Mathematical Insights

The Atoms of Space

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In this brief note, it will be shown that space may have hidden properties normally attributed to elementary particles, such as mass and charge. We will also elucidate the thermodynamic properties of these atoms of space by modelling these atoms as ideal gas entities propagating disturbances at the speed of light. We have only demanded consistency in the formulas for circular motion, Einstein’s mass-energy eqivalance, wave-particle duality, Planck-Einstein equation, Newton’s law of universal gravitation, Schwarzschild solution of general relativity, the Reissner–Nordström metric and black hole thermodynamics. We will then use the adiabatic index formula to elucidate the degrees of freedom of these atoms of space. We will also reinterpret Einstein’s theories of relativity, solve the mystery of the double slit experiment, muse on the physical nature of dark energy, and finally uncover a possible blindspot that may have hampered progress in constructing a consistent and complete theory of quantum gravity.

Euler’s Formula is the Key to Unlocking the Secrets of Quantum Physics

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In this short note, the the key to unlocking the secrets of quantum physics will be elucidated by exploring the fundamentals of Schrodinger’s wave mechanics approach to describing quantum phenomenon. We will show that de Broglie’s wave-particle duality hypothesis which lies at the heart of Schrodinger’s wave-function \psi produces a complex wave equation whose mathematical structure can be described by Euler’s famous equation e^{i\theta}=cos(\theta)+isin(\theta) which basically describes a helical wave in 3D space. By comparing and contrasting the electromagnetic wave with that of a helical wave which Euler’s equation represents, we may have discovered the geometric basis for spin and helicity and antimatter with negative energies that Dirac uncovered in his relativistic reformulation of Schrodinger’s equation.

Visualizing Conway’s Game of Life

What do Conway’s game of life and graph theory have in common? They both can be represented by binary matrices: in Conway’s game of life, a 1 represents a live cell (black) and a 0 represents a dead cell (white); likewise, a graph can be represented by its adjacency matrix, where a 0 or 1 represents no link or a link between two nodes, respectively. Applying a nine-cell two-dimensional outer totalistic rule on a random binary square matrix simulates the evolution of the game of life as well as the evolution of a random network. Thus, although the underlying rule is identical in each case, the computation can be represented graphically in many different ways.