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admiral

Light Speed Limit: Math

Monday, June 4th, 2007 by admiral

The best reason for the light speed limit is that the universe is not infinite. When you look at your monitor, the image appears clear. Look closer and the screen is made up of little glowing dots. If the Universe is made up of little dots of space, then light would have to pass through each ‘point’ in space to get from its source to its destination. That would require everything in the Universe to move at a maximum speed because distance would be inescapable.

I believe that I promised you math in this tirade. As a stand up philosopher, I have no intention of giving you the kind of math that you could be tested on. Instead, I am only going to touch on the source of the math. These tirades are too short for me to go into anything in great depth.

Let us build a clock. This is going to be a simple, but very large, clock. A laser fires against a mirror and the beam takes one second to get back to the detector. This would require that the mirror be about 150 Million meters from the laser and detector. So, we’ll only build the clock in our minds.

Put this clock model on the USS Speed Demon. The beam of light moves to the front of the cabin and bounces back to the laser beside your seat in first class. Feel free to give yourself a seat in first class. Inside the cabin, the clock must keep perfect time or you will know that you are moving very fast. When the beam fires, it is moving at light speed minus the speed that the ship is moving, because light cannot go faster than the speed of light.

When the beam bounces, the detector is moving at the speed of the ship toward the mirror. Even if the beam of light stood still, it would reach the detector because the detector is moving toward where the mirror was when the beam bounced off of it. But, the math requires that the clock be turned to shoot across the cabin instead.

If you fire the laser off across the seat in front of you, the beam of light appears to be moving in a strait line to the passengers of the USS Speed Demon. However, if you see the clock from outside of the ship, the beam of light is moving in the shape of a triangle. Trigonometry allows you to do math with the results.

The beam of light is now moving further than it was when it was facing the front of the cabin. The mirror is moving sideways when the beam is fired at it. In addition to moving toward the mirror, the beam now has to move sideways to catch the mirror and keep moving sideways to hit the detector. Since light has a fixed speed to it, this takes more than a second. For you to not notice this, an actual second has to be longer than it was earlier. And, that is where the math comes from.

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