From: mk_thisisit
Professor Marek Czachor, a physicist from Gdańsk University of Technology, proposes a paradigm shift in physics by introducing “generalized arithmetic” into the field [01:00:00]. He claims to be the first physicist to introduce these generalized arithmetics into physics [00:45:15], [01:40:41].
Core Idea: Arithmetic as a Branch of Physics
Czachor argues that just as Albert Einstein’s work incorporated geometry into physics, making it an experimentally decidable aspect of reality rather than an abstract a priori concept [02:49:00], [03:59:04], so too should arithmetic be considered a branch of physics [02:46:00], [03:50:00]. This means that the rules of addition, subtraction, multiplication, and division might not be universal mathematical truths but rather physical phenomena that vary depending on the context [02:55:00].
He highlights that traditional arithmetic, where “2 + 2 = 4,” might not accurately describe reality in all physical contexts [01:16:00]. He suggests that the “arithmetic of the universe” might differ from our intuitive understanding [00:40:41].
Examples and Applications
Speed Addition in Relativity
A primary example for generalized arithmetic is the addition of velocities in the theory of relativity [09:15:00]. Unlike classical mechanics where c + c = 2c (where c is the speed of light), in relativity, c + c = c [09:15:00]. This “relativistic addition” demonstrates that nature adds speeds differently than our naive mathematical intuition [12:04:00], making it an “arithmetic revolution” [12:48:00].
The Arithmetic of Time and Dark Energy
Czachor suggests that if speed, a quantity derived from distance and time, has a modified addition rule, then space and time themselves, or the operations of division involved, might also follow different arithmetic [12:28:00].
He proposes that the “arithmetic of time” – his own term [19:32:00] – might explain the accelerated expansion of the universe without needing to introduce the concept of dark energy [17:45:00]. By assuming a specific, non-classical arithmetic for time, similar to how speeds are added relativistically, he can reproduce the observational data that currently necessitates dark energy [18:00:00]. In this model, dark energy “disappears in the same sense… as the so-called aether disappeared” with the understanding of the theory of relativity [18:53:00].
Implications for Bell’s Theorem
Czachor’s generalized arithmetic also impacts Bell’s Theorem and Bell’s Inequality [29:01:00]. He argues that Bell’s inequality, which highlights inconsistencies between quantum mechanics and local realism, is derived using specific mathematical assumptions about arithmetic operations. By applying generalized arithmetic, he derives an inequality similar to Bell’s, but one that remains consistent with quantum mechanics [31:03:00]. He suggests that Bell’s inequality relies on “very deep hidden logical assumptions” that are not immediately obvious [29:43:00].
Reception and Future Outlook
Czachor acknowledges that his statements are bold and often treated as an “oddity” by many scientists [00:51:00], [03:35:00]. However, he notes that some mathematicians, particularly those in financial mathematics who also use generalized arithmetics, find his ideas compelling [03:48:00]. He is convinced that this approach, which he calls “experimental metaphysics” [02:16:00], allows for a very fruitful tool in mathematical modeling [03:56:00]. He anticipates that in 100 years, what he is proposing will be obvious to everyone [00:56:00], [03:14:00].