The events cannot be instantaneous, that would break causality. If one is caused by the other, they must be separated in time. Of course, not a whole lot of time, but its still there. Information will not propagate faster than the speed of light, and you need it to propagate for the objects to respond to the collision.
Actually information (laws of physics) is the only thing faster than light. Einstein demonstrated that when changing a neutron to an ion, another nearby ion would be repelled beginning instantly at the moment of the change, before light had time to travel from the first ion to the second. The information that there were now 2 ions and needed to repel each other was transmitted faster than light.
To explain what actually happens in the above example (Newton’s cradle), let’s look at a bigger example.
If you have a button 1 light-year away, the smallest amount of time it could take for you to hit it would be 1 year.
But what if you had a long piece of wood between you and the button? Now you can push the board instantly into the button, right?
Wrong. It would in fact take much longer than 1 year. The atoms inside the board must push each other one-by-one along the length of the board, which happens at the speed of sound.
When a ball hits another in your example, the ball getting hit shrinks in size from the impact point in the direction of the impact. The atoms bounce in that direction until reaching the other side of the ball (restoring the ball to its original width), at which point they bounce into the next ball in line and so on until reaching an end ball.
Nothing is “instant”. By mentally imagining this process you can more easily follow the forces acting on the balls and reason in your mind why 2 balls falling from the left will cause 2 balls to fly to the right.
In computer physics, however, this perfect model is not useful. Impacts are instantaneous. Getting a (reasonably) correct result depends on your contact resolver and how it decides the order in which to resolve collisions (and interpenetrations). The above explanation regarding waves traveling through objects isn’t useful as a mathematical model, but it helps you design your system such that it resolves collisions in a more realistic order.
Even of the time length there, it is a fact (is?) that there is no observable acceleration before the object travels its speed?
All objects accelerate into any new velocity except light (and perhaps quarks or other forms of sub-atomic particles). But in computer physics this is not something practical (or possible) to model. Every iteration of the physics engine performs sudden instant changes from one velocity to the next. It often looks realistic because the changes are typically small, but large instant changes, such as those in Newton’s cradle, are perfectly possible.
L. Spiro
