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As I understand it, the Higgs field is a quantum field that stretches throughout our universe. Particles that carry mass (for example protons and electrons) acquire this property by interacting with the (local) Higgs field. I assume this interaction can be written in the form:

m(j;x,y,z,t) = alfa(j) * H(x,y,z,t)

Here alfa is a coupling constant and j denotes the particle type. H is the effective strength of the Higgs field and x,y,z,t are the space-time coordinates.

I find this intriguing! The mass of a particle used to be considered a fundamental property; just as charge, spin, parity (helicity). But now mass becomes an induced property that results from an interaction with an external field, and its coupling constant alfa(j) becomes the fundamental property.

There is an analogy to Classical Electromagnetism. Molecule can have a electron charge distribution that gives rise a permanent dipole moment d. Molecules can also have a charge distribution which is affected by an external electric field E. This gives to rise an induced dipole moment p = alfa * E. The constant alfa is the polarizability; a key-feature of the molecule.

The problem I have with the "induced mass" concept, is that it requires the Higgs field to be extremely homogeneous on different length and time scales. For example, if electrons in the Andromeda nebula have acquired a slightly different mass than in our galaxy, we would be able to detect this. The light from the Andromeda nebula would have slightly different spectral properties.

My questions are therefore on the homogeneity of the Higgs field.

1. The Higgs field interacts with matter. Hence -by symmetry- matter interacts with the Higgs field. To what extent can this interaction work as a source or sink, resulting in local fluctuations of the field strength?

2. Does the Higgs field have a property to dissipate or smooth out any fluctuations that occur in its local field strength? (e.g. like a conducting metal which responds efficiently and quickly to an excess charge that is applied to it, spreading it evenly out in a short period of time).

3. Is it possible that in certain regions of space (with a length scale L that may range from atomic to intergalactic) there is a small gradient term present in the Higgs field? Perhaps it is even possible that wave-like features can occur?

I thank you in advance!