grav

2007-Sep-09, 12:48 AM

Um, I been thinking quite a bit about this and it seems to me that in order for all observers to see light travelling at the same speed, then the rate of time for what we observe of another observer with a relative speed must be faster, not slower. Now, if length contraction shortens the other in the line of travel by gamma and time dilation also makes their clocks tick slower by gamma, then it would seem to make sense at first that light travelling over a lesser distance in a lesser time would make all observers see light travelling at 'c', right? But if time dilation is meant to counteract the length contraction for this purpose, where the other's rulers shrink in proportion to the length contraction, then they should actually measure a greater distance by laying the shrunken rulers end to end along that distance, shouldn't they?

Consider this. We send a signal to another observer with some relative speed. Let's say that they are travelling away from us at such a speed that the contraction shrinks them to half length. Then by their own shrunken rulers, they should measure the distance between us and them as twice as great, shouldn't they? Therefore, they would measure the speed of light as twice as great since it is travelling over twice the measured distance in the same time. So the only way to counteract that is with time dilation, whereas, their clocks are ticking twice as fast, not half as great. So in the same time that we see the light travelling to them at 'c' over some distance from our point of view (since we cannot go by theirs because to them nothing has changed), they will see the light travelling twice the distance over twice the time, since twice the time has passed for them, in order to also measure the speed of light at 'c'.

Even if we consider the alternate scenario where a pulse is sent between two observers upon opposite ends of a moving rod while we also observe, we would still see the pulse travelling at 'c' from one to the other, but over the shorter distance across the rod, while the travellers think the length of the rod has remained the same, so has travelled over twice the distance for them in the same time. The only way to counteract this, then, so that all observers see the light travelling at 'c' is for them to also measure the transit over twice the time, so that their clocks must be ticking twice as fast, not half as great.

This also makes sense if we consider gravitational time dilation. The stress upon a stationary object in a gravitational field will physically shrink the object somewhat. So the light will travel from one end to the other in a lesser time, and processes occur quicker, clocks tick faster, etc., in inverse proportion to the contraction of the object along the line of contraction, although I'm not sure how that would translate for the other axes.

So what am I missing here? What would the mainstream say about this?

Consider this. We send a signal to another observer with some relative speed. Let's say that they are travelling away from us at such a speed that the contraction shrinks them to half length. Then by their own shrunken rulers, they should measure the distance between us and them as twice as great, shouldn't they? Therefore, they would measure the speed of light as twice as great since it is travelling over twice the measured distance in the same time. So the only way to counteract that is with time dilation, whereas, their clocks are ticking twice as fast, not half as great. So in the same time that we see the light travelling to them at 'c' over some distance from our point of view (since we cannot go by theirs because to them nothing has changed), they will see the light travelling twice the distance over twice the time, since twice the time has passed for them, in order to also measure the speed of light at 'c'.

Even if we consider the alternate scenario where a pulse is sent between two observers upon opposite ends of a moving rod while we also observe, we would still see the pulse travelling at 'c' from one to the other, but over the shorter distance across the rod, while the travellers think the length of the rod has remained the same, so has travelled over twice the distance for them in the same time. The only way to counteract this, then, so that all observers see the light travelling at 'c' is for them to also measure the transit over twice the time, so that their clocks must be ticking twice as fast, not half as great.

This also makes sense if we consider gravitational time dilation. The stress upon a stationary object in a gravitational field will physically shrink the object somewhat. So the light will travel from one end to the other in a lesser time, and processes occur quicker, clocks tick faster, etc., in inverse proportion to the contraction of the object along the line of contraction, although I'm not sure how that would translate for the other axes.

So what am I missing here? What would the mainstream say about this?