In fact, in quantum physics, "negative norm" do pop up from time to time, as a consequence of mathematical computations, and physicists simply choose to eliminate or ignore these cases, saying, "it's un-physical". Kind of like eliminating cases where energy appears to be negative. It's not a "fact" that norms (aka absolute value, or modulus) is NECESSARILY always positive. We have "normed algebras" (i.e., e.g., reals, complex numbers, quaternions, octonions) that behave nicely and allow the existence of norms that are "always" positive. But then we can have sedenions which do NOT have this property, i.e., it lacks multiplicative normedness.

When one tries to make a sweeping claim that the absolute value of a thing can't ever be less than zero, a lot of potentially interesting math is being tossed out the window without the benefit of examination.

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TopNewestIn fact, in quantum physics, "negative norm" do pop up from time to time, as a consequence of mathematical computations, and physicists simply choose to eliminate or ignore these cases, saying, "it's un-physical". Kind of like eliminating cases where energy appears to be negative. It's not a "fact" that norms (aka absolute value, or modulus) is NECESSARILY always positive. We have "normed algebras" (i.e., e.g., reals, complex numbers, quaternions, octonions) that behave nicely and allow the existence of norms that are "always" positive. But then we can have sedenions which do NOT have this property, i.e., it lacks multiplicative normedness.

When one tries to make a sweeping claim that the absolute value of a thing can't ever be less than zero, a lot of potentially interesting math is being tossed out the window without the benefit of examination.

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