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etotheipi

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I was just thinking about this and couldn't decide whether it was a silly question or not, so naturally I thought I might ask. It was partly prompted by one of the questions asked in the homework section.

Every physical law I can think of is "self-correcting" if you substitute negative values for different quantities. E.g. none of ##V=IR##, ##x = u_x t + \frac{1}{2}a_x t^2##, ##\Delta H = \Delta U + T\Delta S## change form depending on whether any of those quantities are negative. So long as the value of a quantity is within its domain (e.g. ##I \in (-\infty, \infty)##), the equation holds true.

Are all of these equations valid for all real numbers by default? Or do we need to use a symmetry argument of some sort to show that the formulae themselves take the same form no matter whether e.g. ##V## is positive or negative?

And furthermore, are there any examples of physical laws where the domain of a particular variable is restricted (ignoring obvious cases, e.g. lengths must be greater than zero)?

Thanks!

Every physical law I can think of is "self-correcting" if you substitute negative values for different quantities. E.g. none of ##V=IR##, ##x = u_x t + \frac{1}{2}a_x t^2##, ##\Delta H = \Delta U + T\Delta S## change form depending on whether any of those quantities are negative. So long as the value of a quantity is within its domain (e.g. ##I \in (-\infty, \infty)##), the equation holds true.

Are all of these equations valid for all real numbers by default? Or do we need to use a symmetry argument of some sort to show that the formulae themselves take the same form no matter whether e.g. ##V## is positive or negative?

And furthermore, are there any examples of physical laws where the domain of a particular variable is restricted (ignoring obvious cases, e.g. lengths must be greater than zero)?

Thanks!

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