PKT_VOL
Veni, Vidi, Vici
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Oh, yeah, and you were asking about my thoughts on the arrow of time. I think this is essentially what the link I provided the other day was dealing with, though, admittedly, I didn't read it that thoroughly. I was simply looking for a source, since I was at work and didn't have any books on hand.
So, during this period of inflation, an arrow of time begins, as we have created essentially a "new universe" even though it is just a local point of inflation in a much larger universe. But as the universe ages trillions upon trillions upon trillions of years to the point that it returns to a homogeneous universe with zero entropy. At this point, time ceases. But other points of inflation, elsewhere in the universe, are experiencing their own Big Bangs, and starting their own arrows of time.
Now the philosophical part. How can a period of inflation begin in a region of the universe with zero entropy, if there is no flow of time? Wouldn't you need to somehow advance time to a point where the inflation could start?
Well, I don't know. But that lends a bit of validity to the notion that time is simply an observance of the conscious mind. Maybe time itself still exists, but an observer wouldn't interpret it moving forward during this period of zero entropy. It wouldn't matter, of course, because there could be no observer in a zero entropy system.
Is time a local phenomenon, where each point in the universe, depending on the level of entropy, time is evolving at a different rate? Similar or even related to Einstein's relativity, where time moves at a different rate due to the effects of gravity.
Maybe it has to do more with entropy than gravity. As a point in space with more mass is going to have higher entropy. Hmmm.... Now my mind is wandering off. Trying to figure out if that's true.
Well, let me start of by saying it all depends on what you believe time is, what you believe the "flow" of time is, and what you believe the nature of time is.
For me, time is a function of 3-dimensional space. There are two ways of thinking about it, either is correct to me. You can simply think about our traditional 3-dimensional space but with an extra dimension connected in a way that would be perpendicular (it is impossible for humans to truly imagine this, but you get the point). Or you can think of it my favorite way being that of a movie reel where the images on the reel are infinitely small splices of 3-dimensional space with vector recognition. Time, or the "flow" of time then is the images moving through the projector at a rate of speed.
Now that we know where I am coming from with my idea of time, we can apply it your hypothetical.
First, zero entropy would not have an effect on my theory of time. Entropy only effects the matter and energy (the stuff) of the universe. It does not effect space. Thus, time would continue until there is no space. Now, the "flow" of time would cease to anyone "watching" such a reel because the stuff within space which gives the illusion of time "flowing" is not there. Basically, there are no points of reference at all where all the atoms are uniformly separated and at absolute zero.
Now to your second question about time in relation to inflation. It depends upon the nature of these "new" spots of inflation within the "old" universe. If they are just random spots of inflation that do not create their own space, meaning they quite literally just randomly and in a violent way spread matter and energy apart, then there would be no effect on time at all on a universal scale. However, there would fluctuations upon the perceived local time due to gravitational and velocity implications. If the "new" spots of inflation create their own space, then the time within that space would be its own separate entity.