I just read this article in the AUSTRALIAN SKY & TELESCOPE magazine, Nov/Dec 2022 Issue 140, on P16, KEEP YOUR DISTANCE: How far away are the objects we see in the universe? And on P23:
"And here is where our story takes a mind-bending turn:"
What does distance even mean in the expanding universe? On scales of the Solar System, we can understand it fairly easily. But for really remote galaxies, cosmic expansion makes the concept of distance quite tricky. In fact, many cosmologists protest that giving distances for anything farther than a couple of billion light-years should be avoided.
Suppose you measure a galaxy's redshift to be z=1.5, meaning that visible light emitted with a wavelength of 500 nm by the galaxy has been shifted by 1.5 * 500 = 750 nm to an observed infrared wavelength of 1250 nm. The Hubble-Lemaitre Law tells you that the light has been travelling through expanding space for some 9.5 billion years. Intuitively, you'd conclude that the galaxy is 9.5 billion light-years away.
However, you can't simply convert the light-travel time into a distance. When the light was emitted 9.5 billion years ago, the universe was smaller and the galaxy was a "mere" 5.8 billion light-years away. Because space is expanding, it took the light 9.5 billion years to reach the Earth. But by the time the light finally arrives here, the galaxy's "true" (or proper) distance has increased to 14.6 billion light-years.
How do they know that the light has travelled for 9.5 billion years? How do you work/figure it out? And, is it now really 14.6 B light-years to the other galaxy or the original/starting point? The other galaxy has also moved away!