Physics of Ownership (DRAFT notes)

While capital by itself has not an appropriate scale to be measured, ownership lets such capital to be traded against a measurable good, usually called money. The study of this spontaneous apparition of scale has only recently attracted attention of modern physicists. Here we accumulate a collection of references, mostly from the point of view of mathematical physics.

From the point of view of fundamental physics, this research is also important, because it provides a different playground for our mathematical tools, then helping us to distinguish between physical principles and sophisticated mathematical tools.

Technical notes

• Experimental input is only widely avalaible from stock markets, so research is centered in the field of finance, where we are interested on study the trajectory of a given "portfolio".
• The "action principle" is usually implemented through the requeriment of "no arbitrage opportunities". Roughly speaking, an arbitrage opportunity is a situation where one can get some benefit without risk. The closest simil in classical mechanics is the existence of conjugate points in a non-minimal trajectory.
• This action principle can be deformed in different ways, by implementing some minimum time unit, by asking for transaction costs, etc.
• While empirical studies of scaling are abundant, the theory lacks yet of the tools usually related to it, such as path integration techniques or Wilson-like perturbations near a fixed point.

Historical notes

• The relationship between ownership and price was first noticed by Tales, who demonstrated it by setting up a speculative operation over oil mills.
• The view of ownership as origin of monetary valuations was first acknowledged and developed by Proudhon and followers?.

Philosophical notes

• It is argued by modern thinkers that the unregulated variant of trade leads to optimal distribution of available capital, but the question remains unsettled, and mostly undefined.
• Past century philosophers have suggested models where ownership (neither private or public) is not introduced, then avoiding the breaking of scale. A good candidate for such "fixed point" economy could be Kropotkine' model, where capital availability goes to infinity, but relative flows of goods between productive units are preserved, being yet driven by private iniciative
• Competition/cooperation.

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