Bouncing ball’s trajectory in general relativity and newtonian gravity


by Paul Mainwood on Quora

This is a conceptually simple and fun piece of work that has been let down by an appalling write-up on
Reading the paper itself, what the authors have done is to put together two fascinating phenomena from 20th Century physics.

  1. At low speeds and with weak gravitational fields, the predictions of Newtonian Physics and General Relativity approach one another, giving rise to dynamics that are so similar that they can be treated as identical.
  2. There are some types of system — chaotic systems — where very small differences can give rise to unexpectedly huge differences in future dynamics.(1)

With these two phenomena written next to one another, there is an obvious path to explore. Why don’t we see if we can come up with a chaotic system whose dynamics can distinguish between the tiny differences between the predictions of GR and NP, even at low speeds and in a weak gravitational field?
And that’s exactly what the authors: Shiuan-Ni Liang and Boon Leong Lan have done, claiming to have found such a desktop system that can distinguish between the predictions of GR and NP when its dynamics becomes chaotic. Fun!
But the write-up of this simple concept veers all over the place, making it sound as though the paper is claiming to contradict General Relativity (it says the opposite). Worse, after happily taking a logically labyrinthine tour through some out-of-context quotes that the authors may have said on the phone, the write-up triumphantly ends with a crashing non-sequitur: “Explore further: Doubly Special Relativity”. (Doubly Special Relativity is a speculative theory with zero connection to anything in the paper.)
So, which one of General Relativity or Newtonian Physics is right? The authors of the paper could not be clearer:

When the predictions are different, general-relativistic mechanics must therefore be used, instead of special-relativistic mechanics (Newtonian mechanics), to correctly study the dynamics of a weak-gravity system (a low-speed weak-gravity system).

(1) Usually in the study of chaotic systems, these small differences are differences in initial conditions: that is, you keep the dynamical laws the same but alter the initial conditions slightly. But you could equally ask what happens if you keep the initial conditions the same and slightly alter the dynamics, which is what they are effectively doing here.