How flexible is the principle of causality?

[Alex K]

Not to split hairs here, and I don't want to act smarter than Wikipedia, but that sounds not like a well defined principle of causality at all. If you have two point masses approach each other, they repulse and fly on their way, what is then supposed to have caused what?

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I apologize if I sound naive (because I am), but wouldn't it have something to do with their gravitational pull which in some instances is known to have the opposite effect (anti-gravity)? Okay so what are the implications you're trying to show me?

I don't want to be so presumptuous as to try and show you the way, since I'm not the high priest of physics, but here's what I think (mainly gathered from what I've learned in classes):

It is well known that in simple Newtonian systems with a few masses, there is no discernible arrow of time. The extreme case is the two body problem, where you have two masses going round each other forever, and if you reverse the clock, it will behave exactly the same, and according to the same laws of physics (the laws of Newtonian physics are the same upon time reversal). Since there is no clear distinction between past and future, I would argue that causality is not really present.

Now if you go to a three body system, it can happen that you set it up as a little complicated three body "solar system" and let it run, and it will run and run, and suddenly after some time, one of the masses will be catapulted out of the system never to return again. Technically, the exact same thing can happen in reverse, with a mass coming flying in from infinity to integrate itself perfectly into a stable three body system. However, this is very unlikely and requires fine tuning of the initial condition. As an observer, you start getting a handle how to at least make a good guess in which direction the movie you watch is rolling, but not 100% certain.

I think it is here that we start to glimpse the effects of entropy, and what causality means: going from less likely to more likely configurations. Let's go the extreme case where you have 1000 gas particles, and you put them in the lower half of a flask. If you now let time run, they will spread throughout the vessel, never in billions of years to return to this state where they all are trapped in the lower half. It is now uniquely possible to tell in which direction time runs, but not because there is an arrow of time built into fundamental physics. It is only because you have as a boundary condition in time a unlikely configuration, which you can therefore associate with past.

So cue say 6 Billion years ago, again, with the same initial quantum state copenhagenously speaking - how different could the world have turned out due to quantum uncertainty? Is that your question?

Yeah.

There would probably be a star in the vicinity here because there was a lot of material nearby, maybe a double star sytem where jupiter has gathered enough mass to ignite, and some planets which bear no resemblance to the ones we know and love. Would there be life? maybe, maybe not.

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p.s.
Incidentally, we today know that the laws of fundamental physics are probably not completely invariant under reversal of time, because of the observation of CP-Violation and the CPT-Theorem. The latter tells you that under reasonable assumptions, the laws of nature remain the same if you reverse the flow of time, left and right, and the sign of all charges simultaneously. Since we know that the laws of nature are subtly different if you reverse all charges and left and right, it is probable that the same happens for the reversal of the direction of time T.

While this may have played an important role to define what is past and future in our world, these subtle effects are not what define the arrow of time in each moment. This is really the statistical mess I describe above.