Waves in an Impossible Sea

Chapter 21 — Basic Unanswered Questions


Note 2: Fields that don’t interact with the Higgs field
  • Quote: If a field doesn’t directly interact with the Higgs field at all, as is the case for the electromagnetic and gluon fields, then the field remains floppy no matter what the Higgs field’s value is.

  • Endnote: The gravitational field, as always, is an exception; though it interacts with the Higgs field, it is not stiffened by it. This reflects the special, universal way in which gravity interacts with everything.

  • Discussion (coming soon)

Note 3: The Higgs field’s value and wavicles’ rest masses
  • Quote: An increase in the Higgs field’s value would simultaneously increase the frequencies of all stiffened fields, as well as the rest masses of all their wavicles, keeping the ratios between any two rest masses the same. (For instance, if the Higgs field’s value increased by ten times, both the top quark’s and electron’s rest masses would become ten times larger, with the ratio of 340,000 between them unaltered.) This would be analogous to tuning all a guitar’s strings uniformly to higher pitches (i.e., transposing the guitar) while maintaining all their harmonies.

  • Endnote: Neutrinos may or may not follow this rule. If the Higgs field’s value increases ten times, their rest masses might increase tenfold or perhaps a hundredfold (i.e., by ten squared). Experiments have yet to weigh in on the matter. More generally, experiments are actively trying to settle several important related questions: why neutrinos’ rest masses are so small, whether they interact in a unique way with the Higgs field, and whether they are their own antiparticles. In this book, I have consistently swept neutrinos to the side, not because they are uninteresting but because they are too interesting and would create a distraction.

  • Discussion (coming soon)

Note 4: Higgs boson interaction tests
  • Quote: As of 2023, ATLAS and CMS have carried out the interaction tests with good precision for the W and Z bosons, with lesser precision for the tau and for the top and bottom quarks, and with poor precision for the muon.

  • Endnote: The data as of 2022 are given in these two papers: “A Detailed Map of Higgs Boson Interactions by the ATLAS Experiment Ten Years after the Discovery,” The ATLAS Collaboration, Nature 607, nos. 52–59 (2022), and “A Portrait of the Higgs Boson by the CMS Experiment Ten Years after the Discovery,” The CMS Collaboration, Nature 607, nos. 60–68 (2022).

  • Discussion (coming soon)

Note 5: Rule of decreasing rest mass.
  • Quote: . . . decays have to satisfy a rule of decreasing rest mass: the wavicles produced in a decay must have less rest mass in total than the original decaying wavicle. More concretely, this means that wavicles in Table 6 can only decay to wavicles that lie lower in the table.

  • Endnote: The origin of this rule is the conservation of energy.

  • Discussion (coming soon)

Note 6: Decays of up and down quarks
  • Quote: Similarly, because (as noted in Chapter 6.4) the number of quarks minus the number of anti-quarks is conserved, up and down quarks are long-lasting, too. None of the wavicles below them in Table 6 are quarks, so they have nothing to decay to.

  • Endnote: Down quarks and up quarks may decay to one another under particular circumstances—this is why neutrons on their own are unstable—but in many nuclei, such a decay cannot occur.

  • Discussion (coming soon)

Note 7: Ordinary material and the Higgs field
  • Quote: Ordinary objects that last days and years must be built from durable wavicles. But long-lived wavicles must have small rest masses, which requires that they have very weak interactions with the Higgs field. Consequently, ordinary objects hardly affect the Higgs field, and it hardly affects them—except by stiffening their wavicles’ fields. This explains why the Higgs force is completely irrelevant to daily life; its effects are beyond tiny.

  • Endnote: There’s a second reason why it is irrelevant. Because the Higgs field is quite stiff, its force declines very rapidly with distance. The same is true of the W and Z fields; this is what makes the weak nuclear force so weak.

  • Discussion (coming soon)

Note 8: Making Higgs bosons
  • Quote: Two wavicles collide head-on, a magic wand touches the collision point, and—ta-da! Higgs boson!

  • Endnote: The most common process that can create a Higgs boson involves the collision of two gluons, one from each of two colliding protons. The process is generated through an indirect effect in which the top quark field is an intermediary, similar to the one briefly described in the main text that allows Higgs bosons to decay to two photons.

  • Discussion (coming soon)


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A decay of a Higgs boson, as reconstructed by the CMS experiment at the LHC