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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!!




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