### Index

Chapter 1 The 4 Dimensions of the Universe

1.1 The 4 Dimensions observed in our Universe

1.2 Definition of 4-dimensional Space and Classical Physics

1.3 Frame of Reference / System of Coordinates

1.4 Space Time Continuum

1.5 Relativity and more dimensions

Chapter 2 The 5th Dimension and Velocity Relationships

2.1 Definition of 5-dimensional Space and Physics in 5 Dimensions

2.2 Relative Velocity between Objects and Observers

2.3 Observer's Perspective of the Relative Velocity of Objects

2.3.1 Observer's Perspective in 5-dimensional space

2.3.2 Observer's Perspective in 4-dimensional space

2.4 Velocity Relationships

2.5 Physical Objectivity

Chapter 3 Relativistic Mass and Momentum

3.1 Relativistic Momentum

3.2 Observer's View of Space and Relativistic Mass

3.2.1 Option 1 - Observer in 5-dimensional space

3.2.2 Option 2 - Observer in 4-dimensional space

Chapter 4 Speed of Light c

4.1 The "common constant velocity" is the speed of light c

4.2 The measured value of c

4.3 The point of view of relativistic mass is critical!

Chapter 5 Relativistic Energy

5.1 Energy of Matter - 4-dimensional space

5.1.1 Deriving 4-dimensional space Expressions of Energy

5.1.2 4-dimensional space Energy and Momentum Relationships

5.2 Energy of Matter - 5-dimensional space

5.2.1 Deriving 5-dimensional space Expressions of Energy

5.2.2 5-dimensional space Energy and Momentum Relationships

5.2.3 5-dimensional space Definitions of Kinetic Energy

5.3 Comparison of Relativistic Energy Relationships

5.3.1 Total Relativistic Energy is Constant

5.3.2 Sharing potential and kinetic energy in 4- and 5-dimensional space

5.3.3 4- and 5-dimensional space energy expressions are compatible

5.3.4 Examples of 5-dimensional Energy Calculations

5.3.4.1 Earth moving around the Sun

5.3.4.2 Electron moving around a nucleus

5.3.5 Energy of Attractive Forces (Gravity and Coulomb calculations)

5.3.5.1 Calculation of the earth's energy relative to the force of gravity

5.3.5.2 Calculation of the electron energy in Bohr's model

Chapter 6 Radiation, Particles, Waves and Origin of Matter

6.1 Thermal Radiation, Planck's Constant and Einstein's Concept of Photons

6.1.2 Classical Theory

6.1.3 Planck's Theory of cavity radiation (1905)

6.1.4 Einstein's Concept of Photons

6.2 Particle Behaviour of Electromagnetic Radiation

6.2.1 Photoelectric Effect

6.2.2 The Compton Effect

6.2.2.1 Auther H. Compton - May 1923 - Quantum Theory of Scattering of X-rays

6.2.2.2 Relativistic relationships in Compton's own paper and 5-dimensional space:

6.2.2.3 Compton's Effect in 5-dimensional space

6.2.2.4 Difference between 4- & 5-dimensional space momentum vectors

6.2.2.5 Compton momentum vectors p & p' related to 4- & 5-dimensional space theory

6.2.2.6 Compton Energy Scalars

6.2.2.7 Validity of the Compton Effect

6.2.2.8 Summary - Compton's Effect

6.2.3 Dual Nature of Electromagnetic Radiation

6.2.4 Photons and X-ray Production

6.2.5 Pair Production and Pair Annihilation

6.2.6 Cross Sections for Photon Absorption and Scattering

6.2.7 Summary - Particle Behaviour of Electromagnetic Radiation

6.3 Wave Nature of Particles

6.3.1 Matter Waves - de Broglie's Postulate

6.3.2 Dual Nature of Matter

6.3.3 The Uncertainty Principle

6.3.4 Single Electron Diffraction

6.3.5 The Properties of Matter Waves

6.3.6 Valid expressions for dE / dp

6.3.6.1 Derivation of the group velocity g

6.3.6.2 5-dimensional space derivation of the group velocity g5

6.3.6.3 De Broglie Vector Diagram

6.3.7 Condition for using De Broglie's Postulate in 5-dimensional space
6.3.8 Summary - Wave Nature of Particles

6.4 The Origin of Matter

6.4.1 5-dimensional Kinetic Energy is Relative to the Observer

6.4.2 De Broglie's postulate linked exclusively with the common constant velocity c

6.4.3 Group Energy of Matter Waves

6.4.4 Hypothesis: The origin of matter is electromagnetic radiation

6.4.5 5-dimensional space and the Uncertainty Principle

6.4.6 5-dimensional space and the Dual Nature of Matter

6.4.7 Summary - The Origin of Matter

Chapter 7 Theory of Quantum Mechanics

7.1 A brief history of wave mechanics

7.2 Schrödinger's quantum theory and equations

7.2.1 Schrödinger's theory of quantum mechanics

7.2.2 Schrödinger Equations

7.2.3 Wave function and its complex conjugate

7.2.4 Born's Interpretation of wave functions

7.2.4.1 Quantum mechanical calculation of the simple harmonic oscillator

7.2.4.2 Classical mechanical calculation of the simple harmonic oscillator

7.2.4.3 Normalising the quantum wave function of the simple harmonic oscillator

7.2.5 Expectation values

7.2.6 The time-independent Schrödinger equation

