The HIggs field appears with spontaneous symmetry breaking
The photon , the particle involved in the electromagnetic interaction, along with the W and Z provide the necessary pieces to unify the weak and electromagnetic interactions. With masses around 80 and 90 Gev, respectively, the W and Z were the most massive particles seen at the time of discovery while the photon is massless. The difference in masses is attributed to spontaneous symmetry breaking as the hot universe cooled. The theory suggests that at very high temperatures where the equilibrium kT energies are in excess of 100 GeV, these particles are essentially identical and the weak and electromagnetic interactions were manifestations of a single force. The question of how the W and Z got so much mass in the spontaneous symmetry breaking is still a perplexing one. The symmetry-breaking mechanism is called a Higgs field, and requires a new boson, the Higgs boson to mediate it.
So the question really asks if one can control the symmetry breaking energy , when the higgs field appears as the electromagnetic and weak coupling constants run into each other.
It is maybe good to think about an analogue in classical physics, a magnet:
When the magnet is strongly magnetized in one direction, it would be hard to guess that the underlying interaction is actually symmetric under rotation. The magnetic field from the magnet is certainly very different if it is rotated 90 degrees, or 180 degrees. The underlying symmetry can only be seen if the energy of the system is raised - heating the magnet to its Curie temperature would remove the directional magnetic field and restore the rotational symmetry of the material.
I find that the Curie temperature can be a function of directions :
In an anisotropic ferromagnet the Curie temperature is a function of the direction of the magnetization. The Curie temperature is high in easy directions, and can drop quite low in harder directions for an anisotropy energy comparable to the exchange energy. Magnetization curves as a function of temperature also depend upon the orientation. In sufficiently hard directions, the magnetization drops from a large value precipitously to zero at the Curie temperature.
This last allows one to imagine that the v.e.v. of 246GeV might be negotiable for some width, i.e. in some specific boundary conditions, but the balances that lead to symmetry breaking have to hold in order to observe the world we observe and have encoded into the standard model. So turning off for the whole universe will both not be possible or desirable ( well it did happen in the Big Bang history at o.1 ns) . Maybe some of these compactified dimensions from strings would give a handle to explore changes in v.e.v. s , if we ever are experimentally sure they exist ;) and can experiment with them. (i.e. allow to modify the boundary conditions that define the electroweak parameters for some specific experiment)
At the moment we have to pursue higher energy experiments with leptons in order to get a handle with enough accuracy to explore differences in coupling constants while approaching the unification energy. This last for the electroweak unification into one coupling constant is at a scale of 10^12 GeV .
