Comment on A little physics riddle
Womble@lemmy.world 5 weeks ago
You dont have sufficient information to calculate the momentum of the third body in the new system. If you are treating the system as Newtonian you need the mass of it to calculate its momentum in the new frame, if you are treating it as relativistic you need its total energy.
pglpm@lemmy.ca 5 weeks ago
Completely agree, which I think is very interesting. In Newtonian mechanics, some scalar and vector quantities such as mass, internal energy, contact forces (stress), heat flux are frame-indifferent. Other, such as velocity and acceleration, are frame-dependent but we do have transformation rules for them. Some quantities – and quite important ones – such as momentum, are in a sort of limbo: they are frame-dependent, but there’s no clear transformation rule for them.
From the point of view of relativity theory, it’s interesting to note that for this particular case of coordinate transformation – note that it is not a Lorentz boost – we can actually calculate the spatial components of momentum in the new coordinate system, if the reported momentum is expressed as a covariant vector (p_µ). This is because its unknown temporal component (energy) gets multiplied by zero in this transformation. But the text is ambiguous on whether the reported components are covariant or contravariant.