# Q & A: speed limit

Q:
Why is it impossible to travel faster than the speed of light?
- Muhammed (age 17)
Sir George Monoux College, London
A:
Muhammed- We're getting to expect these challenging questions from you. As often happens, I'll give an answer that may be only partially satisfying.

The impossibility of travel faster than the speed of light follows directly from the form of the laws of Special Relativity. A special speed enters into these laws, which describe how to transform between the apparent coordinates used by two observers travelling at a consatnt velocity with respect to each other. It turns out that If anything were to travel above that speed, according to any observer, it would have to have infinite energy. That's not esy to get. There are some other limits too. If some conserved quantity, like electrical charge, were to travel faster than that speed according to some observer, then according to other observers it wouldn't always be conserved.

This special speed turns out to be the only speed something can travel at if it doesn't have any 'rest mass'. Light seems to be one such rest-mass-free entity, so it travels at this special speed.

Furthermore, there is a problem with causality if objects can travel faster than light. Events only seem to be able to have consequences in the future -- so far we have not been able to change what happened in the past. Travel faster than the speed of light would allow a traveler to reappear at an earlier time in a similar position, making him able to shake his own hand and create paradoxical situations, such as killing himself before he is able to go on the journey in the first place. This is related to the conservation laws problem -- if the traveler is electrically charged, say, the charge will appear to vanish from everywhere in the universe for some times, and be present twice for other times.

OK, you want to know why Special Relativity should have such weird laws. All I can say (maybe somebody else could give a deeper answer) is that the laws for transforming between different reference frames actually are logically consistent and not very mathematically complicated. We latched on to an over-simplified version classical physics) because it worked well enough for most practical purposes. Time inervals between events may depend on reference frame, but an ancestor who never thought about that possibility while chasing an antelope would not have lost any advantage to one who knew it. In fact, the simple-minded ancestor would probably have an easier time. So it's not surprising we have very strong gut feelings that time and space do not depend on refernce frames.

Mike W. (with Tom)

(published on 10/22/2007)