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If photons are emitted by a star and travel millions/billions of years in a "straight" line, they can be seen by adjacent observers. This makes it seem like there must be an uncountable number of photons emitted from the same region/point on a star. I am aware that there is the wave/particle duality of light, but it still seems that photons must be emitted in an almost uncountable amount in order to be seen by adjacent observers billions of years away. Thanks for any insights.

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  • $\begingroup$ Note that light from other stars in our galaxy does not travel for millions or billions of years… only tens of thousands at most. Light from other galaxies does travel for millions or billions of years, but galaxies can have trillions of stars. $\endgroup$
    – Ghoster
    Jul 16, 2023 at 17:15
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    $\begingroup$ I suggest using the luminosity of the Sun and the average energy of a visible photon to compute how many photons pass through each square centimeter each second on a sphere 50,000 light years from the Sun. $\endgroup$
    – Ghoster
    Jul 16, 2023 at 17:17
  • $\begingroup$ A star emits light in all directions. What would prevent two adjacent observers from seeing the same star? $\endgroup$
    – PM 2Ring
    Jul 17, 2023 at 3:07

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The sun emits $10^{26}$ Joules of energy per second. Each photon of wavelength $700$ nanometres (visible light) carries about $10^{-19}$ Joules. So the sun emits about $10^{26}/10^{19}=10^{45}$ photons per second. That's 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 photons.

A light year is about 9,460,730,472,580,800 metres. So a sphere with a radius of 10 light years has a surface area of $4\pi r^2=10^{33}$ m$^2$.

That means there are about $10^{45}/10^{33}=10^{12}$ photons per square metre per second passing through space 10 light years away. That's a trillion photons. The pupils of your eyes are only a few millimetres across, but that means there would still be millions of photons of starlight entering them every second.

However, if you go a thousand times further out (so 10,000 light years away) you get a million times less light. Now you're down to a few photons per second entering your eyes. Generally speaking, you can't see an individual star the size of the sun from this far away with the naked eye. There are much bigger and brighter stars than the sun, but even these you would struggle to see from so far away. Almost all of the individual stars you can see with the naked eye are no more than a thousand light years away, and about half of them are within only 300 light years of Earth.

When billions of stars are collected together in galaxies, we can see them from a little further. With the naked eye, we can see our own Milky Way galaxy, the Magellanic clouds, small satellite galaxies very close in, and the Andromeda galaxy, our nearest proper galactic neighbour. All the others are too dim to see with our eyes.

Other bright objects are quasars (matter being heated up when falling into giant black holes) and supernovae (exploding stars). These can be hundreds of billions of times brighter than an individual star like the sun.

Big telescopes can see further by collecting light across a bigger area, over a long period of time. The James Webb telescope, for example, has a light-collecting area of about 25 m$^2$, and they leave it staring at a patch of sky for hours, to collect the faint light from the furthest galaxies. Galaxies emit much more light than an individual star. A billion stars means a lot of photons! (Add another nine zeroes to that number above.) But it still requires a huge technical achievement to be able to detect them and make images of them.

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    $\begingroup$ Please, register, so your answers are not lost to posterity! $\endgroup$
    – hyportnex
    Jul 16, 2023 at 23:48
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    $\begingroup$ Why would they be lost? Are you planning to delete them if I don't? Not that I'm very interested in posterity - I do this for fun, and to be helpful, not for reputation. I doubt anyone would remember in 20 years time, anyway. And I have very strong feelings about my philosophical disagreement with the use of 'reputation', 'authority', and 'popularity' in judging science. If you want to link my posts together, for some reason, you guys write the software here so you could do that if you want. But I'm not going to play for points. My deepest apologies if that causes you any problems! $\endgroup$ Jul 17, 2023 at 0:11
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    $\begingroup$ I do not think anybody is deleting them but if I search for your prior contributions physics.stackexchange.com/users/372543/nullius-in-verba only the current shows up, and I think your writings should be preserved. $\endgroup$
    – hyportnex
    Jul 17, 2023 at 0:20
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    $\begingroup$ ...and this has nothing to do with playing for points, 'reputation', 'authority' or 'popularity". It just appears that every time you write something new and unregistered your answer to some previous question is lost. Or maybe I just do not know how to search here and I do not write any software, especially here. $\endgroup$
    – hyportnex
    Jul 17, 2023 at 0:32
  • $\begingroup$ Thank you for answer. I am new, so I can’t give you a good vote, but I would have. $\endgroup$
    – Rich K
    Jul 17, 2023 at 17:14
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You are right, the number of photons beamed at us from for example a distant quasar are uncountably huge (but still finite!), which means there are plenty enough of them to be visible by two adjacent observers with telescopes- even after traveling through space and geometrically diverging for billions of years.

Note that in general, extremely large collections of photons behave mostly like waves and are not discernable as discrete little photon guys. This means that wave-based optical rules govern their behavior i.e., telescopes with lenses in them handle the incoming light from immensely distant objects as waves just fine.

Note that it is possible to equip a telescope with a set of mirrors spaced tens of feet away from the main axis of the telescope, which send collimated off-axis beams of light into the telescope- where they enable interferometry. This illustrates the wave-like behavior of light from very distant sources.

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  • $\begingroup$ Thank you. I am new, so I can’t give you a good vote, but I would have. $\endgroup$
    – Rich K
    Jul 17, 2023 at 17:13

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