Understanding Special Relativity
and Maxwell’s Equations

With Implicattions for a Unified Field Theory

Table of Contents

1.  Space and Time                                                 
    1.1     Reference Frames                                                                                     
    1.2     The Galilean Transformation                                                        
    1.3.    Velocity Transformation                                                                                                                                                                            
2.  Relativistic Kinematics                                                  
    2.1     The Principle of Relativity                                                             
    2.2     The Nature of Light                                                                               
    2.3     The Nature of Time                                                                               
    2.4     Time Dilation                                                                                                        
    2.5     Length Contraction                                                                                
    2.6     The Lorentz Transformation                                                       
    2.7     Relativistic Velocity Transformation                                  
    2.8     Vector Representation of the Lorentz Transformation                                  
    2.9     4-Vector Representation of the Lorentz Transformation                                 
    2.10   Quaternion Representation of the Lorentz Transformation                
                                            
3.  Relativistic Dynamics                                                    
    3.1     Relativistic Momentum                                                                                   
    3.2     Relativistic Energy                                                                               
    3.3     Transformation of Momentum and Energy                         
    3.4     Transformation Law for Force                                                                                      
4.  Maxwell’s Equations                                                      
    4.1     Coulomb’s Law                                                                                         
    4.2     Units                                                                                                              
    4.3     The Electric Field                                                                                              
    4.4     The Lorentz Force                                                                                  
    4.5     Maxwell’s Equations                                                                            
    4.6     Electromagnetic Waves                                                                      
    4.7     Quaternion Representation of Maxwell’s Equations                               
                                                                                                                    
5.  An Alternate Theory of Gravitation                              
    5.1     Newton’s Law of Gravitation                                         
    5.2     A Gravitational Lorentz Force                                                   
    5.3     Gravitational Version of Maxwell’s Equations                                                                     
6.  Toward a Unified Field Theory                                    
    6.1    The Field Equation                                                                                
    6.2    The Dirac Equation                                                                               
    6.3    The Conservation Laws                                                                     
    6.4    The Uncertainty Principle                                                              
    6.5    The Relativistic Invariance of the Field Equation             
    6.6    The Gravitational Field                                                                     
    6.7    Natural System of Units                                                             

Appendix A – Introduction to Quaternions                                               

Appendix B – Fourier Transform of a Gaussian                   

Index