Suppose you're traveling on a space ship at 9/10 the speed of light (.9c). You have a high-powered rifle that shoots bullets at the same speed. Suppose you shoot the bullet perpendicular to your direction of travel.

It appears that the bullet would travel at a 45-degree angle (northeast, if the ship is traveling north and the bullet is shot eastward), at about 1.2728c which is faster than light. Why is this wrong, and what would the actual speed and direction be?

(In reply to re: First thoughts. by Ken Haley)

>>you're on the right track, but not quite there.

Which is why I titled my response "First thoughts" and gave it an unlit lightbulb. I suspected that theta is no longer 45 degrees, so my answer would be incomplete, but it will take some contemplation before I come up with why and find out what it is.

>>To clarify the difference between speed and velocity: Velocity is just speed with a direction attached. Velocity is a vector quantity, whereas speed is simply a scalar (just the rate of movement without any particular direction specified). This is true whether you're speaking in terms of classical or relativistic terms. (Note that c is the "speed of light" not the "velocity of light".)

Yes, that goes without saying. My point was that the direction is as important as the speed in solving the problem. You verified with this when you stated "Nonetheless, you definitely do have to think in terms of speed and direction (ie, vectors) to solve this."

>>The point you make about what the speed is relative to (which is a valid point), would also apply whether we're speaking in classical or relativistic terms.

Which is why I phrased the comment the way I did (as "get[ting] away with ... [not] mentioning the reference frame" in Newtonian physics").

>> We don't need to specify what the at-rest frame is in order to understand and solve it.

>>Nonetheless, you definitely do have to think in terms of speed and direction (ie, vectors) to solve this.

The second statement (along with the whole basis of Relativity) disproves the first (at least in the most rigorous understanding of the problem). However, you are right in that it is easy enough to re-create the missing details in the thought experiment.

Posted by TomM on 2005-01-18 07:52:01