# speed of light flashlights question

This might be a silly question but I take the risk because it's been puzzling me for quite some time :

If you have 2 flashlights, one facing North and one facing South, how fast are the photons (or lightbeams) from both flashlights moving away from one another?

Just adding speeds would yield 2C, but that's not possible as far as I know.

UPDATE : the reference frame here would be the place where the flashlights are and/or UPDATE2 : the beams relative to one another.

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– David Z Sep 24 '11 at 18:24

If you are looking at the frame of reference of the flashlights, then the answer is indeed 2$c$. How can this be so, when nothing travels faster than the speed of light? Ah, but 2$c$ isn't a rate at which anything is actually travelling.
You asked for the rate at which the distance between the photons of the North Beam (the leading ones, say, and supposing we could know their position to some fixed precision; asymptotically speaking, any fixed precision will do) and the photons of the South Beam (ditto) is increasing, in the frame of reference of the flashlights. Nothing is travelling at 2$c$, relative to the flashlights, if special relativity is correct; both beams are travelling at $c$ relative to them.
In fact, the two beams of light can accumulate distance between them at any rate greater than $c$ up to an upper bound of $2c$ for different moving observers, depending on the (sub-light) velocity they have. If their motion is parallel to the line of transport of the two beams, they will also "observe" (they aren't actually observing the light, after it has departed) a distance-accumulation rate of 2$c$. If they travel with some lateral velocity to the light-beam-axis, the rate at which the two beams separate will be less than 2$c$, but strictly greater than $c$.
Note that I mentioned that the rate of growth of the line-segment can achieve any rate of growth between $c$ and $2c$. We can actually find a frame of reference (albeit a somewhat degenerate one) in which the rate of growth between the two beams is precisely $c$; one example, of course, is the frame of reference of the North or South beams themselves (and for which these speeds finally does represent a rate of travel of the beams relative to each other).