If there is a simple explanation for this please share it. Hear my thesis:
There is no special place in the universe in which true velocity can be measured. All speed measured is relative. Therefore if an observerA is travelling .1c relative to observerB, and observerC is travelling at .2c relative to observerB, it would seem that to observerB a vessel travelling at .999c relative to observer would be exceeding the speed of light limit to both observerA and B.
Furthermore, it is possible to perceive motion which exceeds the speed of light limit. A spaceship traveling .99c observing another spaceship traveling .99c towards it would first a. see the spaceship greatly accelerated because of time dilation, then b. see the spaceship cancel out the initial percieved speed gain also because of time dilation. So at the end of the moment, the observed velocity would be .99c+.99c. Perhaps I need to "brush up" on my studies of General Relativity, or perhaps I am right.
You're not right, fortunately! (or we'd live in a very different universe, I imagine). There was a very good discussion on this topic, in this section, a while back. I bet if you dug through or did a forum search you could find it. I'd check it out. Indi posted a link to the relevant equations, and Bikerman has a web script that will let you input velocities and see how everything works out.
| Gagnar The Unruly wrote: |
| You're not right, fortunately! (or we'd live in a very different universe, I imagine). There was a very good discussion on this topic, in this section, a while back. I bet if you dug through or did a forum search you could find it. I'd check it out. Indi posted a link to the relevant equations, and Bikerman has a web script that will let you input velocities and see how everything works out. |
I'll take your word for it. (Netscape enjoys crashing my comp!) | EanofAthenasPrime wrote: |
If there is a simple explanation for this please share it. Hear my thesis:
There is no special place in the universe in which true velocity can be measured. All speed measured is relative. Therefore if an observerA is travelling .1c relative to observerB, and observerC is travelling at .2c relative to observerB, it would seem that to observerB a vessel travelling at .999c relative to observer would be exceeding the speed of light limit to both observerA and B.
Furthermore, it is possible to perceive motion which exceeds the speed of light limit. A spaceship traveling .99c observing another spaceship traveling .99c towards it would first a. see the spaceship greatly accelerated because of time dilation, then b. see the spaceship cancel out the initial percieved speed gain also because of time dilation. So at the end of the moment, the observed velocity would be .99c+.99c. Perhaps I need to "brush up" on my studies of General Relativity, or perhaps I am right. |
No, you are missing the fundamental point of relativity. Each observer exists in their own unique frame of reference (FOR). Within that frame of reference they perceive motion relatively (ie with regard to themselves) BUT the speed of light is an absolute in all frames of reference. This means that the observer (A) who is moving relative to observer (B) observes photons travelling at c AND SO DOES observer B. If observer A is moving away from B at (say) 0.5c then observer A shines a torch, then the photons from FOR A are moving at c AND the photons from FOR B are also moving at c. This is, of course, counter-intuitive as one would expect the photons to be moving at 0.5c with respect to FOR B. The difference is accounted for by the relative time dilation.There is no absolute speed. In that point you are sort of right. Because there is no absolute context to judge it by. Light is always going 1c faster than you. Time for you is always constant although relatively it may change.
| EanofAthenasPrime wrote: |
If there is a simple explanation for this please share it. Hear my thesis:
There is no special place in the universe in which true velocity can be measured. All speed measured is relative. Therefore if an observerA is travelling .1c relative to observerB, and observerC is travelling at .2c relative to observerB, it would seem that to observerB a vessel travelling at .999c relative to observer would be exceeding the speed of light limit to both observerA and B. |
Nope.
Furthermore, it is possible to perceive motion which exceeds the speed of light limit. A spaceship traveling .99c observing another spaceship traveling .99c towards it would first a. see the spaceship greatly accelerated because of time dilation, then b. see the spaceship cancel out the initial percieved speed gain also because of time dilation. So at the end of the moment, the observed velocity would be .99c+.99c. Perhaps I need to "brush up" on my studies of General Relativity, or perhaps I am right.[/quote]
Your examples do not need general relativity, but only special relativity, since no acceleration is involved. This is fortunate because it means that normal people like me can understand the maths.
Velocities don't add the way you think they should.
Taking your second example, if both spaceships are moving towards an observer in between them at 0.99c (as measured by the observer) the velocity that one spaceship observes the other doing is given in Newtonian mechanics by:
w = u + v
where w is the velocity that an observer in spaceship w sees spaceship v doing
and v is the velocity that observer u sees spaceship v doing
and u is the velocity that spaceship w sees observer u doing.
i.e. w --0.99c--> u <--0.99c-- v (from u's frame of reference)
and w <-- 0.99c-- u <--1.98c-- v (from w's frame of reference)
In special relativity the velocities add up as w = (v + u) / (1 + vu / c squared)
So w = (0.99c + 0.99c) / (1 + (0.99c)squared/c squared)
i.e. w = 1.98c / (1.9801) = 0.9999494975c
So even though both space ships are rushing towards an observer between them at nearly the speed of light, the speed of one space ship from the other is still less than the speed of light.
