When we first met the Higgs field, we didn’t say much about it, but
it’s very important and there’s a lot we need to know about it. So let’s talk
Higgs.

As we learned here, the fermionic points in our spacetime have some probability of remaining stationary from one time tick to the next, and some probability of moving to an adjacent point cell. A field, in physics, is simply something that takes a value at every point of spacetime. The Higgs field takes a value of the Planck energy, 10

^{19}GeV, at a stationary point and a value of zero at a moving point. The average value, or vacuum expectation value, of the Higgs field is known to be 246 GeV, and from this we learn that there are about 10

^{17}moving points for each stationary point.

The Higgs field has been in the news a lot lately. For a long time
it was the only part of the standard model of particle physics that hadn’t been
confirmed experimentally. That changed in 2012 when the Higgs boson was
observed at the Large Hadron Collider at CERN in Geneva. In the above
description of the Higgs field there’s nothing about a Higgs boson, but in
quantum field theory any field can fluctuate, and a fluctuation of a field
behaves like a particle. When the fluctuation dies out the “particle” decays.
At the LHC the decay products were found to be exactly what was expected from a
Higgs boson.

The Higgs field is credited with being the source of the masses of
the elementary subatomic particles like the electron and quarks. Ask a
physicist what mass is and how the Higgs field makes electrons massive and
you’ll get a lot of hand-waving. Physicists don’t know what the Higgs field is,
and when it comes to the electron and similar particles, they can’t even tell
you what mass is. In composite particles like the proton, most of the mass
comes from the energy required to bind the quarks together (m = E/c

^{2}). But for the most elementary particles, they see the mass terms involving the Higgs field in their equations, but they can’t tell you what the Higgs or mass might be. We know what the Higgs field is, but what’s its connection with mass?
What is mass? While the mass of a composite particle or a complex
object is influenced by many factors, such as binding energy, defining mass for
a basic particle like the electron, which is a resonance of a single fermionic
point, is actually quite simple. Mass is resistance to acceleration—the larger
the mass, the greater the force required for a given acceleration. Remember f =
ma? But factors other than mass can impede acceleration—for example, the object
may be constrained in some way. The equivalence principle of general relativity
says that we can’t tell the difference between gravity and acceleration. A
similar equivalence principle is at work here. If an object resists
acceleration, we can’t tell if that’s because it’s massive or because its
position is constrained. In fact, a particle has mass if and only if its
position can be known. A massless particle like the photon moves at the speed
of light and has an infinite position uncertainty.

In our spacetime model,

*the mass of a particle that is a resonance of a single stationary fermionic point, that is, an electron, is the same as the degree to which its position can be known—it has mass precisely because its position uncertainty is finite.*Its mass is inversely proportional to the precision with which its position is constrained, that is, the more precisely we can locate it, the greater its mass.
Our fermionic points are pulled together by gravity and held apart
by degeneracy pressure that comes from the Pauli exclusion principle—no two
identical fermions can have the same position. Thus, each point is confined to
a tiny point cell whose walls are other points and whose radius is most likely
the Planck length, 10

^{-33}centimeter. If it were a particle in a spherical box it would have the Planck energy, 10^{19}GeV. The Higgs field takes this value for a stationary point.
This is the ground state energy of the point. To make an electron,
the point has to be excited. The first excited state of a particle in a
spherical box has an energy that is twice the ground state energy. If we
consider the particle to be the energy above the ground state, then the
electron has an energy (or mass, since E =mc

^{2}) that is equal to the ground state energy, which is the Planck energy.
Now, wait a minute! The electron isn’t anywhere near that massive.
Well, no. This is called the

*bare mass*of the electron, or the mass you would see if you knew exactly where it was. If you look up the mass of the electron, what you find is called the*dressed mass*. This is the mass determined by the Higgs field. The Higgs says that there is one stationary point for every 10^{17}moving points, so the best you can say about the electron’s position is that it is somewhere in a volume of space equal to 10^{17}point cell volumes. The electron mass calculated on the basis of a point cell of this size agrees with the experimental value, 0.511 MeV. You can find the calculation in my physics paper. So this is how the Higgs field “gives mass” to the elementary particles.
If the Higgs vacuum expectation value, or vev, were equal to the
Planck energy, only electrons would exist, their mass would be the Planck mass,
and nothing could move. This is a state of very high potential energy, so the
field evolves towards a state of lower potential energy, vev = 0. If vev = 0,
only massless neutrinos would exist and nothing could have a defined position.
It would be possible for fermionic points to be in the same quantum state,
which is impossible. Therefore, the Higgs potential has an infinite barrier at
vev = 0 and the vev settles at 246 GeV. Thus, fermions have mass precisely
because the Higgs vev is greater than zero.

The

*hierarchy problem*asks why there is such a large “desert” between the Planck scale (10^{19}GeV) or the grand unification scale (10^{16}GeV) and the electroweak scale (246 GeV). The reason is that the Higgs field is headed for zero potential, and it’s only because it can’t get there that the electroweak scale exists at all. On the other side of the same coin, the higher the Higgs vev, the more rigid the universe, so life might not be possible without such a desert.
Here’s another little tidbit the physicists don’t know. The Higgs
field has a linear potential energy between zero and the Planck energy, not the
wavy one usually assumed. Since they didn’t know the exact shpe of the
potential, they’ve never been able to calculate the Higgs boson’s mass.The wave
function associated with a linear, or triangular, potential is known, so it’s
straightforward to calculate the mass of the Higgs boson when you know the vev
as well. When I did this I got a mass of 120 GeV for the Higgs boson. That’s
lower than the LHC value of 125 GeV because of a simplifying assumption I made,
but it’s close enough to prove the concept.