[katieHaylor (OP)]

John asks:

Prof Brian Cox in a recent repeat of his lecture on the science of Dr Who, exhibited a candle and said that if there was no roof on the Royal Institution then that light would radiate out forever into, presumably, the far reaches of the universe, at the speed of light. Presumably after that light has travelled a billion light years it will be pretty faint!

Assuming one has a sensitive enough instrument, it could still be detected. How is this possible? The photons will have radiated in all available directions - is there not a theoretical point when they become too weak to detect however sensitive the instrument? How is the light able to 'spread' itself out so thinly - whether light is a wave, photon or both, surely there is a theoretical limit to how far it can spread?

What do you think?

[syhprum]

Whether or not a photon from a particular source can be detected depends as to what degree they have spread out, the collecting area of the receiver and the level of spurious photons in that area.
To take an example at radio frequencies the SETI people claim that with Aricibo size dishes at both ends and multi megawatt transmitters communication would be possible over a 1000 light distance 

[Janus]

A photon is the smallest "energy packet" you can have for a given frequency of light.  No matter how far it travels (for the sake of this discussion we will omit the the effect of cosmological red-shift), its energy will not diminish.  What does happen is that as you get further from the source, fewer photons reach a given point over a fixed time period.
Thus if X number of Photons is striking a 1 cm^2 area per second at a distance of Y from the source, then at twice that distance, 1/4 as many photons strike that surface per second.  Move it far enough away and it starts making more sense to talk about photons per minute or even hour. No matter how far away you move that surface, some photons from the source will reach it if you wait long enough.   The Hubble telescope deals with this issue.  It is looking at objects that are so far away that the rate of photons reaching the telescope is so low, that it has to stare at the object for weeks in order to collect enough photons to form an image.

[Bill S]

David Deutsch (The Fabric of Reality) maintains that a frog’s retina is sufficiently sensitive to observe single photons  If this is the case, as long as its eye is on the trajectory of even a single photon, a frog would see it, whatever the distance.