Researchers from the Austrian Academy of Sciences, the University of Vienna and the University of Geneva, have proposed a new interpretation of classical physics without real numbers. This new study challenges the traditional view of classical physics as deterministic.
In classical physics it is usually assumed that if we know where an object is and its velocity, we can exactly predict where it will go. An alleged superior intelligence having the knowledge of all existing objects at present, would be able to know with certainty the future as well as the past of the universe with infinite precision. Pierre-Simon Laplace illustrated this argument, later called Laplace's demon, in the early 1800s to illustrate the concept of determinism in classical physics. It is generally believed that it was only with the advent of quantum physics that determinism was challenged. Scientists found out that not everything can be said with certainty and we can only calculate the probability that something could behave in a certain way.
But is really classical physics completely deterministic? Flavio Del Santo, researcher at Vienna Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences and the University of Vienna, and Nicolas Gisin from the University of Geneva, address this question in their new article "Physics without Determinism: Alternative Interpretations of Classical Physics", published in the journal Physical Review A. Building on previous works of the latter author, they show that the usual interpretation of classical physics is based on tacit additional assumptions. When we measure something, say the length of a table with a ruler, we find a value with a finite precision, meaning with a finite number of digits. Even if we use a more accurate measurement instrument, we will just find more digits, but still a finite number of them. However, classical physics assumes that even if we may not be able to measure them, there exist an infinite number of predetermined digits. This means that the length of the table is always perfectly determined.To read more, click here.