The Integration Principle A Unified Theory of Force, Energy, and Uncertainty.

Hakan ÜNAL

Hakan ÜNAL

takashi ueda

We present a hypothetical approach showing that the unified field theory (UFT) previ- ously proposed by the author may deterministically include quantum theory. In the UFT, the force is given by F = −H × M2/Mp, where H is the unified energy function. Between a photon and a slit wall, Hnon-self ̸= 0, and the deflection angle of the photon is θphoton = (y + z)M1Dc2 (r 2 − (y 2 + z 2)) FPl . For an electron, the self-term does not vanish, and the deflection angle becomes θelectron = (y + z)M1Dc2 (r 2 − (y 2 + z 2)) FPl − 2M2c 2 zFPl , where M1 = mslit − qslitme/e is the effective mass of the slit wall, M2 = 2me is the effective mass of the electron, y is the projected radius of the slit, z is the particle radius, D is a dimensionless coupling constant, and FPl is the Planck force. The overlap of the radial dispersions from the two slits produces regions of high and low particle density, reproducing the interference pattern. Thus, wave nature can be explained as the statistical con- sequence of the non-equilibrium force from the slit walls. Furthermore, from the photon–electron force derived in the Compton scattering preprint, ∆F = − h(ν − ν ′ ) re , ∆t = re c , ∆p = − h(ν − ν ′ ) c , the relation ∆x ∆p ∼ h can be derived, suggesting that the uncertainty principle may also emerge from the non-equilibrium force and interaction time of the UFT. This paper presents the hypothesis that the UFT deterministically includes quantum theory, and specifies experimental tests.

Rudolph Willis

This paper proposes that quantum uncertainty arises from stochastic mass-energy interconversion at the subatomic level. Integrating Einstein's mass-energy equivalence and quantum mechanics, the hypothesis introduces fluctuating mass terms into mathematical frameworks like the Schrödinger equation, yielding novel implications for the Heisenberg Uncertainty Principle. The theory extends to quantum field theory, string theory, and cosmology, suggesting a dynamic mechanism for phenomena ranging from particle decay rates to black hole evaporation. By bridging quantum mechanics and general relativity through stochastic fluctuations, this framework offers testable predictions for high-energy physics, gravitational wave analysis, and cosmological observations, advancing the search for a unified Theory of Everything.

Wen-Xiang Chen

Kexin An

This article establishes the proof of the Schrdinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrdinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrdinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.