| From: Fluffy | 5/08/99
23:47:04 |
| Subject: Faster than the speed of light? | post id:
28820 |
| Heya, Okay, they say that travel at/faster than the speed of light is impossible. Earlier today Dr Karl had a question from a caller that involved a brief discussion on this topic. Basically, the deal was, you can't travel at the speed of light. The situation involved a vehicle travelling "near" the speed of light, but at 1m/sec slower than light speed. Let's re-use this scenario. We're in a craft travelling at 1m/sec slower than the speed of light. You're at the bow of the ship, I'm at the stern. You say, "Hey, come up the front". If I walk at 2m/sec from the stern to the bow, am I not travelling faster than light speed? Comments please. I need some clarification on this one. Cheers! Jamie | |
| From: James Richmond (Avatar) | 6/08/99
0:47:12 |
| Subject: re: Faster than the speed of light? | post id:
28849 |
| Common sense rules for the
addition of relative velocities are quite accurate at "low" speeds (i.e.
where neither of the two objects being considered is travelling at a
reasonable fraction of the speed of light). However, the common sense
rules are not totally correct, and must be modified if we are to consider
"high" speeds. Consider a spaceship travelling at 99% the speed of light as seen by some "outside" observer. A person walks from the stern to the bow at 2% the speed of light (a brisk walk!) as seen by someone who is stationary relative to the spaceship (i.e. this spaceship observer is also travelling at 99% the speed of light as seen by the outside observer). Common sense tells us that the outside observer will see the walking person travelling at 99 + 2 = 101% the speed of light. But the common sense rule breaks down in this situation because of the large speeds involved, and we are forced to use the full relativistic formula for velocity addition to get the right answer. Here it is: w = (u + v) / (1 + uv / c2). In the formula, u is the speed of the spaceship as seen by the outsider, v is the speed of the walker as seen by someone on the spaceship, c is the speed of light, and w is the speed of the walker as seen by the outsider. Plugging in the relevant numbers here, we find that when u is 0.99c and v is 0.02c, w is 0.99039c. In other words, the outsider sees the walker moving at 99.039% the speed of light (certainly NOT faster than light). The speed of light itself is constant for all observers, regardless of their state of motion. If you're in a car travelling at close to the speed of light and turn on the headlights, both you and all other observers travelling at constant velocities relative to you see the light from the headlights propagating at the same speed (299,792,458 m/s) as it does when the car is stationary. Notice that in the relativistic velocity addition formula, if both u and v are much less than the speed of light c, then the term uv/c2 = u/c times v/c is a number much smaller than one. In this case, the formula reads w = (u + v) / (1 + something very small compared to one) which is approximately the same as the common sense formula w = u + v JR | |