Let's ignore the trivial case where you travel forward in time, and ignore the trivial relativistic take that time "moves" at a different rate depending on one's relative gravitational interaction.

The question Neil poses is: Can we move thru time analogous to the way we move thru space? In other words, is time travel possible?

I have proved elsewhere that it would lead to a logical contradiction when considering living sentient "systems." You might ask: What if there were no sentient being? Would time travel be possible? Ignoring the fact that if sentient beings did not exist, there would be no one to asses any conceptual ideas, including the concept of time, let me prove that time travel would still not be possible.

Consider a general physical system S in a (quantum) state Q, where:

Q = aQ1 + bQ2 + ... + vQn. ... ... eq.1

where the system has been acted on by a (quantum) force (field) described by the Hamiltonian H(t). We then solve the Schrodinger equation and get the probabilities ...