The answer is N3 - and the same reason crashing a car into a concrete wall is twice as severe as a head-on collision of equal relative velocity, since it's the vehicles' speeds relative to the ground that enumerates and underwrites the value of 'velocity' in the KE equation, not their speed relative to one another.
In short, KE is relative, because motion is relative.. but what is that motion relative to? The zero-momentum frame; that is, the FoR from which the net change in momentum in each direction is equal and opposite. The bottom line is that when you accelerate towards or away from the tree, you cause an equal opposite counter-acceleration of the tree-plus-planet, the net mass of which divided by your momentum change gives the infinitesimal but non-trivial counter acceleration of the tree + planet... hence an external observer sees that the net system momentum is constant, and correctly calculates that your motion has virtually all of the kinetic energy of this particular inertial interaction. The property of matter enforcing N3 (and thus, N1) is mass constancy - 1 kg is always 1 kg, regardless of when, or at what speed, it is measured. More specifically, it is the time-invariance of inertia, since this is what we're really dealing with in all the equations of motion and mechanical energy. Doesn't necessarily apply to time-asymmetric gravitational interactions tho (ie. the kiiking principle), wherein momentum can be gained or lost to the inbound vs outboud gravity * time delta.. On Wed, Feb 26, 2020 at 7:21 PM H LV <[email protected]> wrote: > In Galilean relativity if I walk eastward towards a tree with uniform > velocity this is equivalent to saying the tree is moving westward towards > me with the same uniform velocity. As a fundamental proposition of modern > physics this is eminently useful but it is also absurd. It is useful if > what is deemed important about the motion of bodies is the possibility of > past or future collisions (In the absence of such obvious possibilities > the notion of a force was devised to explain changes in uniform velocity). > It is absurd because it is detached from what we actually know about the > world on a personal level. The tree is at rest because it is rooted in the > Earth and I am moving towards it. I cannot get the tree and the Earth to > move towards me by simply declaring I am at rest. There has to be a > property of matter that expresses this non-relative quality of "rootedness" > which has been ignored by physics since the 1600's. > > Harry >
