Thanks for the link. I understand that Roger Penrose's father tought him calculus the evening before he started it at school. It would take me a lot longer, and I don't have the time; so if there is something there that would enlighten me, it will need to be simplified. Lots!
Instead of using the colors on the table make it a distance from the point you choose (you selected the cushion) and write the equation for speed and time.
The formula is straight forward:
distance =
speed ball hit at *
time from ball strike That is the hamiltonian you are describing in your thoughts. So select a table a length (say 2m), select a suitable speed say (0.25 m/sec) now write the distance for each of the 10 seconds following the ball strike.
Do you see the problem with your hamiltonian ... => time from ball strike only conceptually only goes forward then your distance can only ever get bigger. When the ball hits the time reversal pink spot the distance actually starts decreasing the weird behaviour you think is strange.
So what is required is to negate one of the terms in the hamiltonian at the point of reversal.
That can be done in one of TWO WAYS.
1.) Turn speed into a velocity one way being +ve the other -ve
2.) Invert time at the reversal point, notionally its zero at the reversal point so time has a +ve and -ve component
Surprised me but Paul correctly worked that out but he went for both, they don't both reverse you get to choose one.
The problem is there exists no selective process you can choose that tells you which is right or wrong or even if it has physically correct meaning.
What I was trying to get you to realize in your thought experiment was that your statement time reverses at the pink spot is totally SUBJECTIVE.
I can solve your problem in two other ways than your choice
1.) By simply putting time = 0 at the pink spot and it doesn't matter which way time runs the calculation will work. So time is zero at the pink spot and radiates out from that point.
2.) I can simply have an invisible bumper at the pink spot and the ball actually bounced inverting it's velocity.
So even if I could physically do your experiment and view it I would not in any way deduce time had reversed and it introduces no anomaly.
Same way it was before you picked it up.
So now we take the other choice you didn't consider that when the ball reached the pink spot you the observer started going backward in time. If the pink ball is a point with a time reversal why can't the point you are observing from be one.
Picking up the ball is a metaphor for some event that is nothing to do with what is being observed but what the observer does or has done to them.
Your experiment assumes you the observer are GOD and know exactly what is actually happening .. an impossibility for us mere mortals.
