# Time travel + conservation laws

1. Jun 21, 2013

### sWozzAres

Doesn't traditional time travel violate conservation laws?

If I could in effect materialize in the past, then the universe, being an isolated system would have suddenly gained matter/energy out of nowhere! Also, the atoms that make up my body would then be in two places at once since they already exist somewhere else at the time I materialize.

2. Jun 21, 2013

### WannabeNewton

A space-time solution to the EFEs can have closed time-like curves but this won't affect local energy conservation $\nabla^{a}T_{ab} = 0$ which holds for arbitrary space-time solutions to the EFEs. Furthermore, you can even have stationary solutions to the EFEs with closed time-like curves (e.g. Godel space-time) in which case there is a conserved energy current $\zeta _{a} = T_{ab}\xi^{b}$, where $\xi^{a}$ is the time-like killing vector field, and since $\nabla^{a}\zeta _{a} = T_{ab}\nabla^{a}\xi^{b} + \xi^{b}\nabla^{a}T_{ab} = 0$, we have that $E = \int _{\Sigma}\zeta_{a}n^{a}$ is a globally conserved energy by Stokes' theorem. You have to remember that the orbit is in space-time and not just space.

By the way, the standard Friedman models of the universe (which are the simplest models describing our universe that also agree with observation and experiment) don't have closed time-like curves.

3. Jun 21, 2013

### nitsuj

Woo hoo the universe is still physically sane.

4. Jun 21, 2013

### sWozzAres

Are you saying that if CTC's exist then the conservation laws hold across space-time but don't neccessarily hold at any particular instant, allowing the universe to appear as if it has gained energy from nowhere (since it's actually gained/lost it from another time).

5. Jun 21, 2013

### nitsuj

interesting/fun train of thought. I just read a BBC article about "Quantum biology", anyways it mentions some QM phenomenon like "Superposition" & "Tunneling". Both of which I think are with relate to energy "coming from nowhere".

6. Jun 21, 2013

### sWozzAres

Not sure superposition qualifies since we are really talking about stuff that has been measured, but virtual particles might be classed as stuff from nowhere, even if they are short lived.

7. Jun 21, 2013

### Bill_K

Traditional time travel is impossible for many reasons.

Note that in the case of closed timelike curves you DON'T exist in two places at once, rather you reappear in the same place you were already.

No, not at all.

Again, no. In quantum field theory particles (virtual and not) are routinely created and absorbed. But in every such process, energy is exactly conserved.

8. Jun 21, 2013

### sWozzAres

But is violation of conservation laws one of them?

ok then let me try again! CTC's work for individual particles but if an entire body could somehow traverse a CTC back in time a million years then that body would simply be scattered across space as individual particles, therefore a CTC cannot be used to explain traditional time travel (of an ordered collection of atoms that maintain a coherant structure through time)?

9. Jun 21, 2013

Thanks!