7.2.7 Eigenfunctions leading to energy quantisation in the Schrödinger theory.

7.2.8 Energy Quantisation in the Schrödinger Theory

7.2.8.1 Eigenfunction for a higher energy state of simple harmonic oscillator

7.2.9 Summary - Schrödinger's quantum theory and equations

7.2.9.1 5-dimensional space and Schrödinger's equation

7.3 Solutions to time-independent Schrödinger equations

Chapter 8 Quantum Non-Locality & Entanglement

8.1 Non-Local Single Photon

8.2 Predictions of the Quantum Theory of Matter

8.2.1 Sensing without touching!

8.2.2 Description of Physical Reality (EPR) 1935

8.2.3 Schrödinger's cat

8.3 Entanglement - Bell's Theory 1964

8.3.1 Quantum entanglement and the EPR paradox

8.3.2 Bell inequalities

8.3.3 After the inequality

8.3.4 Experimental Bell Tests

8.3.4.1 Experiment 1: Demonstration of single photon non-locality

8.3.4.2 Experiment 2: Demonstration of a Bell-type test of energy-time entangled qutrits

8.3.5 John Bell - The Man

8.4 Summary - Quantum Non-Locality & Entanglement

Chapter 9 Relativistic Space-Time Continuum

9.1 Relativistic Time and Length

9.1.1 Relativistic Time (Time dilation)

9.1.2 Relativistic Length (Length Dilation)

9.1.3 Example of Time & Length dilation: Muon Experiments

9.2 The Space-Time Continuum

9.2.1 Einstein and the Space-Time Continuum

9.2.2 5-dimensional Space-Time Continuum

Chapter 10 Shape of Space

10.1 Hypothesis: Closed Paths in Space

10.2 Hypothesis: Mass and Angular Momentum define all Matter

10.3 Model of local 5-dimensional space

10.3.1 Local space with radius R5s

10.3.2 Characteristics of local space

10.3.3 Limiting conditions of local space

10.4 Philosophy of 5-dimensional space

10.4.1 Two or more bodies form a local space

10.4.2 Local space is associated with a core mass M4

10.5 Summary - Shape of Space

Chapter 11 Motion in 5-dimensional space

11.1 Key data for calculating motion in 5-dimensional space

11.1.1 Relationships of Motion

11.1.2 Prime Data

11.1.3 Units of Measure & Scaling Factors z and A

11.1.4 Mass Number A

11.1.5 Analysis with respect to the prime data

11.2 5-dimensional Universal Equations of Motion

11.2.1 Calculation of zp

11.2.2 5-dimensional constant Б (Cyrillic b) for all particles and bodies

11.2.3 Universal Equations of Motion

11.3 Example results using the Universal Equations of Motion

11.3.1 Electron and the He Atom

11.3.2 Planet Earth

11.3.3 Atomic Number zp

11.4 Properties of parameter P - "local constant of dimensions"

11.4.1 Scaling factors Z and A as functions of velocity

11.4.2 Determining the value of P in local space

11.4.3 Conditions for parameter P to be constant in local space

11.4.4 5-dimensional space and matter waves

11.5 Summary - Motion in 5-dimensional space

Chapter 12 Physics of the Atom

12.2 First Models of the Atom

12.2.1 Thomson's Model

12.2.2 Rutherford's Model

12.2.3 Physical aspects

12.2.3.1 Stability of the atom

12.2.3.2 Atomic Spectra

12.2.4 First models of the atom

12.2.4.1 Bohr's Postulates

12.2.5 Bohr's Model

12.2.5.1 Correction for finite nuclear mass

12.2.5.2 Quantisation and Sommerfeld's model

12.3 One electron atom

12.3.1 Electrostatic equations and quantisation integer n

12.3.2 Electrostatic expression of electron energy E

12.3.3 Universal equations of motion, the quantisation integer n and the electron

12.3.4 Bohr model in 5-dimensional space

12.3.5 Doing away with the proton!

12.3.6 Schrödinger theory and probability densities for one electron atoms

12.4 Rydberg Constant in 5-dimensional space

12.4.1 Comparison of the universal Ru∞ and original R∞ Rydberg Constants

12.4.2 Example calculations of the universal Rydberg Constant Ru∞

12.4.3 Spectroscopic Notation

12.4.3.1 Optical spectra energy level diagrams

12.4.3.2 X-ray spectra energy level diagrams

12.4.3.3 Energy levels in 5-dimensional space

12.5 Multielectron Atoms

12.5.1 X-ray Line Spectra

12.5.1.1 Mosley's empirical data

12.5.1.2 Measured probability that a 82Pb atom will absorb an x-ray photon

12.5.2 Schrödinger Equation, Eigenfunctions and the Multielectron Atom

12.5.2.1 Identical Particles

12.5.2.2 Exclusion Principle

12.5.2.3 Exchange Forces

12.5.2.4 Summary - Schrödinger Equation, Eigenfunctions and the Multielectron Atom

12.5.3 Ionisation Energy of Multielectron Atoms

12.5.3.1 Ionisation Energy in 5-dimensional space

12.5.3.2 Hartree Theory and classical aspects of the Coulomb force

12.5.3.3 Results of the Hartree Theory

12.5.4 "n" as used by Planck, Einstein, Bohr, Hartree and 5-dimensional space

12.5.4.1 Planck and Einstein"n"

12.5.4.2 Bohr "n"

12.5.4.3 Hartree "n"

12.5.4.4 5-dimensional space "n"

