I wouldn't recommend going back to school. You already have a Master's in Physics, which should give you all the math background you need to understand CS algos. I'd even encourage you to start to "translate" your Physics knowledge into code.

Google, FB, Microsoft, et. al. are more concerned with your ability to explain CS concepts at a whiteboard than your degrees.

Have you considered SpaceX? http://www.spacex.com/careers/list

They are usually very interested in cross discipline candidates.