I believe that the idea that a physical ball can bounce infinitely many times is complete nonsense. So let's drill this down a little.Philosophy Explorer wrote: I believe you're referring to post #6. Maybe it does bounce an infinite number of times, maybe it doesn't. Math says it can bounce an infinite number of times in a finite time interval. Also it would take an infinite amount of energy to keep that ball bouncing indefinitely. Therefore I'm saying the ball must come to a stop eventually, with or without an infinite number of bounces.
If each bounce reaches a smaller height than the bounce before, then one of two things must be the case:
a) The bounces get smaller and smaller but never get any smaller than the Planck length.
or
b) The bounces eventually get smaller than the Planck length.
If you believe a ball could bounce infinitely many times, which of the above do you think would be true?
I must confess honestly that I find the notion of infinitely many bounces so profoundly and obviously false that I cannot comprehend the mindset of someone who believes it's possible. But clearly you are one such. So I want to know more about how you think this could happen.
Here's my thought process. Each bounce causes the system to lose some energy, until eventually the ball doesn't have enough energy to get off the ground.
So at some point there is still some nonzero amount of energy in the system, but not enough to get the ball off the ground. In fact a ball sitting on the ground that appears to the eye to be stationary, may still actually be "bouncing," but without enough energy to leave the ground. It's just pulsing internally along the vertical axis ... in other words it's vibrating from the last collision.
For all we know the vibrations never stop ... after a finite number of bounces the ball can no longer leave the ground, but the shape of the ball is still rebounding from the last collision ... and the one before that ... all those waves superimposed to model the actual shape of the ball ...
And some of that compression/expansion energy is converted to heat. So if we carefully measures the air around the ball, we'd see that it's getting warmer as the ball -- still sitting there perfectly still to the naked eye -- is actually pulsating from the sum of all the collisions, giving off heat ... forever? Well actually I don't know.
Now I imagine that this effefct must dissipate at some point ... the rebounding shape must eventually stabilize and stop pulsing. That would also happen in a finite amount of time, but I don't know anything about the physics of compressed, air-filled rubber balls. For that I'd ask a pro basketball player, they know more about this than anyone
Conclusion:
There are three phases:
1) The bounce phase. The ball has enough energy to "bounce," ie separate itself from the earth by an appreciable distance. We'd have to define it but say if there's a space visible to the naked eye, then it bounced. By that definition. there will be a finite number of bounces in this phase. Eventually there won't be enough energy to leave the earth.
2) The decompression phase. This is when the naked eye can no longer perceive the ball as moving. But there's still energy in the ball from all the bouncing, each bounce deforming the physical material a little. If it's "elastic" it bounces well ... elastic is actually a technical term in physics, but I'm really out of my depth on the physics. But in the decompression phase, it's pulsating and giving off heat.
3) The still or "deep" phase. We say the ball is still when it's not only not bouncing, but when it's stopped decompressing from all the bounces it's taken. The balls surface temperature and the local air temp are the same ... it's stopped giving off heat from the decompression.
BUT: But what about all the quarks and gluons and strings and stuff they have these days? Back in the day I kept up at the Scientific American level and knew a photon from a proton. These days they're into some crazy stuff. So who really can say WHEN a ball stops bouncing? Maybe at some deeper level all of the tiny microparticles in there have had their states altered by the bounce? Perhaps at some deeper level, the ball is still striving for equilbrium? And will be forever?
PE, I think I have talked myself into a point of view that sees some merit in what you said. Perhaps a ball does bounce forever ... at some deep level of existence, perhaps a ball that bounces once, never stops bouncing. It wouldn't be a completed process ... but it would be forever. So I think I can imagine a definition of "bounce" that allows the possibility that a ball bounces forever, at some level.
I may have rambled a bit. What do you think?