There are many different theories for time travel theoretically many of the papers published comes under one or more of these theories....
1. Neutron star theory : A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star. These stars have a mass around 466,000 times the mass of the earth, thus exerting a very high gravitational force (1.962×1012 m/s2, earth's is 9.81 m/s2) although they have a diameter of 10-12 Km. As for the Gravitational time dilation, time would pass 30% slower on the surface of such a star, meaning that if someone could travel to such a star and withstand this gravity, they would have a way to "travel" to the future. This theory only serves for time travel to the future, to the past wouldn't be possible.
2. Black hole theory : Black holes are one of the most used resources in time-traveling novels, next to wormholes. The Kerr-black hole theory is the result of Roy Kerr's calculations for relativity. A Kerr-black hole is a singularity that possesses mass and angular momentum, but does not possess electrical charge. This hole spins around a central axis and has two event horizons, which contain a ring-formed singularity. Inside each of the two event horizons, time and space are reversed, so in a Kerr-black hole this swapping occurs twice. In theory, it's possible to escape the ring-formed singularity, although not by the same way you entered it, or simply avoiding it. Crossing the singularity would make you end up in a "negative space" (the definition is still unclear). Avoiding it would cause you to go back in time while you are crossing the first event horizon.
3. Tachyon theory : The Tachyon or a Tachyon particle is a hypothetical particle that always moves faster than light, Most physicists believe that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. The existence of such particles, called tachyons, has not been totally ruled out, but several experiments have tried, without luck to detect them. If they did exist, and they interacted with ordinary matter, it would give us the means to communicate with the past. Tachyons could literally be sent outwards, bounce off a tachyonic mirror, and return before they were sent. This in turn would give rise to a great many logical problems. For example, if you sent a message back in time that caused your grandfather to be killed before your father was conceived, then you would not be around to send the message that prevented your birth, so that you would be around to send the message, so that you wouldn't be around....etc. Despite theoretical arguments against the existence of faster-than-light particles, experiments have been conducted to search for them. No compelling evidence for their existence has been found. In September 2011, it was reported that a tau neutrino had travelled faster than the speed of light in a major release by CERN; however, later updates from CERN on the OPERA project indicate that the faster-than-light readings were resultant from "a faulty element of the experiment's fibre optic timing system....But hpe is still there....
4. Wormhole theory : A wormhole is like a shortcut opened through space and time. There are two holes in it, tied together by a tunnel. Transit time through the tunnel is zero, no matter how far away the second hole is. But there's a catch. The tunnel suffers from super gravity, and collapses as soon as it opens. And that's why we need something to negate the effect of gravity, the so-called 'exotic matter'. It's a substance with negative mass, which repels gravity.The wormhole tunnel is all squished and squashed like this fist of mine. In order to pass through, you need something inside of my hand to oppose the 'grasping force' so that I can not squish anymore.Now, if you stabilize a wormhole with exotic matter injection, teleportation becomes possible. For example, let's say there's a wormhole entrance in paris, and the exit is in LA. Now imagine the hole in LA goes all the way to the end of the universe at near-light speed. And once it reaches the end, it immediately pulls back to LA. According to the theory of relativity, time slows down for objects moving at the speed of light. Meaning the hole that returned to LA would be further in the past than the one in paris. And with those you can enter the wormhole and arrive at LA several years back. However, this cannot yet be called true 'time travel'. It is only 'pseudo-travel'. The so called Urashima effect. The important part is to return to paris from LA through the wormhole once more. Having done that, transit time becomes zero, and you would return to parisa several years back. Time travel complete. The prerequisites for wormhole theory are simpler than the ones for cosmic string theory. First: the wormhole itself. They may exist somewhere in the universe, yet nobody has ever seen one. Second: The energy required to move a wormhole to the end of the universe and back near-light speed. Third: Exotic matter, which by the way, has not been confirmed to exist.
5. Exotic matter theory : Exotic matter, like described in the wormhole theory has a negative mass. However because Exotic matter isnt confirmed to exist the negative mass is also hypothetical, which means it has an imaginary mass much like the Tachyon particle and thus is possibly also able to exceed the speed of light and be used to communicate with the past.
