Relativity Science Calculator - A Simpler Lorentz Transformation Derivation

A Simpler Lorentz Transformation Derivation

light flash at clock 1.png

§ Assume strictly and only  from the Michelson - Morley Experiment ( 1887 ) - that is, we know nothing more than that which is obtained from this famous experiment and its ad - hoc solution:

1).

lorentz length contraction.png,

"Lorentz Length Contraction" of   in frame   moving away from stationary frame    as measured in  .

2).

time dilation.png

"Lorentz Time Dilation"  of   in   moving away from stationary    system as measured in  .

3).  Assume also the extent of the distance of the light flash from

x1 to x2.png

describes a rigid rod.

§ Some definitions:

a).  In system  :

light path.png

b).  In system   :

light path 2.png

since   is moving away from    with velocity .

c).  Because

equations

This latter is true because the entire system   is relatively moving away from system frame     with velocity    in   - time   .

§ Lorentz Transformation Equations Derivation:

I.  Using "Lorentz Length Contraction" ad - hoc assumption of the Michelson - Morley Experiment ( 1887 ),

equations

This part was easy!

II.  We will be using "Lorentz Time Dilation" ad - hoc assumption of the Michelson - Morley Experiment ( 1887 ) in this rather more complicated following derivation:

lorentz time dilation.

Nothing more to say!!