text: this is a category mistake.\n\nADDED COMMENT:\nwell, the way i see it, there are two possible interpretations of your question: a) Does a beam of light ever run out of energy?, or b) Does a beam of light ever stop moving?\n\n(a) is a category mistake because light is energy.  it's not something that has energy.  it just IS energy.  so, the answer using this interpretation is simply no, because it's nonsensical to say that energy loses energy.\n\n(b) can be attacked similarly.  light is being treated as something moving, which seems okay on the face of it, but i don't think it's quite right to treat it that way.  i don't think i'm going to articulate this point successfully (i may be wrong on this anyway), so i'll give you a funny account of why (unimpeded) light will always continue to 'move'.\n\nThe key thing to note is that motion is a relation.  For there to be motion, there have to be at least two things: the thing 'moving' and the thing it is moving in relation to.  if there is only one thing, there is no way to know if it is moving.  if we are to say something is moving, we have to provide the frame of reference too.  e.g. driving in my car, i am moving in relation to the road.  in relation to my car, however, i am not moving.\n\nlight is different than moving objects, however.  einstein's theory of special relativity holds that light travels at the same speed in all frames of reference.  so, it's safe to say that from any possible vantage point (moving at any possible speed), light will always be 'moving' in relation to you, and at the same speed.  so, no, the beam (if unimpeded) will never stop moving.\n\ni hope this is clear enough to be of help.\nalso, if i didn't do your question justice, let me know.  i'd be willing to take another crack at it.