@votingmachine : Thanks for reading, and welcome to PF! Your interpretation of the time dilation equations of Special Relativity is, as bhobba pointed out, a common misconception. See http://www.quora.com/If-a-photon-travels-at-the-speed-of-light-and-time-dilation-at-the-speed-of-light-is-infinite-does-this-mean-that-from-the-photons-perspective-it-takes-no-time-at-all-to-cross-the-entire-universe for a good explanation.
@dayalanand roy Thanks for reading, Dayalanand. Let me respond to your questions in order:
1. This experiment is indeed another type of delayed choice experiment. You can read more about it here:
https://en.wikipedia.org/wiki/Wheeler's_delayed_choice_experiment
2. I chose irreversible examples to imply that entropy is always increasing (the second law of thermodynamics). Entropy is one of the only quantities that requires a specific direction for time. Reversible thermodynamic processes are not particularly interesting to this end since they are performed at equilibrium and keep entropy constant. In fact, it is this conservation of entropy that allows them to be time-reversible! If the entropy had increased, the process would be irreversible, hence the arrow of time. Irreversible processes are primarily what occurs in nature.
3. For a full explanation of why entropy implies an arrow of time, read this:
https://en.wikipedia.org/wiki/Entropy_(arrow_of_time)
4. On this point we can agree somewhat. I don't think time travel is in the cards, either.
5. Spacetime is the fusion of three dimensions of space and one dimension of time into a single continuum. I don't think calling it the "fourth dimension of space" is technically correct. While spacetime was a major leap forward in our understanding of time, note that this experiment was dealing with quantum mechanics instead of relativity, and the two theories are famously incompatible. Our explanations of relativistic time do not account for many of the weird things in QM.
When you get right down to it, I think you're correct that dimensions do not "exist" in a physical sense. They are descriptions we have applied to nature for the purposes of prediction, and they do a great job at that.