Ask Ethan: How Do Quantum Fields Create Particles?

What is our Universe made out of? At a fundamental level, to the best of our knowledge, the answer is simple: particles and fields. The type of matter that makes up humans, Earth, and all the stars, for example, is all composed of the known particles of the Standard Model. Dark matter is theorized to be a particle, while dark energy is theorized to be a field inherent to space itself. But all the particles that exist, at the core of their nature, are just excited quantum fields themselves. What gives them the properties that they have? That’s the topic of this week’s question, coming to us from Richard Hunt, who wants to know:

I have a question about Quantum fields. If we model particle properties as excitations of various independent fields (Higgs field for mass, EM field for charge etc) then what causes these excitation waves to travel around together? Is there really some kind of particle entity underlying these waves?

In other words: what makes a particle have the properties that it does? Let’s take a deep look.

The particles and antiparticles of the Standard Model have now all been directly detected, with the last holdout, the Higgs Boson, falling at the LHC earlier this decade. All of these particles can be created at LHC energies, and the masses of the particles lead to fundamental constants that are absolutely necessary to describe them fully. These particles can be well-described by the physics of the quantum field theories underlying the Standard Model, but whether they are fundamental is not yet known.E. SIEGEL / BEYOND THE GALAXY

The particles that we know of have traits that appear to be inherent to them. All particles of the same type — electrons, muons, up quarks, Z-bosons, etc. — are, at some level, indistinguishable from one another. They all have a slew of properties that all other particles of the same type share, including:

  • mass,
  • electric charge,
  • weak hypercharge,
  • spin (inherent angular momentum),
  • color charge,
  • baryon number,
  • lepton number,
  • lepton family number,

and more. Some particles have a value of zero for many of these quantities; others have non-zero values for almost all of them. But somehow, every particle that exists contains all of these particular, intrinsic properties bound together in a single, stable, “quantum state” we call a particular particle.

Underlying all of it, there are a variety of fields that exist in the Universe. There’s the Higgs field, for example, which is a quantum field that permeates all of space. The Higgs is a relatively simple example of a field, even though the particle that arose from its behavior — the Higgs boson — was the last one ever to be discovered. The electromagnetic (QED) field and color-charge (QCD) field, among others, are also fundamental quantum fields.

Here’s how it works: the field exists everywhere in space, even when there are no particles present. The field is quantum in nature, which means it has a lowest-energy state that we call the zero-point energy, whose value may or may not be zero. Across different locations in space and time, the value of the field fluctuates, just like all quantum fields do. The quantum Universe, to the best of our understanding, has rules governing its fundamental indeterminism.

Visualization of a quantum field theory calculation showing virtual particles in the quantum vacuum. Even in empty space, this vacuum energy is non-zero, but without specific boundary conditions, individual particle properties will not be constrained.DEREK LEINWEBER

So if everything is fields, then what is a particle? You may have heard a phrase before: that particles are excitations of quantum fields. In other words, these are quantum fields not in their lowest-energy — or zero-point — state, but in some higher-energy state. But exactly how this works is a bit tricky.

Up until this point, we’ve been thinking of fields in terms of empty space: the quantum fields we’re discussing exist everywhere. But particles don’t exist everywhere at once. On the contrary, they’re what we call localized, or confined to a particular region of space.

The simplest way to visualize this is to impose some sort of boundary conditions: some region of space that can be different from purely empty space.

Trajectories of a particle in a box (also called an infinite square well) in classical mechanics (A) and quantum mechanics (B-F). In (A), the particle moves at constant velocity, bouncing back and forth. In (B-F), wavefunction solutions to the Time-Dependent Schrodinger Equation are shown for the same geometry and potential. The horizontal axis is position, the vertical axis is the real part (blue) or imaginary part (red) of the wavefunction. (B,C,D) are stationary states (energy eigenstates), which come from solutions to the Time-Independent Schrodinger Equation. (E,F) are non-stationary states, solutions to the Time-Dependent Schrodinger equation.STEVE BYRNES / SBYRNES321 OF WIKIMEDIA COMMONS

In our pre-quantum picture of the Universe, particles are simply points and nothing more: individual entities with a set of properties assigned to them. But we know that in the quantum Universe, we have to replace particles with wavefunctions, which are a probabilistic set of parameters that replace classical quantities like “position” or “momentum.” Cont

Leave a Reply

Your email address will not be published. Required fields are marked *