- A Galilean Multiverse? A Simple Physical Model of a Fractal Cosmos (2008) [Updated 1 decade ago]
- Time Standards and Particle Interactions in a Fractal Universe, with Remarks on Gravity (2005) [Updated 1 decade ago]
- Mechanics of Particles in the Fractal Cosmos (2004) [Updated 6 years ago]

- A Galilean Multiverse? A Simple Physical Model of a Fractal Cosmos (2008) [Updated 1 decade ago]
A new model of a cosmos with hierarchical Universes depends on the existence of three-dimensional (3D) standing wave (SW) patterns of various ranks. Various aspects of this model are explored, both qualitatively and quantita-tively, using simple geometries and simple physical concepts. The number of particles in our Universe is shown to equal the square of the ratio between the radius of the Universe and the effective radius of a particle. It is shown that a series of Universes terminates with our visible Universe.

- Time Standards and Particle Interactions in a Fractal Universe, with Remarks on Gravity (2005) [Updated 1 decade ago]
A fractal particle is a three-dimensional, standing-wave pattern. This paper examines how fractal particles can become shorter in wavelength ? and vibrate faster ? with the passage of time. ?Absolute? time is defined independently of particles, and hence is unchanging. ?Relative? time is based on the period of oscillation of fractal particles; it changes relative to the age of a fractal universe. In this paper, a simple, elegant equation is derived to correlate these two time standards, and calculate the age of our universe. I show here how particle interactions are possible: the standing wave around a source particle interacts with the maximum energy density at the core of a test particle, resulting in a redirection of energy, i.e., a force. For a test particle starting at rest, this electrostatic force increases the kinetic energy of the test particle. Repulsion between like-particles and attraction between unalike-particles is explained by the cylindrical or spherical symmetries of fractal particles. Gravitational attraction occurs because, as particle wavelengths become shorter with time, a portion of the energy stored around the test particle gradually is released in a way that causes an attractive force.

- Mechanics of Particles in the Fractal Cosmos (2004) [Updated 6 years ago]
A fractal particle is a three-dimensional (3D) standing wave (SW) superimposed on much smaller fractal particles, which comprise the finite substrate of one universe within a hierarchical series of fractal universes, or a fractal cosmos. In this presentation, units of absolute time and length are defined with respect to the fram or a fractal cosmos. In this presentation, units of absolute time and length are defined with respect to the frame of reference of a fractal universe. It is then shown that, for a fractal particle in motion, the frequency of vibration decreases (clock retardation) and the wavelength decreases in the direction of motion (length contraction) as the velocity of the particle increases with respect to the rest frame of (i.e., zero-velocity in) the fractal universe. Predications are in agreement with experimental results, yet the equations of "fractal mechanics" are derived without recorse to the controversial two principles of Einstein's special relativity theory (SRT). The present derivation is based on Newtonian mechanics as applied to the built-in clocks and rulers of a fractal particle. It is indicated that Einstein's

*ad hoc*derivation is preposterous and superfluous in the context of the fractal cosmos and leads to unnecessary paradoxes. In conclusion, the fractal cosmos hypothesis is compatible with experimental results relating to clock retardation and length contraction, suggesting that it is a robust theory worth examining in greater detail.