Chapter 19
What are de Broglie Waves?

These are also called matter waves. They were first proposed by Louis de Broglie in 1924 after he reasoned that because light  has both wave and particle properties, then perhaps particles, including macro-objects, should similarly behave like waves. The wavelength of electrons was confirmed a few years later.

de Broglie waves although tiny are a real property of matter. And they are the waves of Schrodinger’s equation, one of the main pillars of quantum mechanics. This will be discussed in a later section.

SED maintains that the dual wave-particle nature of everything exist because of the ubiquity of h or Planck’s constant. This represents the universal quantum of angular momentum or spin. Its definition in the sub-atomic world is h = mcλ, but in our larger macro world the normal expression for angular momentum  is, L = mvr, where L rather than h is used because h is just too small.to be practical. In this expression m is mass, v represents velocity, and r is its radius of motion, and it is their product that creates L. However these are both expressions for real angular momentum. Tiny and big.

Physics also uses an alternative but sometimes more convenient expression for Panck’s constant which is ћ = mcƛ. This is referred to as the reduced Plank constant and in it ƛ stands for the radius of the circular wavelength of the particle rather than its circumference. It only differs by a constant factor of 2π .This puts it more in-line with our larger, macro expression for L above. For they are both the same thing.

Returning to de Broglie waves, the reason for writing all this is because all particles have an effective wavelength that conforms to Planck’s expressions for angular momentum, both sub-atomic and macro particles. This is the essence of wave-particle duality.

Unfortunately modern physics has great difficulty in comprehending what de Broglie matter waves actually are. It often refers to them only in an abstract way as waves of probability because it denies that they actually have any real physical existence, just like it does for sub-atomic spin. SED however disagrees and says that both are real physical phenomena.

Until now physics has had no model to guide it and offer an explanation. It needs the concept of a roton that makes matter and matter waves based on rapidly rotating E-M fields to provide the answer.

The rate of spin of these waves within the roton (i.e. its frequency) define its energy or mass and likewise its size or volume. Yet a roton has no hard edge or surface. The influence of these E-M fields travel with the object through space and well beyond its size. Its spin is always h regardless of whether it is moving or not. So the surrounding space or any measurement made on the particle/object will reflect this because the universe abhors discontinuity.

Even in our much larger macro-world we find composite objects have a wavelength due to their mass in motion. This creates momentum, both angular and linear depending on whether they are moving in a circle or a straight line. We use the symbol L for angular momentum here, and define it as: L = mvr , where v is the tangential velocity and r the radius of motion. For this type of motion there is also an associated de Broglie matter wave that has a wavelength, λ according to Planck’s equation h = mvλ. This wavelength although real is incredibly small and not very significant. This is why it has remained unobserved.

Linear motion produces a similar property or de Broglie wave by virtue of the linear momentum of the object which is given by P = mv. Again its wavelength is obtained from the equation h = mvλ and unsurprisingly this matter wave is real but has a tiny wavelength because momentum is much larger.

Some further remarks concerning matter particles.

Phase velocity

Phase velocity is the velocity at which any single frequency within the wave packet of the  particle travels.

Group velocity

Group velocity is the velocity at which the overall envelope or particle travels. It is what we normally perceive as its motion.

The Origin of Everything
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