Penrose zigzag model of Higgs-electron interaction

[johne1618]

Roger Penrose in Chapter 25 of his book The Road to Reality describes a "zigzag" model of the electron that consists of a pair of massless components one with a left-handed spin (the zig) and the other with a right-handed spin (the zag).

He says that the Dirac equation can be written as a pair of equations which describe each component being continually transformed into the other. The strength of the coupling between these equations depends on the electron mass.

Thus the electron is continually jittering between a massless zig and a zag particle. The energy in this vibrating motion provides the electron with its rest mass. (This is Penrose's explanation of the well-known electron "zitterbewegung")

Penrose then goes on to say that one can think of the Higgs field as taking over the role of the electron mass. One imagines that it is the continual interaction with the Higgs field that causes the electron zig to be converted to the electron zag and vice-versa. Again it is the energy in this vibrating motion that gives rise to the electron's rest mass.

I think this picture is better than the particle-in-molasses picture that one often hears. In my view the Higgs interaction explains the origin of the rest mass/energy of a particle (and therefore its gravitational mass) but not its inertia defined as its resistance to being accelerated. I think inertia might have a "Machian" gravitational cause as outlined in Dennis Sciama's "On the origin of inertia":
http://adsabs.harvard.edu/abs/1953MNRAS.113...34S

 

[Bill_K]

The "zig" and "zag" fields are apparently Penrose's terminology for the right- and left-handed components of the electron.

I think this picture is better than the particle-in-molasses picture that one often hears

Anything would be better than the Higgs-as-molasses picture.

I think inertia might have a "Machian" gravitational cause as outlined in Dennis Sciama's "On the origin of inertia":

A pre-Einsteinian idea, intuitive but primitive, and long ago shown to be false.

 

[Dead Boss]

The "zig" and "zag" fields are apparently Penrose's terminology for the right- and left-handed components of the electron.

Are these right- left-handed components the same as the two components of the spinor?

 

[Bill_K]

Any Dirac spinor can be decomposed into right- and left-handed parts ψ_R and ψ_L using the chirality operators P_R = (1 + γ₅)/2 and P_L = (1 - γ₅)/2. For a massless particle, P_R and P_L commute with H and chirality is a good quantum number. But for a particle with mass, the mass term m(ψ_Lψ_R + ψ_Rψ_L) couples them together. The same holds true whether m is put in by hand or generated by the Higgs field.

 

[Dead Boss]

Ah, thanks. But what is γ₅? I thought there were four gamma matrices?

 

[tiny-tim]

Ah, thanks. But what is γ₅? I thought there were four gamma matrices?

γ₅ is short for iγ₀γ₁γ₂γ₃

 

[johne1618]

Are these right- left-handed components the same as the two components of the spinor?

Penrose works with Pauli 2-spinors rather than the more usual Dirac 4-spinors.

As I understand it a 2-spinor directly represents a spinning particle whereas the Dirac 4-spinor decribes a state with both spin and positive and negative energy components that can't be so easily visualised as a particle.

 

[Bill_K]

Penrose works with Pauli 2-spinors rather than the more usual Dirac 4-spinors.
As I understand it a 2-spinor directly represents a spinning particle whereas the Dirac 4-spinor decribes a state with both spin and positive and negative energy components that can't be so easily visualised as a particle.

johne1618, Did Penrose say that, or is that your own interpretation? The massless Dirac equation decouples into two equations for two 2-component spinors. Although the equations contain the Pauli matrices, the spinors themselves are Weyl spinors. Also the solutions for each equation include both a positive energy solution and a negative energy solution.

 

[johne1618]

johne1618, Did Penrose say that, or is that your own interpretation? The massless Dirac equation decouples into two equations for two 2-component spinors. Although the equations contain the Pauli matrices, the spinors themselves are Weyl spinors. Also the solutions for each equation include both a positive energy solution and a negative energy solution.

Sorry you're right this is largely my interpretation drawing from what Penrose writes in Chapter 24 and 25 of his book - I don't understand the mathematical details myself.

However Penrose definitely does imply that his zigzag particle picture is more directly suggested by a superposition of Weyl 2-spinors rather than the more usual 4-spinor description using the Weyl or chiral basis.