12.5.5 Ground State of multielectron atoms and the periodic table

12.5.6 Simulation of Periodic Table

12.5.6.1 Simulation Method

12.5.7 Stable and unstable multielectron atoms

12.5.7.1 Multielectron atoms in 5-dimensional space

12.5.7.2 Properties of electrons in multielectron atoms

12.5.7.3 Multielectron atoms and radius R5s of 5-dimensional space

12.5.7.4 Unstable transuranic elements

12.5.8 Electromagnetic fields in 5-dimensional space

12.5.9 Relationship between Constants of Physics

12.6 Summary - Physics of the Atom

Chapter 13 Particle Momentum & Energy in 5-D Space

13.1 Charged Pion Decay

13.2 The Photon and Electron treated as particles in Compton's Effect

13.2.1 Change in kinetic energy of a particle with relative velocity v4p&st;c

13.2.2 Wavelength and energy calculations for the Compton Effect

13.2.3 Example of photon mass , momentum and energy in 5-dimensional space

13.2.4 Electron momentum and energy for the Compton Effect in 5-dimensional space

13.2.5 Conservation of energy involves only exchanges of relativistic kinetic energy

13.3 Photons treated as particles in the Mössbauer Effect

13.3.1 Scanning the Mössbauer peak

13.3.2 Conservation of momentum when a nucleus emits a gamma ray with recoil

13.3.3 Conservation of energy when a nucleus emits a gamma ray with recoil

13.3.4 Common ratio of gamma ray parameters resulting from the Doppler effect

13.3.5 Photon frequency in 4- and 5-dimensional space

13.3.6 The Doppler Effect and Wavelength Redshift

13.3.6.1 The Doppler Effect in 4-dimensional space

13.3.6.2 The Doppler Effect for a photon is always a "redshift" in 5-dimensional space

13.4 Summary - Particle Momentum & Energy in 5-dimensional space

13.4.1 Charged Pion Decay

13.4.2 The Compton Effect

13.4.3 The Mössbauer Effect

Chapter 14 Nuclear Decay

14.1 Alpha Decay

14.1.1 Decay Rate, Lifetime T and half-life T1/2

14.2 Beta Decay

14.3 Gamma Decay

Chapter 15 Nuclear Physics

15.1 Nuclear Models

15.1.1 Survey of some Nuclear Properties

15.1.1.1 Nuclear Properties obtained from the study of atoms and molecules

15.1.1.2 Nuclear Sizes and Densities

15.1.1.3 Nuclear Masses and Abundances

15.1.1.4 Binding Energy

15.1.2 Magic Numbers

15.1.3 Shell Model

15.1.4 Moon Model

15.2 Mass Excess calculations in 5-dimensional space

15.3 Reduction of mass - a fundamental feature of 5-D space theory

15.4 Nucleon angular momentum and radius of orbit in 5-D space

15.4.1 Neutron

15.4.2 Proton

15.4.3 Nuclei provide a stable frame of reference with many moving parts

15.5 Summary - Nuclear Physics

Chapter 16 Motion in 5-dimensional local space is Gravity

16.1 Gravity in classical physics

16.2 Gravity-like-behaviour in 5-dimensional space

16.3 The Pound and Snider Experiment

16.3.1 Conservation of Kinetic Energy in 5-dimensional space

16.3.2 Velocity calculations for the Pound & Snider Experiment

16.3.3 More about the Pound & Snider Experiment

16.3.4 The Doppler Effect, Mössbauer Effect and the Pound & Snider Experiment