6. Cosmic String theory : A Cosmic String is a string-shaped crack which has an extreme mass. You can think of the crack as something the width of an elementary particle, and at least the length of a galaxy.It has an immense mass, giving it the property of space-time distortion. If you were to travel through that distortion you could make a full rotation around the string in less than 360 degrees.In short, you can do something resembling a warp. This is called Space-time angular deficit. When you pass through an area of angular deficit, transit time becomes zero.Applying this, once the cosmic string moves approaching light speed, according to the theory of relativity, time will flow slower for the cosmic string in relation to its surroundings. Therefore, passing through the area of angular deficit would cause the zero transit time to become negative. In other words, it will be the 'past' after transit. So, if you use two cosmic strings, you can do a space deficit jump. If you revolve back to your original location, you can return to the same time you started revolving. And that, roughly speaking, is time travel by means of cosmic string theory.By the way, so nobody misunderstands, cosmic string theory is different from superstring theory. With that out of the way, you need three things in order to travel to the past with cosmic string theory. First: Cosmic Strings. Two of them are necessary. Ah, by the way, they are hypothesized to exist only where the universe was first formed, so they might be a little hard to find". Second: Even if you do find the strings, you need the energy to make them move at near-light speed. Just how much energy do you think you'd need to accelerate something as long as the milky way to near-light speed? it's a little bit more than 1,21 jigowatts. Third: a space ship able to go all the way to the cosmic strings. The time traveler must be on board.
7. Quantum Gravity theory : Quantum gravity theory uses Quantum jumps in the use of a "stale state" or a "dead state" where no movement is possible because of density.You can google it or read the feymans lectures to know more....
8. Elementary particle ring and laser theory : This is a theory proposed by Dr. Mallet. What I find interesting about this is it involves some things like the Coriolis metric and the "Sagnac" circularly constrained null (light) geodesics. Frame dragging is apparently the "key" to time travel, which in GR means closed time-like geodesics and/or world lines are possible. Frame dragging is the way time-like curves can be bent around into closed paths. So far, the mass-energy-velocity needed to "close the loop" has been so enormous that it is just an academic thought-experiment (such loops are thought to exist between event horizons in the Kerr metric -- but "thankfully" hidden behind the outer horizon where we would never be able to see it or learn any information about what would happen). But there is a way to do with much less energy. The space-time metric of a beam of light going around in a circle can do the proper frame dragging contortions --actually two beams of light going around in opposite directions (note this would have sort of a "shearing" effect). Now, normally, as above with regular mass, the energy to close the loops would be astronomical, but the "slowing of light" to a crawl by those Bose-Einstein condensates has the effect of amplifying the effect. And there are criticisms of his EFE solutions here, before anyone gets too excited -- they say its wrong. Anyway, from what I understood, the scientist as he said needs a few terawatts of laser power, going around in circles in some BE condensate near absolute zero, and he thinks he'll make a region with closed time-like curves just big enough for some neutrons to squeeze through and be able to observe any funny effects he expects and he said he needs about $1/4 million to do that, and now has the funding and is going to try it.
9. Light speed theory : This is the most simplest as everyone knows it. This is the easiest and most practical way to get to the far future – go really fast. According to Einstein’s theory of special relativity, when you travel at speeds approaching the speed of light, time slows down for you relative to the outside world. This is not a just a conjecture or thought experiment – it’s been measured. Using twin atomic clocks (one flown in a jet aircraft, the other stationary on Earth) physicists have shown that a flying clock ticks slower, because of its speed. In the case of the aircraft, the effect is minuscule. But If you were in a spaceship travelling at 90% of the speed of light, you’d experience time passing about 2.6 times slower than it was back on Earth. And the closer you get to the speed of light, the more extreme the time-travel. The highest speeds achieved through any human technology are probably the protons whizzing around the Large Hadron Collider at 99.9999991% of the speed of light. Using special relativity we can calculate one second for the proton is equivalent to 27,777,778 seconds, or about 11 months, for us. Amazingly, particle physicists have to take this time dilation into account when they are dealing with particles that decay. In the lab, muon particles typically decay in 2.2 microseconds. But fast moving muons, such as those created when cosmic rays strike the upper atmosphere, take 10 times longer to disintegrate.
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