Does time travel violate conservation of mass/energy?

Imagine I exist at time $t_1$ and my mass is $m$. At time $t_2$ I time travel back to $t_1$. At time $t_1$ there is now a net increase of mass/energy in the universe by $m$.

At time $t_3 = t_2 - x$ where $x < t_2 - t_1$, I travel back to t1 again. The net mass in the universe has now increased by $2 \times m$.

Properly qualified, I can do this an arbitrary $n$ number of times, increasing the mass in the universe by $n \times m$. This extra mass, of course, can be converted to energy for a net increase in energy.

Does this argument show that traveling back in time violates the conservation of mass/energy?

Answer

Conservation of Energy is a consequence of Time-translational Symmetry of the system. If this symmetry is broken, there'd be no Conservation of Energy.