Basic argument - Classic physics allows for objects to travel faster than light by continuously applying force - Force is rate of change of momentum with time - So if you keep on applying force, assuming mass doesn’t change, velocity can rise to infinity - But from special relativity we know that nothing can go faster than light - So what must happen is that if you apply constant force, instead of velocity rising to infinity, velocity should asymptotically approach speed of light but mass should keep on rising (hence make it difficult to accelerate further) - Now, energy is required to apply that force - Due to conservation of energy, any energy applied to accelerate an object should increase corresponding energy of the object - If we do the derivations as below, we find that energy required is equal to is equal to gamma * inertial mass * c-square - internal mass * c-square - Which simply means total energy (which is initial energy + this extra energy) must be gamma * internal mass * c-square Convention says, intertial mass is simply mass while relativistic mass is simply energy. Note that in intertial mass, you need to add all energy (potential, chemical or otherwise). A discharged battery literally has less mass as compared to a fully charged one. In other words, energy is mass. It’s simply two ways of looking at the same coin. Even for our bodies, say for protons and hence for molecules, most of the mass doesn’t come from quarks that make up them but rather from their interactions that have potential energy. Even for fundamental particles like electrons, it can be said that they’re moving at the speed of light and hence are massless. Their mass comes from Their energetic interactions with the Higgs field. #### on the conservation of energy It’s interesting to note that while energy is conserved within an inertial frame of reference, it’s not conserved between frames. For example, you’re at rest with compared to 1000 other balls around you and all balls have 0 kinetic energy. Now you start moving at a velocity v (notice your frame of reference changed), suddenly from your new reference frames, all 1000 balls have a velocity of -v and hence combined kinetic energy of 1000 * 1/2 * mv squared. So between reference frames, energy and momentum cannot be compared but within a reference frame, these quantities are conserved. https://leimao.github.io/blog/Mass-Energy-Equivalence-Derivation/