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Who said nothing can go faster than light
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David and Fred were two friends studying physics at the same University. They were both science fiction buffs and had a common dream of one day becoming astronauts and flying to other worlds. To take a break while studying difficult subjects such as electromagnetism and those famous Maxwell's equations, they would indulge in watching some episodes of Star Trek, again and again.
One such evening, after watching the Enterprise zooming through space at warp speed, David turned to Fred a glass of beer in his hand and said pensively, "My wish is to become a great physicist and be able to discover a theory that would manage to break away from Einstein's speed barrier. I would then demonstrate, experimentally, that it is possible to move something faster than the speed of light! Unless we can do that, we can forget about exploring other habitable worlds and hopefully find other intelligent creatures there."
Fred looked at him incredulously and replied condescendingly, "I think you had too much to drink, but if you're serious, well good luck to you! Just remember that many a great minds have tried to disprove Eistein and none has succeeded so far. If you try, you have to be ready for an upward battle with very little chance of success-but I am open minded, as any good future scientist should be. In fact, I'll be happy to be the first one to congratulate you when you receive your Nobel Prize!"
David, the more serious of the two, responded with an embarrassed smile, "Don't make fun of me, it's not a crime to hope, is it?"
"Of course not," said Fred indulgently. He had a great sense of humour and did not take himself or others too seriously. After sipping his beer while pondering about his friend's comment he went on. "Wait a minute, didn't you said that you would like to be able to move 'something' faster than the speed of light?"
"Well yes, that's what I said." He replied, staring at him surprised at the question.
"Then, let me tell you that I can do just that right now."
"Come on, stop making another of your jokes."
"No, no, I'm serious. In fact, I'm ready to bet you $50 that I can show you that I can move something faster than the speed of light."
"Your're on, but I'll hold you to your word then. In fact, I've already decided how to spend your $50! But how long do I have to wait for this demonstration? I hope it's within my lifetime," he said mockingly.
"No, no, in fact I'll do it the first evening it's cloudy."
"And what has that to do with anything?
"Wait, you'll see. In fact I would have done it today but I can't because the sky is clear and the moon is out."
"I won't even try to make sense of what you're saying. You're obviously pulling my leg, or you've had too much to drink. Be it as it may, I can use a break. Call me as soon as you decide that the sky and the stars are in the place of your liking!" David said laughing in his beard.
On these words they parted both in good spirits.
The very next evening Fred called David, "Come to my house-tonight's the night. I'll do what I promised-and don't forget to bring your $50."
"I'll be right over. Make sure you have lots of beer. I'm ready to have a good laugh."
Fred took his friend into the garden. It was a nice overcast evening with just a small breeze.
"Where is your magic machine for the demonstration?" asked David with a sneer. "All I see is you holding in your hand a pair of binoculars and a little gadget."
"Well, that little gadget is a powerful small laser that my parents offered me for Christmas. Ok, so here's the thing. I will now turn the laser on and direct it straight above our heads. Take these binoculars and try to see the spot the laser beam makes on the cloud."
David took the binoculars and after a short while claimed, "Yes, I see the spot-but only fleetingly. Obviously your hand shakes too much!"
"This is not a physiology test to find out how steady my hand is. I only want you to confirm that you can see the spot on the cloud."
"I already said yes. So what?"
"I listened to the airport weather forecast just before you came in. It said that the cloud ceiling is about 1000m. Would you accept this?"
"It sounds reasonable, yes I'll buy that," he said grinning.
"Now just a little bit of geometry if you don't mind."
"You didn't tell me that your demonstration would require me to work! But I'll be a good sport-Go head."
"Thanks. You'll see it will be painless. If I point the laser 45 degrees to the left of the direction straight above our head and then move all the way to 45 degrees to the right, the spot will have moved a total distance of about 2000m over the clouds. You can work it out later if you want."
"No, its about right. Go on."
"Would you further accept that I can sweep the laser spot on the cloud by moving my hand from left to right over the full 90 degrees in about one second?"
"I'll grant you that."
"Then, since speed is given by dividing distance by time, the spot will move over the cloud at a speed of 2000 m/s, or more than six time the speed of sound!"
"That is surprisingly fast," admitted David "but still far from the speed of light."
"I agree with you. But now, I'll ask you to use your imagination and do with me a thought experiment, as Einstein always did."
"You want to flatter me by putting me in his league. OK, you succeeded; my imagination is fully awake! Go on."
"Suppose that instead of the clouds, tonight was clear and the full moon was over our heads. Its average distance from earth is about 400,000 km and its diameter about 3500 km. Now suppose that I have a more powerful laser and sweep its beam across the moon. The angle I would have to cover is tiny, only about .5 degrees. I think you will also agree that I can sweep the laser beam through a full 180 degrees in one second."
"OK I accept that."
"Therefore, as I sweep, the laser spot will intercept and pass through the moon in about .003 sec. That works out to a speed of close to 1.2 million km/sec. But this is four times the speed of light! Do you agree with me so far."
David pondered for a while and answered hesitantly, "I don't see off hand how this can be possible. There must be something wrong with your argument."
"No, there isn't. You worry that it contravenes the laws of physics. But it doesn't. The photons from your laser still travel towards the moon at the speed of light, but only the spot moves faster. You see Einstein's theory is not in peril! On the other hand, I did prove that I could move "something" faster than the speed of light. I therefore won my bet-hand me over the $50!"
David pulled $50 out of his wallet and handed it over reluctantly. "Remind me never to bet with you in the future. You're too tricky for me."
"Don't feel bad, next time you'll probably get me!"
Quickly David recovered his good humor. They went back in, put their feet up, opened their bottle of beer, and became quickly engrossed in a serious discussion about group and phase velocity...
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© 2007 Armand Waksberg
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