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Beyond the speed of light...

Date: Wed Oct 23 20:19:43 1996
Posted by: Matthew Barchok
Grade level: 10-12
School/Organization: Madison High School
City: Madison State/Province: Ohio
Country: U.S.A.
Area of science: Physics
Message ID: 846119983.Ph


Ignoring the factor of gravity from other objects, if two extremely massive objects (with the mass of the sun or greater) were moving towards each other at nearly the speed of light, wouldn't their gravities cause them to accellerate to beyond the speed of light before they collided? Or, if I understand physics correctly, wouldn't both objects turn into energy?

I remember thinking this once when I was first learning about relativity. Couldn't a rocket going just under the speed of light just burn a little more fuel and go past it? Unfortunately, the Universe doesn't work that way.

Albert Einstein, when he formulated the theory of Relativity, was able to describe this problem using math. He found that as you get near the speed of light, the energy it takes to increase your velocity starts to increase very rapidly. The equation looks like this (I'll explain all the variables in a moment):

Energy= constant x  -----------    - 1
                       /     v^2
                     \/  1 - ---

This may look complicated, but it isn't too bad. "Energy" is the energy associated with the velocity, that is, the kinetic energy. For example, it takes more energy to get a baseball moving at 100 kilometers an hour than to get one going at 50 kph. "v" is the velocity at which you're moving, "c" is the speed of light (from the Latin word for light, "celeris"), and "constant" is just a plain old number that doesn't concern us here.

Now look at the number under the square root sign. As your velocity gets near the speed of light, v^2/c^2 gets very close to being equal to 1. 1 - 1=0, so the square root goes to zero. But wait! It's in the denominator, the bottom of the fraction. Anything divided by 0 is infinity! So what this is saying is that as you get very close to the speed of the light, the denominator "blows up" and the energy needed to get to the speed increases very rapidly. It would take infinite energy to go at the speed of light!

This is why the speed of light is considered to be a cosmic speed limit. No matter how fast you go, no matter how much energy you pour into your velocity, you can never quite reach the speed of light. Accelerating through a gravity field still means adding energy to increase your velocity, but you still just cannot ever reach c.

In your example, both objects don't turn into energy either. A very odd thing happens... they reach infinite mass! As objects approach the speed of light, their masses get larger (as observed by someone outside). The amount the mass increases is governed by an equation very similar to the one above. As the velocity gets near the speed of light, the mass increases to infinity. It's just another reason why you can never go at the speed of light.

One more thing: this is only true for things with mass. Photons, or particles of light, have no mass, and so they can go at c. As a matter of fact, it's thought that if you have no mass, you must travel at the speed of light. As someone once pointed out, the Universe is not only weirder than we imagine, it's weirder than we can imagine!

©2008 Phil Plait. All Rights Reserved.

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