Brief Solutions to the Big Problems in Physics, Astrophysics and Cosmology E-Book

Balungi Francis

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

Beschreibung

People have always wanted answers to the big questions. Where did we come from? How did the universe begin? What is the meaning and design behind it all? Is there anyone out there? The creation accounts of the past now seem less relevant and credible. They have been replaced by a variety of what can only be called superstitions, ranging from New Age to Star Trek. But real science can be far stranger than science fiction, and much more satisfying. I am a scientist. And a scientist with a deep fascination with physics, cosmology, the universe and the future of humanity. I was brought up by my parents to have an unwavering curiosity and, like my father, to research and try to answer the many questions that science asks us. I have spent my life travelling across the universe, inside my mind. Through theoretical physics, I have sought to answer some of the great questions. At one point, I thought I would see the end of physics as we know it, but now I think the wonder of discovery will continue long after I am gone. We are close to some of these answers, but we are not there yet. The problem is, most people believe that real science is too difficult and complicated for them to understand. But I don't think this is the case. To do research on the fundamental laws that govern the universe would require a commitment of time that most people don't have; the world would soon grind to a halt if we all tried to do theoretical physics. But most people can understand and appreciate the basic ideas if they are presented in a clear way with equations, which I believe is possible and which is something I have enjoyed trying to do throughout my life. I want to add my voice to those who demand why we must ask the big questions immediate action on the key challenges for our global community. I hope that going forward, even when I am no longer here, people with power can show creativity, courage and leadership. Let them rise to the challenges and act now.

Leseprobe

BRIEF SOLUTIONS TO THE BIG PROBLEMS IN PHYSICS, ASTROPHYSICS AND COSMOLOGY

BALUNGI FRANCIS

Copyright © Visionary School of Quantum Gravity 2018

Copyright © dePhysique Hub2020

Copyright © 2019 by Balungi Francis

Copyright © 2019 by Barungi Francis

All Right Reserved

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, except in the case of very brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law.

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Table of Contents

Dedication

Preface

1. The Problem of Quantum Gravity

2. The Irreducible Anomaly in the Observations of the Deflection of Light by the Sun

3. Is there a Classical Formula of the Force of the Cosmological Constant like that of the Gravitational Force?

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

5. What is the Origin of Mass?

6. How can we derive the Bekenstein-Hawking Area-Entropy Law from first Principles?

7. Can we Quantize Gravity?

8. The Wave Particle Duality Problem

9. What is Semi-Classical Gravity?

10. The Extra Dimension Problem

11. The Theory of Everything

12. How can the Laws of Physics be derived from one Underlying Principle?

13. Is Gravity and the Laws of Physics Emergent?

14. The Galaxy Rotation Problem

15. The Cosmological Constant Problem

16. What is the Radius of a Proton?

Additional Readings

INDEX

Dedication

To my wife W. Ritah for his constant feedback throughout and many long hours of editing,

To my sons Odhran and Leander,

To Carlo Rovelli, Neil deGrasse Tyson and Sabine Hossenfielder, I say thank you.

Preface

In 1900, the British physicist Lord Kelvin declared “There is nothing new to discover in physics. All that remains is to more accurately measure its quantities” today, hardly anyone would dare say that our knowledge of the universe and everything in it is almost complete.

There are still some deficiencies in the standard model of physics, such as the origin of mass, the strong CP problem, neutrino oscillatiobs, matter-antimatter asymmetry and the nature of dark matter and dark energy. Another problem lies within the mathematical framework of the standard model itself.

Some of the major problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomena or experimental result. The others are experimental meaning that there is difficulty in creating an experiment to test a proposed theory.

In what follows, there is given a discussion of what are arguably the most unsolved problems in physics, astrophysics and cosmology. And this book sets to solve them living none untouched. The form of the discussion is not negative: formulating a problem succinctly is essential to a solution. Perhaps the most remarkable aspect of what follows is that many of the problems are interrelated, so the solution of one or a few opens the prospect of widespread advancement.

An excerpt from Lee Smolin’s book “the trouble with physics” explains in detail what this book is all about as given below in Lee’s original words.

To be fair we’ve made two experimental discoveries in the past few decades, that neutrinos have mass and that the universe is dominated by a mysterious dark energy that seems to be accelerating its expansion. But we have no idea why neutrinos (or any other particles) have mass or what explains their mass values. As for dark energy, its not explained in terms of any existing theory. Its discovery cannot then be counted as a success, for it suggests that there is some major fact we are all missing. And except for dark energy, no new particle has been discovered, no new force found, no new phenomenon encountered that was not known and understood twenty-five years ago.

Don’t get me wrong. For the past 25years we have certainly been very busy. There has been enormous progress in applying established theories to diverse subjects; the properties of materials, the molecular physics underlying biology, the dynamics of vast clusters of stars. But when it comes to extending our knowledge of the laws of nature we have made no real head way. Many beautiful ideas have been explored, and there have been remarkable particle aaccelerator experiments and cosmological observations, but these have mainly served to confirm exisiting theory. There have been few leaps forward, and none as definitive or important as those of the previous 200years. When something like this happens in sports or business, it’s called hitting the wall.

What are the major unsolved problems in physics? And what can we do to solve them? These are the central questions of my book.

1. The Problem of Quantum Gravity

Today we are blessed with two extraordinarily successful theories of physics. The first is the General theory of relativity, which describe the large scale behavior of matter in a curved space time. This theory is the basis for the standard model of big bang cosmology. The discovery of gravitational waves at LIGO observatory in the US (and then Virgo, in Italy) is only the most recent of this theory’s many triumphs.

The second is quantum mechanics. This theory describes the properties and behavior of matter and radiation at their smallest scales. It is the basis for the standard model of particle physics, which builds up all the visible constituents of the universe out of collections of quarks, electrons and force-carrying particles such as photons. The discovery of the Higgs boson at CERN in Geneva is only the most recent of this theory’s many truimphs.

But, while they are both highly successful, those two structures leave a lot of important questions unanswered. They are also based on two different interpretations of space and time, and are therefore fundamentally incompatible. We have two descriptions but, as far as we know, we’ve only ever had one universe. What we need is a quantum theory of gravity.

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.

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 demand for consistency between a quantum description of matter and a geometric description of spacetime, as well as the appearance of singularities and the black hole information paradox 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.

For us to solve the problem of quantum gravity (QG) we need to address and understand in detail the situations where the general theory of relativity (GR) fails. That is; General relativity fails to account for dark matter, GR 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. In this chapter, we shall spend a big deal of our time discussing the resolution of classical singularities that plague General relativity.

The two approaches to formulation of quantum gravity leads to string theory, a theory which is problematic and still debatable. In what follows, we modify the uncertainity principle to create a structure called Loop quantum gravity which in turn provides a solution to the information paradox problem and the resolution of classical singularities which plague the General theory of relativity.

(a)Quantum geometry

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 , is the coupling constant and n is a positive number.

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,

(b) Resolution of black hole singularity and the information paradox problem

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.

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 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. And from the uncertainity principle, this 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,

––––––––

(a)Evidence for Maximal Acceleration and Minimal length in Quantum Gravity

Under the assumption of  ( where is the coupling constant), in the Caianeillo maximum acceleration model ( ) , we derive the maximal acceleration and 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.