As I wrote the Compton wave length is not appreciated. It is in Schroedinger equation though obscured but seen in Klein-Gordon and Dirac.
http://en.wikipedia.org/wiki/Compton_wavelength
According to non-locality of the quantum information it might be non-local too. If it is non-local (due to experiments verifying Bell's inequality it has to be) the information about the Compton wave length has to be distributed inversely proportional to the squared distance from the source of the oscillation. Therefore we have a quantum vacuum network made of the information due to Compton wave length.
Here is the background independent Loop Quantum Gravity.
We can't observe an information alone. It is always relative to another information. There ian't quantum jump and perfect empty space doesn't exist. Therefore what we observe as a vacuum it is a set of interacticng informations (cross product). Here we may use a vector field as in Moffad
http://arxiv.org/PS_cache/astro-ph/pdf/0412/0412195v3.pdf
This cross product f(x)*f(y) is essentialy deterministic because f(x) and f(y) don't collapse like in Copenhagen f(x)^2. The distribution is depending on infinity many factors like in Bohm-de Broglie hypothesis but the wave function don't vanish. According to the conservation of the quantum information (Decoherence approach) the superposition remains and goes away into the environment.
The cross product needs absorber and emiter in each point of the space. Therefore the interaction of the wave functions create an atemporal standing wave due to Compton wave length. This is the double quantum loop of Cramer's Transactional Interpretation.
Therefore the vacuum is created by tension between interacting virtual particles-antiparticles.
The fundamental quantum information would be then an information due to Compton wave length. Two particles remains at rest if the distance measured by an amount of the information in that system remains the same. The distance is relative and it is human's perception. The space is a product of the information it is created by information. Smolin wrote about it.
If we have a subset of the particles the information content would be equal a sum of the Compton wave lengthes. The average number for each particle would be radius of the sphere around a subset divided by Compton wave length for one quantum loop. For double loop it is R/2 L = R/h/2*2 pi mc = 4 pi mc R /h
As I deduce of the relation (Planck length)^2 / Compton length(1)*(2) = alfa* F(grav)/F(em) each interaction (standing wave, virtual particle-antiparticle) causes a constant Planck's time dilation and length contraction (frozen length).
To create a space under a sphere one needs to supply N=M/m particles with 4 pi mc R/h information per particle. The interaction (cross product of two double loops ) creates a contraction equal (Planck's length)^2 = hG/c^3.
For a stationary Black Hole the maximum frozen are is equal a surface of the Black Hole with a radius R.
When (M/m) (2*2*2 pi mc R/h) (Gh/c^3) = 4 pi R^2
we have M/c^2 = R/2G
Smolin wrote in conclusion about Compton wave length as a measure of inertial mass.
I think the Compton wave length may be used directly as measure of the information instead of the information as a logarithmic function of the temperature and statistic.
I am sorry for my English. My native language is that of Lewandowski's.
I am not a professional physicist but I noticed the Loop Quantum Gravity has an experimental confirmation in the modern quantum information. The Cramer's Transactional Interpretation can make some problems easier using quantum standing waves as a product of wave functions.
Some calculations seem primitive but they show interesting properties.