Quote by arivero
Just a thinking.
Set [c]=1. Then
[itex][G]=L / M [/itex] and
[itex][h]=L . M [/itex]
So a lot of relationships can be just naive dimensional analisis when M=1 or when you can somehow disregard masses or lengths. This is a peril in this kind of papers, and so they are more careful than usual about doing all the steps explicit.
...

Quote by czes
I thought about it. There are different relations but all of them has its meaning. The question is to find a proper meaning.
For example I studied Planck length and Compton length. I assume it has something to do with a space curvature but is it really ?
We calculate in 3 spatial dimensions. What are the 3 dimensions. Do they exist on the fundamental quantum level?
I assume the space for our observation is made of the information. How many dimensions are between two quantum informations? Do they need any dimension at all?

Czes, I don't want you to be put at a disadvantage by not knowing some relevent background which is familiar to the rest of us. Other people here are aware of an interesting paper on arxiv that touches on elementary dimensional analysis, involving the Planck and Compton lengths, because some of the contributory material was worked on here at PhysicsForums, back in 2005 and 2006.
http://arxiv.org/abs/grqc/0603123
Another thing Czes, do you normally use Tex in your writing? Tex is available here at PF. Just write a formula like L^2 or M_{Planck}
and put symbols "tex" and "/tex" around it. except use square brackets [...] instead of quotes "..."
In other words, copy this without the underline
[
tex]L^2[
/tex]
and you will get
[tex]L^2[/tex]
Copy this without the underline
[
tex]M_{Planck}[
/tex]
and you will get
[tex]M_{Planck}[/tex]