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If I was able to go back in time via Machine or whatever, would traveling back in time not create a paradox? I was not there, so how could I exist where I did not exist in the passed? i would have to assume that we could never go backwards in time in any way shape or form.

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Someone retag with time travel. And likely duplicate of physics.stackexchange.com/questions/7823/… but I won't call it quite yet. These both seem to be about standard Back to the Future kind of time travel, which might be already addressed sufficiently. –  AlanSE Aug 15 '11 at 17:32
Neither question (nor most of the answers to 7823) are coached in sufficiently precise language to be dealt with well. There are attempts to deal with the possibility of closed time-like curves, and the properties they must have (or not have), but as yet they must be formulated in fairly opaque mathematics. –  dmckee Aug 15 '11 at 17:40
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This question is directly about the apparent paradoxes that are present in what I will refer to "Back to the Future" time travel. This is the time travel depicted in several major movies where a time machine is created and someone goes back into the past and changes something.

A simple solution to time travel paradoxes

This might be better handled by a philosophy perspective, but since it's being asked here, I'll start with a slightly less relevant of a physical example where something can be taken to be traveling backward in time. Hawking radiation involves a particle radiating away from an event horizon after being spontaneously created from quantum fluctuations with an antiparticle that falls into a black hole.

Hawking radiation

In this case, the antiparticles can be interpreted as the particle itself traveling back in time. On can not escape the event horizon of a black hole, but it can if it travels backward in time. The "lame" thing about this situation is that time travel happens without any conflicting world-lines. There is a singular story of what happened, and no multiple universes are required.

Hollywood time travel often does involve conflicting (and often hopelessly confused) world-lines. This generally comes in the form of someone from the future affecting the series of events that leads to the creation of a time machine. Developing a plot should depend on several philosophic physical questions like:

  • Can a given outcome be guaranteed, or does the world exhibit determinism / fatalism?

One could potentially take the above example of particles and antiparticles and replace it with an intrepid time traveler. In that case, the time traveler is moving forward in time, until at one point in spacetime he goes into reverse and begins traveling backward in time. This would be observed as the existence of 2 versions of the time traveler colliding and then disappearing. Then if he reverses back into the forward direction, then at some other point in spacetime, before his "first" reversal (first, perceived in his time), there is an apparently spontaneous creation of 2 versions of him, one of them going backward in time and one of them going forward in time.

There is no way to create time paradoxes because the versions that have time traveled already exist by the time the time machine is used.

Entropy arguments

Yet another way to time travel goes back to the definition of entropy and time itself. The laws of physics are (to the extent of my own knowledge) fully reversible, and the reason time progress in one direct was due to the low entropy at the big bang, which allows us to have a memory of the past and not the future.

You could just create something that has a decreasing entropy. There, finished. What does this mean? This means that you create an item that has a decreasing number of degrees of freedom. For instance, a gas that starts with chaotic-seeming motion of particles that are really precisely engineered to converge on a single point in the middle. The event of that gas contracting is identical to saying that the gas is expanding backwards in time.

Again, you should find Hollywood disappointed with the proposal because no privileged information is gained. No one can use this to win the lottery, and the systems required to decrease entropy of a chunk of matter are drastically more elaborate than the system that is created. On the plus side, we are getting closer to the point when we can technologically do this.

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The universe lives in a continuum evolving present . The past do not exist, neither the future; there are no such places. The equations are symmetric irt time and they only told what will be the next state in face of the actual snapshot and similarly we can derive what was the previous state, eg. the Earth will progress to the next position in space and not to the position it occupied a moment ago.
I'm looking to the night sky and I'm receiving energy (photons) released billions of years ago as measured by our local clock or by the cosmological clock used to describe the evolution of the universe as a whole by an independent observer (not attached to the matter properties).
If in the next moment, say $t_{+1}$, I intended to be in my past $t_{-1}$ I will have to deconstruct all past events that already happened in the whole universe between $t_{-1}$ and $t_{0}$. All photons that are hitting my eyes now must be sent back into space to some other evolving position. All other people normally evolving will have to be deprived of that light. Can we erase stars from the sky? No. Can we substitute one photons by others? No. Now lets admit that you arrived to your desired past. What photons are you seeing? In what position in space is the Earth? Was it moved at your will to any other place except that one that physical laws will determine? With all its present inhabitants ? With all past and dead inhabitants, those that are now flowing in the rivers or buried down in the Earth (possibly some atoms of them are now integrated in my body) ? How much energy will you need to recall all that matter from its present locality to your desired position? Will you go and at the same moment stay here? Will you have two consciences? Some atoms in your body could belong to someone else in the past. To return there will you destroy him? or will you reassemble some other matter locally available to reconstruct your body? What happens to your present body?
All matter radiates gravito/electromagnetic energy into space always. How do you reassemble back that energy into the particles to have the world of the past? There is no way!
In the universe there is a currency, called energy that has to be paid to do any action. All the matter/energy in this universe is allocated, engaged in this trip. If we want to construct an alternative reality we have to assume other simultaneous universe like a shifted copy modified, of this one. The object of physics is only the universe that we observe. Some theoretical instances wrote about other realities, mental constructs, desires, much like many others constructed other places like Heaven and Hell. When some believe in other universes we have two situations: if they interact or leave some trace in this one then we are only talking about this one and if they do not interact then they are out of the domain of physics.
Using Einstein SR equations we describe the viewpoint of a moving body and get prisoner of our local clocks and we think about closed time-like curves. If we adopt another viewpoint, above all moving bodies and with instant vision to acknowledge the events,not the kind of the Einstein referential, we will have a broader view and see that there is no chance to travel to the past.
The energy argument and the choice of a more proper referential should be enough to put an end to the dream of time travel. But because we are humans it is nice to have dreams.

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Thank you a great answer to my question. Witch brings me to think that if we could travail back in time it would only be during the 'big crunch' thus the universe itself being the time machine. Maybe some day the notion/study of the Déjà vu could prove with calculations that we are constantly being looped froward and backward in time and that we have time during our Déjà vu to change history of that particular big bang expansion, Thus only effecting the one we are in at the moment and no others. and if that being true why? –  Sifimichael Aug 17 '11 at 5:31
The universe is absolutely fascinating without Big Crunch, Big Bang, DM, DE, BH, time travel, etc. I've experienced once or twice the Déjà Vu. Its a mirage. My brain is a marvelous construction that took 57y of my own time, 30 of my parents time, more 30 of my grand-parents,.... and some of the neuronal constructs of the past may have survived in my brain and the pattern matching that our brain constantly do can activate false memories. In some future ;) I can add to this answer more about quantity of information, emitter and receiver stations and the notion of 'time' local and cosmological. –  Helder Velez Aug 17 '11 at 7:26
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