Zeno argued that the smoothness of the continuum of space stops all motion.  Louis deBroglie argued that all particles are waves in space, and as such must have a velocity. They have to move.

These two diametrically opposed positions can be reconciled if we make the assumption that all quantum mechanical particles (particles that can exhibit interference) move by making precision wavelength jumps across space-time. At the end of each jump they appear for a moment and then they jump again continuing their journey. It is this type of discontinuous motion that is the bedrock of quantum physics. Technically speaking, nothing ever moves but everything changes. From the changes we can calculate a fictitious velocity. There is no such thing as velocity. Velocity is something we assume (invent) to make sense of how particles (and energy) change positions and time.

This type of pseudo motion (wavelength hopping aka λ-hopping) satisfies Zeno because particles never have a velocity where they appear. A particle never needs to “move” to the point closest to it. Particles by their nature jump over points in the continuum in a very curious fashion, they leave space-time. Particles never have an actual velocity but they digitally change their position. Even though they do not have a velocity at their position, a velocity  can be calculated for a particle over a wavelength.

This type of jumping motion also satisfies Louis deBroglie with the caveat that a particle’s velocity is always a calculation using the particle’s appearances at each wavelength hop.

With this wavelength hopping (λ-hopping) motion for particles we can develop a model of reality that can explain both quantum mechanical and gravitational phenomena in a way that can be visualized. This website is my attempt to advance this model of reality. I am Don Limuti creator of this website Digital Wave Theory and the concept of wavelength hopping (λ-hopping). You can find out more about me in Section 37.

This illusion of velocity is strictly applicable to quantum particles that have wavelength. Classical objects with a mass greater than the Planck mass can be considered to move continuously, even though their constituent quantum parts do not (see Section 29). This fundamental split of reality between the quantum realm and the classical realm will be developed in this presentation and will help to explain the nature of time (see Section 32).

Note that the classical notions of space and time are considered valid in DWT, they are continuous and do not have discontinuities. However, DWT maintains that the motion of quantum mechanical particles (and electro magnetic energy and gravitons) are discontinuous on this background of a continuous space-time.

Humanity in general has a genetic predisposition that demands that all objects (including particles and light) must have a continuous existence.  This predisposition comes from our history of handling and studying classical objects which do behave as continuous things.  However, the quantum mechanical world does not exist continuously!  This is a fact of nature and cannot be deduced by using the standard model of particle physics which is a continuous theory.  This is the cause of much of the controversy regarding Bell’s theorem, which essentially states that there is no way of saving quantum mechanics from being goofy (if you insist that phenomena must be continuous).

A wikipedia entry states that: Later in his life, Bell expressed his hope that his work would "continue to inspire those who suspect that what is proved by the impossibility proofs (of local variables) is lack of imagination." (click for link)

λ-hopping is the missing link, no lack of imagination here!  And Einstein was correct that quantum mechanics is goofy.  However, it may be the discontinuous way quantum mechanical things move and not a missing local variable that is causing the goofiness. See Section 6 for a new way to look at the EPR experiment.

The Philosophical Underpinning of Digital Wave Theory (DWT):

Calculus cannot break Zeno’s argument that motion is impossible.  The calculus definition of velocity as dx/dt is a failed attempt to justify the human genetic defect that demands that motion must be continuous.  See Section 12  Paradoxes.

Authors Note:   Some if not most of my readers will find my models of physical reality quite strange.    This is because my starting position is that reality (at the quantum mechanical level) is non-continuous. There is no proving (or disproving) this as Bell tried to do.  There is no finding a missing local variable as Einstein tried to do.  As soon as a scientist has a starting position that quantum mechanical objects must exist continuously, they are in a soup of confusion with many  contradictions and arguments that turn out to be silly when it is realized that their starting axion of continuity is not the way that nature operates on the quantum level.

The principles of superposition and uncertainty patch up this misreading of nature and have made it    possible to develop the standard model of particle physics. The Standard model of particle physics    is a marvelous, workable structure, but it is at its limit. It is time to begin developing our models of    nature starting with the truth that quantum mechanical particles do not move (they change    positions).  I contend that the models of reality presented here in DWT give a better understanding    of our world than those models of reality based upon continuity, superposition and uncertainty. Keep on reading, it gets much more interesting !