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When we study black body radiation, we often make calculations assuming a continuum of radiation with some amount of flux. In reality, there is a very very large number of photons being emit per unit time from some entity in some very very large number of directions. No matter how large of a number, there are still only finitely many photons, and finitely many directions.

Consider a black body that emits four photons in four directions once per second. For any given distance from the black body, it is easy to say that an instrument designed to detect photons would have to be a certain size in order to guarantee that the device would detect anything at all.

Doing some rough calculations, if photons are emit uniformly from the surface, it seems to me that a star similar to our sun could exist in our own galaxy, and the earth's orbit is simply too small to ever have a chance of coming across a photon. I'll polish up my calculations and share them if my hypothesis isn't nicely thrashed by people much smarter than myself.

Is this a reasonable hypothesis, or is this something quantum field theory proves impossible? Even if the quantum field does exist in a continuum, might there be a credible reason why there might be tiny 'shadows' in it? Has this been considered as an explanation for dark matter?

Jonny
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    Sounds like you're describing something similar to a pulsar. How does QFT play into it, though? – HDE 226868 Sep 15 '14 at 23:37
  • I'm just talking about a garden variety star. We say it emits radiation in 'all' directions, but certainly finite photons can only emit in finite directions -- or, if they do emit in infinite directions (like a quantum field), certainly could there be a finite size shadow just big enough to cause something the size of the earth to miss? – Jonny Sep 15 '14 at 23:41
  • What do you mean by "garden variety star"? Might just be an expression I haven't heard of. – HDE 226868 Sep 15 '14 at 23:43
  • That question looks quite similar. The accepted formula fits my calculations: when you make the distance 10,000 to 30,000 lightyears the flux gets a lot smaller. However: does QFT guarantee that it is possible to detect every radiating body from every direction as long as it is unobstructed by other bodies and exists long enough for its radiation to reach the Earth? – Jonny Sep 15 '14 at 23:59
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    1W of visible radiation creates on the order of 1e19 photons per second. This means that 1W of visible light from an isotropic radiator is easily detectable to a distance of approx. 1e9m (i.e. 1 million km) if there is no background. You will gain one order of distance for every two orders of power, i.e. 1MW will be detectable from a billion km. 1000GW will be detectable from 1 trillion km distance. A sunlike star generates approx. 4e26W, which would be detectable from 2e19km. That's about 20,000 light years. One could see it from >10 times that distance by working a little harder. – CuriousOne Sep 16 '14 at 00:02
  • And, yes, theoretically one can detect it from any distance, it would merely take really large detectors. – CuriousOne Sep 16 '14 at 00:03
  • If I am understanding correctly, the size of the detector serves only to increase the probability that a photon will interact with the detector, but any size detector still have some chance. This negates the possibility of stars that happen to be located in a position to have a zero probability of being detected. – Jonny Sep 16 '14 at 00:16
  • The size of the detector AND the exposure time, which is again just an arbitrary limit that we set. Indeed, you can trade detector size against exposure time at will, as long as resolution is not important. – CuriousOne Sep 16 '14 at 00:23
  • Might the pigeon hole principle apply then? Given the finite energy emit by the radiating body, there can only be a finite amount of matter that will interact with it at any given instant. Lets call that amount $x$. If there was more than $x$ amount of matter around to interact, we can know for sure that the difference is the minimum amount of matter that will not interact with the radiation at a given instant. Any reason why my detector couldn't always be the excess matter than never gets interacted with over infinite time? – Jonny Sep 16 '14 at 00:41
  • In all of physics the "you get what you pay for" principle applies. If you pay for a larger detector and more exposure time, you can see fainter objects. I am not sure what exactly you are struggling with. This is absolutely trivial. – CuriousOne Sep 16 '14 at 00:46

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