Inquiring Minds

All About Light
All About Light Main Page  |  Classical  |  Relativistic  |  Quantum

Relativistic - 0.9 Plus 0.9 Is Never 1.8

c and Einstein  |  c Top Speed  |  Speed & Speed  |  Faster than c?
Mass Gain  |  E=m*c^2  |  Age Slower  |  Time Dilation  |  Twin Paradox
Dopper Shift  |  Ticketed  |  Simultaneity  |  Competition  |  Fast Strudel
Paradox? No!  |  Confusions  | 
On the previous page I stated that the speed of light in a vacuum is the ultimate speed in our universe. But you might say, "What?? Why do you say that?" There are many counter examples:

Imagine you are traveling in your car with a speed of 50 mi/h with respect to the road. If you have an apple in your hand and you throw it forward with speed of 20 mi/h with respect to your car, everybody knows that the apple will hit the road with a speed of 50 + 20 = 70 mi/h.

Thus one can easily create objects traveling faster then the speed of light!! How? Take a car traveling with the speed of, let's say 90% of the speed of light in a vacuum. Throw the apple with a speed, again, of 90% of c, but with respect to the car. What you eventually get is an apple traveling with respect to the road with a speed 1.8 times higher than the speed of light !!! Got it? But wait a minute. Didn't I say that nothing can exceed the speed of light?

The solution is hidden in the title of this page. Einstein's theory of special relativity dictates a different law for adding velocities. We cannot simply take the scalar sum of the speeds! For completeness I will show you the formula for adding two velocities (car with respect to the road) and (apple with respect to the car). Relativity theory dictates that the resulting speed (apple with respect to the road) is given by:

Try this exercise yourself. You'll find that no matter what speeds and you enter (assuming they are less then c), is always smaller than the speed of light!

On the next page I will discuss the fact that at Fermilab we have particles moving with speeds higher than the speed of light!!!

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last modified 1/5/2001   email Fermilab