4 Sep 2005 [To Steuard Jensen] >> Will the light beam still bounce back to the receptor... >> >> 1. During acceleratiion? > > No. From the point of view of an observer on the rocket, the light > bends in the "gravitational field" that she feels. Because it > bends away from its previously straight path, it will miss the tiny > mirror. > > From the point of view of an _inertial_ observer outside the rocket > ship, the answer is still no (remember, all observers must > certainly agree on the answers to "physical" questions like "did > the light reach the receptor"). > > Imagine that from his point of view, the rocket had been moving at > some constant speed when the laser and mirror were aligned. Then > what he saw at that point was that the laser was carefully aligned > to aim at where the mirror _would be_ when the light got there > (much as a football quarterback throws a pass to where he expects > the running receiver to end up). > > But when the rocket starts accelerating, the mirror will keep > moving faster _after_ the laser has already been aimed and fired. > Because the mirror ends up moving faster than the laser was set to > expect, the beam of light will miss. To continue the football > analogy, imagine that the quarterback throws the ball, but then the > receiver speeds up faster than the quarterback expected. The ball > will fall behind him, for an incomplete pass. > > Does all that make sense? Yes, it confirms what I thought the answer was. >> 2. At the end of acceleration (once again in uniform motion but >> without deceleration)? > > Yes, the laser will hit the mirror and bounce back to the receptor. Oops. Here is one point where I have a problem. My brain is thinking that even though the space ship is once again in constant speed, it is going faster than it was before the acceleration took place. Previously, the beam was aligned to hit the top mirror at the point where the mirror would be by the time the beam got to the mirror. If the mirror has not been adjusted for the new, faster speed, won't the alignment be off at the new, faster speed, since the beam is aligned to hit the mirror at the point the mirror would have been at the slower speed. I know that is convoluted language, but do you get my concern?? In an earlier portion of your last answer you stated: "Then what he saw at that point was that the laser was carefully aligned to aim at where the mirror _would be_ when the light got there (much as a football quarterback throws a pass to where he expects the running receiver to end up)." If the rocket ship is now going faster, wouldn't the beam have to be adjusted to lead the receiver by a bigger margin before we would get a bounce back? > From the point of view of the observer on the rocket, the > "gravitational field" has now gone away. Thus, the laser's > previous alignment is no longer being disturbed, and the light will > bounce off of the mirror just as it did before. > > From the point of view of the observer who was in an inertial frame > the whole time, the laser is once again aiming at just the right > angle ahead so that it will hit the mirror. That angle has to be > different, of course, since the rocket is now moving at a different > speed than it was before. Okay, the above statement seems to confirm that at the new faster constant speed the beam would not hit the mirror unless and until the angle of the beam were adjusted to account for the faster speed. Is this interpretation of what you said correct?? > But if you give it a few minutes' thought, you'll see that it's not > surprising that the angle looks different now: that doesn't even > depend on relativity. To use a different sports analogy, imagine a > pair of basketball players inside a train car (one with lots of > windows so that we can see in), passing the ball back and forth > perpendicular to the direction the train is moving (perpendicular > from their point of view!). If we watch them doing this from the > outside, we will see the ball moving in a zig-zag pattern: the ball > "inherits" the motion of the train along the tracks even though the > people inside feel like they're passing it straight back and > forth. The same thing works for our laser in the rocket ship (even > if the math involved in "inheriting" the motion is a bit more > complicated when relativity is involved). > > This basketball player example can give some insight into the > acceleration part of your scenario, too. If one player passes the > ball but the train accelerates before it reaches the other player, > the pass will go off center (because it was aimed at where the > receiver was supposed to be before he accelerated out of the way). > But once the train's speed stabilizes again, their passes will stay > on target... and the observer on the platform will see a more > "stretched out" zig-zag because the ball is now "inheriting" the > train's faster sideways speed. > > I hope those explanations aren't overly complicated! But let me > know if I've managed to make things more confusing instead of less. :) Still on this same point, in case I have misunderstood you, I understand a basketball inheriting the speed of the train. However, I thought light was special and did not inherit the speed of the emitter. Am I getting in deeper or am I starting to see the light? I can't tell. >> If the photon beam misses the mirror during or after acceleration, >> that supports the previous idea of the light pulse from one space >> ship reaching the other space ship even though the two ships are >> receding from each other at 120% the speed of light. But then, it >> also seems to support some kind of stationary spatial concept >> (similar to but not identical to the ether idea), doesn't it? > > The light pulse from one ship will most certainly reach the other > one, but _without_ any need for a notion of "stationary space". > Let me explain what each of the three observers sees, given your > premise that one observer (on Earth, say) sees each ship moving at > 60% of the speed of light in opposite directions. > > From the point of view of the emitting ship, the other ship is not > moving away faster than the speed of light. (In fact, when you > work through the math, people on the emitting ship will see the > other one moving at about 88% of the speed of light.) So they > certainly expect to see the light catch up with the other ship > eventually. Why is this? If they are receding from each other at 120% the speed of light, why does ship A think ship B is moving away at 88% of the speed of light. Is it because light emitted from (or bouncing off of) ship B will reach ship A because ship A is receding from the point of emission (or bounce) at on 60% of the speed of light? > From the point of view of the observer on Earth, the light pulse > still moves at the speed of light, even though it was fired > "backwards" from the emitting ship. (That's where the weirdness of > relativity comes in.) So the Earth observer certainly expects to > see the pulse of light catch up with the receiving ship eventually. I think I'm okay with that. > From the point of view of the observer on the receiving ship, the > light pulse _still_ looks like it's moving at the speed of light. > Given that that observer thinks that he is sitting still, he will > expect the pulse of light to reach him without trouble (it won't > even have to "catch up" with anything!). > > > But for the record, the three observers won't agree on everything! > If the emitting ship emits a _series_ of pulses (say, one pulse per > second as they measure it), the three observers will disagree on > what the rate of pulses is. Okay, I think I get that. > The Earth observer will see about one pulse every [1.5] seconds, and > the receiving ship will see about one pulse every [2.1] seconds. For > that matter, since the frequency of light determines its color (and > since frequency is a lot like a pulse rate), the Earth observer > will see the pulses a bit more red than the people on the emitting > ship do, and the people on the receiving ship will probably see the > pulses all the way down in the infrared range (and hence invisible > to the naked eye). I'm okay with that, too. >> If the photon beam hits the mirror during or after acceleration, >> doesn't that support the idea that the travel of the light is >> somehow related to or influenced by the acceleration or >> deceleration of the emitter? > > That's at least somewhat accurate, too. But only in the sense that > I discussed with the basketball player example: if I see the > emitting device moving, then I will see that motion "inherited" to > some extent in the motion of the emitted light. If another > observer were in the rest frame of the emitter, she wouldn't see > any motion of the emitter that the light could "inherit". So the > motion of the light is "influenced" by the motion of the emitter > only in a fairly weak sense: things that travel together, travel > together, no matter who's watching. Tilt! I'm a lost again. I don't get how the light beam inherits the motion of the emitter. I guess that is the central question I am hung up on. Does it inherit the motion of the emitter, and if so, how, why and to what degree? Certainly not to the same degree as a bullet from a gun or basketball being tossed, does it? If my previous interpretation of what you said was correct, then it seems (assuming our ability to construct measuring devices of nearly infinite accuracy) that we would be able to calculate the speed of the light clock through space by measuring the changes in the angle of aim required to hit the mirror. But if that is true, that indicates there is some sort of stationary point in space that is the reference point for speed. And, it seems like that point would be the point where the light beem started its travel. Am I going in circles?