That would mean that in every possible direction we might look, we should see intensely bright light coming in (from that direction) from a star surface. So Olbers said that that would imply that the night sky should be all brilliantly lit up everywhere, as bright as the surface of the brilliant Sun is, and at least as bright as daytime! He then noted that we all go out to a dark sky at night, so that clearly was not true. He just did not know why, and so his interesting observation came to be known as the Olbers Paradox.
For many years, no one could answer it. Eventually, astronomers discovered that there are many clouds of gas, particularly inside our Galaxy but elsewhere too, which do not emit light. So they are dark clouds of gas. They act somewhat like our atmospheric rain clouds do in partially or completely blocking the light of the Sun from us.
Therefore, the current understanding regarding the Olbers Paradox is that there is enough dark gas floating around in the Universe as to block the light from billions of distant stars. We now know that we cannot even see the region of the center of our own Galaxy, only 30,000 light years away, because there is so much interfering gas in the way!
When most atomic particles or nuclear radiation passes through us, there are usually clear effects when collisions occur with our body's atoms. Cancer can be caused, or genetic mutations, radiation disease, or thousands of other effect, most of which happen to be bad for us! So it is a good thing that neutrinos nearly always pass completely through us without hitting anything! More than that, standard physics agrees that nearly all neutrinos pass completely through the entire Earth without hitting anything, and so they come out the other side just like they went in!
Neutrinos are described as having no electrical charge, no magnetic characteristics, and possibly no mass at all. They are essentially nearly non-existent. Physicists first decided they must exist because there is a property of angular momentum that protons and neutrons and electrons have, usually called "spin". When a neutron decays into a proton and electron, the amount of this spin appears to not be conserved. But Newton proved that angular momentum must always be conserved. So the neutrino was invented, with essentially no characteristics at all EXCEPT spin!
For quite a while, no one could figure out any experiment that might confirm the existence of neutrinos. With ONLY spin, they wouldn't really ever cause any effect that we could record or measure! But after about 30 years, a couple experiments were created, and a small number of neutrinos were claimed to have been confirmed. There are still only a very small number of results of such experiments, and all the results are rather indirect as to actually being confirmations of neutrinos.
I am not entirely sure about that logic, because the Earth's rocks contain many radioactive materials, Radon gas, Radium, Uranium, and hundreds of others. It seems to me that if some Radon gas seeps up near that detector, or if there happens to be some Uranium nearby, then the results of the experiment would become meaningless. If a Uranium atom fissions, or even if a neutron is emitted from any nearby atom, a neutrino would be emitted that would act exactly like the ones that would allegedly come from the Sun.
However, I am not sure that is the biggest problem! The experiments are designed on calculations based on expected neutrino emissions from the Sun. And, once in a while, an event is recorded, and it is nearly always automatically attributed to the Sun. (The oldest running experiment, around 35 years, cannot tell what direction a neutrino might have come from, only that an event happened. Newer experiments are attempting to determine the direction as well.)
Keep in mind that VERY few such events are recorded! This is not like a chemical reaction where countless billions of reactions occur. A few events per year is not unusual.
We do experiments deep in underground caves and mines to detect neutrinos from the Sun, but shouldn't we actually be receiving around 200,000 times that rate of neutrinos because the total angular area of the sky is around that much larger than the angular area of the Sun? Every one of those stars that sends photons toward us must be creating an equivalent number of neutrinos in the process, right? So it seems that we should be inundated by random incoming neutrinos from every possible direction.
It seems to me that the experiments intended to find Solar neutrinos, should all be being swamped by even larger numbers of neutrinos from all those other stars. Doesn't that seem to make the Solar neutrino experiments somewhat pointless, UNLESS the precise direction of the neutrino was identified as coming from a VERY small area in the center of the Sun? (NOT from the whole visible area of the Sun but a tiny, tiny source location at the very center of the Sun!) In that case, if a large number of neutrinos were detected that came from that tiny originating space, then, yes, such experiments might make sense. Otherwise, at best, the results of such experiments seem to only imply SOME possible source of neutrinos.
And if that is NOT the case, then either the neutrinos have some sort of limitation on their mean path length or that the "map" thus created should give some indication of any non-sphericity of the Universe. In both cases, new thought seems necessary.
In other words, I do not see why the Olbers paradox should not apply to neutrinos.
( http://mb-soft.com/index.html )
C Johnson, Physicist, Physics Degree from Univ of Chicago