An innovative new "Waves of Space" model is presented, providing more unified and inter-related explanations of phenomena in physics. It might help to bridge gaps between general relativity and quantum mechanics, and to resolve other mysteries. Space, composed of uniform quantized units ("volons"), is proposed as the fundamental substance of the universe, and the medium of waves and fields. That agrees with super-substantivalist philosophy, and provides physical mechanisms that help make that concept feasible. Included are intuitive new conceptions of gravitation (deletion of space units, bringing bodies together, with gravitational potential energy absorbed into spatial pressure), and of the Hubble expansion (accelerating addition of space units, pushing bodies apart). Universe expansion and contraction phases might alternate, a "Big Bang" alternative. Waves and other processes in space produce properties of matter and most energy. "Standard model" particles are actually waves in the medium of space. Most are unsustainable and inconsequential transitional waves. Time is a relationship to repetitive motions in space. Four-dimensional spacetime is geometrically optional and complicates calculations. Space deletion in moving bodies generates the Lorentz transformations. Thermodynamics’ second law is a probability phenomenon, not universal. "Singularities," dimensionless points, and infinity lack physical reality. Mass can survive matter shrinkage or disintegration. Supporting this model, space has known physical properties and is expanding; particles have wave forms. This alternative to current theories offers causal mechanisms where currently only equations exist. New plausible hypotheses from outsiders have been resisted, but may be needed for physics, and associated philosophy, to progress.