QUESTION #169

If you're in a car traveling at the speed of light and you turn your headlights on, does anything happen?

Your question contradicts Einstein's Special Theory of Relativity which states that no object with mass CAN travel at, or above, the speed of light (c). As your car approaches c, its resistance to acceleration (mass) increases so that it would take an impossibly infinite force to actually reach c. Your question, then, is based on an impossible premise. It's like asking 'What would happen if I reached the North Pole and kept going north?'

As you approach the speed of light with your headlights on, however, you would still measure the light beam racing away from your car at 186,000 miles per second (c). A 'stationary' observer watching this happen, though, would not then measure the beam's speed at almost twice c. Relativity says that all observers always get the same measurement for c.

While that may not sound logical or plausible, it happens because what we normally think of as fixed concepts--length and time--are both variable at high speeds. If you observed a car travelling past you at close to c, its length in the direction of travel would appear shortened and the passage of time on board would appear slowed down.

Although these ideas sound strange to all of us not used to moving at relativistic speeds, they have all been confirmed experimentally.
Answered by: Paul Walorski, B.A. Physics, Part-time Physics Instructor

First of all, you need to realize that when you say you are traveling at the speed of light, that has to be with respect to, or relative to, something else. It is an underlying fundamental assumption of Einstein's special theory of relativity that uniform, non-accelerated motion has no meaning of and by itself. That is, there is, by assumption, no meaning to the idea of moving uniformly at the speed of light in an empty universe. That state is completely equivalent to being at rest in an empty universe..

I preface my answer with this comment because it leads immediately to the answer to the question. Imagine that you are in your car 'traveling at the speed of light' and that you turn on your headlights. That state of motion is utterly equivalent to being at rest in an empty universe. Since, when at rest, the light from your headlights would be launched forward from your car at the speed of light, relative to you, with a certain color spectrum, that is exactly what would happen if somehow you could be moving instead at the speed of light.

In other words, the presence or absence of other objects or matter in the universe relative to which, if present, you could make a determination that you were moving at the speed of light makes absolutely no difference to your own experiences and experiments. The light that you launch behaves in exactly the same way whether the other referential matter exists or not.

This leads into another interesting question, however. And that is whether the rest of the matter (mass) in the universe in some way affects your own local observations. So far this question has come up in relation to theories of gravity. If effect, the question is how does the universal gravitational constant, G, which determines how strongly gravitating masses attract each other, know what value to assume if there is no other mass in the universe. Mach proposed, essentially on philosophical grounds, that G must be determined by the sum total of all of the mass in the universe. Einstein assumed in his General Theory of Relativity that G is simply a universal constant, independent of the specific mass distribution of the universe. On the other hand, Brans and Dicke later proposed a so-called scalar-tensor theory of gravity in which the local value of G depends upon the rest of the mass in the universe through an additional scalar field that does not appear in Einstein's theory.
Answered by: Warren Davis, Ph.D., President, Davis Associates, Inc., Newton, MA USA