Minimum Energy Requirements of Information Transfer and Computing

In 1961/1962 this author proposed that the uncertainty principle of quantum mechanics imposes fundamental limitations upon computers (Bremermann, 1962a, 1962b). As Von Neumann (1958) pointed out, computers represent data by physical markers. In the course of computation, data are transferred between subunits. This implies that the physical markers that represent data must be measured whenever data are stored, retrieved, transmitted, or entered into the arithmetic unit, central unit, etc. Measurements are subject to error margins because of the Heisenberg uncertainty principle of quantum mechanics. In practice signal energies are large and markers are spaced far enough apart for quantum uncertainties to be insignificant. As computers are being miniaturized and signal energies are reduced the safety margins are shrinking, while at the same time computing power per pound of hardware is increased. Eventually a limit is approached where the quantum uncertainties prevent further miniaturization and an upper limit of computing power is reached. Data processing in a Von Neumann-type computer consists of several kinds of operations: input, output, storage and retrieval, logical and arithmetic operations, and control. Transmission between subunits lends itself most easily to a quantum uncertainty analysis. A unit that receives data from another unit must interpret the markers that are transmitted. We propose that the receiving unit is subject to the same uncertainty laws as the entity of quantum mechanics known as observer. In other words, the