From: mk_thisisit
Traditionally, metaphysics has been considered a branch of philosophy, dealing with statements or hypotheses that cannot be experimentally confirmed within science [01:35:00]. However, Professor Marek Czachor, a physicist from the Gdańsk University of Technology, proposes a shift towards “experimental metaphysics,” asserting that certain metaphysical questions can indeed be addressed by physics [01:55:00].
Historical Precedent and Decidability
The concept of integrating metaphysical questions into physics is not entirely new. Czachor references a Polish book from the 1980s by Hibner, titled “About the Decidability of Metaphysics” [02:17:00]. This book argued that disputes about concepts like absolute space or entities existing independently of an observer, previously considered purely philosophical, could be made decidable based on physics [03:10:00].
While acknowledging the significance of this idea, Czachor qualifies it, suggesting that claiming all such issues are decidable purely by physics might be an exaggeration [03:38:00]. This applies especially to issues related to Bell’s inequality and the objective existence of things [03:47:00].
Arithmetic as a Branch of Physics
A core tenet of Czachor’s proposed “experimental metaphysics” involves the reclassification of arithmetic. He argues that just as Albert Einstein’s work incorporated geometry as a branch of physics (as seen in general relativity) [20:49:00], [39:04:00], arithmetic structures should be treated similarly [25:50:00], [39:22:00].
The Relativistic Revolution in Arithmetic
Czachor highlights that the special theory of relativity already demonstrates how seemingly fundamental arithmetic operations differ in physics. For example, the addition of velocities at high speeds does not follow classical arithmetic [11:22:00]. While for an ant walking on a hand, velocities add up classically (10 cm/s + 1 cm/s = 11 cm/s) [10:10:00], this is not true for speeds approaching the speed of light [10:28:00].
“The theory of relativity basically uses modified arithmetic. In fact, I claim that the relativistic revolution, these particular relativities, this is an arithmetic revolution.” [12:41:00]
This observation leads Czachor to propose that if nature adds speeds in a “strange” way, it implies that every physical quantity might be added in a non-classical manner [14:15:00].
The Arithmetic of Time and Dark Energy
Applying this idea, Czachor hypothesized that time might also have a unique arithmetic. He explored what would happen if time’s addition followed a relativistic-like rule [15:27:00]. This approach allowed him to create a model that reproduces observed cosmic acceleration, which is typically explained by the hypothetical “dark energy” [17:04:00].
“I turned and I said that there is no dark energy but we don’t know how time is added. I wrote the equation, I solved it, I simply compared it with the model for which they got the Nobel and I got the arithmetic of time. It turned out that it is simply the arithmetic of time… I reproduce these data exactly.” [17:45:00]
In this model, the need for dark energy disappears, much like the concept of the aether was eliminated by the theory of relativity [18:53:00]. Czachor introduced the term “arithmetic of time” [19:32:00] and believes he is the first physicist to introduce these generalized arithmetics into physics [19:39:00].
The appearance of dark energy, in this context, is seen as a “clash between two different arithmetics” – humanity’s classical arithmetic and the universe’s inherent arithmetic [24:50:00].
Rethinking Bell’s Theorem
Czachor also applies his concept of variable arithmetic to Bell’s theorem. He suggests that Bell’s inequality, which is central to the theorem, relies on “certain type of calculations that use a certain type of pluses, a certain type of integrals and things like that” [29:03:00]. He compares it to the seemingly obvious geometric axiom that the sum of angles in a triangle is 180 degrees, which holds only in Euclidean geometry [29:23:00].
“I derive the Bell inequality, which is the same inequality as I derived Bell. Only that in my case, these signs, which there are these crosses, lines, or pluses and minuses, mean slightly different things, but it is the same as his. But my inequality is simply consistent with quantum mechanics, and his is inconsistent with quantum mechanics.” [30:48:00]
Czachor claims to have found a “hidden assumption” in Bell’s theorem which, when manipulated, allows for the standard Bell inequality to be broken while still meeting other key assumptions like locality and experimenter free will [34:12:00]. He states that he has provided a counter-example to Bell’s theorem [31:28:00].
A Paradigm Shift
Marek Czachor views his work as proposing a fundamental paradigm shift in physics [07:29:00], [38:55:00]. This shift involves treating arithmetic structures not as a priori truths but as something to be explored and determined experimentally, analogous to how geometry became an empirical branch of physics through general relativity [39:22:00].
He anticipates that this perspective, which allows for “loosening” mathematical structures to better describe reality, will prove to be a “very fruitful tool” for mathematical modeling [35:56:00]. Czachor is convinced that this approach will lead to further experimentation and an expanded understanding of fundamental physical quantities, asserting that his ideas will be “obvious to everyone” in 100 years [00:56:00], [03:03:00].