Another Time-Travel Paradox?

[GenePeer]

So I've read that there's nothing that rules out time travelling, but there's something I've never seen discussed: mass-energy conservation.

Let's say in the year 2020, a time machine/portal is created and Sam moves back to 2010. He then lives the next 10 years doing doing whatever he likes. By the year 2020, a Sam somewhere will move back in time while this one continues his "normal" life.

Therefore, in the time period 2010-2020, there were two Sams. Before and after that time, there's just one. Will this not violate the law of conservation of mass? Maybe the extra mass was converted from energy, but that would require E = mc² amount of energy. For the mass of a normal person, this is a ridiculous amount of energy. So why do scientists think time travel is still feasible?

[euler]

But if the universe consists of all space AND all points in time then Sam travelling back 10 years in time is nothing more than Sam travelling 10 metres in a particular direction in space.

[Lord_Farin]

In fact, there is a paradox at work here. This is because when assuming FTL (faster-than-light) travel, one necessarily violates the equations of relativity theory. It will therefore be void to discuss about the equation $E = m c^2$ (which as you mentioned, already disposes of conservation of mass; conservation of the total of mass and energy is typical these days). Simply put: time travel will disprove our current theories of physics. No problem; this has happened a lot of times before We will always have only theories, no truths (despite us calling them 'laws').

[timday]

David Deutsch's book "The Fabric of Reality" has some interesting ideas about paradoxes of time travel; specifically how they simply go away in an Everettian many-worlds multiverse. It's a good read, although be aware it's very personal, opinionated "Theory of Everything As The Author Would Like It To Be".