# Infinitely divisible vs finitely divisible time

1. Jul 2, 2004

### mercmisfire

I have a bad habit of hearing a very basic discussion of something and then acting on that discussion without further investigation -- and that is a habit that I will continue with here . My question is about time, and whether the uncertainty principle requires it it to be infinitely or finitely divisible. The problem :

As I understand it, it is not only true that we cannot know with precision both the velocity and position of a particle, but that they do not possess either of those qualities for us to know. If you cannot say that electrons EVER have a definite position or speed, then you have to admit that time is infinitely divisible.

The reasoning :

If time were finitely divisible, then definite smallest moments exist and you could pin down one moment and completely freeze a particle in that moment, since within that one moment of time, no action can occur -- action is change over time, change over time requires at least two moments of time. This would allow you to definitely know the particle's position, since everything that exists spatially, must exist in space, and to exist in space must exist in a position at any given time; if you know the time/freeze a particular moment, then you know the position. In pinning the same particle down in the next moment, you can definitely know its velocity, by comparing its two positions, which you know definitely, and how they differ across a definite amount of time, which you also know (since you have finitely divisible moments and have only allowed one to pass from one position to the next). So, if you have finitely divisible time, then particles must have definite positions and definite speeds. However, if time is infinitely divisible, then you cannot pin down one moment and it is impossible to definitely determine either position or speed -- you can only get closer and closer by making the chosen moment smaller and smaller --> however, there is no one smallest moment so you will never get small enough to allow the freezing of a particle in time (there is no such thing as one moment, so within any amount of time, there is always room for change since there is always more than one "moment" in any amount of time you chose) and so you can never know position or velocity definitevely (only approximately according to the smallness of the chosen moment). So, how about it --> is time finitely or infinitely divisible ? Am I way off base in my understanding ?
thanks,
-->merc

2. Jul 2, 2004

time, unlike quantum mechanics is infinitelly divisible, there is no set unit of time, like a quantum. You have answered your own question.

3. Jul 2, 2004

### mathman

There is a unit of time (very small - around 10-43 sec.) called Planck time. According to current ideas (subject to change), time intervals smaller than this are meaningless.

4. Jul 3, 2004

who are scientists to say what is meaningless. Nevertheless, it is meaningless to us, but in the quantum world, it is not.

5. Jul 3, 2004

Meaningless as in there is no distinction between "now" and "then."

6. Jul 3, 2004

### mathman

It is precisely the quantum world which is making time less than the Planck time meaningless. It is not something dictated by scientists.

7. Jul 3, 2004

### dilasluis

Probably I miss understood you all

How can you say that the Planck time constant is insignificant... It's precisely in the now and then of it that resides the knowledge of the universe beggining. His constant is the time between the big bang and everything we know from the universe at this point. If one could tell what happened during that time interval many thing's would be explained. Some say that during that time interval the laws of physics as we postulat weren't applied... Who's to say?

So, one thing, not even space is finitely divisible... we would reach the notions of sources and sinks... punctual positions is space... that's fairly unlikely. I think if you could get a punctual mass (an electron isn't the case - It's vey big to be one...) you would probably know it's position precisely in the fourth dimension (time) ....
.... so i really didn't get this post...

8. Jul 23, 2011

### cubzar

The universe looks different at different scales therefore time and space must be discrete. If space was continuous, two items of different volumes would contain the same number of points, so measurement would not make sense. Calculus uses 'tending to' notation to avoid having to deal with the contradictory infinitesimals.
At one time it was commonly assumed that matter was continuous, but now we know that it is made of particles. If space and time are quantised, then it is possible interactions between these quanta could form particles and explain the laws of physics.

9. Jul 23, 2011