system
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human
Given enough time, will photons ever fall back towards their source?

I've been wondering about the end of the universe lately. Where do all the photons go over very long time scales? Does the answer change if the universe is finite? Infinite?
gpt
> Given enough time, will photons ever fall back towards their source?

Only in a few very specific cases with black holes. 

Photons do this thing where the follow a geodesic, which is basically a straight line in curved spacetime (specifically, they follow a certain type of geodesic called a "null geodesic" but that might be too technical for our purposes here). In the handful of solutions we have for general relativity, these lines can generally just be thought of as out and away, but with things getting interesting near massive objects. The basic principle of general relativity is this: mass tells spacetime how to curve, and curved spacetime tells mass (and light) how to move. For example, when you get close to black holes, there is a certain distance from the black hole that light will actually *orbit* the black hole, so that if you are close enough to a black hole and you look forward, you'll see the back of your own head. This would be one example. 

Black holes have this interesting property inside in that *all geodesics converge at the singularity* - no matter how you move inside of a black hole, you are getting closer to the singularity at the middle. Weird, right? Well this means that if you drop a blinking LED into a black hole, if it is still emitting after it passes through the event horizon, both the LED and all the light it emits will come back together at the singularity in the center. 




> I've been wondering about the end of the universe lately. Where do all the photons go over very long time scales? 

They just keep going until they hit something. But since you asked about the end of the universe, I'll mention that the universe is expanding. This is causing the clusters of galaxies in the universe to spread out, and as they move apart, the light we see from them get's *redshifted*. This is like the doppler effect that makes sound wave changes frequency when the car goes by- it makes light look *less energetic* if it's source is moving away from us. As things in the universe begin to recede faster and faster, eventually the light we receive from them will be redshifted away to almost nothing.