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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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.
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:
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.
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.
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.