# Quantitized dimension

1. May 6, 2005

### scilover89

Recently I was thinking about these statement:
1. Dimension is as if a 3-D graph, which every coordinate is the smallest unit for dimension.
2. Volume of an object is a whole number multiply the volume of the dimension unit.
3. Distance is a whole number multiply the length of the dimension unit.
4. When object travel from one dimension unit to the other, it do this by "looping".

Are there proves that can support this statement or show that this statement is untrue?

2. May 6, 2005

### kleinwolf

I don't really understand 1.

But for 2-3 : Why should this a whole number, I can have a volume of .000001 units of volume ??

3. May 6, 2005

### scilover89

A simple analogy will be the 'paint' aplication in the windows. Let say you draw a square. And you click the option zoom. You will find that the square is consist of many small square. The small square is the smallest unit.

I don't know why should(or shouldn"t)2-3 be ture either. This statement just flow through my mind.

4. May 6, 2005

### ZapperZ

Staff Emeritus
Think again. Your "coordinates" or tick marks on the graph are NOT your smallest unit for "dimension". If it is true, you have no way of describing a value that in between those units - unless you practice the discarding of data points that do not fall into clear values. Furthermore, it would be meaningless to draw a continuous curve on your "graph", since you are assuming the existence of an infinite set of continuous values all along the line.

I'm not saying quantized spatial dimension doesn't exist (this is still a research area and conclusive proof is still not here yet). I'm just saying the impetus you are using to argue for its existence is faulty.

Zz.

5. May 6, 2005

### kleinwolf

Maybe we could understand this more if we look at how was the conclusion drawn that energy is quantized for example.....

This will show that this approach is not good to understand if space-time is quantized :

In fact only the Action is quantized, this comes from the old Bohr-Sommerfeld quantization, starting from the experimental values of Hydrogen levels :

Starting from it : $$S=\int_{t_a}^{t_b}L(q,q',t)dt=nh, n\in\mathbb{N}^*$$ L is the Lagrangian.

What can we deduce : suppose the particle is moving freely :
$$L=\frac{mv^2}{2}$$

hence : $$t_b-t_a=nh\frac{2}{mv^2}$$

So if you try to find out if time is quantized, then you have to show that the energy of a free particle is quantized.....but the Energy is E=hw...where omega is the pulsation of the wave...hence the energy of a free particle is quantized iff time is quantized...so it's a tautology