How far has a 13.7 billion year old photon travelled

Question

I've read that the size of the observable Universe is thought to be around ~46 billion light years, and that the light we see from the most distant galaxies were emitted ~13.7 billion years ago as a result of the expansion. So is the actual distance the photons have travelled 46 billion light years, or 13.7 billion light years?

Answer 1

Light always travels at the speed of light when in a vacuum. Space is a pretty good vacuum. So if it's been travelling for 13.7 billion years, then it has travelled 13.7 billion light years.

There is no contradiction here. Yes, those galaxies are now 46 billion light years light years away, but this is because the universe has expanded. You can find lots of questions related to this on Physics SE.

e.g. How can a quasar be 29 billion light-years away from Earth if Big Bang happened only 13.8 billion years ago?

Why is the observable universe so big?

Are the distances we measure to objects in the universe incorrect because of their relative motion?

Answer 2

A community Wiki answer recording someone else's (Ben Crowell's) comment that I think is worthy of being a permanent answer.

The proper length is zero, because the photon's path is lightlike. If you want to define the photon's "odometer," you can't do it in the photon's frame, because a photon doesn't have a rest frame. The 13.7Gyr is measured on a clock that's at rest relative to the Hubble flow. The 13.7Glyr is measured on a chain of rulers, each at rest relative to the Hubble flow.

Here the "Hubble flow" is simply the motion of astronomical objects that is owing wholly to spacetime expansion (defined by the derivative $\dot{a}(t)$ of the scale factor $a(t)$ in the FLRW metric)

Answer 3

Simple calculation: Age of observable universe is 13.8 billion years. Distance light travels in one year is 6 trillion miles. So 13.8 billion x 6 trillion = 8.28e+22. (Mic drop...)

Answer 4

Age of universe is roughly 13.8 billion years, so anything with longest traveling record can only travel 13.8 billion light years at most (in any direction; not necessarily to Earth) because nothing can travel faster than light.

Now, we are at the center of the observable universe (which is spherical with visible radius 13.8 billion years), so longest traveling record holders are the oldest ones and are at the edge of the observable universe and they have traveled 13.8 billion light years so far.

The actual calculated radius 46 billion light years is different from the visible radius because the universe has expanded.

So, the answer to your question is 13.8 billion light years.