NOVIKOV'S SELF-CONSISTENCY PRINCIPLE, HAWKING'S CHRONOLOGY PROTECTION CONJECTURE, & EVERETT'S MANY WORLDS INTERPRETATION

Are There Reasons Why Time Travel Is Not Possible?

There are severe complaints which can be leveled at the idea of time travel, both physical and philosphical. Some of the physical complaints can be eased by looking at rotating black holes where you don't have to pass through the singularity, but the problem is still severe in that event horizons are one-way membranes.
There are other types of wormholes which do not suffer from some of the physical problems. For example, there are Schwarzschild wormholes formed by gluing black hole and white holes back-to-back so that the singularity is not cloaked by event horizons in all universes. These do not suffer from the one-way nature of event horizons but they do suffer from other problems.
As stuff passes through the throat of a wormhole, it is compressed and so its density i(mass/volume) goes up and the gravitational force, GM/r², amplifies and the throat pinches itself off. To get around this problem, Thorne, Morris, & Yurtsever postulated that some arbitrarily advanced civilization (AAC) could develop a new form of matter to hold open the throat of the wormhole. In this case, one could travel from place to place in spacetime and, under the right circumstances, could travel in time. That is, wormholes could act as time machines!!

Is Time Travel Possible?

The impossibility of time travel has never been proven, and so it might be possible. However, there is also no evidence that time travel has occurred and if time travel were allowed then, potentially, we would have serious problems as laid out in notions like the grandfather paradox and various other inconsistencies which could arise in history. Time travel is not something with which we want to deal at this time (or at any time really). It is better that it were not possible. Someday if we can show and understand why time travel is not possible then we will have done something quite significant. There is nothing in our current theories which tells us why time is special and why time flows as it does. (There is no reason to believe, based on theory, why cause must precede effect in our Universe--What defines the Arrow of Time?) Since cause always precedes effect, this probably means that there is a physical reason for why time flows as it does. Unfortunately, the reason escapes us at this time. If we could understand why time travel is not possible, it might help us to understand the fundamental nature of the Universe.

Novikov's Self-Consistency Principle
The Novikov self-consistency principle asserts that if an event exists that could give rise to a paradox then the probability that the event occur is zero. To support his conjecture, Novikov did not look at a classical paradox such as the Grandfather Paradox, but rather considered a rather simpler problem which we now discuss.

Polchinski's Paradox
Imagine the two mouths of a wormhole have been manipulated so that they exist at two different times. (Imagine the Twin Paradox where one end of the wormhole is the traveling twin and the other end of the wormhole is the stay-at-home twin. In this case, one end of the wormhole will be younger than the other end.) If a billiard ball enters the wormhole at one point in space-time, but then returns at an earlier time through the other end of the wormhole, we could then have the uncomfortable possibility that if the billiard ball hits the original billiard ball, it could deflect the ball and not allow it to enter the wormhole. Ooops.
There are many possbilities for the trajectories of the balls in this scenario consistent with one timeline (outcome of events) (Echeverria, Klinkhammer, & Thorne 1991, Phys. Rev. D, 44. 1077). For example, suppose the original billiard ball was not going to enter the wormhole,but that the returning billiard ball slightly jostles it so that it does enter the wormhole. The billiard ball is itself the thing which causes it enter the wormhole and so to return from the other end (the future). That is, the billiard ball goes into the past but cannot alter the outcome of the scattering.

Hawking's Chronology Protection Conjecture
Hawking propoed that quantum mechanical effects always conspire to prevent time travel where classical physics might allow otherwise. The chronology protecion conjecture states that solutions in General Relativity which allow closed time-like paths are physically meaningless.

Everett's Many Worlds Interpretation and Wavefunction Collapse
If we imagine say, an electron, contained in a box or some arbitrary space, the electron may be anywhere (position) with any momentum allowed by the equations. Before the electron is observed, quantum mechanics says that the electron is in no particular state, (with given (position,momentum)-pair), but that it is in a superposition of all possible such states. This superposition is described by what is called its wave function. Before you observe the electron, no one state can be considered more real than any other state. It is only after the system is oberved that the electron settles in, that is, the wavefunction collapses to only one state. To illustrate this idea (as did Schrodinger in the 1930s), consider Schrodinger's Cat

Schrodinger's Cat A cat is placed in an isolated box along with a vial of poison and a box of radioactive material. The vial of poison and the radioactive material are hooked up in such a way that if the particle decays, the hammer is released and the vial is broken, releasing the poison gas killing the cat.

Now imagine the above experiment is set-up. Let the observer wait an hour or so to allow the particle to have a chance to decay. After an hour, the observer opens the lid of the box to check on the cat. The observer finds a dead cat. The naive observer then says that the particle must have decayed before the box was opened and then that the cat must have been killed sometime in the last hour. This sounds sensible.
What does quantum mechanics say (the Copenhagen version of quantum mechanics)? Well, it says that before the observer opened the box, the system existed in a quantum superposition of states--the cat was neither alive nor dead. That is, the state where the particle decayed or the one where the particle did not decay were, in a sense, on equal footing with neither preferred nor being more real. It was only after the observation that the wave function collapsed into the single observed state where the particle decayed. This is odd.
It is against this backdrop that Everett introduced his Many Worlds interpretation of quantum mechanics. Everett suggested that whenever a quantum event occurs such that one state out of many is selected, that what actually happened was that not only was one state selected, but that multiple timelines for the other possibilities were also spawned. This would remove the need to collapse the wave function but it introduces the foliation of multiple histories at every quantum event. Is this notion any better?
The Everett Many Worlds Interpretation of quantum mechanics may allow one to escape the paradoxes inherent in time travel. For example, travelling back in time where one saves President Kennedy would not necessarily change history in our Universe, because we could actually be travelling back in time to the Universe where President Kennedy survived. This idea is appealing but it is not clear whether such journeys between the multitudes of timelines is possible.