3.4.4.1  Wave-Particle Duality

As we have already noticed in chapter II, since the early history of ancient philosophy and up to the current modern theories, there had been always two opposite views, manifested in various ways, such as: the continuum and discretuum structure of space, the atomic and substance theories of matter, the geocentric and heliocentric models of the Universe, and the modern relativity and quantum theories. We also explained that the reason why scientists and philosophers are facing these conflicts is because they are studying the various phenomena of physical multiplicity, each from their own perspective, while reality is metaphysical and indivisible, and although other philosophers have studied the metaphysical or ontological oneness of nature, but they could not make any application of it, because their theories were all abstract and incomplete.

The wave-particle duality is another manifestation of this conflict between the two contrasting views of space, time and matter: whether they are infinitely divisible or indivisible, or whether they are discrete or continuous. The corpuscular theory of light is attributed to Descartes as we have seen in chapter II (section 13), who proposed that light is made up of small discrete particles called “corpuscles”, or little particles which travel in a straight line with a finite velocity and possesses impetus. This was based on atomistic description advocated by Democritus who argued that all things in the Universe, including light, are composed of indivisible atoms. We also mentioned in section 16, of the same chapter, that Newton also developed and championed the corpuscular hypothesis, arguing that the perfectly straight lines of reflection demonstrated light’s particle nature, because only particles could travel in such straight lines. On the other hand, other scientists at the time, such as Hooke and Huygens, and Fresnel at a later time, all argued for the wave nature of light, which was subsequently experimentally supported by Young’s double-slit interference in 1803. Another important support for the wave nature of light came after Maxwell formulated his four equations, when he discovered that he could apply them to describe the propagating waves of oscillating electric and magnetic fields. It quickly became apparent that light was actually electromagnetic waves.

As we have introduced above, the quantum nature of radiation was suggested by Planck in 1900, and after five years Einstein applied it to explain the photoelectric effect by postulating that a beam of light is a stream of particles, which were later called photons, whose energy is proportional to their frequency according to Planck equation. This meant that the photon is a particle that is still described as a wave with frequency. Einstein was awarded the Nobel Prize in Physics in 1921 for this discovery which explained the photoelectric effect.

In 1924, de Broglie claimed that, not only light, but also matter particles, such as the electrons, may have the same nature of waves, and he proposed the relation that gives the length of the wavein terms of the particle momentum:

This equation is a generalization of the relation between the energyand momentum:

Here of courseis the speed of light in vacuum, which naturally equals the wavelength of light by its frequency:, and thus by taking into account Planck’s equation 3.15:, we can easily get the above formula of de Broglie.

Through the observation of electron diffraction, De Broglie’s hypothesis was confirmed three years later, and he was awarded the Nobel Prize for Physics in 1929 for this remarkable discovery.

Later experiments in 1929 have clearly shown that neutrons and protons exhibit wave properties. Other recent experiments also confirmed the wave behavior of atoms and molecules. In 1999, the diffraction of C60 fullerenes was reported, and in 2003, the wave nature of tetraphenylporphyrin was also demonstrated. More recently it was shown that we can use macroscopic oil droplets on a vibrating surface as a model of wave-particle duality, localized droplet creates periodical waves around and interaction with them leads to quantum-like phenomena.

The wave-particle duality is deeply embedded into the foundations of Quantum Mechanics, because all the information about a particle is encoded in its wave-function that evolves according to the Schroedinger equation. Even for particles with mass, this equation has solutions that follow the form of the wave equation, whose propagation leads to wave-like phenomena such as interference and diffraction.

The particle behavior is evident in Quantum Mechanics when measurement are performed, where the location of the particle can be determined. But before the measurement, the position of the particle could only be determined within the constrains of the uncertainty principle, that will be discussed further in section 4.4.2. The measurement causes the wave-function to collapse to a sharply peaked function at some location. For particles with mass the likelihood of detecting the particle at any particular location is equal to the squared amplitude of the wave-function there. The measurement will return a well-defined position, (subject to uncertainty), a property traditionally associated with particles. It is important to note that a measurement is only a particular type of interaction where some data is recorded and the measured quantity is forced into a particular eigenstate. The act of measurement is therefore not fundamentally different from any other interaction.

The more localized the position-space wave-function, the more likely the particle is to be found with the position coordinates in that region, and correspondingly the momentum-space wave-function is less localized so the possible momentum components the particle could have are more widespread.

Conversely the more localized the momentum-space wave-function, the more likely the particle is to be found with those values of momentum components in that region, and correspondingly the less localized the position-space wave-function, so the position coordinates the particle could occupy are more widespread.

However, although the wave-particle duality has been successfully used in quantum physics, its actual meaning has not been understood yet, because particles and waves are two contrasting phenomena, so they cannot describe the same thing at the same time. Actually, this fundamental fact of nature cannot be explained on the level of physical multiplicity, where things are either discrete or continuous, not the two together. Hence, according to the Single Monad Model, and the complex-time geometry that resulted from the Duality of Time postulate, discreteness and continuity are two emergent properties of the same linear time recurrence, as we shall explain further in chapters IV and V.

In anticipating this fact, Bohr regarded the wave-particle duality paradox as a fundamental or metaphysical fact of nature, and he saw it as one aspect of the concept of complementarity. Bohr regarded the renunciation of the cause-effect relation, or complementarity, of the space-time picture, as essential to the quantum mechanical account. Heisenberg saw the duality as present for all quantic entities, but not quite in the usual quantum mechanical account considered by Bohr. He saw it in what is called second quantization, which led to the new concept of quantized fields that are the basis for Quantum Field Theory, from which ordinary Quantum Mechanics can be deduced as a specialized consequence. Einstein described this puzzling duality by:

“It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.” Einstein and Infeld (1966)

The wave-particle duality is an ongoing conundrum in modern physics. Most physicists accept wave-particle duality as the best explanation for a broad range of observed phenomena; however, it is not without controversy. Alternative views, which are not generally accepted by mainstream physics, include: Both-particle-and-wave, Wave-only view,Particle-only view, Neither-wave-nor-particle view.

The different interpretations of Quantum Mechanics explain the wave-particle duality in different ways. De Broglie himself proposed that the particle is accompanied by a pilot wave-function derived from Schroedinger’s equation. David Bohm extended this model and explicitly included it in his interpretation, as we shall see in section 4.5 below.