Energy Conservation, Lorentz Invariance and a Second Dimension of Time
The law of conservation of energy can be stated: Energy can neither be created or destroyed but only converted to from one form to another. Laboratory experiments demonstrating that no energy is lost or gained during a conversion have been rare. Interestingly, there is a close connection between energy conservation, Lorentz violation and the possibility of a second dimension of time. We explore this connection within a model of Lorentz invariance that incorporates a second dimension of time. The model's Lorentz transformation matrix reduces to the well-known one-dimension of time version in the limit of a parameter that defines the relative size of the extra dimension. If the parameter is finite, one might misinterpret the energy equivalence of mass or observe a deviation from the accepted time dilation formalism. We explore different experimental limits on this new parameter including Lorentz violating parameters from the Standard-Model Extension.