16.3.5 Summary of the Pound & Snider Experiment and their results

16.3.6 Shape of 5-dimensional space for the Pound & Snider experiment

16.3.7 Physical Effect of the Pound & Snider Experiment

16.3.8 Summary - The Pound & Snider Experiment

16.4 Constrained motion of an object in 5-dimensional space

16.5 Conservation of energy within local 5-dimensional space

16.5.1 Common "energy change" scalar z

16.5.1.1 Change of kinetic energy is K5 in 5-dimensional local space

16.5.2 The limits of 5-dimensional local space

16.5.2.1 "Pre-local-space" and "Start-of-local-space"

16.5.2.2 "End-of-local-space"

16.5.2.4 5-dimensional space theory forecasts the natural mass limits for both nuclei and black holes

16.5.3 Energy in 5-dimensional local space

16.5.3.1 Conservation of energy within 5-dimensional local space - E = m c² = Va + Vf

16.5.3.2 General expression for the energy E of a body in 5-dimensional local space

16.5.3.3 Observer's view of energy in local space

16.6 Shape of local space and the central mass M4

16.6.1 Shape of 5-dimensional local space - Origin of the model

16.6.2 5-dimensional space and time has physical objectivity

16.6.3 Membership of local space and the angular momentum of the central mass M4

16.6.3.1 Maximum Angular Momentum

16.6.3.2 Angular Momentum for the Schwarzschild radius

16.6.4 Common location of matter waves in 5-dimensional local space

16.7 Motion in 5-dimensional local space and gravity-like-behaviour

16.7.1 Conservation of energy expression in 5-dimensional local space

16.7.2 General energy expression for the conservation of energy

16.7.3 All systems of coordinates apply to 5-dimensional local space

16.7.4 General energy expression and the Pound & Snider Experiment

16.7.4.1 Frame of reference of the gamma ray

16.7.4.2 Frame of reference of a "falling" body

16.7.4.3 Time dilation in the Pound & Snider experiment

16.8 Deflection of Light by the Sun

16.8.1 Photon and the path of closest approach to the Sun

16.8.2 Pound & Snider experiment related to photons passing the Sun

16.8.3 Key parameters for calculating photon deflection by the Sun

16.8.4 Deflection of the photon

16.8.5 Refractive Index of the space around the Sun

16.9 Summary: Motion in 5-dimensional local space is Gravity

Chapter 17 Structure of the Universe

17.1 Physics of the Doppler Effect in 4- and 5-dimensional space

17.2 5-dimensional space Astronomical/Cosmological Redshift

17.3 4-dimensional space Astronomical/Cosmological Redshift

17.4 5-Dimensional space and the Structure of the Universe

17.4.1 Finite physical boundary and unlimited time

17.4.2 Built-in Redshift

17.4.3 Distances between objects and observer

17.4.4 Creation and Loss of Matter in the Universe

17.5 Summary: Structure of the Universe

Appendix A Relativity and the Problem of Space

Appendix B Copenhagen interpretation

Appendix C Parameter change with"n" in 5-dimensional space

Appendix D Angular Velocity

Bibliography