Kolmogorov Complexity, Causality And Spin

A novel topological and computational method for ‘motion’ is described. Motion is constrained by inequalities in terms of Kolmogorov Complexity. Causality is obtained as the output of a high-pass filter, passing through only high values of Kolmogorov Complexity. Motion under the electromagnetic field described with immediate relationship with Subscript[G, 2] Holonomy group and its corresponding dense free 2-subgroup. Similar to Causality, Spin emerges as an immediate and inevitable consequence of high values of Kolmogorov Complexity. Consequently, the physical laws are nothing but a low-pass filter for small values of Kolmogorov Complexity.

💡 Research Summary

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The paper proposes a highly speculative framework that attempts to reinterpret motion, causality, and spin through the lens of Kolmogorov complexity. The author begins by drawing an analogy between various observational “filters” (radio, X‑ray, infrared) and a hypothetical “complexity filter.” In this view, a high‑pass filter passes only strings (or trajectories) with large Kolmogorov complexity, while a low‑pass filter admits only those with small complexity. The high‑pass output is described as endless Brownian‑like, irreversible motion—a “foam ocean”—whereas the low‑pass output yields simple geometric objects (lines, circles, points).

The formal development starts with a topological space (X) and a finite alphabet (W). A quantization map (Q: X \to W^*) assigns to each point a finite word. Concatenating the words along a continuous path produces a “path word” (w); its Kolmogorov complexity (K(w)) is then used as a measure of the motion’s informational content. The author claims that high values of (K(w)) correspond to irreversible dynamics, while low values correspond to reversible, deterministic dynamics.

Next, the paper introduces the notion of a “Maxwellian Robot,” a mobile Turing machine with bounded memory and program length (m). The robot’s state is given by a universal turning machine (!), a self‑delimiting program (p), and initial conditions (c_0). Motion is modeled as the inverse image of the quantization map applied to the output of (!) on ((p,c_0)). External influences (forces, potentials) are represented by a transformation (E: W^* \to W^*) that perturbs the word (w). The robot is also capable of self‑replication, reminiscent of fork() or Quine programs, which the author uses to argue for a kind of computational self‑generation of space.

A central claim is that causality emerges only in the high‑complexity regime: the high‑pass filter isolates non‑reversible sequences, which the author equates with a well‑defined cause‑effect ordering. Similarly, spin is said to be an inevitable consequence of high Kolmogorov complexity; the paper suggests that when the informational content of a trajectory exceeds a certain threshold, rotational degrees of freedom (spin) must appear. No mathematical proof or physical model is provided to substantiate this link.

The author also attempts to connect electromagnetic motion to the exceptional Lie group (G_2) and its dense free 2‑subgroup, invoking the holonomy of a (G_2) manifold. However, the discussion remains purely verbal; no explicit representation, connection form, or curvature calculation is given. The statement that “the electromagnetic field is described with an immediate relationship to the (G_2) holonomy group” is therefore ungrounded.

Finally, the paper posits that conventional physical laws (Newtonian mechanics, Maxwell’s equations) are essentially low‑pass filters: they operate on low‑complexity, reversible structures. High‑complexity phenomena, according to the author, lie outside the domain of standard laws and are governed by the high‑pass filter, producing irreversible, stochastic behavior.

Overall, while the manuscript is imaginative and introduces intriguing metaphors (complexity filters, computational robots, self‑replicating space), it lacks rigorous definitions, theorems, and empirical validation. The mapping from Kolmogorov complexity to physical quantities is not specified, the role of (G_2) holonomy is not mathematically developed, and the claims about causality and spin are not supported by derivations or experimental evidence. Consequently, the work reads more like a philosophical speculation than a concrete contribution to theoretical physics or information theory. Future progress would require precise formulations of the complexity‑motion correspondence, explicit models linking (G_2) geometry to electromagnetic fields, and testable predictions that could be verified experimentally.