Momentum in Time: 4th Dim & Gravitational Fields

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OK, time (or perhaps sqrt(-1) X time) is our fourth dimension. Do we have momentum as we move through time? When we encounter a gravitational field, does it act to accelerate (decelerate) our "velocity" through time?
 
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The time-momentum is just the energy! In relativistic physics, energy and the three space components of momentum are viewed as a single entity called 4-momentum. Even in non-relativistic physics, there are indications that energy and momentum have very similar nature (see books on advanced mechanics).
 
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