@Brain: We didn't do anything robust with it, but we messed around with what the electron would see if the CPT inversion operation were performed on it. In it's own frame of reference, it's charge, parity and time would be negative, forward and forward; but the rest of the universe relative to it would appear to be CPT inverted.
The upshot seems to be that the notion of forward and backward in any given direction in space and time aren't really that meaningful. Provided the CPT conservation holds, it is not any different to talk about a (positive, forward, forward) and a (negative, backward, backward).
Frankly, direction isn't truly meaningful even if the CPT does not hold, as long as there's an inverse function to the laws of the universe. That is, you could hold that the universe is in fact running backwards using these inverse laws, rather than forwards with the usual laws. In this scenario, we would be hopelessly doomed to enact our "past" (which is in fact a premonition). There isn't really any way to know for sure in what direction time "moves", except that it's more natural (simpler) to assume it runs towards higher entropy.
Even if there is no inverse function to the laws of the universe, there may be an inverse relation (a 1-to-several mapping, which can lead to a backwards-bound tree of universes, or a non-deterministic path). There again, there is no way to know whether our memories are memories or premonitions, for the laws we use to understand the universe may be the inverse laws of what the universe actually uses to compute present from future and past from present.
Now here's an illustration of how reversing time flow could actually be productive, because I think it's cool: imagine that some particle A can decay into either particles B and C, or into particles D and E, seemingly at random. This would seem like the universe is not deterministic. Now imagine that no other physical phenomenon ever involves creating B+C or D+E. The inverse function of the laws of physics would then map the collision of B and C, or of D and E, to particle A, always. No uncertainty is at all involved. So you would have a case where the laws of physics are non-deterministic when running towards the future, but fully deterministic when running towards the past. Thus one could consider the idea that the universe really does actually run backwards, and that all "randomness" is just information loss. Such a model would be predictively worthless, yet it very well might be correct!
All this to say that the direction in which time "truly" flows is impossible to determine and is more a matter of usefulness or taste than science.
One funny point that I have read is that since the future hasn't happened yet, it doesn't exist, and since the past is no longer here except as a memory, it doesn't exist anymore either. The only time that exists is the exact present. But the duration of the present is 0, so consequently no time exists.
If the past exists, that pretty much means that the universe backs itself up as it goes, leaving a trail. Alas, if we were to go in these backups, there's no way to know what kind of rules apply to them, so it's unclear what would happen - at worst, these backups are in cold storage and time travel effectively jams you in a precise time in the past, like flies in amber.
Also, out of curiosity, how do you classify the various time travel implementations I posted earlier?
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About free will: the issue with free will is that I have never seen a definition of it that wasn't either inadequate (too broad) or outright unintelligible (self-inconsistent) (except for the one I will present below). One massive stumbling block is the concept of "self": if you want to determine whether "you" have free will, you need to know what kind of thing you are. And once you've determined what kind of thing you are, you need to explain what it means for that thing to choose to do something.
Here's the closest I think one can get to a coherent definition of free will (well, it's the best I could find):
Let B be an actual brain in the real world and let P be the
person represented by B.
1) P is defined as the
collection of all possible specific entities E such that B, upon inspecting its own behavior in a new situation and the behavior of E in the exact same situation, could not determine which of the two it is.
2) "P can do Y" is defined as "there exists E in P such that E does Y" (assuming E is reified and put in situation).
3) "P has free will" is defined as "there is a sizable number of non-trivial actions Y such that P can do Y and P can do not-Y"
The first definition seems reasonable, because it mirrors the fact that any of us can imagine ourselves doing many things. This suggests that the "self" assimilates more than what it is in reality, and is preserved under several changes. That is, there's probably an infinity of different brains that you would readily associate to yourself, not just the one you actually have - the "self" is like a blurry cloud of different people that are so similar to us that we can't tell them apart from us, and believe that we can do whatever any of these people would actually do. Regardless of whether one accepts this definition of free will or not, I think that at the very least this is essentially why we
think we have it - we simply think that we are all these people at once.
Here's another way to look at it: our consciousness and introspection capabilities are clearly insufficient to precisely determine our brain state. The best we can do when introspecting ourselves is to place constraints on what we are, and these constraints lead us to modelize ourselves as the set of all brains that fit them. Therefore, if we consider the action of pressing a button, it is likely that neither pressing it nor not pressing it runs against any constraints. In fact, the human brain is so complex that it will usually fail to see any constraints on its behavior that are not glaringly obvious. Therefore, our brain will consider that it
can do either: it cannot tell apart any brain which fits the constraints, so as long as one of them would press the button and another wouldn't, the conclusion is that both are possible. In a sense, this is foolish, because only one of these outcomes will actually happen. But here's the thing: when we say "self", what we
mean is precisely this internal representation of ourselves that our consciousness built. And when we say "can"... well, you get the picture. Most free will arguments might very well be strawmen, the saddest thing being that both proponents and opponents are guilty of it.
I'm sorry about the tangent, I didn't intend to write that much :(
