Let's try this from another standpoint:

There is nothing in current theory that rules out the possibility of the existence of tachyon particles. These super-luminal particles would flow backwards in time. To them, yesterday most certainly would still exist.

If, to some part of the universe, yesterday still exists, then every moment back to the Big Band still exists. We simply don't have the ability to travel that direction on time's arrow.

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your hypothesis relies on the supernatural viewpoint in order to dispense with time. The cosmos cannot, by definition, exist within 'extra-cosmic space'

I didn't say it had to. In fact, I specifically explained why it didn't have to: "The same several-dimension structure could still exist as filling the entire area into which it formed - in which case there is no extra-cosmic space"

The analogy is not dependent on an outside figure. My point was that any "time traveler" that isn't bound to the same inexorable time dimension as us, be it a guy in his extra-cosmic workshop or a humble tachyon particle, can only exist if time is a static dimension.

I mentioned my Catholicism in the spirit of full disclosure. I'm well aware that it puts a sudden suspicion on all I say, but don't do yourself the disservice of assuming that my viewpoints ever are influenced by it to the point of not accepting scientific fact. When science produces information seemingly contrary to my faith, I ponder it until figuring out how they fit together - I'm not one of those folks who denies science for folly. I only brought up my Catholicism at this particular time because it just happens that the nature of time is something that I've had to ponder on quite a lot in order to reconcile my faith with science. The tachyon particle is key to that reconciliation. It hasn't been found yet, but it hasn't been ruled out yet, either.

w