Waves and Particles: An Inscrutable Duality

Wave and Corpuscle: the enigma that changed physics

The inaccessibility of the quantum world

The world of particles such as the electron, the photon, the proton, the atom, is not accessible through our organs of perception, including the brain. No image, no interpretation can represent the reality of the quantum world, even the words of our language are approximate for describing quantum phenomena.

All that can be said and shown of this reality is false, but I will nevertheless try to give you an idea of this fundamental concept of quantum physics, wave-particle duality, although this term is now obsolete because we should speak of fields.

Superposition of states

In quantum mechanics, we often hear that a particle is both a corpuscle and a wave. In reality, it is neither a corpuscle nor a wave but a superposition of all the states of the particle.

The modern definition of a quantum particle

The technical definition says this: A quantum particle is a fundamental entity representing a quantization of energy and information localized in space-time, governed by the principles of superposition, entanglement and indeterminism, and described mathematically by a state function (state vector) in a Hilbert space.

In other words, a quantum particle that is neither a corpuscle nor a wave can be defined as a quantified excitation of a fundamental field described by quantum mechanics and quantum field theories.

Modern description of the experiment called the double-slit experiment.

The experimental setup

The four observed behaviors

• When corpuscles (solid objects) are sent onto a wall pierced with two slits, each corpuscle passes through one or the other slit, bounces in all directions and impact points mark the screen somewhat randomly, behind the slits.
• When a wave is sent onto this same wall, the wave passes through both slits and the passage through the slits creates two small waves that will superimpose, at certain places they add up and at others they cancel out, interference fringes appear on the screen.
• When a quantum object is sent, it passes through both slits, it interferes like a wave but when it hits the screen, it suddenly reduces to a point, rather where the two small waves add up. After a large number of trials, both impacts appear as with corpuscles and interference fringes as with waves.
• But if an observer is added to know through which slit the particle passes, the wave now reduces to a corpuscle at the level of the slits and only passes through one slit at a time. We then measure impact points on the screen and not interference.

N.B.:
How to interpret this experiment? If one wants to determine the state of a quantum system, one must observe it, but this observation has the effect of destroying the state in question.

When matter dances: wave-corpuscle duality deciphered

The quantum scale

The scale of quantum physics is so small that it is impossible to see a quantum object as one sees a wave or a ball on a beach. The size of a hydrogen atom is 53 pm (53 x 10^-12 meters), one can align 10 million atoms on one millimeter.

Observation and wave packet reduction

Young's experiment shows us that when we measure a quantum object, it changes its nature. Sometimes it is a corpuscle, sometimes a wave, and moreover, it depends on the measuring device or the observer.

What Young's double-slit experiment also tells us is that when the quantum object is free from any environment, it presents itself as a wave. But if the environment (screen, wall, observer or even air molecules) forces it to interact, the object or rather its energy suddenly reduces to a point and takes on the appearance of a corpuscle.

We notice on the screen that the wave front does not reduce just anywhere, it reduces where the wave is intense, that is to say on the crests or troughs. In other words, the probability of reduction is greater at the top and bottom of the wave than on the slopes. It is even zero where the waves are in opposite phase.

If we send the particles one by one, the most astonishing thing is that over a large number of measurements, in the end, despite the reduction of the wave packet, we obtain interference fringes.

Max Born's probability wave

An explanation was proposed in 1927 by Max Born (1882 - 1970). The particle is a Probability Wave. This terrible definition shows the difficulty encountered when one wants to speak of quantum objects.

In simpler terms, it is the amplitude of a wave at a given position that predicts the probability that the particle is at that position. A high amplitude does not mean that this is where the particle is, but it is where we have the greatest chance of finding it (after the reduction of the wave packet).

What to remember

The probabilistic nature of the quantum world

In quantum mechanics, one cannot know if the particle is at a precise point in space, but what is the probability that it is there. It will have a position only if it must interact with the environment; before that it has no position, it is everywhere and its nature is wave-like. Exactly like a photon emitted by a star. While it has traveled freely for millions of years, as a wave, it will die upon reaching your retina, with which it will interact.

The equations of quantum mechanics prove to be astonishingly precise as soon as one accepts that it is a matter of probability. All matter that constitutes the universe (stars, planets, trees, you, etc.) is made of atoms and subatomic particles governed by probability and not by certainty.