Question

The two-mile linear accelerator at Stanford University in California "appears" to be less than a meter long to the electrons that travel in it. Explain.

Answer 1

For the moving electron, length contraction
reduces the apparent length of the 2-mile long
tube. Since electrons move with nearly the
speed of light, the contraction is very signifi-
cant.
Length contraction is the relativistic physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer.

L = 2 miles = 3218.7 m is the length observed by an observer in relative motion with respect to the object,
Lₒ =3219.7 m is the proper length (the length of the object in its rest frame),
L=Lₒ•sqrt(1 -β²),
1- β² =(L/ Lₒ)²,
β = sqrt{1 –(L/ Lₒ)²}=
= sqrt{1 – (3218.7/ 3219.7)²} =0.025
β = v/c,
v = β•c = 0.025 •3•10^8 =7.5•10^6 m/s.