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Supposing it's possible to see some distant galaxies with an earth telescope, then, at the tip of the telescope lens there are photons comming from the distant galaxy...

So, if I extend my hand in a dark night without visible moon, and far from city lights, photons from distant galaxies are in my hand skin... if it is true... is kind of amazing...

Then at that moment if photons of EVERY visible galaxy (from an earth telescope) are in my hand, then why my hand didn't bright? knowing (from photoelectric effect) that photons act as a whole or don't act, then why my hand didn't bright?

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I'm not sure, but I think this question is about what is generally known as Olbers's paradox: If, at any given moment, light from all light sources in the Universe are illuminating any given point, one might expect every point to be extremely bright.

To be precise, consider all of the light sources in a spherical shell of radius $R$ and thickness $dR$. If the Universe is uniform, the number of such sources is proportional to $R^2\,dR$. The apparent brightness of each source is proportional to $1/R^2$, so the total light striking your hand from all such sources is simply proportional to $dR$. If the Univers is infinite, then the total that results from integrating all such sources is infinite.

In reality, distant sources will be blocked by nearby sources, so the power striking your hand won't be infinite, but it will be as large as f the entire sky were filled with sources of the same temperature as a typical star. (To see this, note that every line of sight ends on the surface of a star. The surface brightness (watts per steradian) due to a source doesn't depend on distance: the brightness goes down like $1/R^2$, but so does the solid angle. So the entire sky has the surface brightness of a star.

That's the paradox. What's the resolution?

The main thing is simply that we shouldn't integrate out to $R=\infty$. The Universe has a finite age, which means we can see out only to a finite distance. If you consider only the sources within our observable volume, the integrated brightness of all those galaxies still turns out to be very small. Galaxies are luminous, but they're far away. (There's also the fact that distant sources are receding from us, so the light from them is highly redshifted.)

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Isn't the fact that we are not at star temperatures an argument in the proof that the universe is finite? –  anna v Feb 14 '11 at 19:43
It's a proof that one of the assumptions that goes into Olbers's paradox is false. Those assumptions include that the Universe is infinite in spatial extent, infinite in age, homogeneous in space, homogeneous in time. It doesn't say which assumption is false, so it's not a proof that the Universe is finite. –  Ted Bunn Feb 14 '11 at 20:08
The entire sky would be infinitely bright, not the brightness of a star. You can't just "block" distant sources. They would absorb the energy hitting them, heat up, and radiate more brightly. –  Mark Eichenlaub Feb 14 '11 at 21:41
Another resolution of Olbers paradox is that distant sources will have their light redshifted below the visible range. The CMB was originally as bright as the surface of a star, after all. –  Jerry Schirmer Feb 14 '11 at 23:59
Yes, I'm sure. "With enough photons," things will look bright, but there wouldn't be enough photons. Space is big and the galaxies are far away. –  Ted Bunn Feb 15 '11 at 20:29
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