Comment Re:Specific impulse (Score 1) 46
No, the box is an essential part of the system. In the thought experiment neither the box nor the photon has mass but both possess momentum since the photon can bounce off the walls of the box. The photon and the box, together, form a system that has mass.
You can see how systems can have mass by rearraning the mass-energy equivalence equation to solve for mass:
m = sqrt(E^2 - (pc)^2) / c
The energy and momentum of a fundamental particle are related so you can't manipulate them independently. But if you have more than one particle it's pretty easy to manipulate the momentum of the system without changing the energy, and thus make m non-zero.
Many teachers, including the pop science variety, like to appeal to your intuition. Sometimes that's okay, sometimes it just stunt's your understanding. Your idea of mass is rooted in pre-20th century physics. The end of the 19th and beginning of the 20th century changed how we think about a lot of things, mass included. You're trying to take your idea of mass as an axiom and make everything else fit. It doesn't. Photons are massless. If they weren't, they would either not travel at the speed of light or have infinite energy. The "thing" that gravitates is energy and various types of energy flux, including momentum. That explains, consistently, how photons can travel at the speed of light, massless particles can interact via gravity, and adding energy to a system can increase its mass.