|Long Exposure of double pendulum with LED at end of each pendulum|
It is hoped that a final, overall rotation will again deliver the required cup de grace – Quantization!
To deliver the appropriate conditions, let us choose a Compound Pendulum as our starting point, for even without any of the intended extra additions, these produce fascinating and complex behaviours. So, that if it is successively modified and appropriately “tuned”, it will take us through a range of stabilities, and even a final extra example of quantization – entirely as a result of oscillations and rotations alone.
But the usual form of a compound pendulum will require several additions in order to tune it into the possible stable forms that we are seeking. The diagram below shows the necessary construction.
This new form would commence by changes to the structure of the pendulum and the overall vertical vibration to attempt a “Walker-like” stability. Once this has been achieved, we could add a horizontal rotation via the included motor, and see the effects achieved at different rates.
If the discoveries of the Couder “Walker” experiments are applicable generally in appropriate circumstances, when driven by an overall vibration as a key component, that is also a continuous source of energy, we should expect to get both the establishment of a stable system, and, even more important, the clearly quantized results of the various added horizontal rotations.
Who fancies having a go at this task?