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Relativistic Effects Help (page 3)

By — McGraw-Hill Professional
Updated on Sep 18, 2011

High-speed Particles

You’ve heard expressions such as electron rest mass , which refers to the theoretical mass of an electron when it is not moving relative to an observer. If an electron is observed whizzing by at relativistic speed, it has a mass greater than its rest mass and thus will have momentum and kinetic energy greater than is implied by the formulas used in classical physics. This, unlike spatial distortion, is more than a mere “mind experiment.” There is little practical concern about spatial distortion in most situations, at least nowadays. (A thousand years from now, when we are roaming among the stars, we should expect that things will be different!) When electrons move at high enough speed, they attain properties of much more massive particles and acquire some of the properties of x-rays or gamma rays such as are emitted by radioactive substances. There is a name for high-speed electrons that act this way: beta particles .

Physicists take advantage of the relativistic effects on the masses of protons, helium nuclei, neutrons, and other subatomic particles. When these particles are subjected to powerful electrical and magnetic fields in a device called a particle accelerator , they get moving so fast that their mass increases because of relativistic effects. When the particles strike atoms of matter, the nuclei of those target atoms are fractured. It takes quite a wallop to break up the nucleus of an atom! When this happens, energy can be released in the form of infrared, visible light, ultraviolet, x-rays, and gamma rays, as well as a potpourri of exotic particles.

If astronauts ever travel long distances through space in ships moving at speeds near the speed of light, relativistic mass increase will be a dire concern. While the astronaut’s own bodies won’t seem unnaturally massive, and the objects inside the ship will appear to have normal mass too, the particles whizzing by outside will gain real mass. It is scary enough to think about what will happen when a 1-kg meteoroid strikes a space ship traveling at 99.9 percent of the speed of light. But that 1-kg stone will mass more than 22 kg when u = 0.999, that is, at 99.9 percent of the speed of light. As if this is not bad enough, every atomic nucleus outside the ship will strike the vessel’s shell at relativistic speed, producing deadly radiation.

Experimental Confirmation

Relativistic time dilation and mass increase have been measured under controlled conditions, and the results concur with Einstein’s formulas stated earlier. Thus these effects are more than mere tricks of the imagination.

To measure time dilation, a superaccurate atomic clock was placed on board an aircraft, and the aircraft was sent up in flight to cruise around for a while at several hundred kilometers per hour. Another atomic clock was kept at the place where the aircraft took off and landed. Although the aircraft’s speed was only a tiny fraction of the speed of light and the resulting time dilation was exceedingly small, the accumulated discrepancy was large enough to measure. When the aircraft arrived back at the terminal, the clocks, which had been synchronized (when placed right next to each other, of course!) before the trip began, were compared. The clock that had been on the aircraft was a little behind the clock that had been resting comfortably on Earth.

To measure mass increase, particle accelerators are used. It is possible to determine the mass of a moving particle based on its known rest mass and the kinetic energy it possesses as it moves. When the mathematics is done, Einstein’s formula is always shown to be correct.

Practice problems of this concept can be found at: Special and General Relativity Practice Problems

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