Symmetric Sampling and the Discrete Laws of Physics (2): Measuring Quanta arriving in a Sensor

The classical sampling theorem was refuted in part-1 of this series due to its circular proof: the proof is always true, whether the input signal is under-sampled or not. The symmetric-sampling theory of part-1, is here presented, while minimizing on the mathematics. The classical sampling theorem [Shannon 1949] is based on sampling deterministic signals and produces a finite number of measurements at specific sampling points. At each sampling point, however, the measurement must reach infinite precision. That creates a measurement problem in sampling theory, which is mirrored by an equally fundamental measurement problem in Quantum Mechanics and in all of Physics. Deterministic Classical Physics does not include measurements; it only includes predicting infinitely precise results postulated by “Laws of Physics”. Those postulated results serve only to confirm theoretical predictions. Physics must rather be based on collecting information, that is, on learning from the real physical experiments. Classical Physics is thus constructed with “inverted logic”. Solving this measurement problem calls for a reformulation of the Laws of Physics in discrete form. The mathematical details of such a Discrete Physics are covered in part-3 of this series. Discrete measurements (the act of information collection) on a physical system can never lead to deterministic results since measuring anything to infinite precision requires an infinite amount of energy. Representing a deterministic function in a digital computer to infinite precision, is equally impossible. Symmetric-sampling allows one to assess the physical world by measurements and calculations, without ever deranging into singularities or infinities: not at the small-scale (high-frequency) limit, and not at the large-scale (low-frequency) limit. Symmetric-sampling, combined with a coherent information harvesting strategy, resolves the measurement problem in Physics, including Classical Sampling; Quantum Mechanics; General Relativity, etc. Jumping ahead to the overall conclusions of this series: the 1920s Classical Quantum Mechanics is not only “incomplete”, but it is also superfluous. That conclusion will allow us to leapfrog straight into the realm of a discrete version of Quantum Field Theory (QFT) in future parts of this series.