When light leaves a star, it spreads out. When it spreads out, it covers a larger area and the luminosity declines as a result. The same amount of light is spread thin across more space.
For stars that are very far away from us, an awful lot of spreading has been done by the time their light reaches us. By that token, stars get dimmer to us as the universe expands and they get farther away.
If we were able to pintpoint a start that we knew was going to become so far and so dim that we’d fail to be able to detect or observe it, it would get fainter until that happened.
The light will become redder (longer wavelength) and redder (longer wavelength) until almost all the emitted light will be in the infrared. At this point you wouldn’t be able to see them even with a super giant telescope, although we can still see them in telescopes that use imaging systems capable of seeing in the infrared.
The James Webb Space Telescope has been specifically designed to look in the deep infrared precisely because these distant objects are redshifted so much.
The light undergoes something called a “redshift.”
Ever have an ambulance or something go past you, where it sounds different coming toward you than it does going away from you?
That’s the Doppler affect at work. When the siren is coming toward you, the sound waves are compressed and the pitch changes. When the siren is moving away from you, the same thing happens except this time the sound waves are stretched out, and it sounds lower-pitched.
The same thing happens with light. With light, when something is moving toward you, the wavelength of the light is compressed. This makes it turn more blue, and the phenomenon is called “blueshifting.” When something is moving away from you, the wavelength of the light is stretched and the light turns redder. That’s called “redshifting.”
When something moves out of the observable universe, it’s not crossing some magic boundary where it’s instantly either in or out of the observable universe. It moves away from us at some rate, and with the universe expanding that rate gets faster and faster over time.
So the light from, say, a star that’s moving away from us toward the edge of the observable universe will undergo more and more extreme redshifting over time. This means the light will get redder and redder (as well as dimmer and dimmer as it gets further away) , shifting into the red, then infrared, then radio spectrum, until we can no longer see it.
Once it crosses the border of the observable universe, no new light that it emits will be able to reach us. But the light it has been emitting as it travels will be able to, and it’s that light that undergoes the redshifting.
As I’m sure you know the ‘observable universe’ is the area of the universe which is moving away from us slower than the speed of light, which gives photons from that area a chance to reach us. Any further and the relative space between us and those points expands faster than the speed of light and the photons will be forever on our way to us, but space is being stretched out in front of them faster than then can travel through it.
Now for the stars in right on the edge of the observable universe, it helps to think of the light that is emitted in a one-year time span, which will span over the distance of one lightyear when it is expelled from the star. Over the course of time when the light travels to us, this one lightyear span of space will have stretched out, effectively distributing the original amount of photons over a longer span of space.
Take this to the extreme, right on the edge of the observable universe, and the one lightyear span of space will stretch out into an infinitely long distance. Since the hypothetical star will slowly move over the edge of the observable universe, we can say that the density of photons we can record from the star will asymptotically reduce to 0.
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