## The Guiding Wave

To be able to signal at any instant and location the return of energy/momentum needed to achieve energy conservation, the accumulating deficit must be accessible to the particle instantaneously over a wide area of the interface of the void with spacetime. The fluctuating accumulation of deficit must therefore be moving at the speed of light in the form of a two-dimensional cloud spread across an extended region of the spacetime interface before, after, and multiple times around the deviating particle. To work, the correction process must be non-local, in the sense of not being confined to a single point.

*Here a particle is moving into the screen. All around it is a
continuous space that appears as a series of concentric regions. The
correction process must be spread out over this region to be able to
respond instantaneously. It must therefore be non-local.*

The momentum of a photon is located at the particle, a point traveling in spacetime. The potential energy in the bulk is without its own dimensions or structure except at the two-dimensional spacetime surface. For the bulk, the spacetime interface appears as a continuum of rounded hills and angular valleys, formed by the outside surfaces of packed spheres. When the cloud of required corrective energy/momentum travels over an assembly of concentric surfaces like this, it will be shaped by the periodic pattern of the interface. That is, it becomes a wave.

*Spaces in the continuous medium around quanta form a wave
structure around a particle. The frequency of the wave will be a very
distant subharmonic of that shown here, and will have some random
jitter. It will match the moving potential energy in the void to the
kinetic energy of the electron or photon.*

The result is a complex wave of energy/momentum spread out laterally and vertically, deviating in consort with a particle. It donates the needed increments of momentum then accepts their return in the zero-sum exchange that sends the particle back to its proper track at regular intervals. The wave’s potential energy must match the kinetic energy of the particle. As the energy of a wave is proportional to its frequency, this sets the frequency of the guiding wave. I suggest that in the transmission of light through a vacuum, the frequency of the guiding potential energy wave correcting particle paths in spacetime is the frequency attributed to a photon or electron when it is thought to become a wave.

The guiding wave can be revealed by a screen with two parallel slits about 2 mm apart, placed in front of a monochromatic light. Arrival of light from the slits is registered on a display. At very low intensities of the source. Individual photons causing flashes on the display arrive at random times and positions (angles of flight), showing the randomness of their paths. However, as time passes, the arrival points coalesce into the stationary pattern of a wave.

The wave resembles that forming when two waves collide in water (in a harbor with two entrances, for example). Moving crests of two incoming waves of the same wavelength continually meet at the same location. There, they combine, and form a stationary peak. Where troughs meet, they form a stationary trough. The rest of each wave provides a smooth transition between peaks and troughs, transforming the kinetic energy of the moving waves into a stationary wave of potential energy.

To produce a stationary wave at the display, the twin slits are dividing a wave of potential energy traveling with the particles into two components with the same wavelength and phase that combine after the slits. The resulting standing wave pattern steers particles emerging from the slits at different angles to different points in the pattern. The standing wave does not provide path-correction, but signals the presence of a wave arriving at the slits that does.