> Where philosophy intersects with physics, it is called "physics".
And yet, so many physicists have no idea how important self-consistency is in their physics.
> We've never managed to go without need for experiments.
Well, I never made such claim.
Also, Chicken or the egg, physics and philosophy, only a physicist ignoring self-consistency would bother trying to collapse this.
> We can observe the dimension of time with a clock.
Please, I think you are both too small and too slow to see it for what it really is when you look at a clock. You assume it is a dimension as we all do, since for our scale of things, this works pretty well.
> No, it's not. Something is static if it doesn't change with respect to time. Any parameter changes with respect to itself at rate 1.
Again, please I refer to time "itself" to try and catch you before you trip. When I say in this circumstance, time "itself" is static, I mean to say that if it can be reversed along with physical actions and you get back what you started with, then it is independent and unchanging, predetermined and all that that implies - essentially, static.
> This isn't at all a problem. After all, we can already observe in every unit of space, time moving forward or backwards as we see it.
No. I'll stop here. This is just wrong, so I won't go any further with it.
I don't think the reversing the syllogisms holds in this example. It is not sufficient to say that because T is violation that T would not be in violation if the universe were flipped and all CPT were now opposites. Just managing to show that things do not reverse equally in this universe, does not mean that by inverting everything, you also invert false to true.
I think you have misunderstood the implications of this finding. Just like gravity waves and their observation (or lack of), I think it only takes a small philosophical thought experiment to realise that there are problems with the questions being asked here and so the results alone will only serve to confuse.
For a start, let's assume that time is a dimension - this is an assumption that most physicists hold dear, some do not.
In this circumstance, the arrow of time appears arbitrary since positions in a spatial dimension appear arbitrary - it could this far along and a sequence of actions moved it in this direction, reversing all the actions perfectly moves everything the other way.
Of course, even if this were definitely true, you would still be faced with the dual direction problem - i.e. it looks like if time is a dimension, then it runs the same way forward as backward - as long as actions are reversible. This is just another way to say that time itself is static, the chosen direction itself is arbitrary and one could say that in a inverted universe my reverse is your forward. What I'm really saying here is that if time is a dimension, then the real problem is having a universe where time runs both forwards and backwards in different regions of space and that it would be possible to observe one from the other. This violates relativity.
So, if time were not a dimension, merely a product of components of the universe being able to interact consistently with other components of the universe (i.e. for this to happen, you need causality and change), then it would appear to have a direction to observers too small or slow, but this would be an illusion because the observer can not exist outside of the realm being observed. It's like a physicist is doing a thought experiment without realising he doesn't actually exist outside of the realm he is imagining to be our universe.
Time is a process - Time has no direction at all because it is the process of change that allows observers to do anything at all, imagining it running another direction is actually happening in this universe. Time is the result of a universe struggling with a paradox of it being one solid indivisible thing, or a multitude of things that appear to interact. If it contains components, they require time to observe each other with consistency, being the result of the causality required to keep things consistent. If there were no relativity, the universe would have no discernible objects and its only consistency would be to remain a single, solid unchangeable, unobservable thing.
so CPT invariance implies that the universe is the same thing, just being viewed differently - you still can't run it forwards and backwards in different regions of space and this whole thing of it being viewed differently is just a thought in someone's very real head that also cannot run time differently - it cannot be "viewed" from outside at all. I nearly said you can't run time forwards and backwards in the same universe, at the same time! But of course, the absurdity of that just illustrates that some questions are just improperly formed and do not have meaningful answers because the questions themselves are self-inconsistent and meaningless.
Kleeneness is next to Godelness.