Lorentz-Fitzgerald Length Contraction

We now have

which tells us that the length L measured for the moving meter stick is shorter than the length L_o measured when it is a test. This difference in length is called the Lorentz-Fitzgerald contraction.

How can this be?

Observer B will complain that this unexpected value for the length is because the ends of the meter stick were not marked at the same time. For x_A = L_o and t_A = 0 , the Lorentz Transformation equations give us

or

That is, observer B will see event E₂ occur before event E₁ --s he will insist that A has measured a shorter length because he first marked the front of the meterstick, waited until the rear of the stick moved closer to that mark, and then marked the rear. Non-simultaneity is not an explanation of this length contraction. They are both consequences of the lack of absolute time or space.

Applications of the Lorentz Transformations			Applications of the Lorentz Transformations
Return to Ch 27, Special Relativity

(c) Doug Davis, 2002; all rights reserved