Question

What exactly is it that make the speed of light a "speed limit" for all material things, no matter the kind or amount of force exerted upon it? I know it has something to do with mass or relativity, but I would like to have a more specific explanation laid out.

Answer 1

there is a limit as to how we can explain that question.

we can say that due to relativity, an object slows down and the length contracts just enough so that it's speed stay below the speed of light.

we can also say that the mass increases as speed increases, using equations like:
\[\vec{F}=\frac{d\vec{p}}{dt}=m(\gamma\vec{a}+\vec{v}\gamma^{3}\frac{\vec{v}\cdot\vec{a}}{c^{2}})\]What this equation says is if the force is in direction of acceleration, gamma is to the power of 3. If perpendicular, then gamma is to the power of one.

however, this is just a math construct. mass, as we usually define it, does not change.