That's a common misconception.No time elapses at the speed of light.
Time DOES slow down as the speed of light is approached.A number of posts in this thread have been removed, as they were driving the discussion off-topic.
I'd like to remind the participants about the Physics Forums rules about personal theories. They are not allowed unless supported by peer-reviewed publications or other scientifically accepted sources - and the books that pump out misleading half-truths like "time slows down as the speed of light is approached" aren't that).
Its misleading. Proper time, for example, remains the same. Suppose you have two inertial frames moving close to the speed of light relative to each other. Each has a clock placed at the origin. Each will read the same time on their clocks, but see the other clock as running slower. Which is correct? Which runs slower?Time DOES slow down as the speed of light is approached. Where is there any evidence of the opposite?
Highly grateful having such an illuminating reply.@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 [Broken] 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.