ASTRONOMY FUNDAMENTALS - Chapter 1, Exercise 2 Solution ========================================================== Light-Travel Distance vs. Comoving Distance PROBLEM ------- Explain why the observable universe's light-travel radius (13.8 billion light-years) and its comoving radius (46.5 billion light-years) are both correct, and what real physical process explains the difference. SOLUTION -------- Both numbers are correct because they answer two genuinely different questions about the same photon's journey. The 13.8-billion-light-year figure is the LIGHT-TRAVEL DISTANCE: it is simply the age of the universe (13.8 billion years) multiplied by the speed of light. It answers the question "how long ago was this light emitted?" A photon reaching Earth today, having traveled for the entire history of the universe, was emitted 13.8 billion years ago - that part is a straightforward multiplication. The 46.5-billion-light-year figure is the COMOVING DISTANCE: it answers a different question - "how far away is the source that emitted that photon RIGHT NOW, at this present moment?" This number is larger because space itself has been expanding for the entire time the photon was traveling toward us. The source that emitted the photon 13.8 billion years ago has not stayed still - the space between us and it has been stretching the whole time, so by today, that original source is actually much farther away than the photon's own travel distance would suggest. WHY THIS WORKS AS AN ANSWER ---------------------------- This isn't a measurement error or a rounding issue - it's a real, physical consequence of cosmic expansion described by general relativity. Space itself is not a fixed, static backdrop that light travels through unchanged; it is actively stretching, and it has been stretching for the universe's entire history. A useful way to picture it: imagine a photon on a treadmill that is itself slowly getting longer while the photon runs. The photon's own total distance traveled (13.8 billion light-years) is smaller than the treadmill's own current length at the far end (46.5 billion light-years), precisely because the treadmill kept stretching the whole time the photon was in transit. This is exactly why cosmologists distinguish "light-travel distance" (sometimes called lookback distance) from "comoving distance" - using the wrong one for the wrong question produces a genuinely misleading picture of the universe's real current size.