As special relativity is a theory and not fact it is in a certain sense speculative (in that it has non discharged assumed premises within the conclusion of the argument) If the reality of time is speculation it is useful speculation that allows man to engage in art, math and science, whereas, a subjective universe (like the one you have suggested)is not a particularly useful theoretical construct. Also this view has considerable metaphysical problems. For instance how do you account for the homogenous quality of human experience that allows for standard observation in a universe that works as you have suggested?

The Hawking Theory you guys are referring to is called the Hawking Chronology Protection Conjecture. Also a reason we might not be inundated with time travelers right now is that many theoretical time machines allow for time travelers to only travel as far back as when the time machine was first turned on or created (and we haven't created a time machine yet).

If some form of monistic idealism accurately maps the state of reality then psyche could work (by psyche I assume you mean mind). If the universe is compatible with a materialist framework however time travel will be a feat achievable only through the application of advanced theories in physics. The metaphysics of reality is not knowable with absolute certainty by any current human standards. That being said planes fly, bombs explode, satellites communicate the wonders of man and the universe every second of the day, therefore, it seems like the materialist postulation of metaphysics is the most reliable.

As far as I can tell time is analogous with change. This answer is very basic but if time is not a fundamental dimension of space time then why is the theory of relativity so successful? If we remove time as the 4th dimension the theory of special relativity can no longer make sense of the time dilation we routinely observe around black holes and neutron stars. If you can not come up with a better theory than Einstein for why this occurs then you must accept that the reality of time is at very least the most plausible physical understanding of the universe humans are currently capable of employing.

The question which initiated this debate really implies two questions not one. Is time travel physically possible? Is time travel metaphysically possible? Between Gott, Davies and others I am inclined to believe that time travel seems like it might be a physical possibility as far as the theoretical physics go. As for the metaphysical problems with time travel like the grandfather paradox I'm not sure whether they can ever be fully resolved unless the past is completely determined even for time travelers and even this theory has strange implications like highly unlikely events becoming increasingly likely i.e. If I tried to kill my grandfather in the past I would in theory be prevented from doing so by slipping on banana peels,having a heart attack or some other statistically unlikely occurrence.

Time is observed as Quantifiable and constant throughout the universe, therefore, not subjective. If some people perceive the flow of time differently (like people who blackout a lot)their perception has no bearing on the objective flow of time. If a person were to travel near the speed of light from a certain perspective (i.e. people who are stationary)the personal time of the stationary observer and the light speed traveler would diverge but this is not an effect of perception it is an effect of time dilation and that time dilation is measureable, therefore, objective and not subjective. This many worlds, subjective, quasi-solipitical understanding of time you seem to be employing is completely unverifiable, without justification and is not represented in any major school of thought.

People experiencing time differently like the Haefield effect for instance merely creates a distinction between personal time and external time.

Also Richard Gott theorizes that the non Euclidean geometry around cosmic strings would allow for you to beat light at slower than light speeds thus travelling back in time.

Also Richard Gott theorizes that the non Euclidean geometry around cosmic strings would allow for you to beat light at slower than light speeds thus travelling back in time.

McTaggerts unreality of time essay says about the same as you have been if you are not already familiar. I haven't read everything here but the philosopher David Lewis thought that people could travel back in time but he also believed that the past is determined even regarding the actions of time travelers.