ursaminortaur wrote:MrFoolish wrote:Let's say I'm standing still in space (whatever that means). I observe a large clock with my telescope. The clock is moving at close to the speed of light. How do I see the clock evolving in the following two scenarios...?
1. It is moving away from me.
2. It is moving towards me.
I'm interested in the relative time of the moving clock compared to my own clock; and if it's appearing larger or smaller in the sky (as you'd expect with something being closer or further away).
A simple question, no doubt!
The factor used in the lorentz transformation for calculating length contraction and time dilation is (1 - v^2/c^2)^-0.5. since it incorporates the square of the velocity the time dilation and length contraction are the same whether the clock was moving towards or away from you. It should also be noted that the length contraction only happens in the direction of motion and not in directions perpendicular to that motion. Hence a clock heading towards or away from you at close to the speed of light which is face on to you would appear to be ticking slower but its clock face would only appear to be smaller because of its distance rather than because of its speed.
One difference though which you would see between a clock coming towards you versus one moving away would be that the light by which you saw the clock face would be blue shifted if it was approaching and red shifted if it was moving away.
Relativity may be hard, but talking about relativity is harder. The math is clear but words do not mean what you think they mean, a pre-Newtonian world view is baked into English.
MrFoolish asked what he would see. In this case the "appear" in the first bolded statement does not mean "see".
Imagine that there is an electrical charge on the second hand of the clock. This circling electric charge will emit a 1/60 Hz radio wave* in the clocks frame of reference. For a physical observer this will be red shifted or blue shifted depending on if the clock is approaching or receding. But the frequency of that wave is also what you see as the frequency of the clock. What is seen does depend on whether the clock is approaching or receding. The approaching clock is seen to be running fast.
The resolution is that while the approaching clock is slow in the observer's reference frame that is not something that can be seen directly. You can only "see" at the speed of light. A physical observer has to correct for the speed of light delays to figure out where and when the clock ticks appeared to occur in his frame of reference. The difference in time between two events occurring and the difference in time between the light from the two events arriving at the observer are not the same thing.
* Or whatever they call radiation in that part of the spectrum. If that bugs you add a split-split-second hand that circles at 60 Hz.