To synthesize gravity theory and quantum theory we extrapolate the common element of the relativistic lines of thought of Einstein and Heisenberg. Both substantially simplified and regularized some of the fundamental groups of physics. Extrapolating this process leads to a theory with a simple group. This requires one to modify the commutation relations for both general relativity and the standard model, but the change can be as small as desired. As an unexpected reward, all observables of the simple theory have finite spectra. The main singular non-simple group today is the Heisenberg group. The least change that simplifies it replaces each canonical pair p,q of the usual singular quantum theory by an SO(3) triplet ?p, ?q, ?r with large quantum number l and replaces Planck’s constant by an action variable ?r . The resulting finite quantum theory unifies space-time coordinates, energy-momentum variables, and dynamical variables in a way that preserves exact Lorentz invariance.
For exercise we first simplify a toy linear harmonic oscillator. It becomes a rotator with high fixed angular-momentum quantum number l. In the Heisenberg quantum theory all oscillators are isomorphic, but the finite quantum theory has distinct classes of soft, medium, and hard oscillators. Medium oscillators approach the familiar ones of the singular limit, but soft and hard oscillators have negligible zero-point energy and grossly violate equipartition and the Heisenberg uncertainty relation. Their energy is almost entirely kinetic for soft oscillators and potential for hard. Similarly, in the Heisenberg quantum dynamics all times are alike but in the finite quantum dynamics any time variable has distinct early, middle and late eras. This breaks invariance under time translation except as a singular limit, but exact conservation of energy is still possible.
Credit reporting companies serve as sources of information about consumers' use of credit as reported by those from whom consumers borrow. Lenders use this information to supplement whatever data they have already directly acquired about a borrower's creditworthiness to make lending decisions. As part of this system, lenders have incentives to report their own experiences with borrowers so as to gain access to other creditors' data in the future.
The credit data essentially represent a consumer's credit "reputation," based as it is on his or her borrowing and repayment behavior over time. In the past, this "reputation" was usually maintained by lots of local agencies working with local lenders with incomplete and often unverifiable information. Today, regulation and consolidation have led to highly automated national firms that compile far more detailed and complete information and comply with a range of policies designed to protect the interest of consumers.
How can the use of credit in anonymous exchange be supported in equilibrium? Does history offer examples of institutions that accomplish this? Financial instruments only arise when trust or enforcement are strong enough to break the one-shot character of anonymous barter and cash transactions. Before the advent of the modern territorial state with its law enforcement tools, traders could hardly hope for contract enforcement by authorities, whose reach was incomplete and at best only local. Under those circumstances, transactions that were asynchronous across space and time were ruled out, or limited to small minorities where group cohesion afforded the necessary level of enforcement, see Greif (1993).
