If we interpret waves literally, then you can have a wave doesn’t have an exact location, but instead has a density or quantity function given a location. That is, I can’t tell you where a wave is, though I can delimit its boundaries, and provide a function that, given a coordinate, will tell you the density or quantity at that point. If information is conserved physically, and I show it isn’t in some cases, simply because energy is not conserved, unlike momentum, which is, apparently, always conserved, as far as I know. Specifically, gravity causes unbounded acceleration, which violates conservation of energy (macroscopic potential energy just doesn’t make any sense), but you don’t need to violate the conservation of momentum, if you assume that either an offset occurs when gravity gives up energy (e.g., the emission of some other particle or set of particles), or, gravity has non-finite momentum to begin with (see Equations (9) and (10) of, A Computational Model of Time-Dilation). Gravity is by definition unusual, since it cannot be insulated against, and appears to have the ability to give up unbounded quantities of momentum to other systems. At a minimum, the number of gravitational force carriers that can be emitted by a mass of any size appears to be unbounded over time. As a result, the force carrier of gravity is not light. The same is true of electrostatic charge and magnetism, neither of which can possibly be carried by a photon, given these properties.

If information is conserved in this case, then when a particle transitions from a point particle to a wave, the amount of information required to describe the particle should be constant. Let’s assume arguendo, that the amount of information required to describe the properties of the particle in question doesn’t change. That is, for example, the code for an electron is the same whether it’s in a wave state, or a point state. If this is the case, then the only remaining property is its position, which is now substituted by a function that describes the density of the electron at all positions in space, which will in turn delimit its boundaries, if it has any (i.e., a density of zero at all points past the boundary). Again, assuming information is conserved, it implies that the amount of information required to describe the density function of the wave will be equal to the amount of information required to describe its position, as a point particle. If it turns out that space is truly infinite, then that function cannot have finite complexity.