Can Time Loops Create Paradoxes?

[Blouge]

Hi, I have some questions about time travel. My understanding is that it is an accepted theoretical consequence of General Relativity. If the scenarios I'm describing are too ridiculous then perhaps analagous microscopic scenarios would be more palatable.

Consider these scenarios:

Scenario #1:
You are trapped in a burning building locked from the inside. Someone throws a key under the door and you are able to escape. Some time later, you decide to travel back in time to thank the stranger. But, when you arrive, no one is there, so you simply throw the key under the door.

There are two problems here: (a) where did the key really come from? Is it anything like a virtual particle - would the time loop here be limited to a duration based on the inverse rest mass energy of the key? Or would it not be so limited? Another problem is (b) there is a contradiction. The key you gave up is not the key that you obtained. Some atoms may have flaked off. The oil from your skin has corroded it. If you ignored this contradiction and continued watching the time loop, the key would continue degrading until nothing was left. (c) What if it's not a key, but an electron, and a spontaneous decay process is theoretically forbidden - will the contradiction be sidestepped?

Scenario #2:
The exact same scenario as #1, except the building is locked by a computer that requires you to factor a gigantic composite number and type the factors on a keyboard to open the door. Instead of throwing a key, the stranger is yelling the factors at you.

Again, similar questions: (a) since this time it is mere information - lacking rest mass - would it elude the limitations on its duration of existence as pondered in 1a? (b) Since it is information, can it be reproduced without degradation? Or is even the brain, as a physical information storage device, subject to being in a superposition of states, which will continuously degrade the information just as the key was degraded? In other words, can information actually exist in the universe or is information a mere ephemeral state of some physical object which can't be infinitely and precisely copied?

Is it possible that the information "degrades" slightly when you receive it, but by the time you give the information back, it has "degraded" in precisely the opposite way, avoiding a contradiction? Or does a superposition of states involving complex/real coefficients, and not integer coefficients, make this dubious? If the information is a small enough amount of data, say spin up vs. spin down, and is exchanged over a small amount of time, would this help avoid the degradation problem, or not?

Answers to these questions might forbid or severely restrict the possibility of objects or information that semingly come out of nowhere as a result of "time loops".

 

[RUTA]

Hi, I have some questions about time travel. My understanding is that it is an accepted theoretical consequence of General Relativity. If the scenarios I'm describing are too ridiculous then perhaps analagous microscopic scenarios would be more palatable.

Consider these scenarios:

Scenario #1:
You are trapped in a burning building locked from the inside. Someone throws a key under the door and you are able to escape. Some time later, you decide to travel back in time to thank the stranger. But, when you arrive, no one is there, so you simply throw the key under the door.

There are two problems here: (a) where did the key really come from? Is it anything like a virtual particle - would the time loop here be limited to a duration based on the inverse rest mass energy of the key? Or would it not be so limited? Another problem is (b) there is a contradiction. The key you gave up is not the key that you obtained. Some atoms may have flaked off. The oil from your skin has corroded it. If you ignored this contradiction and continued watching the time loop, the key would continue degrading until nothing was left. (c) What if it's not a key, but an electron, and a spontaneous decay process is theoretically forbidden - will the contradiction be sidestepped?

(a) In GR one finds a solution to Einstein's equations (EE) for the entire spacetime manifold in question. So, one can always ask, "Whence that spacetime region?" The answer to that question lies beyond GR. All GR provides is a rule (EE) for the metric and stress-energy tensor (SET) to be compatible. Keep in mind that there is no global conservation of momentum-energy in GR. The divergence-free nature of the SET is stricty local. So as long as the SET and metric satisfy EE, which entails a divergence-free SET, there is no answer to "where did the key come from?" anymore than "whence the entire spacetime region?"

(b) I assume the worldline of the key is a closed time-like curve (CTC). If you've constructed a solution to EE, then the SET for the key on this CTC is divergence-free so it marries up nicely everywhere along the CTC and there is no problem. If you want to say it "degrades" so that a divergence-free SET for the key along this CTC cannot be created, then you don't have a solution to EE and you're functioning outside GR.

(c) Ibid.

 

[Dmitry67]

Also check this

http://en.wikipedia.org/wiki/Novikov_self-consistency_principle

I really like this part:

A common example of the principle in action is the idea of preventing disasters from happening in the past and the potential paradoxes this may cause (notably the idea that preventing the disaster would remove the motive for the traveller to go back and prevent it and so on). The Novikov self-consistency principle states that a time traveller would not be able to do so. An example is the Titanic sinking; even if there were time travellers on the Titanic, they obviously failed to stop the ship from sinking. The Novikov Principle does not allow a time traveller to change the past in any way, but it does allow them to affect past events in a way that produces no inconsistencies—for example, a time traveller could rescue people from a disaster, and replace them with realistic corpses seconds before it occurs. Providing that the rescuees do not re-emerge until after the time traveller first journeyed into the past, his/her motivation to create the time machine and travel into the past will be preserved