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Question:
If it were possible to travel in a car at light speed, and...you achieved light speed with your headlights off, and...you then turned on your lights, what would happen? Since you are traveling at the same speed as the light from your headlights, would they "light your way"? I teach H.S. Earth/Space Science and this question comes from my 16 year old son. He is really beginning to show an interest in Physics so I want to make sure he gets the right answer and not just "Mom's best guess". Thanks.



Replies:
You have stumbled straight into relativity, which does not lend itself to intuitive explanation. For what it is worth, the speed of light is a fundamental constant. The speed of light is the same in all reference frames. This is highly counterintuitive. If you observe a photon approaching you at the speed of light from your left, and another one from your right, they both appear to have speed c, the speed of light. If you place your frame of reference on one of the inbound photons, you may expect that the other photon would appear to be approaching with speed 2c, but it does not. It appears to approach at the speed of light, c. I wish I could explain this easily (I would be the first person to do so). There is much literature on this in any introductory book on relativity, and much has been written in layman's terms as well.


As an object with a nonzero mass reaches higher and higher velocities v, the force required to accelerate it increases without limit. You cannot reach v = c (c being the speed of light) in your car, because an infinitely large force would be required to accelerate you to that speed. However, you can get as close to v = c as you like by simply installing a larger and larger engine and gas tank. With the V-8 from an old GTO you should easily be able to attain 99% of c or better.

Ahem. Well anyway. When you are very near the speed of light, as others have mentioned, your headlight beams will of course depart from you at c from your point of view, the constancy of c being a cornerstone of modern physics. (If they do not, by the way, you are encouraged to write to "Physical Review Letters" as soon as you slow down.) So they will light your way. Or sort of. Because as you approach c objects and distances in your path will appear to contract, and the garbage truck that pulled out six blocks ahead of you will seem to have done so only inches ahead, and even at the speed of light the reflection from your headlights will not get back to you in time to do much good. Hey, that is why we have speed limits. An amusing book for your son is "Mr. Tompkins in Wonderland," by George Gamow, which relates tales of what would happen if c = 30 MPH, say, or Planck's constant were so large that ordinary objects had strong quantum mechanical behavior.

christopher grayce


This is a great question. Even if it is difficult to move at the velocity of light, it is important to ask the question that push our understanding. The important idea behind special relativity is that no matter what speed you are moving the speed of light for you is the same as anyone else. So, in your car moving at almost the speed of light, the light from the headlights will v move off from the car at the speed of light. In relativity speeds do not combine by simple addition. If you want to know something about the formula, let me know by email or by another question. Your source of questions is a very smart person who is thinking like a scientist. Our favorite question is "What if?"

samuel p bowen



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