Motion Is Discontinuous and Random

What quantum mechanics describes is discontinuous motion of particles.
Foundations of Physics Letters, 17(2), (2004) 181

The motion of particles described by the wave function is an intrinsic random process.
International Journal of Theoretical Physics, 45(10), (2006) 1949

A Brief Argument

[Premise]
A moving object is in one position at each instant.

[Argument]
No causes determine the change of its position*;
The change without cause is random;
The random change of position is discontinuous;

[Conclusion]
The motion of objects is discontinuous and random.

[*] Note that the velocity property, even if it exists, cannot determine the change of the instantaneous position of an object. On the one hand, velocity may not exist for some forms of motion such as Brown motion. Its valid definition requires that motion is continuous and the trajectory is differentiable relative to time. But it is still unclear whether or not the motion of objects is continuous, and thus the continuity of motion and the existence of velocity should not be a precondition when we analyze how the objects move. On the other hand, even if velocity may exist for the motion of an object, it does not count as part of the instantaneous state of the object. Thus velocity cannot determine the change of the instantaneous state such as position of the object.

For a detailed and complete argument see the new book Quantum Motion and relevant papers.

A Complete Argument

A Popular Argument New

Relating Ideas

Its Brief History

My Recollection (2000, in Chinese)