The latest theories and fundamental laws of physics, all in one place. From thermodynamics and electromagnetism to astrophysics, quantum mechanics, and particle physics—explore research and insights written with academic depth, yet made perfectly accessible.
Quantum fractal electronics redefines circuit behaviors beyond classical Ohm, Kirchhoff, and Maxwell laws through fractal dimension (𝐷𝑓), multiscale resonance, and quantum entanglement motifs. The goal here is to explain electron flow not only with linear resistance/capacitance but with self-similar energy distributions.
The laws of fractal optics are a new framework that explains the behavior of light beyond classical optical laws through multi-scale and self-similar structures. In this approach, fundamental laws such as reflection, refraction, and diffraction become scale-dependent; light produces both regular and chaotic patterns.
When we map cell organelles to functions in a quantum system, each operates like an operator. Thus, we can view the cell as a complete “quantum metabolism model”.
Quantum fractal electronics is an advanced field that unifies classical electronics with quantum mechanics through the principles of self-similarity (fractal) and multiscale resonance. These lecture notes present a systematic framework ranging from fundamental concepts to application areas.
Fractal Mechanics is not merely a theoretical framework; it is a powerful model used to explain multi-scale dynamics across different disciplines. Here are its main application areas:
Fractal Mechanics defines the motion and energy flows in nature through self-similarity and multi-scale dynamics. Instead of the classical 𝐹 = 𝑚𝑎, the fractal derivative expression is used: 𝐹fr = 𝑚 ⋅ ( 𝑑𝛼𝑣 / 𝑑𝑡𝛼 ) Here, 𝛼 represents the fractal dimension of the system.
Dyson spheres are mathematical structures built upon infinite energy density and vacuum fluctuations in the classical sense. According to fractal mechanics, however, these spheres are not single-scale; they are explained by multi-scale self-similarity motifs. That is, a Dyson sphere is not a flat sphere, but an energy lattice containing fractal sub-spheres on every edge.
According to fractal mechanics, the void is not “nonexistence”; it is a multi-layered carrier of self-similar energy and information flows. Both the void within the atom and the void in space are filled with fractal motifs: they gain structure through invisible but constantly changing flows of entanglement.
The constancy of the speed of light can be explained with different interpretations beyond classical physics, according to both relativistic and fractal mechanics. Let us unfold this through patterns and energy flow:
Fractal potential wells are an extension of classical quantum potential wells with fractal scale dependence; energy surfaces are modulated with wavy, self-similar structures, and the probability distribution of particles is shaped by multi-scale fractal motifs. This approach offers a wide field of application, ranging from atomic transitions at the micro-level to the energy flow around black holes at the macro-level.