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by danparsonson 1881 days ago
> 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.

1 comments

Well, OK.

  $ /bin/units
  You have: 1 Gly
  You want: m
   * 9.4607305e+24
   / 1.0570008e-25
  You have: 1 Gly
  You want: km
   * 9.4607305e+21
   / 1.0570008e-22
  $
But I got mixed up on starting the road length, reading it as 60 mi. Fair's fair.
I got mixed up between m and km so I guess we're even :-)