Lorentz contraction

One way to understand special relativity is to see how time dilation and Lorentz contraction of objects parallel to motion can be used to explain the null results of the Michelson-Morley [1] experiment, which was performed to measure the velocity of earth in relation to an assumed ether. The result was that the expected influence of such an ether on the velocity of light was not found. Let us now study this double-pass example, where one arm of a Michelson interferometer was perpendicular to the velocity of the earth s surface, while the other... 

The Lorentz contraction of the parallel arm is more complicated and cannot be measured directly as it is not permanent but disappears when the velocity (v) disappears. Thus, I find the discussion of assumed contractions or elongations of a moving object meaningless as they are, by definition, invisible. I look at them as only theoretical tools, and in the following section we will solely study how the stationary world appears deformed when studied and measured by an observer traveling with a velocity close to that of light. 

This result is identical to the accepted value of the Lorentz contraction [14], but our graphic derivation shows that this is true only for objects that just pass by (Fig. 17). Objects in front appear elongated by OC/BD, while objects behind appear contracted by OC/BE. 

Figure 12. To the traveler an arbitrary point (G) of the stationary world appears to exist at H. which is found by drawing a line of constant Y value from G to the sphere. As the traveler directs the telescope in her direction BH, her line of sight in the Tester s universe will be GB. As the traveler directs the laser in his direction BH, the direction of the laser beam will appear to be AG to the rester. The Lorentz contraction is MN/ED.

The Lorentz contraction, which is found to be a special case of apparent expansions and contractions... 

The reason is that the measuring rod that moves with the rotating circumference suffers Lorentz contraction, but not for measurement along the radius. The only interpretation is that euclidean geometry does not apply to K. ... 

Hence lengths in the second system appear from the first system to be shortened (the Fitzgerald-Lorentz contraction). On the other hand, if are the times of two events at the same place x in the first system, then... 

Figure 5. Behavior of a positive-energy wave packet under a velocity transformation. The right image shows the wave packet after a Lorentz transformation (boost) with the indicated velocity. The relative motion between observer and wave packet causes a Lorentz contraction.

Figure 6. A superposition of positive and negative energies before and after a Lorentz boost. Apart from the Lorentz contraction, the relative motion between observer and wave packet produces interference effects. The interference is caused by the separation of the negative and positive-energy parts in momentum space.

Lorentz contraction - The reduction in length of a moving body in the direction of motion, given by the factor (1-v /c ) , where v is the velocity of the body and c the velocity of light. Also known as the FitzGerald-Lorentz contraction. 

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