Physical Quantities and Measurement

Enrico G. Beltrametti

Ragne Emardson

Wolfgang Orthuber

Every physical measuring needs a finite, different from zero measurement time and provides information in form of the choice of a measurement result from all possible measurement results. If infinitely many (different) measurement results would be possible, the choice of a measurement result could deliver an infinite quantity of information. But the results of physical measurings (of finite duration) never deliver an infinite quantity of information, they describe past, finite reality. Therefore the set of all possible measurement results a priori is finite. In the physical reality only a finite information quantity can be processed within a finite time interval. For mathematical models whose representation requires a processing of an infinite quantity of information, for example irrational numbers, no (exact) equivalent exists in the physical reality. So mathematical calculations, which have an equivalent in physical reality, can include only rational (finitely many elementary) combinations of rational numbers. Conclusions arise from this for the foundations of mathematical physics.

K. A. Tsokos

Luca Callegaro, Francesca Romana Pennecchi, Walter Bich

The paper ``Physics without determinism: Alternative interpretations of classical physics'' [Phys. Rev. A 100, 062107 (2019)] defines finite information quantities (FIQ). A FIQ expresses the available information about the value of a physical quantity. We show that a change in the measurement unit does not preserve the information carried by a FIQ and therefore that the definition provided in the paper is not complete.

Jean-Louis Basdevant