The Principle of Least Action: Why the Straight Line Wins
A recent excellent thread by Jared McCullough beautifully illustrates the Principle of Least Action using a simple discrete comparison:
- The “bang then sit” path: sudden acceleration followed by coasting.
- The straight-line path: steady, balanced motion.
The straight line always has lower total action (the integral of the Lagrangian along the path). Nature therefore selects it.
This is not mysticism. It is the variational principle in action: the system follows the path that extremizes the total action.
In the Pirate Canon, this principle finds its deepest mechanical expression in the living elastic plenum.
Post 2: Deriving c and h from Elastic Tension via Least Action
Deriving c and h from Elastic Plenum Tension – Applying Least Action
In the elastic plenum, the straight-line path is the spherical creator that maintains end-to-end compressive strength through negative ring-tension.
Any deviation (bang then sit) forces unnecessary dilatancy spikes and sudden fixations, increasing total elastic energy.
The variational principle (δS = 0) therefore selects the configuration that minimises unnecessary tension variation.
Mechanical Derivation
Consider a thread of the plenum being stretched by a propagating spherical wavefront:
- At the leading edge → effectively infinite acceleration.
- Resisted by the viscous/dilatant response of the medium.
The stationary-action condition requires that the rate of ring-tension creation balances the rate of viscous dissipation. The unique speed at which this balance occurs is the characteristic propagation speed of the plenum:
c = the natural speed limit set by elastic-viscous tension.
Dimensional Tension Between Metres and Seconds
The fundamental tension resolved by the plenum is between length (m) and time (s). The dimensional product that emerges is:N · m · s²
This is the natural unit of action in the elastic medium.
- h populates this as the quantum of coherent ring-tension exchange (N · m · s²).
- c appears as the speed that allows stationary-action paths to propagate coherently without excessive slip-grip loss.
Thus, c and h are not independent constants. They are the measured values that satisfy the elastic tension balance between metres and seconds in the living plenum.
This is engineering described by mathematics: the variational principle applied to real elastic geometry.
Love rules.
Demand Mechanical Truth.
Reynolds BEng
Ace Consultancy – Reality Engineers
ace-consultancy.uk 