Is time travel Impossible Because time Doesn't Exist?

[AFTT47]

It seems many of the questions raised in this thread are philosophical in nature, not scientific. I therefore don't feel particularly competent to answer them as a physicist. At least I might be able to offer some perspective or correct scientific misconceptions.

If you argue that time travel backwards might be impossible because the past doesn't exist, there is little in the way of scientific."proof" to pitch against that. But I find it unlikely for one reason: the concept of "now" in the theory of relativity is much more complicated than the Newtonian view or common sense for that matter. If you go beyond your immediate  location in space X and ask the question: what time is it "now" in location Y, you get vastly different answers depending on the velocity at which you move. An observer which moves relative to you with velocity v, will see a slice through spacetime as "now" which is at an angle with respect to yours, because different frames of reference have times which differ by lorentz transformations. This becomes particularly obvious in General relativity when considering the time of someone falling into a black hole. They never reach the event horizon as seen by an outside observer, but  cross it in finite time from their perspective. There is a complete disconnect between what different observers consider the moment now, going so far that events happen for observer B that never happen for observer A, or only in the infinite future.  This lack of a well-defined concept of now (for lack of a global unique time for all places in the cosmos) lets me think that both the past and future hold an ontological existence.

I believe the distinction between past and future to be a statistical phenomenon (as has been alluded to elsewhere in this thread) caused by the increase of entropy. This is obvious in classical physics, but more difficult to argue in quantum theory because of the apparent wave function collapse which only proceeds from past to future - but that is likely an artifact of the formalism because it is not present in all interpretations of quantum theory

Alex, is General Relativity right or isn't it? Does not General Relativity assert that space and time are a 4-D construct of space-time or doesn't it? As far as I understand it, General Relativity asserts that the past, present and future all exist and that any observer's viewpoint is equally valid. I thought we settled this > 100 years ago. Am I in error in my understanding of General Relativity?

I'm not asking about the possibility of travel back in time. I understand that while GR may not forbid it, the prohibition of decreasing entropy might. I'm asking about the 4D construct of space/time where the past, present and future exist - irrespective of the theoretical ability to travel back and forth along the time axis. Does GR assert the existence of the 4D space/time construct or doesn't it?