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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?

yters
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  • There is a related concept for wormholes about a feedback loop amplifying virtual particles and destroying it. See part of http://en.wikipedia.org/wiki/Wormhole#Time_travel – Brandon Enright Apr 30 '14 at 20:24
  • I actually wanted to close this as "unclear what you're asking" (there's no question in it), but the consensus among others was non-mainstream. Regardless, I think this does need some edits. – David Z May 01 '14 at 05:42
  • Thanks for the clarification, David. I was confused regarding the reason below, because there are numerous other questions about time travel on this site. – yters May 01 '14 at 18:35
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    For those who put my question on hold due to being off-topic, can you point out what is not established science in my question? That way I can reword it to fit within the guidelines. – yters May 01 '14 at 19:55
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    This does not sound off-topic to me. It begs the question "given what we know to be true about the universe, can we conclude that time travel must be impossible?" – Sildoreth May 29 '15 at 15:00
  • As I mentioned above, I don't think this question is particularly far outside the mainstream. I would invite input from others on whether it's suitable for reopening in its current form, or if not, why not. (I'm on the fence myself) – David Z May 30 '15 at 12:33
  • FWIW, six/seven years later: I found a searched (Ecosia) for "time travel conservation of energy." This was the top result. FWIW. – zedmelon Aug 13 '21 at 15:01

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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.

Earth is a Spoon
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  • You can still have time translation symmetry in a chronology violating spacetime, the simplest case being the torus spacetime $S \times \mathcal{M}$. If you assume really basic classical behaviour though, there needs not be violation of conservation of energy, at least in the GR sense. But you may not be able to create time paradoxes willy nilly. – Slereah Apr 30 '14 at 20:35
  • @Slereah Time-translational Symmetry is more than geometry of Spacetime. If your worldline is in loop, you're going to crash with yourself. How can GR explain extra mass crashing with original mass? The challenge in time travel isn't twisting Spacetime.. But, it is the flaw in the concept. – Earth is a Spoon Apr 30 '14 at 20:50
  • So does the "law" of conservation assume time travel is impossible, if the two are mutually exclusive? – yters Apr 30 '14 at 22:34
  • @yters Actually, conservation laws don't dictate the possible/impossible things in the universe. See Spontaneous Symmetry Breaking events, for example. The thing is: We don't have a solid theory for time travel. But, it can exist successfully violating conservation laws. – Earth is a Spoon Apr 30 '14 at 23:11
  • To expand on your answer, I found this question discussing the conditions for conservation. http://physics.stackexchange.com/q/296/ – yters Apr 30 '14 at 23:48
  • You can't really crash in yourself if you just solve the Cauchy problem in a smooth manner (if such a solution exists, of course). Some CTC spacetimes, so called benign spacetimes, don't even have any physical weirdness and you can just extend the solution from some initial data. But of course you have to impose self consistency as a rule. – Slereah May 01 '14 at 09:15
  • @Slereah What you're saying is only possible if the loop already exists when you start the time machine... That's plain simple crazy sci-fi stable time loop thing. Before you first started the time machine, you already are time traveller? – Earth is a Spoon May 01 '14 at 12:41