Think Physics: Beginner's Guide to an Amazingly Wide Range of Fundamental Physics Related Questions

THINK PHYSICS

BEGINNER’S GUIDE TO AN AMAZINGLY WIDE RANGE OF FUNDAMENTAL PHYSICS- RELATED QUESTIONS

Copyright ©2020 Balungi Francis

All rights reserved.

TABLE OF CONTENTS

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PREFACE

The Minimum mass limit of a gravitationally Collapsed star

Emergence of Gravity

The Simple Link between Quantum Mechanics and Gravity

Proof of the Proton Radius

Reinventing Gravity

On the Deflection of Light in the Sun’s Gravitational Fields

A new Approach to Quantum Theory

The Volume Entropy Law of a Black Hole

Space-time Singularity Resolution

Glossary

About the Author

PREFACE

Balungi explains deep ideas in physics in an easy-to-understand way. Think Physics is a series aimed to solving the big problems in physics. The book targets topics that researchers and students spend time wondering about, like the origin of gravity and the universe. It also goes into the theories that seem right but are wrong and shows why they are wrong a rarity in science books. Think Physics series is a rigorously correct, lighthearted, and cleverly designed problem solving book for physicists of all ages.

❖  Has been tested, rewritten, and retested to ensure that you can teach yourself all about major unsolved physics problems

❖  Requires no math-mathematical treatments and applications are included in optional sections so that you can choose either a mathematical or nonmathematical approach. No Calculus

The Minimum mass limit of a gravitationally Collapsed star

The smallest black hole would be one where the Schwarzschild radius equals the radius of a mass with a reduced Compton wavelength which is the smallest size to which a given mass can be localized. For a small mass M, the Compton wavelength exceeds half the Schwarzschild radius, and no black hole description exists. This smallest mass for a black hole is thus approximately the Planck mass, the micro black hole.

Contrary to the above observation, torsion (see Einstein-Cartan theory) modifies the Dirac equation in the presence of the gravitational field causing fermions to be spatially extended. This spatial extension of fermions limits the minimum mass of a black hole to be on the order of , showing that micro black holes (of Planck mass) may not exist. Another mass limit is from the data of the Fermi Gamma-ray space telescope satellite which states that, less than one percent of dark matter could be made of primordial black holes with masses up to .

The major aim of this book is to prove theoretically the existence of a minimum mass limit of a gravitationally collapsed star and thereafter prove Chandrasekhar  wrong (see Chandrasekhar 1983 Noble lecture concluding statement below)

We conclude that there can be no surprises in the evolution of stars of mass less than 0.43Solarmass ( ). The end stage in the evolution of such stars can only be that of the white dwarfs. (Parenthetically, we may note here that the so-called ‘mini’ black-holes of mass   cannot naturally be formed in the present astronomical universe.)

In what follows the above given statement may prove to wrong according to a detailed derivation given below.

From the theory of white dwarf stars, the radius limit of a white dwarf of mass M is given by the following equation,

(1)

Where and is the proton and electron mass respectively

Just like the Compton wavelength, there must exist another radius for the consistitution of stars that differs from the radius given in (1) above. For example, in the same way the Planck mass is deduced (i.e by equating the Schwarzschild radius to the Compton wavelength) is the same way in which we are to prove the existence of the mass limit of a gravitationally collapsed star.

We start from first principles. Let it be known that the derivation of the Chandrasekhar mass limit will follow the equipartition of the gravitational potential energy of a star to its electron degeneracy pressure. In the same way, if the gravitational binding energy is given by,

Where is the Planck mass and µ is is the average molecular weight per electron

And the electron degeneracy energy pressure of the star is given by,

When then we obtain the mass limit of the white dwarf star as,

If then this is true, then the formula (2) for the gravitational binding energy of a star is true. This therefore implies that the following assumption will also be true.

When the binding gravitational energy of a star is equal to the Newtonian gravitational potential energy we obtain the radius which is the smallest size to which a given mass of a star can be localized as,

(3)

This can be rewritten in the form,

Where which is smaller than the Planck length of

Therefore equating Equation (1) to Equation (3) we deduce the mass limit of a gravitationally collapsed star as,

The value is in excellent agreement with other theoretical and experimental observations

The radius of this black hole from Equation (3) is thus  larger than the radius of the sun of .

In conclusion therefore the end stage in the evolution of a star can only be that of the black hole with a mass   and size of in contrast with the Chandrasekhar observations.

Note that the radius given by Equation (3), above is similar to the Equation for the size of the Planck star that was given by Rovelli and Vidotto, where is the Planck length and n is the positive number. This is a clear indication that singularities in black holes can be resolved.

Emergence of Gravity

Starting from first principles and general assumptions we present a heuristic argument that shows that Newton's law of gravitation naturally arise in a theory in which space emerges