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Higgs Asteroids

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So, the zero value Higgs field has energy. Is it an energy that is reachable simply by temperature reduction? Could a ferrous asteroid fall low enough in temperature to be accelerated by a magnetic field to the speed of light?

If the energy density with respect to the ground state is non-zero and the field has the same non-groundstate value everywhere, then in an infinite universe the total energy difference is infinite. I don't see where temperature, a magnetic field, or the acceleration of an asteroid come in.

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