This is really starting to annoy me. Its possibly one of the simpliest parts of the special theory of realivity but its not clicking. I keep on asking myself why, I get it explained, I understand it for a few...then the next time it comes up its just goes over my head and Im asking why once more. Something's not clicking and when that happens its either because Im missing something, or there's something wrong with the whole thing. So it has to do with the classic example of the car speeding away from the clock near the speed of light. What I don't understand is, why does the clock appear to be clicking slower? Lets say the guy in the car's name is Bob. Bob looks back the clock. Since the clock is speeding away from him at .9c, time dilation will occur and the clock will be going slower, I get that. But then I have it explained to me that it takes each individual light particle to get to Bob since hes moving away so fast. That makes no sense to me because then light wouldn't be going C anymore, it'd be going slower relative to him kinda like a bullet being shot at a moving car. Is there something Im not getting or can I assume the explainer is wrong? The taking the same scenerio, lets say Bob speeds towards the clock at .9c. Time dilation will still occur, the clock will still slow down so the light particles are neither reaching him any quicker or slower than it would if he was sitting still right?
And then...lets say there are Ashley and Bob go straight at each other at .9c then flash then send a pulse of light at each other. For some reason I can't even think of the results, probably beucase its like 2:30 in the morning right now. But how fast would they be going relative to each other?
As written it appears their speed would be 0.9c but having asked the question I think you meant each had a velocity of 0.9c relative to some initial inertial rest condition. In the later case the SR answer is v = 0.994475c, not 1.8c as intution would have you think. The formula called "Velocity Addition" is v' = (v + u) / (1 + vu) where v and u are the two respective velocities being considered.
Ok but to a third observer (lets say John), both Ashley and Bob have the same time dialistic effect since, relative to John both Ashley and Bob are going the same speed, but relative to each other, Ashley and Bob both have different time dialistic effects. If they were both to deaccelerate at the same rate at the same time to 0 velocity, then who would have aged faster?
Sorry, according to John. For some reason I thought it would be the same for all, I just realized though Ashley and Bob would disagree with each other... which kinda answered my question, but Im still unsatisfied. Can someone predict the outcome?
Sure, just use the Lorentz transform. You will get the "official" answer every time. -Dale PS One nice shortcut to keep in mind for these kinds of problems is that "aging", or elapsed proper time, is equal to the spacetime interval and is a Lorentz invariant quantity. So for any worldline between any two events John, Ashley, and Bob will all agree on the aging measurement.
