# What is the probability of a photon being emitted by the sun actually being absorbed by matter in the visible universe?

In the Hubble ultra-deep field image it is apparent that the visible universe has a lot between us and our light horizon, but what is the likelihood that a photon emitted by our sun actually "hits" anything on its way to the bounds of our observable universe?

• Interesting question. Perhaps, your answer will pretty much be related to olber's paradox. en.wikipedia.org/wiki/Olbers%27_paradox – Rishabh Jain Oct 5 '19 at 14:33
• "between us and our light horizon" - There is no evidence of the existence of the particle horizon. It depends on the cosmological model and has not been experimentally confirmed. – safesphere Oct 5 '19 at 17:19
• I don't understand the purpose of your comment? I am asking what are the chances that light will hit matter within our observable universe, I am not saying anything about a particle horizon. – Joe Oct 6 '19 at 14:12
• You do mention the horizon, but there is no evidence it exists. For example, if the whole universe is observable and closed, then light would be circling forever until it is absorbed by something eventually. Then your probability would be a function of time. Or, in the Milne model, any light would eventually be absorbed by the expanding singular border of the universe. It is unclear if your question is limited to the Ftiedman model (that mismatches the observations by 95% of the matter content in the universe and produces non physical singular results for the initial state of the flat space). – safesphere Oct 6 '19 at 16:19
• Also please address your replies with the @ sign for people to get notified. – safesphere Oct 6 '19 at 16:22

That likelyhood changes over time, in the early universe when everything was dense the mean free path of a photon was rather short, while in the meantime it has grown to approximately 10 billion lightyears, see

Paul Davies wrote: The mean free path is about a Hubble radius (10²⁸ cm = 10²³ km).

Wikipedia wrote: The mean free path of a photon is about 10²³ km, or 10 billion light years.

That distance will grow with time, since the density of the universe dilutes with its growing volume.

If your question is not in the cosmological but in the astronomical context, meaning that you are looking for the amount of the sunlight that hits the planets and their moons and the asteroid and Kuiper belt objects of the local solar system, you have to calculate their angular size in the frame of the sun and substract that from the 4π sterads of the celestial sphere, which I won't do here since there are a lot of small bodies to add up.

Since we really don't know how big the universe is what I suggest you do is take the size of the observable universe and then use the inverse square law along with the average photons the sun outputs in whatever given amount of time you want and then use the average density of matter in our universe and use all of those variables to calculate your answer.

• I don't know that much about physics but I am slowly learning more so don't judge if I'm wrong. – T. Fisher Oct 9 '19 at 22:42