What is the relationship between the Higgs field and General Relativity?

Question

We are told the Higgs field gives particles mass, therefore how does this relate to gravity according to Einstein's theory? Since gravity interacts between mass, surely there is a connection.

Answer 1

General Relativity used to go camping in Higgs' Field.

No, seriously, there is sooo much we don't understand about gravity, and I'm not sure you will get good answers on here;-))

(Did you hear a few years back about the supercooled ceramic discs which were supposed to negate gravity somewhat?  Russian scientists were welcomed to the USA, given BIG grants, and nothing heard of positive results since!)

Answer 2

While it is believed that the Higgs boson (carrier of the Higgs field force) is responsible for particle mass, gravity is such a negligible force on the particle level as to have virtually no effect on individual particles. It's only when there are enough particles to have an impact in our macroworld that gravity is able to exert any influence.

In a way, it's like asking the effect of individual letters on the stock of a bookstore. It's only when the letters are combined in enough concentration to create books that their effect on the stock carried in the bookstore matters.

Remember that Relativity is concerned mainly with the world of the very large. Gravity in the quantum world is still not well understood (there is no valid theory of quantum gravity, for example).

Answer 3

Unfortunately the two great corner stones of twentieth century physics, namely General Relativity and Quantum Mechanics, are not able to mathematically incorporate one another. General Relativity, mathematically breaks down when it attempts to deal with the very small and, furthermore, the original Heisenberg and Schrodinger formulations of Quantum Mechanics were not relativistic. Dirac derived a relativistic equation for the electron and there are a number of other partially relativistic particle theories.

The LHC at CERN will be searching for, among other things, the Higg's boson, which gives particles their mass. The prediction for this particle comes from the 'Standard gauge Model' of particle physics. This model is non-relativistic and deals with the strong nuclear and weak nuclear forces along with their exchange via bosons between the quarks and leptons (electron family).  Thus, the Higg's field and its boson are not describable using general relativity.

Below I will try and outline how the Standard Model of particles physics requires the Higg's field and boson.

The weak interaction  is mediated by spin-1 bosons which act as force carriers between quarks and/or leptons. There are three of these intermediate vector bosons, which were all discovered at CERN in 1983. They are the charged bosons W+ and W- and the neutral Z0. Their masses are measured to be: -

M(W) = 80.3 Gev/c² and M(Z) = 91.2 Gev/c²

which gives their ranges as: -

R(W) ≈ R(Z) ≈ 2 x 10^-3 fm

Their decay modes are as follows: -

W+ -> l+ + vl

W- -> l- + vl'

Z0 -> l+ + l-

Where the l's stand for leptons and the v's for neutrinos with the prime ' indicating an anti-neutrino.

This introduction sets the scene for what follows!

The intermediate vector bosons gain their mass from the Higgs boson. Please allow me to explain.

During the nineteen-sixties the theoretical physicists Glashow, Salam and Weinberg developed a theory which unified the electromagnetic and the weak nuclear forces. This theory is known as the ‘electroweak’ theory, it predicted the neutral vector boson Z0, and weak nuclear force reactions arising from its exchange, in what are known as neutral current reactions. The theory also accounted for the heavy charged bosons W+ and W-, required for the mediation of all observed weak interactions, known as charged current reactions. These particles were discovered in 1983.This unified theory is a ‘gauge invariance’ theory, which means that if the components of its underlying equations are transformed, in position or potential, they still predict exactly the same physics. Because the force carrying particles (Z0, W+ and W-), of this theory, are massive spin-1 bosons a spin-0 boson is required to complete the theory. This spin-0 boson is the as yet unobserved ‘Higgs’ boson.

The masses of the force carrying bosons (Z0, W+ and W-), for the electroweak theory, are derived from their interaction with the scalar Higgs field. Unlike other physical fields, the Higgs field has a non-zero value in the vacuum state, labelled φ0, and furthermore this value is not invariant under gauge transformation. Hence, this gauge invariance is referred to as a ‘hidden’ or ‘spontaneously broken’ symmetry. The Higgs field has three main consequences’. The first, is that the electroweak force carrying bosons (Z0, W+ and W-) can acquire mass in the ratio: -

M(W) =cosθ(W)

_____

M(Z)

Where θ(W) Is the electroweak mixing angle. These masses arise from the interactions of the gauge fields with the non-zero vacuum expectation value of the Higgs field. Secondly, there are electrically neutral quanta H0, called Higgs bosons, associated with the Higgs field, just as photons are associated with the electromagnetic field. Thirdly, the Higgs field throws light on the origin of the quark and lepton masses. In the absence of the Higgs field the requirements of gauge invariance on the masses of spin-½ fermions (quarks and leptons etc,) would set them at zero for parity violating interactions (non-mirror image interactions). Parity is a conserved quantity in strong nuclear force and electromagnetic interactions but is violated in weak nuclear force interactions, which would make quark and lepton masses zero in this later case. However, interactions with the Higgs field can generate fermion masses due to the non-zero expectation value φ0 of this field, as well as with interactions with the Higgs bosons. These interactions have a dimensionless coupling constant g(Hff) related to the fermions mass m(f) by the expression: -

g(Hff) = √ (√2G(f)m(f) ²)

Where G(f) is the Fermi coupling constant and f is any quark or lepton flavour. However, this theory, that the fermion masses are mediated by their interaction with the Higgs field, does not predict their mass m(f). However, with the future discovery of the Higgs boson the above equation can be used to confirm the observed coupling constant g(Hff).

At CERN, the Large Hadron Collider (LHC) will search for the Higgs boson at an energy of up to 1 TeV by colliding protons in the reaction: -

p + p -> H0 + X

Where X is any state allowed by the usual conservation laws.