Suppose you have a ball, bouncing between 2 walls. Now suppose that instead of losing energy and slowing down with each bounce, the ball was given more energy and it's speed doubled. (This is possible, just think of two people hitting the ball as it reaches them - although the amount of energy required for the next bit will get very large so it's not the best of analagies)

As the speed doubles each bounce, the time for the journey between the walls halves. As the number of bounces tends to infinity, the total time for all journeys will sum to a finite number.

Say the first journey takes 1 minute. The next will take 1/2 a minute, then 1/4, 1/8, 1/16 and so on. Without much effort you can see that as the number of bounces tends to infinity, the times sum to 2 minutes.

The ball will perform an infinite number of bounces and journeys and will never stop bouncing. Yet it will never bounce for 2 minutes or more.
:confused:

Anyone who understands whats wrong with this please help:(

That's because you limit all the hits within the two-minute time frame, not because the ball stop bouncing after 2 minutes. If you can squeez infinite hits in two minutes, you don't need more than two minutes to make the ball bounce infinite times.

But as an observer, time continues past the 2 minute barrier. But for the ball, infinite energy can't be reached, and without it neither can the 2 minute barrier. So what is observed?

It would only if the observer never passes the 2-minute barrier, an infinity bounce could reach. Once the observer is willing to pass the time barrier, he will see a finite number of bounces of the ball.

The scenario implicitly defines an abstraction, the “infinitely bouncing ball”, as the two minute limit of the described process. Let’s label that limit IBB2. Now at three minutes it’s going twice as fast, IBB3 = 2 * IBB2 = IBB2, since twice infinity is still infinity. So if one accepts that the limit IBB2 exists then the “value” stays at IBB2 for all time. If one doesn’t accept that the limit IBB2 has any meaning then one doesn’t have to worry what happens after two minutes as the model is already "broke".

Math is great for abstract calculations and transformations. Whether the abstractions have any real world meaning is a separate question of little interest to many mathematicians. (Give a mathematician an “infinitely bouncing ball” and he’ll tell you everything except what an “infinitely bouncing ball” is. Hehe.)

How to observe an “infinitely bouncing ball”? Hmmm…use an infinitely bouncing eyeball? Hehe.

Elmo,

There's nothing wrong with your scenario in a mathematical sense. Lots of infinite sums add to finite quantities.

In a physical sense, of course, your ball would be limited to the speed of light as its maximum velocity.

Why is the speed of light 3x10^8 m/s and not infinite anyway? What makes that number so special? I mean, if it takes infinite energy to reach that speed (assuming the object has rest mass) and a photon has no rest mass, shouldn't it be able to travel at infinite speed? I find it a bit strange that a photon can travel 3x10^8 m/s but not any faster (that is, the entire waveform of a pulse of light), if it can get that fast, what is keeping it from accelerating any further?

Xelios,

Nobody knows why the speed of light is 3 × 10⁸ m/s. Nobody knows why the electron has a charge of 1.6 × 10^-19 Coulomb. Nobody knows why Planck's constant is 6.63 × 10^-34 Js.

Maybe some future theory will explain why the fundamental constants have the values they have, but at this stage science does not have the answers.

Well then, I guess there's still something for me to research after all, after I graduate anyway ;)