What is Real? E-Book

Balungi Francis

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

Veröffentlichungsjahr: 2020

Beschreibung

What exactly is physical reality? In elegant and accessible prose, theoretical physicist Balungi Francis leads us on a wondrous journey from space-time singularities to Quantum Black Holes without information loss, from the Bekenstein-Hawking Area entropy law to his famous Volume entropy law of Black holes, from Modified Newtonian Dynamics, Dark Matter to Planck mass particles, from White Dwarfs to Black Holes and from General Relativity to his own work in Quantum Gravity. As he shows us how the idea of reality has evolved over time, Balungi offers deeper explanations of the theories he introduced so concisely in Quantum Gravity in a Nutshell1. Balungi invites us to imagine a marvelous world where space breaks up into tiny grains, singularities disappears, information loss in BHs resolved, time disappears at the smallest scales, and black holes are waiting to explode.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.

Leseprobe

WHAT IS REAL? 

Space -Time Singularities or Quantum Black Holes? Dark Matter or Planck Mass Particles? General Relativity or Quantum Gravity? Volume or Area Entropy Law?

BALUNGI FRANCIS

Copyright © BalungiFrancis, 2020

The moral right of the author has been asserted.

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.

TABLE OF CONTENTS

DEDICATION

PREFACE

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

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

Stellar Mass Black Holes or Primordial Holes

Additional Readings

Hidden in Plain sight1:  A Simple Link between Quantum Mechanics and Relativity

Hidden in Plain sight2: From White Dwarfs to Black Holes

Appendix 1

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

Epilogue

Glossary

Bibliography

Acknowledgments

DEDICATION

To Carlo Rovelli

PREFACE

What exactly is physical reality? In elegant and accessible prose, theoretical physicist Balungi Francis leads us on a wondrous journey from space-time singularities to Quantum Black Holes without information loss, from the Bekenstein-Hawking Area entropy law to his famous Volume entropy law of Black holes, from Modified Newtonian Dynamics, Dark Matter to Planck mass particles, from White Dwarfs to Black Holes and from General Relativity to his own work in Quantum Gravity. As he shows us how the idea of reality has evolved overtime, Balungi offers deeper explanations of the theories he introduced so concisely in Quantum Gravity in a Nutshell1. Balungi invites us to imagine a marvelous world where space breaks up into tiny grains, singularities disappears, information loss in BHs resolved, time disappears at the smallest scales, and black holes are waiting to explode.

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.

Balungi Francis 2020

Space-time Singularity or Quantum Black Holes?

It has been known for some time that 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.

In summary, a Black hole is that object created when a dying star collapses to a singular point, concealed by an event horizon, it is so dense and has strong gravity that nothing, including light, can escape it. Black holes are predicted by general relativity, and though they cannot be “seen,” several have been inferred from astronomical observations of binary stars and massive collapsed stars at the centers of galaxies.

Black holes formed by gravitational collapse require great energy density but there exists a new breed of Black holes that where formed in the early universe after the big bang, where the energy density was much greater allowing the formation of Primordial Black holes with masses ranging from, . Therefore the formation of primordial, min or quantum black holes was due to density perturbations forming in it a gravitational collapse in the early universe.

A Black hole might not actually be a physical object in space but rather a mathematical singularity, a prediction of Einstein’s General Relativity theory, a place where the solutions of Einstein differential equations break down. A space-time singularity therefore is a position in space where quantities used to determine the gravitational field become infinite; such quantities include the curvature of space-time and the density of matter. Singularities are places where both the curvature and the energy-density of matter become infinitely large such that light cannot escape them. This happens for example inside black holes and at the beginning of the early universe.

Singularities in any physical theory indicate that either something is wrong or we need to reformulate the theory itself. Singularities are like dividing something by zero. The problems in General relativity arise from trying to deal with a point in space or 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.

Singularities are a sign that the theory breaks down and has to be replaced by a more fundamental theory. And we think the same has to be the case in General Relativity, where the more fundamental theory to replace it is quantum gravity.

If black holes are as a result of the solutions to the Einstein’s differential equations breaking down, then what is real?

Whether in gravitational collapse or the early universe, we now know that the formation of Black holes or space time singularities requires great and much greater energy density. This we know because while the left hand side of Einstein field equations representsnts the metric of space-time curvature, the right hand side represents the matter- energy content of the classical matter fields of pressure and energy density. This therefore means that quantum mechanics which plays an important role in the behavior of the matter fields has no place in the Einstein field equations and this is what brings on the singularities that plague the general relativity theory. 

Because of this, one therefore has a problem of defining a consistent scheme in which the space time metric is treated classically but is coupled to the matter fields which are treated quantum mechanically.

What is not real is to use the stress energy tensor (classical pressure and energy density) on Black holes instead of the quantum mechanical energy density.

The approximation I shall use on my journey to quantum gravity (Quantum Black holes) is that the matter fields, such as scalar, electro-magnetic, or neutrino fields, obey the usual wave equations with the left hand side replaced by a classical space time second order curvature ( ), where R is the radius of curvature) while the right hand stress-energy tensor replaced by the quantum mechanical energy density (   (1) ) Where F is the force involved in an interaction α is the coupling constant that determines the strength of the force, and ћ is the reduced Planck constant. The equation represents the coupling constant () as a function of the energy density for any force (F) exerted in an interaction. The application of this equation is the Franzl Aus Tirol curve on Wikipedia’s “Coupling constant”. Another application is the derivation of energy stored in the electromagnetic field (see Appendix 1).Therefore the general theory of quantum mechanics in curved space –time will be given by this simple equation, , where

Where, is the Planck energy and is the Planck mass

From the above given equation we see that high space curvature will always be achieved when the square of the force involved increases. According to the theory given, this will only occur at the Planck energy level where space is discrete or granular in nature (its building blocks being exactly the Planck mass, simply put, the atoms of space). There is no change in energy because the only energy involved in the process is the constant Planck energy of the Planck mass.

As we said earlier, that the formation of a black hole due to the process of gravitational collapse occurs in the presence of great energy density and also that the formation of primordial black holes in the early universe occurs in the presence of a much greater energy density, our theory suggests that this energy density is high because of the strong gravitational force involved in the process. According to general relativity, this force is a constant and is given by,  . Therefore from equation (2), when this force is present the curvature of space scales as the inverse of the square of the Planck length,

Where is the Planck length.

This implies that, in the theory of quantum mechanics in curved space-time for the gravitational collapse of a star, the star does not collapse to a singularity but instead to a Planck sized star of Planck length close to  and this will happen only when .Finally, in the theory of quantum mechanics in curved space-time, 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.Since the energy density or pressure is expressed as in equation (1),

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. And from the uncertainity principle, this repulsion force is given by,

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

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