SPECIAL RELATIVITY:
The thing that is special is light. Things like distance and time are the ones that are relative; light is the absolute boss. To summarize special relativity, the speed of light is constant to all observers, and the rest of it is a lot of ooing and ahhing over the consequences of this fact. Einstein came up with this in 1905, and it has survived all kinds of scrutiny ever since.
Here is the essense of it: Light goes 300 meters in a microsecond. (We call the speed of light c, and c = 3 x 108 m/s.) Suppose you build a space vehicle 300 m long (wow) and put light detectors attached to the two ends so that you can measure the time it takes for light to go from one end to the other. You trigger a flashbulb in front of the vehicle, and since the rear end is 300 m farther away, the reading on the timer is 1 microsecond. It took 1 microsecond for the light to get from the front to the rear. Now here is the amazing thing about nature-- if your vehicle travels toward or away from the source of light, or if the source of light travels toward or away from the vehicle, you get the same reading on the timer, 1 microsecond. This would be true even if you could travel almost as fast as light!
If that isn't amazing, you are not thinking. If you experimented with timing a bullet or a battleship or a sound wave, the time would vary. Consider a gun that fires a bullet at 300 m/s. It would pass from front to rear of your vehicle in 1 second if there is no relative motion between the gun and the vehicle. Then if you travel toward the gun at the rate of 200 m/s, it is like having a bullet travel at the rate of 500 m/s. It would go from front to rear of your 300 m vehicle in 3/5 s. At low speeds like that of a bullet (low compared to light, that is), common sense prevails. Distance and time are reasonable, and there is almost zero error in the 3/5 s calculation.
But it turns out that as relative speeds increase, strange things happen to distance and time. To the person in the vehicle, the length of it remains 300 m and her pulse is 70/minute. To an outside observer zooming by at high speed (or the vehicle zooming by the observer), these things change. The length is shorter and the time between pulses is longer (by the same factor-- why ?).These things are functions of the velocity in such a way as to keep the speed of light constant, relative to all observers. On the highway, if you are traveling at 29 mph and another car is going 30 mph, you will observe that it will get ahead of you and increase the separation between you at the rate of 1 mph. But if you travel at the rate of 99% of the speed of light, the light would zip past you as if you are standing still! Its speed relative to you would be c!
We
use the Greek letter gamma (g
) to represent the factor mentioned above. (g > 1 for a moving body.) The
sketch at the right shows a sphere at rest. Under it is an identical sphere
moving to the right or left at about 0.99 c. In the 300 m spaceship example, an
observer on Earth would see the moving ship as having a length 300/g , and while ten
years go by on Earth, the astronaut would age 10/g
years. Here is how to calculate g . First find the speed of the thing as a fraction of
the speed of light. Let's call the fraction b . For example, if an electron is
going 2 x 108 m/s, b = 2/3.
Now square b and subtract the result
from 1. In our example we get 5/9. Gamma is the inverse of the square root of
this result. I.e.,
g = (1-v2/c2)-1/2.
In this example we get 1.34.
If you know g and you want v, here it is: v = c(1-1/g 2)1/2.
It turns out that mass acts like it increases by this same factor, gamma! Furthermore, it can be shown that mass and energy are two aspects of a more general entity which we can call mass-energy. (Some people say mass is converted to energy or energy converted to mass, but this kind of talk can lead to a misunderstanding of the subject.) See E = mc2 for more.
There are two possible approaches to start to develop the idea of the
constancy of the speed of light to all. One is experimental- the
Michelson-Morley experiment (which was done here in
The second approach is theoretical- if it were possible to go the speed of light and travel along side of a light wave, you could observe a spatial wave with its electric field up in one location, then down at a location half a wavelength away. If this is possible, then we ought to be able to create such a stationary wave in the lab. But we cannot. It would violate Maxwell's equations. Or to put it another way, if you succeed in doing it, you will get a Nobel prize and force the revision of Maxwell's equations and of Einstein's relativity. (We can never know that we have the ultimate truth in our knowledge of the universe.)
A thought: face, facial; space, spatial. Who invented that?
Now go back to more mundane stuff, or you might look at a little general relativity.
My main pages:
mechanics
fluids, heat, electricity and magnetism
vibrations and waves
quantum
Comments, questions: fredrick.gram @tri-c.edu