Reflecting Photon Velocity

Hi Mike- there was a question earlier that someone posed about a photon being reflected off a surface and whether its speed would be considered to be zero at the instant of reflection. I was wondering if it was correct to say that its velocity has changed (i.e. direction) but that its speed was always the same. Its been 35 years since I took calculus but I seem to remember there being a distinction between changes in direction along a curve that are smooth and differentiable ( had a tangent equal to zero, and constituted local maximums or minimums) and changes in direction of a function that appear as sharp instantaneous changes in direction of the function, which aren't differentiable at that point ( where there is no tangent). Does this relate in any way to the scenario of the reflected photon in the sense that, mathematically, a function can seem to go from increasing to decreasing ( or the reverse ) without ever going through a point where the derivative is zero?
- Annette (age 55)
Toronto, Canada

Hi Annette-

I think the old answer you have in mind is follow-up 18 on  
Certainly if you say it's the same photon it's correct to say that the velocity has changed but the speed hasn't. 

Yes, you can think of the velocity of each "piece" of the photon wave as changing discontinuously, but since there's a smooth continuum of "pieces" the overall change is still continuous. That's one way to avoid having any part ever have zero velocity. The intermediate value theorem only applies to continuous functions, as you remembered from those old courses.

I guess if we were to get very careful then in addition to the wave coming in at c and the one leaving at c (both of which we're calling part of the same photon) there's some wave in the reflecting material, coupled with excitations of the electrons there. Offhand, I'm not sure how to describe that part in terms of local velocities.

Mike W.

(published on 02/18/2015)