Suffice to say, then, light emitted a billion years ago has travelled substantially farther than a billion x 9.46e12 km, according exactly to how much the bit of universe it traversed expanded on the way.
No, the other way around - the distance light would have travelled if the universe had stopped expanding at the time it was emitted would have been a lot less than a billion light years. The light ended up travelling a billion light years because of the expansion.
Try a thought experiment. You're driving at 60mph between two towns on a straight road that's 10 miles long when you set off but is growing in the direction of travel. You arrive an hour later - how far have you travelled?
You contradict yourself. In that billion years, either the light travelled (1) a distance we call "a billion light years (a measure adjusted to account for expansion of space during transit)", or (2) it travelled "more than a billion light years (a measure that neglects expanding space)". In either case, substantially greater than 9.46e24 meters.
If the road grew while I was on it, then it would take longer than an hour to get there. If it took an hour to get there anyway, I went faster than 60 mph. If I went 60 mph for an hour and got there, then the road did not grow.
You can fool with "light years" as a unit all you like ("instantaneously 9.46e12 m, but more as travel time increases"), but you don't get to fool with meters. If no numbers change, expansion is meaningless, the only thing that changes is light wavelengths. Then you are just talking about tired light.
> If the road grew while I was on it, then it would take longer than an hour to get there. If it took an hour to get there anyway, I went faster than 60 mph. If I went 60 mph for an hour and got there, then the road did not grow.
I'll start with this because it's the easy one and I think you've maybe just misread. The road is 10 miles at the outset. Your speed is 60mph. If the road doesn't expand, the journey would take 10 minutes. Instead the journey takes an hour - 60mph for one hour is 60 miles. So in total you've travelled 60 miles. To switch back to our 'light travelling through space' discussion, by analogy - light travels at C; if light travels for 1 billion years, it travels a distance of C * 1 billion == 1 billion light years. When it set out on its journey towards us, the distance between there and here was less. Therefore it has travelled 1 billion light years to reach us only because space was expanding. It hasn't travelled more than that, it can't - the speed of light is a constant in every reference frame. X years at light speed is necessarily X light years.
> You contradict yourself. In that billion years, either the light travelled (1) a distance we call "a billion light years (a measure adjusted to account for expansion of space during transit)", or (2) it travelled "more than a billion light years (a measure that neglects expanding space)". In either case, substantially greater than 9.46e24 meters.
(note that I think you mean 9.46e21 meters, since conventionally, 1 billion is 1e9; I'll run with that figure for consistency).
For the record, option 1) is what I'm saying. However, one billion light years is 9.46e21 meters, so I'm totally stumped as to what you mean when you say "In either case, substantially greater than 9.46e2[1] meters". Those are the same thing. What am I missing? Light travels one billion light years, 9.46e21 metres, in one billion years. That's it. Where am I misunderstanding you or contradicting myself? I'm honestly confused.
You're both right and talking past each other. The light moved between two points that if measured at the start was fewer light-years apart than the time it took to cross the gap, or a greater number of light-years if measured now.
I think the most correct and relevant thing to say is that the light moved 1 light-year per year and covered exactly the specified distance, if you integrate the distance over the trajectory of the light as it moved across the universe. Inflation simply changes the geometry of the space before (or after) the light passes through.
> I think the most correct and relevant thing to say is that the light moved 1 light-year per year and covered exactly the specified distance, if you integrate the distance over the trajectory of the light as it moved across the universe.
Yes, so light travels X light years in X years, not substantially more than that which is how I read (or misread) the parent comment. Language is fun I guess.
Try a thought experiment. You're driving at 60mph between two towns on a straight road that's 10 miles long when you set off but is growing in the direction of travel. You arrive an hour later - how far have you travelled?