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In the conventional formalism of physics, with 1-time, systems with differentHamiltonians or Lagrangians have different physical interpretations and areconsidered to be independent systems unrelated to each other. However, in thispaper we construct explicitly canonical maps in 1T phase space (includingtimelike components, specifically the Hamiltonian) to show that it isappropriate to regard various 1T-physics systems, with different Lagrangians orHamiltonians, as being duals of each other. This concept is similar in spiritto dualities discovered in more complicated examples in field theory or stringtheory. Our approach makes it evident that such generalized dualities arewidespread. This suggests that, as a general phenomenon, there are hiddenrelations and hidden symmetries that conventional 1T-physics does not capture,implying the existence of a more unified formulation of physics that naturallysupplies the hidden information. In fact, we show that 2T-physics in(d+2)-dimensions is the generator of these dualities in 1T-physics ind-dimensions by providing a holographic perspective that unifies all the dual1T systems into one. The unifying ingredient is a gauge symmetry in phasespace. Via such dualities it is then possible to gain new insights toward newphysical predictions not suspected before, and suggest new methods ofcomputation that yield results not obtained before. As an illustration, we willprovide concrete examples of 1T-systems in classical mechanics that are solvedanalytically for the first time via our dualities. These dualities in classicalmechanics have counterparts in quantum mechanics and field theory, and in somesimpler cases they have already been constructed in field theory. We comment onthe impact of our approach on the meaning of spacetime and on the developmentof new computational methods based on dualities.

Generalized Dualities in 1T-Physics as Holographic Predictions from 2T-Physics