Can Distant Stars Fill the Universe with Photons?

[Burnsys]

suppose we look to distant galaxies or stars tru a telescope like hubble.

We can see an image of the star becouse it's emiting photons and this photons are reaching the Hubble telescope...

Knowing the size of the universe, the size of the star, the size of the Hubble telescope, and it's distance from the star. then if the photons from the star reach a soooo tinny spot like the Hubble telescope then we can say almost the entire universe is filled with photons from this star?

 

[chroot]

The photons from a star leave in all directions, in a radially-symmetric fashion. Light travels one light-year per year. Thus, around a star that's been shining for N years, you can think about a large sphere centered on the star, with a surface N light-years away. Anyone inside that sphere can see the star. You could reasonably say that the entire sphere is full of photons from the star.

When you're really, really far away from the star, though, the photons would be very diffuse. It still might take a long time before one happens to hit your telescope, even though technically you are within that sphere.

- Warren

 

[gonzo]

Wait, I think I understand the question, and it bothers me too. I understand the shell idea, but here's the problem as I see it, and as I think the original poster meant it.

At any given time T a star emits a finite number of photons, correct? In all directions, sure, and as the speed of light sure, but since each of these light-shells won't have infinite photon density, won't "gaps" start appearing between photons as you get farther and farther away from the star?

Do you see my point here?

Anothe way to look at it might be this--if there are infinite "directions" something can shoot out from a star, but only a finite number of photons at a given instant, then many directions won't have a photon. While many of these directions differ but an incredibly small distance that might not matter most of the time, as the distances increase, even small differences become significant and should produce gaps.

Assuming I'm being clear in my question here, can someone explain what I'm missing? Thanks.

 

[chroot]

gonzo,

You are correct. The photon density in each "shell" decreases with square of the distance. The further away you are, the less likely you are to encounter a photon from the star, as I said in my previous post.

- Warren

 

[Janus]

Wait, I think I understand the question, and it bothers me too. I understand the shell idea, but here's the problem as I see it, and as I think the original poster meant it.

At any given time T a star emits a finite number of photons, correct? In all directions, sure, and as the speed of light sure, but since each of these light-shells won't have infinite photon density, won't "gaps" start appearing between photons as you get farther and farther away from the star?

Do you see my point here?

Anothe way to look at it might be this--if there are infinite "directions" something can shoot out from a star, but only a finite number of photons at a given instant, then many directions won't have a photon. While many of these directions differ but an incredibly small distance that might not matter most of the time, as the distances increase, even small differences become significant and should produce gaps.

Assuming I'm being clear in my question here, can someone explain what I'm missing? Thanks.

The answer lies in the phrase "in any given instant". In the next instant a whole new group of photons will be emitted and after that another group and another and another... Each of these groups of photons are emitted in random directions so later photons fall in the gaps left by earlier ones. At any finite distance from a light source, any given area (such as the aperature of the hubble) takes up a certain percentage of the photon "shell" at that distance. So if you wait long enough, a good number of photon have to hit your telescope. The longer you wait, the more photons you collect.

This is what the Hubble does; it uses long exposure times and multiple exposures of the same object to get a single image. There is one image that took 800 exposures spread over 4 months to get.

 

[Chronos]

Due to the wave nature of light, a photon occupies a lot more volume than it would if it were a particle.

 

[DB]

Does this mean that anything can be seen as long as the photons have reached our eyes no matter what the distance?

 

[chroot]

DB,

Theoretically, if you can take a long enough exposure to collect enough photons, you will be able to see the object, no matter how far away it is.

The problem with photographs is the limitation of technology -- all photographic media, including digital imagers, collect random noise as well as real photons. The signal from the real photons has to be larger than the "signal" from the random noise, or the signal will get "lost" in the noise.

- Warren

 

[gonzo]

Thanks Janus, that also occurred to me later.

One more question, what is the cross sectional area of a photon, if such a question even makes sense and is known? (in other words, how much are on each shell does each photon occupy?)

 

[Nereid]

It doesn't make sense gonzo, or at least not without considerable qualification.

Think of X-rays, or gammas, or photons that are sufficiently energetic that our recording devices count them (works just fine with other wavelengths too, but most folk find it easier to grasp thinking of the clicks of a geiger-müller counter), and imagine we have a 'perfect' X-ray telescope (it detects all X-ray photons in energy band A from a region of sky b" x b"; there is no internal noise, and no photons from other directions are detected). Now do the inverse square calculations (e.g. if our telescope is recording (an average of) 1 photon per second now, then if the steady source were twice as far away it would drop to 1 per 4 secs, etc), including the collecting area (assumed normal to the direction the photons are coming in) - e.g. double the collecting area and the rate goes up to 2 photons/sec. In principle it' pretty easy to calculate the photon flux from a (point) source at any given distance ... in fact, here's a good heuristic ... 10,000 photons of wavelength 5000 angstroms (per angstrom) pass through every square cm from an A star of magnitude 0 every second at the top of the atmosphere. Now the HUDF detected distant galaxies of (B) mag 30, so how many photons from such a distant galaxy did it collect (assume an integrated collection time of 1 million secs)? What other assumptions do you need to make to get a simple answer?

 

[gonzo]

Hmmm, maybe i was asking how many photon could dande on the head of a pin?

I was trying to think more about what I meant. I know that photons have this measurement of wavelength that is the only relevant "size" measurement of a photon. And if I remember correctly from a million years ago (when I studied this stuff), this would affect what type of matter a photon would be likely to interact with, but now I'm confusing myself. Isn't most photon/matter interaction basically a photon hitting an electron (most of the time)? Can a photon of any wavelength interact with an electron?

So, I was thinking about maybe my question was on the size of a detector ... not the whole detector, but the individual detecting units. But if all of our photon detectors are based around a photon interacting with an electron, then the size of the surrounding "machinery" doesn't really seem relevant anymore.

Maybe I was really asking then what the theoretical maximum number of parallel photons is that could strike a detector at "the same time". Of course, I realize again this is probably meaningless since in any practicle sense since our ability to detect this at all is limited by detector size. Though maybe there's a theortical answer in there? Near inifinite?

I think I've managed to totally confuse myself now, and probably lost any question I might have had. But here, I'll come up with one at the end maybe that to me seems related.

Can two photons travel in parallel and occurpy the same space at the same time, and if so what does this mean? Or if they get "close enough" do they automatically join to become one higher energy photon? And would there be any way to even theoretically tell this experimentally?