Bell-type Field Theory: the universe may be made of particles not fields
The alternative quantum field theory
The alternative quantum field theory
Most physicists have concluded that the universe, all space, time, and matter, is made of fields. As far as we know these fields have no smallest, indivisible constituent. In doing so we have turned away from centuries of progress in the opposite direction towards a particle model of the universe. It is not too late to go back.
First some history:
Over 2000 years ago, there were two theories of matter. Greek philosopher Artistotle posited that all things were made of the four elements (air, water, earth, and fire), and that matter was infinitely divisible. Another Greek, Democritus, however, suggested that matter was made of tiny, indivisible particles called atoms.
Artistotle was so highly regarded in the ancient world through the medieval times that he won out on sheer clout.
It wasn’t until the 18th century Enlightenment that Democritus’s ideas gained popularity again as Natural Philosophers such as Isaac Newton and Robert Boyle proposed new theories of matter. In his treatise on Optics, Newton even proposed his “corpuscular” theory of light which presaged the discovery of photons. But it was, at the time, all speculation.
It wasn’t until the early 19th century that Robert Dalton put the atomic theory on scientific footing. His theories formed the foundation of modern chemistry. Meanwhile, Italian scientist Avogadro developed his understanding of how particles relate to chemical proportions. If you took high school chemistry, you probably heard about Avogadro’s number, a large number of particles (6.02214076×10²³) that make up one mole of a substance.
The atom theory turned out to be incredibly successful from then on and experiments continued to confirm it. Later, subatomic particles such as electrons and protons were discovered. Particle accelerators were developed in the early 20th century that could smash them together and observe still more particles.
It was a particle world.
Then came quantum mechanics which showed how particles could also be waves, and this was when the particle model started to break down. If particles were waves, then they were more like fields, like Artistotle had suggested. Depending on how we looked at them, they acted like either waves or particles. It was a particle-wave duality.
So, was Artistotle really correct or not?
Many physics textbooks say yes and no, but that’s not really what the mathematics of modern physics says. It says emphatically yes and that’s a problem.
Here’s what happened:
In the 1930s and 40s physicists like Dirac, Feynman, Schwinger, and others worked to build a theory of quantum mechanics that could explain what happens inside particle accelerators, where matter moves so quickly, you need to incorporate Einstein’s theory of special relativity that governs matter moving near the speed of light. They came up with what has become the gold standard for theories of matter, forces, and energy: quantum field theory.
Quantum Field Theory (QFT) seemed to answer the question, with its more sophisticated view of particles, about what matter is. While we can measure particles or waves, both are really manifestations of fields (hence, the name). When we observe a field as a particle, it is because a field is “on mass shell” which means that it has the right amount of energy to equal the mass of a particle of that type. When the particles acted like waves, it was because of the sum total of the field’s influence on and off mass shell.
The off mass shell part of fields are not detectable, and we call them fields of “virtual particles”, but they aren’t particles in the model at all. They are just continuous fields. Worse, they are mathematically “imaginary”.
The ontology (theory of what is real) of quantum field theory is that fields are the hidden reality and that particles are manifestations of fields that have particular configurations.
This ontology did not sit well with some people. In particular, it did not sit well with David Bohm, who developed Bohmian mechanics in the 1950s. Nor did it sit well with John Bell, who developed his famous theorem on quantum probability. Bell and Bohm both insisted that the correct ontology was still that of Democritus. The particle was the hidden reality, not the field while the wave was a separate but related entity.
Bohm’s theory, sadly, did not work as well as QFT. It only explained quantum mechanics, the theory of well-defined, slow moving particles, not particles smashing into each other in an accelerator.
To solve this problem, Bell took Bohm’s theory and developed a version of it intended to rival QFT. In doing so, he created the first of what we now call Bell-type Field Theories, QFTs where fields are manifestations of many, many particles and their associated waves. Particles are the fundamental reality, just as they are with water, air, and other things we know in chemistry.
Bell and his successors had to deal with a few issues in order to make this work. The first thing that QFT had over Bohm’s theory is that in a particle accelerator particles can be created and destroyed. That is the whole point of particle accelerators! We want to see particles that we’ve never seen before like the Higgs Boson. We spend billions of dollars to build larger and larger accelerates to make new particles. A theory that can’t take that into account is useless in High Energy Physics.
Fields create new particles easily because they pretty much create all their particles from nothing (okay, not nothing but just incoming energy and matter that we then ignore). The fields interactions can generate any particles that are allowable provided the energies are right. That is one of the advantages of field theories.
In a particle theory, you have to model creation and destruction of particles explicitly. Bell and others do this by modeling particles as having so-called “jump” trajectories. A jump trajectory is a way for a particle to simply appear, follow a trajectory for a while, then disappear. It also allows a particle to be moving along, jump to a new location entirely, and continue along as before.
While this doesn’t happen in our world, it happens in quantum mechanics all the time. Imagine trying to go bowling if your bowling ball just disappeared and ending up in the parking lot? Or some ball you never saw before suddenly appeared in your lane, hit the pins, and vanished? Or your ball rolled down the lane, split into two tennis balls, which collide to form a bowling ball again? That is normal in the quantum realm.
Bell-type field theories work by essentially having a random process that makes particles appear and disappear by jumping around in its “configuration space” or the space of all possible configurations of particles. That random process, called a Markov process, makes it possible for new particles to appear just like in standard QFT.
Let’s take an example: for quantum electrodynamics, suppose you have three types of particles: electrons, positrons, and photons.
Suppose I want to cause two electrons to interact and create an electron positron pair that appears and then vanishes.
In field theory, I would just take the “perturbation term” of the field theory that involves those interactions. (A perturbation term is sort of like one particle interaction scenario in field theory.) A perturbation term would have a Feynman diagram associated with it, something like this one:
The Feynman diagram isn’t really a depiction of what’s happening in time. It has a time order to it from top to bottom but doesn’t really say when each particle is created or destroyed. Instead, the diagram is just a depiction of one of an infinite number of things a field is doing at any time.
In a Bell-type field theory, however, you would model each particle’s trajectory in time. I would first have two electrons coming in. Then an electron emits a photon. The photon travels for a while, disappears, and an electron and positron pair appears. They travel for a bit and then collide with each other. The photon reappears and continues on to the other electron where it is absorbed. The other electron does the same in the reverse direction. The result is the electrons move apart, repelling one another.
In the end, Bell-type Field Theory and QFT can make the same predictions. Yet, it is hard to argue for all the other things that the fields are doing that we can’t measure such as virtual particles. Nor does it seem to make sense to propose mathematical constructs that are invisible and impossible to interpret physically in order to make our predictions work out.
Dürr, D., Goldstein, S., Tumulka, R., & Zanghi, N. (2004). Bohmian mechanics and quantum field theory. Physical Review Letters, 93(9), 090402.