Question about fundamental particles

Question

When we say that light behaves as a particle and as a wave, we say that light is an electromagnetic wave, and it's a photon. Both EM waves and photons have physical definition. On the contrary an electron wave is just the probability amplitude, in other words the definition for the so called wave nature of electron is not physical as it is for a photon. Obviously electrons belong to the group of particles known as fermions while photons belong to the class of particles known as bosons. I think that this is a way to differentiate between the two. I would like to know if this is the case with all bosons and fermions.

Answer 1

Your question shows some misunderstanding about a supposed fundamental difference between the wave behavior of light and beams of electrons. However, your guess about some different behavior between fermions and bosons has some basis.

Let's start with the misunderstanding. For that, it is better to leave aside as much of the theory as possible and stick to the experimental facts.

Working with not demanding experimental set-ups, it is possible to show that light displays the same phenomenology as macroscopic waves in the matter. It is then attempting to assign to the light an intrinsic wave-like behavior, although it is clear that some important difference with waves in materials exists since light can propagate even in the vacuum. Notice that we can say a lot about the wave-like behavior of light without making hypotheses on the physical nature of such waves. However, more refined experiments show that the wave-like picture is only part of the phenomenology associated with light. Other experiments (I would just cite Compton's experiment as an example) suggest that some behavior we usually associate with particles is also shared by light.

On the other side, electrons, when they were discovered at the end of the nineteenth century, first were considered rays of something and their nature of particles was suggested by the first experiments. However, also in that case more refined experiments showed, without doubt, some wave-like behavior. Notice that the experiment by Davisson and Germer. unambiguously displays electron diffraction, without any indication about the nature of the underlying wave.

Summarizing, the experimental evidence shows that both light and electrons share a dual behavior. Some experiments are compatible with a wave-like behavior, while others with a particle-like behavior.

Notice, however, that nowadays we know much more than physicists working a century ago and we can go beyond a generic claim of duality that is more a historical remnant than a physical theory.

What we know for sure, again from experiments, is that if the intensity of light or electron beams is small enough, both systems behave like beams of particles whose dynamics is definitely different from the classical mechanics of particles. In the case of electrons, a theoretical description of such puzzling behavior is to associate to the dynamics of the electron a probability wave, controlled, in the non-relativistic regime, by the Schrödinger equation. And this is the level where the wave of probability amplitude appears.

However, the full inclusion of relativity in the theoretical description of electrons and photons requires a further step forward, and a consistent description able to account for all the experimental phenomenology of electrons and photons is provided within Quantum Field Theory, in particular Quantum Electrodynamics (QED). At that level of description, the behavior of photons and electrons is described in a unified manner by a spin-1 and a spin-1/2 quantum fields that are able to account for all the apparently contradictory wave-like and particle-like behaviors observed in the experiments.

Where the fermionic or bosonic nature of the fields enters to explain the differences between electrons and photons at the macroscopic level?

When we move from single-particle experiments to macroscopic experiments, the Bose statistics allows the build-up of macroscopic coherent states which in a way amplify at the macroscopic level the fundamental wave-like behavior of the one-particle level. This allows the possibility of obtaining a macroscopic behavior that we can describe in terms of classical fields. The same possibility is not allowed for fermions, making it impossible to observe the electronic analogous of a macroscopic electromagnetic field.

Answer 2

There is some misconception on this topic due to the popular treatment of the topic, which is unfortunate. Let's first treat the whole business of how the electromagnetic field and the photon are related and where does the so called "dual nature" comes in.

• The dual nature simply corresponds to the fact that the position observable and momentum observable are incompatible in quantum mechanics. This means that a physical system cannot have both a well-defined momentum and a well-defined position at the same time. An implication of the particular way in which a system cannot have both well-defined momentum and well-defined position (in technical terms, an implication of the commutation relation of the position and the momentum operator), the quantum state of a system which has a well-defined momentum has a probability amplitude distribution which looks like a wave in the position spectrum. In other words, the probability amplitude of finding a particle at a particular position in space, say $x$, for a particle which has a well-defined momentum, say $p$, would be proportional to $e^{ipx}$. This is the whole and the only reason, a particle with a specific momentum was given the label of representing the wave nature in the old quantum theory. It was said to represent the particle nature when it had a well-defined position (and thus, no well-defined momentum) because we more intuitively associate particles with having specific positions in classical mechanics (although, particles also always have specific momentum in classical mechanics but a particle with no specific position is just harder to accept, whereas waves in classical mechanics can have specific momentum without having specific positions). So, the wave-particle duality has everything to do with the quantum state of a particle. The electromagnetic field is not the dual of a photon, a photon state with a specific momentum is the wave-dual of a photon, and a photon-state with a (fairly localized) position is just a photon, if you wish.
• The way photons and electromagnetic waves/fields are associated comes from a totally different place. It comes from quantum field theory. In quantum field theory, one starts with a quantum field. "Excitations of this quantum field" are what are called particles. So, we start with a quantum electromagnetic field and its excitations are called photons. Now, in the classical limit of this theory, i.e., via taking the limit that there are many many photons (technically $N\to\infty$), the description of the system is given by classical electromagnetic waves/fields. So, the way photons are related to the electromagnetic waves is that the electromagnetic waves are the classical limit of the quantum theory of photons obtained by taking the limit of the quantum theory in which the number of photons is very high. The "dual" of the photon in the de-Broglie sense is not what the classical electromagnetic wave is.
• OK, so what happens with electrons? That is interesting because electron is a fermion as you notice. Here again, we start with a quantum electron field. Its excitations are what are electrons. In order to arrive at a classical electron field like we have the electromagnetic field corresponding to photons, you would have to take the classical limit of the quantum electron field theory. But, since electrons are Fermions, you cannot take a limit in which the number of electrons is high in the same state (due to Pauli exclusion principle, you can say). Thus, we do not arrive at a classical field for the quantum electron field like we arrive at the classical electromagnetic field. However, there are other ways to take classical limit or the large $N$ limit of the quantum theory of electron fields, you can find a more detailed discussion on this topic here: Classical field limit of the electron quantum field

Answer 3

Both EM waves and photons have physical definition. On the contrary an electron wave is just the probability amplitude, in other words the definition for the so called wave nature of electron is not physical as it is for a photon.

Photons and electrons are elementary particles, and at the level of one particle at the time they display the exact same behavior their differences in interactions reduced to charge and spin effects.

You cannot get more physical than a double slit experiment one particle at a time.

Here are the photons:

Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

Each photon footprint is like a random dot on the screen on the left. The accumulation shows the probability wave nature for finding the photon at an (x,y) of the camera screen.

And here are the electrons,

Electron buildup over time

The behavior of single particles leaves a particle footprint both for photons and electrons, and a probability interference pattern when the number becomes large.

The fact that the photons can build up by superposition the classical electromagnetic wave, should not be surprising, as the wave function of the photon is a solution of a quantized Maxwell equation.