Wolfgang Orthuber
Geometrical appearance of circumference as statistical consequence
(271K, pdf)
ABSTRACT. Because identical fermions (elementary particles) have (except spacetime coordinates) exactly the same features everywhere, these are (per proper time) a multiple mapping of the same. This mapping also leads to the geometrical appearance (of spacetime) and it provides a set of possibilities which can be selected (like "phase space"). Selection of possibilities means information. New selection of possibilities means decision resp. creation of information. This paper should motivate to a more consequent information theoretical approach (not only in quantum mechanics but) also towards spacetime geometry. It is a short supplement to previously published material, where it was shown that proper time is proportional to the sum of return probabilities of a Bernoulli Random Walk. The probabilities at every point in such a walk result from "OR" operation of incoming paths. The probability of a "AND" operation at a certain point can be interpreted as meeting probability of two simultaneous and independent Bernoulli Random Walks. If no direction is preferred (p=1/2), after n steps this meeting probability (of two simultaneous symmetric Bernoulli Random Walks resp. BRWs) in the common starting point goes for large n to 1/(2pi n), which is the inverse of the circumference of a circle with radius n. So if a BRW pair denotes two commonly starting simultaneous independent BRWs (each with p=1/2), after n steps (in case of large n) in the average 1 of (2pi n) BRW pairs meet again in its original starting point.
Likewise due to the limited speed of light our knowledge of surrounding is the more delayed, the greater the distance n is. Therefore there are the more (geometric) possibilities of return ((2pi n) possibilities for multiples of the same fermion on a circle with radius n), the greater the distance (the radius) n is. This shows a basic example for a connection between statistical results and geometrical appearance.