Mass Distortion Help

High-speed Particles

You’ve heard expressions such as electron rest mass , which refers to the 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 fact, unlike spatial distortion, is more than mere fodder for “mind experiments.” 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. When this happens, energy can be released in the form of infrared (IR), visible light, ultraviolet (UV), 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 practical concern. While their own bodies won’t seem to be more massive from their own point of view and the things inside the ship will appear normal to them, the particles whizzing by outside will become more massive in a real and dangerous way. 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. However, that 1-kg stone will mass more than 22 kg when u = 0.999. In addition, every atom outside the ship will strike the vessel’s “prow” at relativistic speed, producing deadly radiation of the same sort that occurs in high-energy particle accelerators.

Experimental Confirmation

Relativistic time dilation and mass increase have both been measured under controlled conditions, and the results concur with Einstein’s formulas stated earlier. Therefore, 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 awhile 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 therefore was exceedingly small, it 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 registered a time slightly earlier than 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.

Mass Distortion Practice Problem

Problem

Suppose that a small meteoroid, whose mass is 300 milligrams (300 mg), strikes the shell of a space vessel moving at 99.9 percent of the speed of light. What is the apparent mass of the meteoroid?

Solution

Use the preceding formula for relativistic mass increase, considering u = 0.999. Then the mass is multiplied by a factor m as follows:

m = (1 − 0.999 ² ) ^−1/2

= (1 − 0.998) ^−1/2

= 0.002 ^−1/2

= 1/(0.002) ^1/2

= 1/0.0447

= 22.4

The mass of the meteoroid when it strikes the vessel is 300 × 22.4 mg, or 6.72 grams (g).

Practice problems of these concepts can be found at: Relativity Theory Practice Test