relativity - Wouldn't backwards time travel break the law of conservation of mass?

We know from the law of conservation of mass that the amount of mass in the universe is constant. Suppose there were a way for a person to travel backwards in time. Let's call this mass $m_t$ for some time $t$. Assume you are traveling backwards in time from $t_n$ to $t_0$ where $n$ is the amount of time (let's say the unit is seconds) since the time traveled back to. This allows for negative subscripts of $t$. If the law of conservation of mass is true, then it is true for all times. Then $m_{t=-1}=m_{t=0}$. However, since you have traveled through time to $t_0$, you have added your mass to $m_{t=0}$. That means that according to conservation of mass, a quantity equal to your mass has been subtracted from something else. But mass doesn't spontaneously disappear in order for time travel to occur, so that's impossible. Doesn't it follow that by the law of conservation of mass, backwards time travel (and by similar logic but in reverse, forwards time travel) is impossible?