From: mk_thisisit
Professor Marek Czachor, a physicist from the Gdańsk University of Technology, proposes a fundamental shift in how we understand the relationship between mathematics and physics [01:08:00]. He asserts that the traditional arithmetic we use does not fully fit the description of reality, suggesting a need for a generalized arithmetic in physics [00:45:15], [01:16:00]. Czachor states that he is the first physicist to introduce these generalized arithmetics into physics [00:45:15], [01:39:00]. He believes that his ideas, which he refers to as changing the paradigm of physics, will be obvious to everyone in 100 years [00:56:00], [01:00:00], [03:8:14], [03:17:00].
The Limitations of Traditional Arithmetic
Czachor argues that the inherent operations of mathematical calculus, such as addition, subtraction, multiplication, and division, are built upon a specific type of arithmetic [08:30:00], [08:34:00]. He compares this to the freedom observed in geometric axioms, where non-Euclidean geometries emerged after Euclid’s axioms were challenged [08:48:00], [08:50:00]. He suggests that our understanding of “plus” might not be what occurs in nature [09:00:00].
Relativistic Addition of Velocities
A key example demonstrating the limitations of traditional mathematical operations in physics is the addition of velocities in the theory of relativity [09:15:00].
- If one adds the speed of light (c) to the speed of light, the result is still the speed of light, not 2c [09:15:00], [09:19:00].
- While an ant walking on a moving hand adds its speed to the hand’s speed linearly (e.g., 10 cm/s + 1 cm/s = 11 cm/s) [10:07:00], [10:10:00], [10:20:00], particles moving at near-light speeds in an accelerator do not [10:30:00], [10:33:00]. For example, adding 0.9c to 0.9c results in approximately 0.994c, not 1.8c [11:14:00], [11:19:00], [11:22:00].
- This discrepancy highlights that nature adds speeds differently than traditional arithmetic [10:41:00], [10:50:00], [10:55:00], [10:57:00]. Czachor labels the special theory of relativity an “arithmetic revolution” [11:36:00], [12:48:00].
The Arithmetic of Time and Dark Energy
Czachor applies this concept of generalized arithmetic to other physical quantities, specifically time [14:03:00], [14:05:00]. He suggests that the addition of time, or the passage of time, is a process whose arithmetic is not fully understood [14:48:00], [14:50:00].
He proposes that if time has a certain arithmetic similar to how speed is added in relativity, it could explain phenomena like the accelerating expansion of the universe without the need for “dark energy” [15:27:00], [15:42:00]. Dark energy was introduced to explain why the universe’s expansion is accelerating, contrary to standard theory predictions [16:11:00], [16:13:00], [16:17:00], [17:27:00]. Czachor’s model eliminates the need for dark energy, much like the theory of relativity eliminated the concept of aether [00:30:00], [00:33:00], [18:51:00], [18:53:00]. He obtained the “arithmetic of time” by solving equations and comparing them to models that account for the accelerating expansion [17:56:00], [18:00:00]. He emphasizes that the “arithmetic of time” is his own term [19:30:00], [19:34:00].
Arithmetic as a Branch of Physics
Czachor argues that arithmetic, like geometry, should be treated as a branch of physics [20:46:00], [20:49:00], [20:51:00], [25:50:00], [25:53:00]. He draws a parallel to Einstein’s inclusion of geometry into physics, which led to general relativity [03:59:00], [04:08:00], [20:51:00], [39:04:00]. Just as geometry ceased to be purely abstract and became subject to experimental verification, Czachor believes arithmetic should follow suit [39:08:00], [39:13:00], [39:15:00], [39:22:00]. This means treating arithmetic operations as potentially variable and subject to experimental verification [25:55:00], [26:04:00], [26:09:00].
Experimental Metaphysics
Czachor touches upon the concept of “experimental metaphysics,” which he defines as statements or hypotheses that were previously considered purely philosophical but can now be addressed by physics [01:44:00], [01:47:00]. He references a book from the 1980s titled “About the Decidability of Metaphysics” by Hibner, which explored whether issues like the absolute nature of space or the independent existence of entities could be resolved by physics [02:14:00], [02:17:00], [03:07:00]. Czachor’s work aligns with this idea, proposing that questions about how existence operates can be addressed through physics, challenging classical notions of reality, like whether the moon exists when not observed [04:08:00], [04:12:00], [05:04:00]. He differentiates his stance by emphasizing that his model does not face the same issues with free will as some interpretations of Bell’s theorem [03:42:00], [03:45:00], [03:47:00], [03:49:00].
Bell’s Theorem and the Role of Arithmetic
Czachor claims to have found a “hole in the whole” of established physics [00:16:00], [07:21:00]. His work provides a counter-example to Bell’s theorem [03:28:00], [31:28:00]. Bell’s inequality, a key part of Bell’s theorem, relies on specific mathematical assumptions about addition and integrals [02:59:00], [03:01:00], [03:03:00], [29:01:00], [29:03:00]. Czachor argues that Bell’s inequality, much like the 180-degree sum of angles in a Euclidean triangle, contains deeply hidden and non-obvious logical assumptions [29:12:00], [29:15:00], [29:23:00], [29:43:00].
He has derived his own version of Bell’s inequality where the mathematical operations (“pluses and minuses”) mean slightly different things, making his inequality consistent with quantum mechanics, unlike Bell’s [30:48:00], [30:52:00], [30:54:00], [31:03:00]. He discovered a hidden assumption in Bell’s theorem which, when manipulated in his model, breaks the standard inequality [34:12:00], [34:16:00].
Czachor is confident that there is at least a new arithmetic [25:06:00], [25:08:00], [25:11:00]. He believes the universe might have its own arithmetic, leading to a “relativity of arithmetic” similar to the relativity of geometry [25:28:00], [28:30:00], [28:32:00], [28:35:00], [28:41:00].
Reception and Future Outlook
While Polish scientists might treat his statements as an “oddity,” Czachor notes that there are a few people globally, particularly in financial mathematics, who utilize generalized arithmetics [00:49:00], [00:51:00], [03:37:00], [03:42:00], [03:48:00], [03:50:00]. His work is peer-reviewed and published, with a group of people who understand his concepts [03:17:00], [03:18:00].
Czachor believes his approach provides a “very fruitful tool” for mathematical modeling by loosening up mathematical structures and then using that “looseness” to describe reality [03:51:00], [03:54:00], [03:56:00]. He is convinced that this paradigm shift will lead to future experimental confirmations [03:40:00], [04:09:00]. He predicts that in 100 years, his current statements will be considered obvious [03:17:00], [03:19:00].