11  The Concept of Wavelength-Hopping                        Table of Contents     Previous    Next

Louis deBroglie’s famous equation is λ=h/(mv), where the wavelength λ is the distance a particle λ-hops.

Satisfying Zeno and deBroglie with the concept of λ-hopping.

  (Nothing moves and yet everything changes)

Velocity is Δx divided by Δt. There is no velocity at the position of the particle.  

Velocity is a property we calculate for a particle not a property that the particle has.  The logic of this is as follows:

1. Particles appear at a point of space-time then disappear and reappear “nearby” at another point     in space-time.  Wavelength (λ) is the distance between these two points in space-time.

2. A particle moves by going from a point in space-time, to another point in space-time. This is called λ-hopping. See Section 30 for a more complete model of λ-hopping.

3. During the hop the particle cannot be found in space-time. However, the particle can appear before or after its scheduled landing if it either emits or absorbs a photon (accelerates or decelerates) which it can only do during the hop. This action resets the hop after which the particle continues hopping at its new wavelength. It has a new wavelength because it has new calculated velocity. I do not have an reason for λ-hopping. It is just a way of interpreting the deBroglie equation that makes it meaningful. Thus it is a starting axiom. All quantum mechanical particles move by λ-hopping.  Note that Schrodinger interpreted the deBroglie equation as a continuous particle motion describable as a linear differential equation, the Schrodinger equation. This is somewhat workable but distorts the underlying reality (IMHO).

Particles are considered things that demonstrate the property of interference. So, electrons are   particles and so are C60 buckyballs in that both have been shown to demonstrate the property of interference.  A case will also be made that photons (energy) also moves by λ-hopping even though they are not quite particles (do not have a Compton wavelength). A case will also be made that gravitons (gravity particles) also move by λ-hopping. These gravitons do have a Compton wavelength and do carry a small amount of mass. This graviton mass will be shown to account for the dark stuff in the universe (see Section 19).

4. The wavelength λ cannot be known via one measurement. It takes at least two measurements to get a λ and the measurements always involve the emission or absorption of photons and thus has to be made with care because the measurement will effect the λ and the motion of the particle.

5. Once the wavelength λ is known by subtracting the second position from the first position (x2 - x1) we can then use it in the above deBroglie equation (if we know the mass of the particle) to calculate v the velocity of the particle.

6. Alternatively if we have a clock we can calculate the velocity of the particle as:  v = (x2-x1)/(t2-t1). 
7. Interestingly, Chemists when they consider the motion of electrons in atoms, think of them as hopping from energy level to energy level. The loss of continuity does not seem to bother them too much. It is not much of a stretch from this viewpoint to having electron movement in general to consists of hops.

A particle can propagate but it is never seen moving                      

a. At the instant a particle appears it has neither velocity nor acceleration; it just is. We infer motion by the history of the particle’s appearances. Note that this type of propagation is not true for ordinary objects like golf balls. The golf ball has so many random λ-hopping particles that they fill in all the space-time and leave no gaps for the golf ball to clear its own dimension, and the concept of a single λ-hop for the golf ball is not possible even though the golf ball is composed of many particles that do λ-hop (see section 29).

b. An observer and a memory (or persistence) of the past are needed to calculate the propagation speed of a particle. In many instances our senses and instruments do this automatically.

The concept of λ-hopping motion satisfies deBroglie, because all particles have a “movement” (velocity) that can be calculated (but is never seen directly).

Zeno is also satisfied because a particle is never seen moving, it just makes appearances. Said another way, particles do not have the property of velocity, velocity is given to them by their history.

A more detailed investigation into λ-hopping is found in section 30 (A tale of two wavelengths). It is very similar to what is developed here initially but goes on to speculate that light (and gravitons) are characterized by a single wavelength, while particles are characterized by two wavelengths (a deBroglie wavelength and a Compton wavelength).  Pure fun, check it out.

Where will a particle hop?
If conditions are simple, the particle will maintain its λ-hopping mode unless it is acted upon by other particles and/or energies (photons).  This is similar to Newton’s law of motion, saying that a body will maintain a steady motion unless it is acted upon by an outside force.

b.  I believe that Feynman’s sum over histories technique is also an answer to the question of where will the particle hop, but without the probability interpretation. Feynman needed probably because he considered the electron as having a continuous existence. A sum over histories technique taking into account λ-hopping will predict exactly where the electron will hop. Thus, where a particle will land depends upon the history of all other particles. This is very similar to Newton’s observation that a particle in motion will remain in motion unless acted upon by an outside force.

c.  In Section 16 the mechanism of Compton scattering is introduced.  This mechanism is also a way of understanding how a particle moves when it is “hit” with photons.

d.  In Section 29 the mechanism of Spin is introduced.  This spin mechanism is also a way of understanding how a particle has properties of mass, charge and anti-particleness. Sorry for the term anti-particleness.  Check out Section 33 and you will see why I introduced it, and if you have a better term let me know (don.limuti@gmail.com)....thanks.

The problem in visualizing λ-hopping:

When the λ-hops are short, we can think of the movement of photons and particles without much trouble. When the λ-hops are light years in length, our notions of a continuous particle become nebulous. This is because we do not have any experimental feel of this type of stuff. And when it comes to a minuscule graviton mass (see section 17) that spans hundreds of light years we are very much at a loss. How do we visualize and measure a very long string of nothingness? In section 19 I postulate that this string of nothingness has a very small mass and is actually dark matter and dark energy. 
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 superposition and uncertainty. Keep on    reading, it gets much more interesting !

Albert Einstein on λ-hopping:
Albert Einstein (1879-1955) Germany-Switzerland

"On a Heuristic Viewpoint Concerning the Production and Transformation of Light."

"Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt." Annalen der Physik. Leipzig 17 (1905) 132;

From the last two paragraphs of the introduction:

It seems to me that the observation associated with black body radiation, fluorescence, the photoelectric effect, and other related phenomena associated with the emission or transformation of light are more readily understood if one assumes that the energy of light is discontinuously distributed in space. In accordance with the assumption to be considered here, the energy of a light ray spreading out from a point is not continuously distributed over an increasing space, but consists of a finite number of energy quanta which are localized at points in space, which move without dividing, and which can only be produced and absorbed as complete units.


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