Endnotes
Note 2: The Higgs field’s feedback
- Quote: Every field that the Higgs field interacts with produces powerful feedback; the stronger their interaction, the stronger the feedback. This makes the top quark field and the W and Z boson fields, at the top of Table 6 (p. 253), especially important. Bosonic fields push the Higgs field to the right of Fig. 51, while fermionic fields push it to the left. Adding to the chaos is the Higgs field’s own large impact on itself.
- Endnote: The Higgs field interacts with itself, and so it, too, feeds back on its stiffness.
- Discussion (coming soon)
Note 3: The effect of the feedback
- Quote: The Higgs field stiffens various other fields, but because those fields’ enormous vacuum energy then depends on the Higgs field’s value, they in turn stiffen the Higgs field even more than it stiffens them. As a result, the Higgs boson’s rest mass—the energy-of-being of a tiny standing wave in which the Higgs field’s value vibrates around its average value—would be gigantic by wavicle standards, comparable to the Planck mass. Or so goes the theoretical argument.
- Endnote: This is a significantly oversimplified argument because the energy involved could be both positive and negative, while in my reasoning, I’ve tacitly assumed it’s always positive. But it gives a sense of the scale of the problem.
- Discussion (coming soon)
Note 4: Quantum field theory and the cosmological constant problem
- Quote: Discarding quantum field theory would seem an easy way out, eliminating both the cosmological constant problem and the hierarchy puzzle.
- Endnote: Actually, the cosmological constant problem is worse than I’ve made it sound. Even if the fields’ vacuum energy were absent, the problem would remain, because effects from cosmic phase transitions (see the next chapter) also contribute to the universe’s energy density. But conversely, there is an argument, called the anthropic principle, that offers a plausible resolution of the cosmological constant problem. Unfortunately, this argument can’t resolve the mass hierarchy puzzle unless one makes powerful and dubious assumptions that create an equally serious challenge, sometimes called the artificial landscape problem.
- Discussion (coming soon)
Note 5: The hierarchy puzzle
- Quote: Not surprisingly, physicists have spent a lot of time thinking about the mass hierarchy. Some have pointed out mechanisms by which the universe could control the feedback. A few have argued that the hierarchy isn’t puzzling at all—that the puzzles it poses are philosophical, not scientific. (Personally, I find their arguments lacking in perspective.)
- Endnote: To explain this point of view requires a long, careful discussion of the mass hierarchy and quantum field theory. I have written about it elsewhere.
- Discussion (coming soon)
Note 6: Principled mechanisms concerning feedback
- Quote: A number of principled mechanisms have been suggested over the years. For example, it could be that the feedback balances automatically: for every fermionic field whose feedback tends to make the Higgs field’s average value large, there’s a bosonic field with exactly the same strength trying to make it zero, such that the feedback from each pair almost perfectly cancels out. Alternatively, it might be that each field’s feedback is far weaker than we might naively think. That would happen if the Higgs field were composite, because the very same forces that could create a composite Higgs field would limit its stiffness. It could also happen if the gravity between objects at extremely short distances, beyond the reach of our best experiments, differs significantly from what Einstein’s theory predicts. Yet another possibility is that the history of the universe itself generated a stabilizing effect that controlled the feedback, driving down the Higgs field’s stiffness and value and leaving them small and nonzero.
- Endnote: Buzzwords that go with these classes of suggestions include supersymmetry, composite Higgs field, large extra dimensions, and the relaxion. There’s no experimental evidence for any of them as yet.
- Discussion (coming soon)
Note 7: The LHC’s golden opportunity
- Quote: On the face of it, it’s a golden opportunity: the same particle accelerator suitable for finding and studying the Higgs boson might also be able to give us insight into how the hierarchy
problem is resolved. Unfortunately, there’s no guarantee that this will happen.
- Endnote: Regrettably, some particle physicists stated or implied in public that there was indeed a guarantee. I do not fully understand why they did so.
- Discussion (coming soon)
Note 8: Goals of the LHC
- Quote: The LHC’s primary purpose was to help physicists find and study Higgs bosons and any of their cousins. In that regard, it has done its job well. Secondarily, scientists hoped it would provide clues to other unresolved questions in particle physics, including the hierarchy puzzle. But as of 2023, the LHC has yet to do so. We have seen nothing unexpected that might clarify the hierarchy’s origin or help us address other problems facing particle physicists. Since the LHC was the opportunity of a generation, this has been a significant disappointment.
- Endnote: A further goal of the LHC was to reveal secrets of the strong nuclear force; here, it has been a remarkable success, full of interesting surprises that will someday deserve a book of their own.
- Discussion (coming soon)
