Relativity Length

Profile of Goery (Like Alfred Hitchcock) which gets thinner as speed increases.

Or you flying like superman in the hold of your spacecraft or outside your spacecraft.

Or you standing in a spacecraft flying upward

Or show the length of a car in the hold.

Enter speed as a fraction of the speed of light.

[v ] 0 - 0.999999

[ ] print speed in miles per hour and kilometers per hour.

You are [(1-v^2)^0.5 ] as thick( e.g. 0.5)

Animation

Print the profile reduced in thickness.

Use a slider to control the speed.

Illustration: The length of a moving object follows the arc of a circle with speed as the x axis and length as the y-axis.

Prove It!

Length of a "bunch" of particles in an accelerator.

Particle accelerators like the Stanford Linear Accelerator, or SLAC, accelerate bunches of electrons. The bunch of electrons has a length which is measured to be shorter as the electrons go faster.

Explore It!

The length of SLAC as viewed by an electron

The depth of the atmosphere viewed by a muon.

To a muon created 10 km above the earth moving at high speed toward the earth the thickness of the atmosphere appears 10 times thinner or a mere 1 km thick. The half-life of a muon is 1.56 microseconds, at nearly the speed of light muons can travel about 1560 ft. or 500 m before half of them decay. Muons actually make it to the surface of the earth where they are observed in the Exploratorium's cloud chamber.

10 km is 20 times 500 m so it would take 20 half lives of muons to reach the surface and only 1/2^20 would reach the surface. Many more actually reach the surface, so that muons must see the atmosphere length contracted.

The pole vaulter runs through the barn.

An observer sees a relativistic pole vaulter run toward a barn at 0.87 c so that gamma = 2, The pole at rest is 20 feet long the barn is 10 feet long. The pole is length contracted to half its rest length. so it is 20 feet long and fits into the barn.

To the pole vaulter the barn is length contracted to 5 feet long. What he sees, is that the front of the pole exits the front of the barn before the back of the pole enters.

Timing of events at different locations changes in the relativistic view.

Do the Math!

The circle of length versus speed.

The length, L, of a moving object is observed to be its rest length L0 divided by g where

g = (1-v^2/c^2)^-0.5

Why is it shorter? Because two observers can't agree on simultaneous measurement time.

For an object at rrest you can measure the position of the front and the back at any time, however the front and the back position of a moving object must be measured at the same time. Simultaneous times are not the same as viewed by two observers in motion.

 Scientific Explorations with Paul Doherty © 2005 8 May 2005