It also seems that, if each kilometer is thought of as expanding over a period of time, wouldn't much of the expansion between us and the other star be happening behind the light as it traveled? To my mind, this means that any light we're seeing didn't actually travel the entire distance from there to here.
This is essentially correct. See
page 11 of Steven Weinberg's
Cosmology for starters, but check out chapter 1.6 (page 46) for accelerated expansion. I have been attempting to calculate the distances in question that I might be able to give an answer myself, but my calculus isn't up to it yet, and I'm pretty sure you'd not want to wait around. (I'm not allowed to take calculus or physics till next year.)
I seems to me that if the velocity of expansion at the emitter is Hd, and the velocity of expansion of the absorber is 0, then the average velocity of expansion for the trip would be Hd/2. But this may be a violation of point 5.
However, I offer some corrections to statements in preceding posts:
- In an accelerating universe the observable universe is getting smaller as the distance at which the expansion becomes superluminal draws nearer.
- Don't think of it like trying to throw a football to your friend who is running away from you, while you are running backward. Firstly, that would be an effect caused by their own peculiar motion rather then cosmological expansion and there are significant differences. Secondly, lest one confuse the velocity of the two travelers as being subtracted from the velocity of the ball it's best not to. This is exactly the idea that SR flees screaming from.The photon emitter and the photon absorber would both see the photon moving at c.
- There can be no center of the Universe.
- The energy of the light is not conserved. Wave length is inversely proportional to energy. Red-shift = longer wave length = lower energy.
- It seems like I'm making it harder than it needs to be. Particularly bogus and non-triumphant.
Correction I: In point number 4 I wrongly understood Taq to mean that the photon retained all of its energy. I used a bad choice of words, of course the energy is conserved.
Correction II: Upon further reading I'm less certain of this, but I don't abandon it yet. In an accelerating universe atoms will eventually be torn apart by expansion. Where would that put the horizon?
Edited by lyx2no, : Grammar
Edited by lyx2no, : Consistency.
Edited by lyx2no, : Missed point 3.
Edited by lyx2no, : Bad choise of words.
Edited by lyx2no, : Correction II.
Genesis 2
17 But of the ponderosa pine, thou shalt not eat of it; for in the day that thou shinniest thereof thou shalt sorely learn of thy nakedness.
18 And we all live happily ever after.