No basis for an arrow of time can be found in any of the laws of physics. All fundamental physical processes can happen in either time direction. On the scale of everyday experience, one time direction is highly more probable than the other for many observed processes, but this is the statistical result of the large number of particle involved and their largely random motions.
On the quantum scale, events are found to depend on the future as well as the past, which makes them seem very strange. Weird effects occur, such as particles appearing simultaneously at different places ("nonlocality"). These and other quantum paradoxes can be easily understood in terms of time symmetry. On the other hand, the time travel paradox, in which you go back in time and kill your grandfather, does not occur at the quantum level. Thus quantum time travel is not paradoxical.
Time symmetry at the quantum level makes it possible to draw a model of underlying reality that is simpler and more symmetric than the conventional view. This reality is timeless, with no beginning, no end, and no arrow of time. Observations at the smallest distances and highest energies reveal a picture of localized, discrete material bodies moving along definite spacetime paths in an otherwise empty void, with no fundamental distinction between past and future and no need to introduce "real" continuous fields. This is the picture revealed to us by the standard model of elementary particle and forces, which is fully consistent will all empirical data.