2.2 Particles and Fields

summary

Particle physics attempts to answer many questions about the properties of particles and fields.

An elementary question: Why is every electron exactly the same, and how can we know that every single one has the same properties?
Physicist John Wheeler once postulated that this was because there was only one electron in the entire universe.
Suppose the electron is allowed to go forward and back in time—it could stand next to itself at any point in time, essentially creating a clone of itself.
An electron traveling backwards in time looks to us in the forward-time direction as its antiparticle—a positron.
Suppose the electron traveled through space backwards and forwards in time, creating a “knot” in spacetime. A cross-section at any point in time could have any number of identical electrons and positrons all in different places at the same time.
The theory would have to imply that there were the same number of electrons and positrons at every time, so it wasn’t developed further. But this line of reasoning led Wheeler’s graduate student, Richard Feynman, to develop the symbolic formalism now known as Feynman diagrams.

In quantum mechanics, nearly anything is allowable, provided it happens fast enough before detection occurs.

For instance, a particle might split into two “virtual” particles—ones that might violate various laws of physics—that are undetectable. They exist only in calculations.
Consider vacuum fluctuations—a pair of particles appearing out of nowhere and then annihilating and disappearing again.
Even empty space is filled with these dynamic processes. The Dutch physicist Hendrik Casimir was the first to notice these physical forces—the Casimir effect.
Vacuum fluctuations imbue spacetime with physical energy (much like dark energy), which is computable in principle.
However, it would be very difficult to compute this energy since virtual particle interactions are involved in everything in the universe. We would need a fundamental framework connecting all processes.

Symmetry is a unifying principle underlying all of modern physics.

In quantum mechanics, there is gauge symmetry—we can rotate a wavefunction in complex space. But this requires the use of a vector potential, providing a direct connection to electromagnetism and the electromagnetic field.
A modern way to look at the electromagnetic force is that it is transmitted by quanta of the field—these so-called “virtual” particles.

Understanding symmetry is key in understanding all of the forces relevant to particle physics.

For example, the strong nuclear force acts on quarks, which come in three “colors.” Quarks can be thought of as a sort of vector in “color space,” as a combination of the three elementary colors.
You can think of force fields as collective “waves” in this color space.
Different colored quarks can change type by interacting with different kinds of gluon, the mediating particle of the strong nuclear force. Put differently, when quarks change type, their vectors rotate in color space.
Our universe exhibits local gauge in symmetry, in which the vector of each individual particle can rotate independently in color space.
Gluons themselves can also interact, fusing together to change type.

Mathematically, symmetry provides a simplified and elegant way to understand the Standard Model.

In some sense, the only thing you have to know about the Standard Model is what the symmetry group is:$$\underbrace{U(1)\times SU(2)}_{\text{electro-weak force}}\times\underbrace{SU(3)}_{\text{strong force}}$$ and how it acts on matter. That is, what the “color” of each particle is.
Although symmetry provides a unique way of understanding particle physics, many questions still remain. What’s so special about this particular symmetry group? Why not some other symmetry group?