For whatever reason, time has an apparent direction that follows the path of increasing entropy. It seems to be a one way street from the past to the future. So, what are the prospects for actually controlling the movement through the 4th dimension?
Travelling Forward
No one disputes the concept of travelling forward in time. This type of time travel relies on an effect called time dilation. As you approach the speed of light, time contracts. So, a person moving at 0.9 times the speed of light might experience 1 year pass by but to an outside observor (who is stationary with respect to the moving person) they would experience 2.3 years. In affect when the travelling person comes to a stop, they would have travelled 1.3 years into the future. There are no foreseeable problems with this type of time travel as it doesnt affect what we percieve as the past. This type of time travel isnt theoretical. It is experimentally verified. For example, scientists know the lifetime of certain particles generated in the upper atmosphere from cosmic rays. This lifetime is much shorter than the time it would take the particles to reach the surface where they are detected. Since the particles are highly energetic (travelling near the speed of light), they are able to make it to the ground due to this time dilation effect which to an outside observer(the person detecting them) makes their lifetime seem longer. In reality, the particle still experiences the same lifetime.
Travelling Backwards
This form of time travel only exists within a few special(extreme) theoretical models. The thing all of these models seem to have in common is they require immense amounts of energy or matter. Most of them are toy models in that they are nonphysical and are only investigated for the purpose of looking at how the physics works in them. There are a few which might actually be conceivable. One such model uses Einstein-Rosen bridges (wormhole) and time dilation to create a link between the past(when the wormhole is created) and present(where the other end of the time dilated wormhole ends up). The problem with these models is it isnt possible to go back beyond the point where the time machine was created. So for example, you could never witness the Pyramids being built or prevent the JFK assasination. There might be other problems also but a quantum theory of gravity would be needed to understand them. One possible problem is that the wormhole might collapse if anything tries to pass through it. Even though the equations of stable wormholes work on paper now, there isnt a guarantee they will be possible once you incorporate quantum theory with general relativity.
Paradoxes
A lot of good stories have centered around the possible inconsistencies that travelling back in time might create. The classic example is the Grandfather Paradox. In this paradox, a person travels back in time and prevents their grandfather from producing their father. The paradox is said to exist because the time traveller shouldnt exist to go back in time to prevent the birth of his father at that point. It is my belief that paradoxes do not occur. That the only reason we believe there will be a paradox is because of a linear mindset with regard to time. If you look at the amount of energy needed to actually generate a portal back in time, it seems to me that it is causing a different excitation of the universe. Just to explain what I mean here. Most mainstream scientists do not think that the multiple universe vision of quantum mechanics is true. For example, Roger Penrose thinks that once you include gravity that mass will cause multiple states to collapse into a definite state. So, you will not have the superposition(a system being in multiple states simultaneously) of macroscopic objects (see Schrodinger's cat thought experiment). So, at any given moment of time there are an infinite number of possible states for the universe to be in. However at that moment, it actually only exists in very few. By excitation, I am saying that backward time travel is essentially pumping energy into the earlier universe so that a particular state is populated(realized).
Travelling Forward
No one disputes the concept of travelling forward in time. This type of time travel relies on an effect called time dilation. As you approach the speed of light, time contracts. So, a person moving at 0.9 times the speed of light might experience 1 year pass by but to an outside observor (who is stationary with respect to the moving person) they would experience 2.3 years. In affect when the travelling person comes to a stop, they would have travelled 1.3 years into the future. There are no foreseeable problems with this type of time travel as it doesnt affect what we percieve as the past. This type of time travel isnt theoretical. It is experimentally verified. For example, scientists know the lifetime of certain particles generated in the upper atmosphere from cosmic rays. This lifetime is much shorter than the time it would take the particles to reach the surface where they are detected. Since the particles are highly energetic (travelling near the speed of light), they are able to make it to the ground due to this time dilation effect which to an outside observer(the person detecting them) makes their lifetime seem longer. In reality, the particle still experiences the same lifetime.
Travelling Backwards
This form of time travel only exists within a few special(extreme) theoretical models. The thing all of these models seem to have in common is they require immense amounts of energy or matter. Most of them are toy models in that they are nonphysical and are only investigated for the purpose of looking at how the physics works in them. There are a few which might actually be conceivable. One such model uses Einstein-Rosen bridges (wormhole) and time dilation to create a link between the past(when the wormhole is created) and present(where the other end of the time dilated wormhole ends up). The problem with these models is it isnt possible to go back beyond the point where the time machine was created. So for example, you could never witness the Pyramids being built or prevent the JFK assasination. There might be other problems also but a quantum theory of gravity would be needed to understand them. One possible problem is that the wormhole might collapse if anything tries to pass through it. Even though the equations of stable wormholes work on paper now, there isnt a guarantee they will be possible once you incorporate quantum theory with general relativity.
Paradoxes
A lot of good stories have centered around the possible inconsistencies that travelling back in time might create. The classic example is the Grandfather Paradox. In this paradox, a person travels back in time and prevents their grandfather from producing their father. The paradox is said to exist because the time traveller shouldnt exist to go back in time to prevent the birth of his father at that point. It is my belief that paradoxes do not occur. That the only reason we believe there will be a paradox is because of a linear mindset with regard to time. If you look at the amount of energy needed to actually generate a portal back in time, it seems to me that it is causing a different excitation of the universe. Just to explain what I mean here. Most mainstream scientists do not think that the multiple universe vision of quantum mechanics is true. For example, Roger Penrose thinks that once you include gravity that mass will cause multiple states to collapse into a definite state. So, you will not have the superposition(a system being in multiple states simultaneously) of macroscopic objects (see Schrodinger's cat thought experiment). So, at any given moment of time there are an infinite number of possible states for the universe to be in. However at that moment, it actually only exists in very few. By excitation, I am saying that backward time travel is essentially pumping energy into the earlier universe so that a particular state is populated(realized).