Waves in an Impossible Sea

Chapter 20 — The Higgs Field in Action


Note 6: The rest mass of wavicles from the Higgs field
  • Quote: Our second step would be to ask whether the field is intrinsically stiff or whether it has a stiffening agent.

  • Endnote: As an example of how rest mass arises for a wavicle that gets its mass from a stiffening agent, consider the Z field. Its stiffness is provided by the Higgs field H , which creates a restoring effect proportional to ( yz vh )2 z , where vh is the Higgs field’s nonzero average value, z is the Z field’s value, and yz is the strength of the interaction between them. The resonant frequency for the Z field and the Z boson’s rest mass are then proportional to √( yz vh )2 = yz vh . Similarly, the electron field’s frequency and the electron’s rest mass are proportional to ( ye vh )2 , where ye is the strength of the interaction between the Higgs and electron fields. The ratio of the Z boson’s rest mass to that of the electron is then simply yz/ye . More generally, the rest mass of a wavicle is equal to the product of (1) the strength of the interaction between its field and the Higgs field and (2) the Higgs field’s average value.

  • Discussion (coming soon)

Note 7: The Higgs field and the weak nuclear force
  • Quote: Experimental studies of the weak nuclear force (for which the W and Z fields serve as the intermediaries) were critical, as were theoretical arguments that clarified the experimental results. These gradually made it evident that none of the elementary fields then known could be intrinsically stiff.

  • Endnote: Intrinsically stiff fields would be symmetric in a mirror. But it turns out that processes involving the weak nuclear force are not symmetric; this was discovered in 1957 by Chien-Shiung Wu, one of the foremost experimenters of her generation, after a proposal by theorists Tsung-Dao Lee and Chen-Ning Yang. (The fact that only the theorists won a Nobel Prize for this achievement is widely considered a historic injustice.) From this it was gradually understood that the known stiff fields need a stiffening agent. .

  • Discussion (coming soon)

Note 8: The curtain shifts the waves’ frequencies
  • Quote: Even with this encumbrance, the string will still have traveling waves, as at the left of Fig. 48. If its ends are attached, it will still have a familiar standing wave, as in the center of Fig. 48. Qualitatively, these waves are much as they were without the curtain.

  • Endnote: Quantitatively, these waves’ frequencies will be somewhat larger than they were without the curtain. .

  • Discussion (coming soon)

Note 12: More on the Higgs field’s effects
  • Quote: This explanation of the Higgs field is in many senses incomplete, and you may or may not be satisfied with it.

  • Endnote: Most notably, I have omitted fascinating details about how the Higgs field affects the W and Z bosons and the photon, and thereby the weak nuclear and electromagnetic forces.

  • Discussion (coming soon)


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