E = mc²
The Holy Grail of modern physics is a so-called theory of everything, a unified field theory, a theory which unifies all known “forces.” That is, unifies all the fundamental interactions of nature. The three “quantum” interactions (electromagnetism, weak, strong) and gravitation.
A conventional sequence of theories depicts final unification as occurring at the Planck energy (density) level.
… electroweak unification occurs at around 100 GeV, grand unification is predicted to occur at 10^16 GeV, and unification of the GUT force with gravity is expected at the Planck energy, roughly 10^19 GeV.
Electroweak unification is a broken symmetry: the electromagnetic and weak forces appear distinct at low energies because the particles carrying the weak force, the W and Z bosons, have non-zero masses of 80.4 GeV/c2 and 91.2 GeV/c2, whereas the photon, which carries the electromagnetic force, is massless. At higher energies Ws and Zs can be created easily and the unified nature [symmetry?] of the force becomes apparent.
A recent Symmetry Magazine article (below) was inspiration for this post. I’ve encountered the topic – unification of forces at high enough energies – many times before. But this latest article, while an experimental milestone, struck me as quite particle oriented, not helping advance visualization based on quantum field theory (QFT).
The premise of Grand Unified Theory models is merging of gauge interactions at extreme energies, energy densities possibly in the quite early universe.
A Grand Unified Theory (GUT) is a model in particle physics in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although this unified force has not been directly observed, the many GUT models theorize its existence. If unification of these three interactions is possible, it raises the possibility that there was a grand unification epoch in the very early universe in which these three fundamental interactions were not yet distinct.
I like to imagine that at high enough energies, all localized vibrations – excitations in the various fields associated with “particles” – become a mash-up of energy transformations. Where direct vs. conventional mediated interactions alter hallmark designations. Unfettered field interactions.
• Symmetry Magazine (A joint Fermilab/SLAC publication) > “LHC creates matter from light” by Sarah Charley (August 24, 2020) – Scientists on an experiment at the Large Hadron Collider see massive W particles emerging from collisions with electromagnetic fields. How can this happen?
The Large Hadron Collider plays with Albert Einstein’s famous equation, E = mc², to transform matter into energy and then back into different forms of matter. But on rare occasions, it can skip the first step and collide pure energy—in the form of electromagnetic waves.
Last year, the ATLAS experiment at the LHC observed two photons, particles of light, ricocheting off one another and producing two new photons. This year, they’ve taken that research a step further and discovered photons merging and transforming into something even more interesting: W bosons, particles that carry the weak force, which governs nuclear decay.
This research doesn’t just illustrate the central concept governing processes inside the LHC: that energy and matter are two sides of the same coin. It also confirms that at high enough energies, forces that seem separate in our everyday lives – electromagnetism and the weak force – are united.
If you try to replicate this photon-colliding experiment at home by crossing the beams of two laser pointers, you won’t be able to create new, massive particles. Instead, you’ll see the two beams combine to form an even brighter beam of light.
“If you go back and look at Maxwell’s equations for classical electromagnetism, you’ll see that two colliding waves sum up to a bigger wave,” says Simone Pagan Griso, a researcher at the US Department of Energy’s Lawrence Berkeley National Laboratory. “We only see these two phenomena recently observed by ATLAS when we put together Maxwell’s equations with special relativity and quantum mechanics in the so-called theory of quantum electrodynamics.”
Inside CERN’s accelerator complex, protons are accelerated close to the speed of light. Their normally rounded forms squish along the direction of motion as special relativity supersedes the classical laws of motion for processes taking place at the LHC. The two incoming protons see each other as compressed pancakes accompanied by an equally squeezed electromagnetic field (protons are charged, and all charged particles have an electromagnetic field). The energy of the LHC combined with the length contraction boosts the strength of the protons’ electromagnetic fields by a factor of 7500.
When two protons graze each other, their squished electromagnetic fields intersect. These fields skip the classical “amplify” etiquette that applies at low energies and instead follow the rules outlined by quantum electrodynamics. Through these new laws, the two fields can merge and become the “E” in E=mc².
The LHC is one of the few places on Earth that can produce and collide energetic photons, and it’s the only place where scientists have seen two energetic photons merging and transforming into massive W bosons.
Just as photons carry the electromagnetic force, the W and Z bosons carry the weak force. The reason photons can collide and produce W bosons in the LHC is that at the highest energies, those forces combine to make the electroweak force.
 And as to whether current QFT is incomplete – only a mathematical model of effective field theories. And the question as to whether unification requires additional dimensions and/or fields and interactions. Wiki notes:
Yet GUTs [Grand Unified Theories] are clearly not the final answer; both the current standard model and all proposed GUTs are quantum field theories which require the problematic technique of renormalization to yield sensible answers. This is usually regarded as a sign that these are only effective field theories, omitting crucial phenomena relevant only at very high energies.
Is there a limit to probing those energies?
• YouTube > Sabine Hossenfelder > “Does nature have a minimal length?” (Feb 2, 2020)
The Planck length seems to be setting a limit to how small a structure can be so that we can still measure it. That’s because to measure small structures, we need to compress more energy into small volumes of space. That’s basically what we do with particle accelerators. Higher energy allows us to find out what happens on shorter distances. But if you stuff too much energy into a small volume, you will make a black hole.
 As Wiki notes, extreme energy GUT models characterize such a state by a single unified coupling constant with yet several (so-called) force carriers. That is, in such a state, “particles” (excited fields) experience a single interaction strength while still mediated separately?
GUT models predict that at even higher energy, the strong interaction and the electroweak interaction will unify into a single electronuclear interaction. This interaction is characterized by one larger gauge symmetry and thus several force carriers, but one unified coupling constant.
 Sometimes the tone of theories of everything strikes me as casting perfection onto the universe akin to that of ancient celestial spheres. A mathematical perfection or symmetry. Yet the universe need not play by any such vision. Perfection a quixotic quest.