Time-travel theories

There are many different theories for time travel. Steins;Gate uses the black-hole theory mostly, by compressing the data of the brain (2.5 Petabytes), to a size sendable by the phone microwave.

In the VN, Kurisu mentions that although there are many theories, 11 of them are widely accepted in the scientific world. Listed below:
 * 1) Neutron star theory
 * 2) Black hole theory
 * 3) Light Speed theory
 * 4) Tachyon theory
 * 5) Wormhole theory
 * 6) Exotic matter theory
 * 7) Cosmic String theory
 * 8) Quantum Gravity theory
 * 9) Cesium Laser theory
 * 10) Elementary particle ring and laser theory
 * 11) Dirac antiparticle theory

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 ranging from 449.482 to 665.900 times the mass of the earth in a diameter of 12 Km. That means they have a very high density, thus very high gravity ( 7 × 1012 m/s2, earth's is 9.81 m/s 2 ). 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.

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. Here's a Penrose diagram of two time travelers making their way through the black hole. The dark-blue one avoids the singularity and the light blue one crosses it:

Tachyon theory
See page: http://www.macrobiotic.org/health11.html

Wormhole theory
Wormhole theory, as Cosmic String theory, is explained by Makise Kurisu during her press conference:

-"In that case, why don't we go to our next example, wormhole theory? It may be a little more realistic than cosmic string theory. By the way Hououin-san, do you know what wormholes are?"


 * -Kurisu Makise, chapter 1 of the VN

-"It's like a shortcut opened through space or something... right?"


 * -Okabe Rintarou, chapter 1 of the VN



-"Yes, that's correct. There are two holes, 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."

''-"If you stabilize a wormhole with exotic matter injection, teleportation becomes possible. For example, let's say there's a wormhole entrance here in Akihabara, 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 Akihabara. And with those co'ndition, Hououin-san 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 Akihabara from LA through the wormhole once more. Having done that, transit time becomes zero, and Hououin-san would return to Akihabara 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.'"''


 * -Kurisu Makise, chapter 1 of the VN

Cosmic String theory
In the VN, Makise Kurisu explains the cosmic string theory at her conference:



-"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? I'm pretty sure 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. What do you think Hououin-san? Care to take on the challenge of cosmic string theory time travel?"

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.

Dirac antiparticle theory
The theory of Paul Dirac represents an attempt to unify the theories of quantum mechanics and special relativity. That is, one seeks a formulation of quantum mechanics which is Lorentz invariant, and hence consistent with special relativity. For a free particle, relativity states that the energy is given by. Associating E with a Hamiltonian in quantum mechanics, one has

If H and p are associated with the same operators as in Schrödinger theory, then one expects the wave equation

This is known as the Klein-Gordan Equation. Unfortunately, attempts to utilize this equation are not successful, since that which one would wish to interpret as a probability distribution turns out to be not positive definite. To alleviate this problem, the square root may be taken to get

However, this creates a new problem. What is meant by the square root of an operator? The approach is to guess the form of the answer, and the correct guess turns out to be

With this form of the Hamiltonian, the wave equation can be written

In order for this to be valid, one hopes that when it is squared the Klein-Gordan equation is recovered. For this to be true, equation 63 must be interpreted as a matrix equation, where and are at least matrices and the wavefunction is a four-component column matrix.

It turns out that equation 63 describes only a particle with spin 1/2. This is fine for application to the hydrogen atom, since the electron has spin 1/2, but why should it be so? The answer is that the linearization of the Klein-Gordan equation is not unique. The particular linearization used here is the simplest one, and happens to describe a particle of spin 1/2, but other more complicated Hamiltonians may be constructed to describe particles of spin 0,1,5/2 and so on. The fact that the relativistic Dirac theory automatically includes the effects of spin leads to an interesting conclusion--spin is a relativistic effect. It can be added by hand to the non-relativistic Schödinger theory with satisfactory results, but spin is a natural consequence of treating quantum mechanics in a completely relativistic fashion.

Including the potential now in the Hamiltonian, equation 63 becomes

When the square root was taken to linearize the Klein-Gordan equation, both a positive and a negative energy solution was introduced. One can write the wavefunction

where represents the two components of associated with the positive energy solution and represents the components associated with the negative energy solution. The physical interpretation is that is the particle solution, and represents an anti-particle. Anti-particles are thus predicted by Dirac threory, and the discovery of anti-particles obviously represents a huge triumph for the theory. In hydrogen, however, the contribution of is small compared to. With enough effort, the equations for and can be decoupled to whatever order is desired. When this is done, the Hamiltonian to order can be written

where is the original Schrödinger Hamiltonian, is the relativistic correction to the kinetic energy, is the spin-orbit term, and is the previously mentioned Darwin term. The physical origin of the Darwin term is a phenomenon in Dirac theory called zitterbewegung, whereby the electron does not move smoothly but instead undergoes extremely rapid small-scale fluctuations, causing the electron to see a smeared-out Coulomb potential of the nucleus.

The Darwin term may be written

For the hydrogenic-atom potential, this is

When first-order perturbation theory is applied, the energy correction depends on. This term will only contribute for s states (l=0), since only these wavefunctions have non-zero probability for finding the electron at the origin. The energy correction for l=0 can be calculated to be

Including this term, the fine-structure splitting given by equation 58 can be reproduced for all l. All the effects that go into fine structure are thus a natural concequence of the Dirac theory.

The hydrogen atom can be solved exactly in Dirac theory, where the states found are simultaneous eigenstates of H,, and , since these operators can be shown to mutually commute. The exact energy levels in Dirac theory are

This can be expanded in powers of, yielding

This includes an amount due to the relativistic energy associated with the rest mass of the electron, along with the principle energy levels and fine structure, in exact agreement to order with what was previously calculated. However, even this exact solution in Dirac theory is not a complete description of the hydrogen atom, and so the the next section describes further effects not yet discussed.