# Does it take work to bend light?

We all know that light always travels in a straight line. Would it not then stand to reason that changing the path of light requires energy? If so, would this not violate Newton's laws of motion if bending the light did not exchange energy thus changing the color of the light in the process?

• Light isn't explained by newtonian mechanics. Commented Feb 8, 2021 at 9:53
• Accelerating an object does not automatically imply changing its energy. Commented Feb 8, 2021 at 9:57
• A magnetic field will cause a charged particle to curve, but without doing any work on the particle. Commented Feb 8, 2021 at 15:11
• @ProfRob The case that you are alluding to is a circular orbit. For light bent by the sun the orbit is very much hyperbolical so the argument does not apply. Commented Feb 8, 2021 at 16:19
• @CalWitthoft See my previous comment. Commented Feb 8, 2021 at 16:20

You can use Newton mechanics in the limit to m=0 and will see that work is simply $$\int \mathbf{f} \cdot \mathbf{ds}$$. No net work is performed when integrated over the full hyperbolic orbital. In summary, it does not take work to bend light in Newton mechanics. I am not sure if the concept of work exists in General Relativity.