When two light sources flashlights are facing each other and turned on simultaneously what is the closing speed of the beam?

Answer 1

They close at c, the speed of light. From the frame of reference of the two flashlights, the beams leave at c, travel at c and arrive in the middle at t= d/v (time = distance over velocity--in this case v=c, so t=d/c). If you try to measure the close rate from the frame of reference of either wave front (which I suspect is what you are trying to do), the laws of Special Relativity apply. If you could ride on one front and measure the arriving front, you would measure it arriving at c, but greatly blue-shifted. Likewise if you select the other beam as your frame of reference. Confusion arises if we compare this to the closing rates of two cars traveling at high speed. The intuitive approach is to add the two speeds. But when you do that as an external observer, you are unconsciously projecting yourself into a different frame of reference. Here's why frame of reference must be so rigorously observed (and remember, you can only measure, not intuit): We take two cars moving at 60 mph on a collision course. If I stand at the starting point for car A (don't worry about acceleration times), and measure their speeds, I observe that A is moving away from my position at 60 mph and car B is approaching my position at 60 mph. The measurements are the same but reversed at the starting point for Car B. If I stand at the projected point of impact, I measure car A approaching at 60mph and car B approaching at 60 mph. The only vantage point from which I can measure a close rate of 120 mph is from inside or moving alongside one or the other of the two cars. That is the only frame of reference that permits that addition of speeds. The same applies to relativistic speeds, but at those speeds time dilation becomes a factor so cremains absolute and constant regardless of the observer's frame of reference. You can't stand aside watching the beams and intuit an additive speed.