors in a Reissner-Nordstrom space-time geometry will have a horizon at a distance bounded by a minimal value limit (Where is the Planck length and  is the fine structure constant 1/137)  and  (ii), a commoving observer accelerating with respect to his neighbors in a Schwarzschild  space-time geometry  will have a horizon at a distance bounded by a minimal value limit . Therefore the generic bound on length and acceleration implies that the resolution of singularities is general and must be taken seriously.

Here we consider the gravitational collapse of a perfect fluid sphere- a gravitating body of mass M and radius R. Then for a test particle or an observer falling freely from infinity to a distance from the gravitating body, the spherically symmetric solution to the Einstein field equation will be given by;(13)

Where,   is the Schwarzschild radius of a gravitating body and   is the gravitational coupling constant that determines the strength of the gravitational force, G is the gravitational constant and c is the constant speed of light.

Therefore a commoving observer accelerating with respect to his neighbors in a given space- time geometry will have a horizon at a distance bounded by a minimal value limit . Correspondingly, the growing acceleration approaching a classical singularity is bounded by the existence of a maximal acceleration

.

The existence of minimal length and maximum acceleration is of course something long expected in the quantum theory of gravity. Below we derive two important results for minimum radius and maximum acceleration supporting the results in loop quantum cosmology and black holes.

(i) Considering a test particle at the event horizon in the Reissner-Nordstrom metric (RN), . Where e is charge on an electron, is the permittivity of free space and is the reduced Planck constant. The minimum radius (size) to which a gravitating body can collapse in a commoving frame is;

=.

This also implies a maximum acceleration of . Then in terms of the Planck length we have, (14) Where is the Planck length . Taking fourth powers on both sides of the equation we have, (15). Where - the fine structure constant.

(ii) Considering a test particle at the event horizon in the Schwarzschild metric, .The minimum radius to which a gravitating body can collapse in a commoving frame is; . This also implies a maximal acceleration of,

.

Therefore a commoving observer accelerating with respect to his neighbors in a Reissner-Nordstrom space-time geometry will have a horizon at a distance bounded by a minimal value limit . Where is the Planck length and  is the fine structure constant 1/137. Correspondingly, the growing acceleration approaching a classical singularity in this metric is bounded by the existence of a maximal acceleration where M is mass.

Also, a commoving observer accelerating with respect to his neighbors in a Schwarzschild space-time geometry  will have a horizon at a distance bounded by a minimal value limit . Correspondingly, the growing acceleration approaching a classical singularity in this metric is bounded by the existence of a maximal acceleration .

It has been deduced in (i) above that, the resolution of singularities occurs as a result of a fundamental discreteness of space. This is based on the fact that the minimum radius or size is proportional to the Planck length (14). This is one of the promising results of this essay. The presence of implies a discreteness of space or length spectra which is manifested by the presence of the fine structure constant (15).However, in (ii) singularities are avoided in a limit (Planck mass), by imposing a minimum length. Therefore the generic bound on length and acceleration implies that the resolution of singularities is general and must be taken seriously.

Unlike other models, the cosmological model (13) created in this example directly predicts a limit on the length and acceleration, thus providing evidence for the resolution of the classical singularity. The derivation in (i) is unique in that the value of the fine structure constant comes out as a direct result of the theory, which has never been witnessed in any promising theory of quantum gravity, not even in LQG or string theory.

Remark: In a more general form we can express (13) as,, where s= 0,1,2,3,......,1/2, Such that when s=0, . What name should be given to s is left for the reader to decide. However we can denote s as an extra dimension number.

We have clearly modified the geometry of Rindler space by the introduction of the coupling into the formula for acceleration. We have witnessed that the presence of into the formula for acceleration leads to an exact evidence for the existence of the maximal acceleration and minimal length for both the Reissner-Nordstrom and Schwarzschild black holes in quantum gravity. The split horizon in a Rindler wedge at a distance R= /a for the acceleration a has been modified here, hope you have witnessed how changes all of this. This implies that there is some fundamental limitation on how much acceleration a particle could experience based on the strong-field behavior of the fundamental force causing it.

Results of the maximal acceleration and minimal length for the Reissner Black hole have not been derived anywhere in literature. These clearly impose a general bound on acceleration and length (in Reissner space time geometry) with implications. For example, a black hole the size of an electron (), imposes an acceleration of  . So this accelerated frame would detect a Unruh radiation at K. Also the minimal length result implies the existence of the discreteness (granular nature) of space and cures the singularities that plague General relativity by imposing a general bound on length of .

In conclusion, a corrected Rindler space geometry directly proves an existence for the maximal acceleration and minimal length in quantum gravity, not only for the Schwarzschild metric with a horizon distance half of the Schwarzschild radius but also for the Reissner metric. Therefore the introduction of in the formula for acceleration must be thoughtfully investigated as this solves all the problems brought about by the General relativity theory.

2. Mass Ain’t What It Used To Be

The origin of mass problem is at the forefront of those big unsolved problems in the standard model of physics. My first insight about mass came in 2000 in a lecture about Newton’s mechanics probably about the study of Newton’s second law of motion. The problem is important to me because the primary role of mass is to mediate gravitational interaction between bodies, and no theory of gravitational interaction reconciles with the currently popular standard model of particle physics. But because the problem started with inertia, we again revisit Newton’s law to create a model through which all the masses of elementary particles can be generated.

Recall from the previous section, the modified Rindler space with an acceleration given by,