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A question of Quantum Time: Does a minimum interval of time cause wave-like behavior? If we think about the uncertainty principle, could it derive from a quanta of time? Does plank’s constant somehow derive from the quanta of time?

Hypothesis: When delta t is larger than a quanta of time, then particles behave like particles. When delta t tries to be smaller than a quanta of time, then we have uncertainty because delta t cannot be smaller than a quanta of time. So when the delta t is smaller than a quantum of time, we don’t have the granularity in time to be certain of momentum, or location of a particle at a later time smaller than a quanta.

Interference waves seem to be caused by particles that compress to the point where they influence each other. E.g. an atom of H2O behaves like a particle until it is organized with many atoms of H2O at a certain point of density where the atoms all influence each other. At this point the action/reaction caused be adjacent contact creates an interference wave of movement over time. Another way to say this is that a certain minimum level of distance between two particles, the unit of distance cannot be condensed further, and interference waves are generated. Could this happen with time as well. Could it be that that time can only move in a quanta, and this causes the interference wave?

Additionally, could this help explain the limit of the speed of light? If time has a minimum value (a quantum), then how does an observer measure speed for distances traveled faster then the minimum value of time?

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Fun fact: planck length/planck time=c. Well, sort of obvious since these planck values can all be obtained via dimensional analysis. – Manishearth Mar 2 '12 at 16:28
Related: – Qmechanic Mar 2 '12 at 16:30
My understanding of Planck time is the length of time it takes for light to travel a Planck length. Does the concept of Planck time say that Planck time is the smallest possible unit of time? In the context of the original post above, I am asking if there us a minimum unit of time. I imagine a minimum quanta of time would be smaller than a unit of Planck time. – user7940 Mar 2 '12 at 19:08
@JoeDonahue Nope. Below planck time, time loses its meaning. Welcome to the world of Quantum mechanics. – Manishearth Mar 3 '12 at 3:12
wave-like behaviour is already ubiquitous without a minimum time. The question is pure speculation. – Arnold Neumaier Mar 9 '12 at 11:15

Since none of the big guns have answered this I'll give it a go. You're really asking several questions. Shout if I'm misrepresenting you, but it seems to me you're asking:

  1. is time discrete?
  2. could discrete time account for wave particle duality?
  3. could discrete time account for the speed of light?

Taking 2 and 3 first, there are already excellent descriptions of wave particle duality and the speed of light that don't require discrete time, so there is no reason to start looking at discrete time to explain them. You'll find plenty of questions on this in this forum. For example, look at my answer to What is the relationship between the speed of light and virtual particle production for a discussion of the speed of light.

Going back to 1, there are currently no useful theories that rely on discrete time. It's a common mistake to think that quantum mechanics requires space and time to be discrete, but this isn't the case. Luboš Motl's answer cited by Qmechanic explains this more elegantly than I could.

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