What happens when it's all mounted to a rotating wheel is getting a bit ahead for now, but on the face of it, i consider it a foregone conclusion that all GPE outputs and inputs sum to unity.eccentrically1 wrote:After the actuator fires, the 1kg upper mass will have to dragged around like you say. That is the reaction, just delayed. The lower mass, or an angular replacement, will begin to lose momentum at the end of the actuator travel as the upper mass's reaction kicks in. Then, as always, the next question is how much does it cost to reset the actuator.
Looking forward to the results.
The form of gain here is very specific - with an effective N3 break, we can buy momentum at a fixed energy rate per unit from within the accelerating system. Each asymmetric inertial interaction leaves an accumulating excess of momentum, and so each subsequent interaction begins at a progressively-higher starting velocity. However the cost of operation of the asymmetric inertial interaction is speed-invariant, so it doesn't increase with rising velocity. From the external reference frame however (ie. us observers, outside the system) the value of the energy being expended on-board is being inflated by the ever-rising ambient momentum of the system inside which those interactions are being applied.
For example, suppose the internal acceleration applied by the jack is 1 kg by 1 meter / sec, then, per the standard KE term (KE = 1/2 mass times velocity squared), it is performing just 1/2 a Joule of work.
If however the system is already moving at some speed, say 1 meter / sec, then the on-board acceleration of 1 m/s brings its net momentum, relative to us stationary observers, up to 2 m/s.
Normally, due to N3, net system momentum is conserved, and the on-board forwards-acceleration will decelerate the net system by an equal amount, keeping net momentum constant. This is why you're not supposed to be able to change a system's net momentum from within that system - an external force must be applied.
And so while the on-board mass is accelerated by 1 m/s, the net system decelerates by the same amount, and only the relative velocity between the system's on-board components changes, ie. its internal distribution of momentum. Externally, the net momentum's constant, and us static observers see a net 1/2 m/s acceleration of the on-board mass, along with a 1/2 m/s deceleration of the net system.
On-board, the work performed was still a 1 kg-m/s acceleration, at a cost of 1/2 a Joule, but the net system momentum remains constant, and 1/4 of a Joule is spent accelerating some of its mass, while the other 1/4 of a Joule was spent decelerating the corresponding counter-momentum.
With an effective N3 break however, the net system is not decelerated - because we fiddled our way out of inducing the corresponding counter-momentum in the first place!
And so the static observer sees the on-board acceleration of 1 kg-m/s, at an on-board cost of 1/2 a Joule, as an acceleration from an initial 1 m/s, up to 2 m/s. And at 2 m/s, a 1 kg mass has 2 Joules - an increase of 1.5 J from the 0.5 J it began with..
And so while only 1/2 a Joule has been spent internally, externally, the system energy has risen by three times more than the internal work performed.
If we had some kind of accurate KE sensor sat on our desk monitoring the experiment, it would record an impact energy of 2 Joules. If we calculate the mass's energy as a function of its speed relative to us, we get 2 Joules. So the mass quite objectively has 2 Joules. Yet, the system only performed 0.5 Joules of work...
That is the gain principle, and yet to be demonstrated.. What we have here, so far, is an apparent N3 break - the secret sauce. The actual stir-fry comes next, but all the gravitational interactions will be a zero-sum game - the same amount of mass will rise and fall against the same gravity field, for zero net cost or benefit, besides skewing the distribution of momentum during the inertial interaction, and hence causing an N3 break and net momentum rise.
Likewise there's gonna be frictional losses etc. in a real-world build, but if you extrapolate the asymmetry i've described to higher velocities, you'll quickly see that the potential gain margins are many times greater than the potential entropic losses of even the shoddiest build..
Bottom line is that either this is an effective N3 violation or it isn't. If it is then we're in business. So far, i'm still confident.. moreso than ever in fact..