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Q & A: Car traveling at the speed of light?

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if you were in a car traveling at the speed of light and turned on the headlights, would a beam of light project outwards? or would the light simply not light up the area in front of the car?
- Anonymous

The good news is that cars do not travel at the speed of light. Only massless particles, like photons, may travel at the speed of light, and in fact massless particles may travel at no other speed. An object which has some mass, like a car, requires ever more energy to accelerate it to speeds approaching the speed of light, and no matter how much energy you give the car, it will always travel at a speed less than the speed of light.

The question might then be what would the situation be like if the car were going at 0.9999999 times the speed of light? If you are in the car, and look only at stuff which is traveling along with you at your speed, you would not notice the difference, and the headlights will work normally. If another car is ahead of you traveling at the same speed, then your headlights will light up that other car and you will see it normally. This happens because the laws of physics are the same in all inertial frames of reference (where "intertial" means "moving uniformly without accelerating". Rotating also involves acceleration, so the frame of reference cannot turn).

The road might look strange, however. It will appear to be shortened (Lorentz contracton), and the photons from your headlights will bounce off of the road and back at you with very large energies because of blueshifting. You may not see your taillights reflected on the road either (they will be redshifted), but the car behind you traveling at the same speed will be illuminated by your taillights in the normal way.

If you are not in the car but are standing at the side of the road, then the headlights of the car will make a beam of very high-energy photons (maybe x-rays, maybe gamma rays, depending on how fast the car is going). The light rays from the headlights will actually not spread out but will become more directed along the line of motion of the car because the component of the momentum of the photons along the car's direction will increase due to blueshifting but the transverse components will stay the same.

Tom J.

(republished on 07/23/06)

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