I Have a Theory

nope, once you die you're done, no second or third tries

How do you know this is true?

Nothing is ever what it is until observed, quantum theory makes free will possible...The arrow of time is a one direction trip guaranteed by entropy... $.02

Unfortunately, determinism is dead. Heisenburg killed it (or maybe it's neither dead nor alive, like Schroedinger's cat.) On the quantum level, it's all probability. If you play the universe over again, it won't be the same.

not to mention the path that the table fabric will have worn into it

'If' everything is exactly the same - one could argue repeatable results even at the smallest level, but things are never the same to the degree necessary to repeat at the smallest level.

I still don't think we've been able to mathematically model the tip of a flame, or the transition from laminar to turbulent, have we? Too many variables and too many non-repeatable conditions.

It's CHAOS, and there is no repeating with the exact same initial conditions. And the conditions change as they play out.

Thanks for giving it a name I could look up, determinism. Interesting topic, granted maybe not the right forum but engineering being the appliance of science I thought I'd ask.

Apparently determinism isn't dead as conflicting theories are far from complete. People I've spoken to agree that with the same initial conditions the snooker ball theory is correct but don't believe it can be scaled up to the universe, but they don't know why they think that.

I'm not saying that if we rerun the big bang the universe will be the same, as the initial condition may well be different. The problem I can't get my head around is for this big bang there was one initial condition. If there are multiple outcomes then it suggests there is either something outside the system which could influence the outcome or the snooker ball theory doesn't workwork. Assuming there is no God influencing it, where does the snooker ball theory fall down? I'm not talking about repeatability rather the idea that for a unique initial condition there is one and only one unique outcome?

So maybe you are onto something considering only non-living things. (planets/stars/comets) However, when you bring living creatures into the equation, can we be sure they will choose exactly the same every time? Is the thought process based on physical entities only? We still know far too little about the actual thought process to say that, for example, Hitler will attack Russia again and fail to pull out in winter. That would make a big difference in the order of things today, would it not?

No. Random quantum variations play an important part in the structure of our universe.

There would be no way to insure the same set of conditions and as such, outcomes would most likely be wildly different with each throw of the dice.

This is one of the fundamental differences between the macro world (your snooker table example) and the quantum world.

Even the snooker ball analogy won't work, anywhere except on the equator, then only if released exactly parallel to the Earth's rotation due to the Coriolis effect.

Depends on the level of accuracy you want to measure at.

The universe is another matter. A tiny deviation in anything would be huge after 13.8 billion years.

But if you measure it....

I distinctly remember distinctly remember him asking the same question 17 and a half billion years ago ago.

Nothing stays the same; change is always occurring. Otherwise God would get bored and since we were created similar, image-wise, we have to deal with that. Randomness occurs on a quantum level and the choices we make, even unreasoned random ones are not ultimately preordained. Entropy occurs. The challenge is to try yourself to create exact same starting circumstances with your pool balls on the surface of the table on the surface of the rotating revolving planet within the rotating galaxy within the expanding universe influenced by gravity acting on all objects from constantly varying relative positions. Go on, try it. Let me know how it turns out.

Another factor is that after the initial roll of the ball the medium through which it has to push its way will be different. The exact number of molecules of oxygen, nitrogen and other gasses will be altered, there could still be a currents that the first role set up that completely alter the second roll. In a Platonic world in theory maybe repeated roles would be possible (though I doubt it) but in the real universe initial conditions could never be repeated. Well, okay, maybe by random chance once ever 10^100 years or so.

Have a look at chaos theory: especially the pendulum with three magnets problem.

..there's a butterfly out there somewhere...!

You forget that each time the snooker ball rolls on the felt, a minute amount of wear of the felt occurs, the felt is ever so slightly compressed, and subsequent rolls may take the ball ever so slightly farther each time it is rolled. That is why tables get recovered. Don't know if that would have any effect in your scenario…Intereseting thoughts...

My take, for what it's worth, would be there's new felt each time the ball is rolled.

Then there is variation in the felt, lot to lot, and batch to batch.

Temperature and seismic variations and we can't forget the Moon.

Chaos theory supporst free will. In the sense that we still dont know what is our future. But once we can predict, then chaos wont be chaos anymore.