From: mk_thisisit
Professor Marek Czachor, a physicist from the Gdańsk University of Technology, proposes a paradigm shift in physics, suggesting that the arithmetic we currently use may not accurately describe reality, especially at extreme scales [01:03:00], [01:16:00]. He states, “I am changing the paradigm of physics” [01:05:35]. Czachor believes that arithmetic concepts are not abstract mathematical truths but rather physical properties that should be subject to experimental verification [02:50:00], [03:51:00].
Generalized Arithmetic in Physics
Czachor claims to be the first physicist to introduce generalized arithmetic into physics [00:45:45], [01:39:00]. This approach suggests that fundamental operations like addition, subtraction, multiplication, and division might behave differently in nature than our conventional understanding [08:30:00], [09:00:00].
Speed Addition and Einstein’s Special Relativity
A key example demonstrating this concept is the addition of speeds, particularly in the context of light [09:15:00].
- Classical Addition: For everyday objects, like an ant walking on a hand, speeds add linearly (10 cm/s + 1 cm/s = 11 cm/s) [10:07:00], [10:20:20].
- Relativistic Addition: However, for speeds approaching the speed of light, as demonstrated in a CERN accelerator, velocities do not add up in the classical sense [10:30:00]. For example, two speeds close to the speed of light will not sum to twice the speed of light but will remain at or below the speed of light [11:11:00], [11:19:00]. This phenomenon is explained by Einstein’s special theory of relativity [11:33:00].
Czachor asserts that the relativistic revolution was, in fact, an arithmetic revolution [12:46:00]. He posits that if speeds add up differently, then other physical quantities like space and time might also have a different underlying arithmetic [12:30:00].
The Arithmetic of Time and Dark Energy
Applying this concept, Czachor investigated the “arithmetic of time,” a term he coined [18:22:00], [19:32:00]. He suggests that the passage of time is a process of nature “adding” time, but how it does so is largely unknown [15:01:00], [15:10:00].
He performed a calculation assuming that time’s arithmetic behaves similarly to the relativistic addition of speeds [15:20:00]. This led him to a model where dark energy may not be necessary to explain the accelerating expansion of the universe [17:45:00], [18:00:00]. In his model, dark energy “disappears in the same sense… as the so-called aether disappeared as a result of no understanding of the theory of relativity” [00:33:00], [18:57:00].
“Dark energy at this point is a clash between two different arithmetic” [24:50:00].
Bell’s Theorem and the “Hole in the Whole”
Czachor’s first public appearance on the subject of Bell’s theorem was an inscription he made on a wall in a detention center, symbolizing his search for a “hole in the whole” in physics [00:09:00], [06:30:00], [07:17:00]. He claims to have found such a “hole” [00:16:00], [07:23:00].
Bell’s inequality, a core component of Bell’s theorem, is derived using specific mathematical assumptions about arithmetic operations [02:50:00], [29:00:00]. Czachor argues that these assumptions contain “very deep hidden logical assumptions” that are not experimentally testable [29:43:00], [30:05:00]. By manipulating these hidden assumptions within generalized arithmetic, he claims to derive a version of Bell’s inequality that is consistent with quantum mechanics, unlike the standard one [30:50:00], [31:06:00], [34:12:00].
He also touches upon the concept of free will in relation to Bell’s theorem, stating that if the observer lacks free will, it is difficult to prove Bell’s inequality [31:31:00]. However, in his model, there is no such problem with free will, as all assumptions are met [33:42:00].
Arithmetic as a Branch of Physics
Czachor draws a parallel between his proposal and Einstein’s inclusion of geometry in physics with general relativity [20:49:00], [39:04:00]. Just as geometry ceased to be purely abstract and became subject to physical laws, Czachor argues that arithmetic should be treated similarly [39:08:00], [39:22:00].
“Arithmetic becomes like a branch of physics at this point, just like geometry became a branch of physics” [25:50:00].
This view suggests that physicists should not assume a fixed arithmetic but rather “compare with the experiment and see which arithmetic agrees with the experiment” [26:09:00], [39:36:00]. He refers to this as “experimental metaphysics” or “experimental mathematics” [01:47:00], [28:50:00].
Czachor believes that the universe might have its own “arithmetic” and “geometry” [28:41:00]. This perspective leads to the idea of the “relativity of arithmetic,” where different arithmetic structures could be equally valid, and the challenge lies in understanding how to translate between them across different physical levels [22:45:00], [25:27:00], [30:00:00].
This approach offers a “very fruitful tool” for mathematical modeling by “loosening up” mathematical structures to describe reality [35:56:00], [36:02:00]. Czachor is convinced that his research points to a “new arithmetic” [38:38:00], and that in 100 years, his ideas will be obvious to everyone [00:56:00], [38:17:00].