Lately however, as the search closes in on any remaining stones unturned, it is clear to me that we're looking for a symmetry break between input GPE and output KE, and that such an open thermodynamic system can only arise from a reactionless acceleration between inertially isolated velocity reference frames. The means for applying such an acceleration may simply be gravity itself; the hand merely needs release the weight, for it to unilaterally accelerate away.
Hence for some time now i've been considering weight drops in an elevator car travelling up or down at constant velocity. Because gravity's an ambient acceleration, it's invariant of velocity; drop a weight whilst riding an elevator car at constant speed and it'll experience exactly 1 G, basically exhibiting the same transformation of GPE to KE relative to the lift car regardless of whether it's rising, falling or stationary.
The changes in absolute GPE and KE however are of course subject to the elevator's state of motion. When we compare the energy metrics between these two inertial reference frames, we appear to see tantalising hints of a potential symmetry break, as yet unrealised..
For example, consider an elevator travelling upwards at a constant 1 m/s. A 1 kg weight is latched to the ceiling. After say 1 second, the latch is released, dropping the weight to the elevator floor. If we make the elevator car - and thus relative drop height - about 2 m tall, and model the system right up to the moment prior to impact such that all GPE is converted to KE relative to the elevator car, then we find a surprising outcome: within the rising elevator, the relative conversion of GPE to KE is unremarkable, but from the external, ground frame of reference, the absolute GPE and KE deltas appear disparate, and it is the potential opportunity in the emergence and nature of this apparent disparity that i intend to investigate here.
Below is a simple model of that system; initially stationary, after 1 second the weight is released, the sim pausing in the final frame prior to impact, hence a full conversion of GPE to KE relative to the elevator car:
Now a moving example, the elevator rising at a constant 1 m/s:
rel delta GPE = -15.69 J
rel delta KE = 15.69 J
But look at the absolute figures:
abs delta GPE = -0.28 J
abs delta KE - 11.09 J
The weight's initial half-Joule of upwards KE inverted back down to zero and climbed up again as the weight's absolute vertical velocity flipped direction, from slowly rising to rapidly falling, ending up with 10.59 J, hence a total dKE of 11.09 J.
However the absolute initial and final GPEs of the weight itself have hardly changed; with a little more finesse we could tune the interaction such that the absolute net change in GPE was zero..
..and thus you see the connection to the opening context of lifting and dropping the point of application of a weight, as opposed to the weight itself; since here we appear to have pretty much that same outcome, of an absolute change in KE yet divorced from a corresponding absolute change in GPE. If no weight was actually dropped, then what converted to KE?
Of course in the round, we still lifted and dropped the weight; i'm not suggesting there's any anomaly here - a full accounting including the work done by the elevator car will obviously resolve to unity - however in the search for an exploit, this seems a potentially interesting dynamic for further investigation.
The objective would be an effective symmetry break between relative and absolute values of 'height' and 'velocity' in the GPE and KE formulas; usually, both remain relative to ground and thus the absolute FoR, due to the actions of Newton's third law. The chink in the armour, if there is one, would be the fact that GPE is invariant of constant absolute vertical velocity - that 1 J of GPE will convert to 1 J of KE relative to the elevator car, regardless of its absolute constant velocity or direction relative to ground, and hence in spite of disparity with the absolute energy metrics.
We can underline the potential disparity between the speed-invariant GPE-KE conversion onboard the moving elevator versus its absolute quadratic relationship to velocity by simply increasing the elevator speed in the next example to, say, 10 m/s:
Aboard the rising elevator, Alice would report dropping 15.69 J of GPE, neatly converting to 15.69 J of KE at impact with the car floor. Bob watching from ground level however would see gravity decelerate the weight's absolute KE by 40.33 J; the same change in velocity worth different energies in their respective velocity frames of reference. Again, what is constraining the net system to unity regardless is the work done by the piston driving the elevator car, and specifically the reciprocation of forces per Newton's third law. Opening the system to a disunity requires breaking that energy equivalence between different velocity frames, ultimately by causing the inertial reference frame of the 'elevator' to diverge from that of the ground / absolute frame, by exploiting an effective circumvention of N3.. somehow, courtesy of gravity.
Don't expect any whirlwind developments here, i'm just kicking this out there half-baked to try crystalise my thoughts on the matter; it's a meditation on a potential route to a solution - the potential seed of an exploit - not necessarily the solution itself.
For a final thought however: "I don't want to go into the details here of how suddenly the excess weight is caused to rise. You can't comprehend these matters, or see how true craftsmanship can rise above innate lowly tendencies (as does a weight above the point of application of a lever)".
