The digital randomness of black-body radiation

TL;DR

This paper analyzes the fractional part of black-body radiation energy using classical probability, revealing its binary independence and connection to zero-point energy, suggesting it acts as a natural random number generator.

Contribution

It introduces a classical probabilistic analysis of the fractional energy part in black-body radiation, linking zero-point fluctuations to random number generation.

Findings

Binary variables are independent at different positions.

The distribution of the fractional part can be recovered from independence.

Zero-point energy can be viewed as a natural random number generator.

Abstract

The statistical properties of the fractional part of the random energy of a spectral component of black-body radiation have been analysed in the frame of classical Kolmogorovian probability theory. Besides the integer part of the energy (which satisfies the well-known Planck-Bose distribution), the realizations of its fractional part (related to 'round-off errors') has been represented by binary sequences, like z = 0.001011000010.... It has been shown that the binary variables realized by the 0-s and 1-s at different positions are independent. From the condition of independence the original distribution of the fractional part z can be recovered. If these binary variables have the same distribution, then they describe a temperature-independent random energy, whose expectation value is just the zero-point energy. Thus, the zero-point fluctuation can be considered as a physical representative of an ideal random number generator.