Planck Length and Quantum Geometry

[Hamid]

The advancement of technology is based on the developments in tool and measuring instrument production. The measurement of dimensions is based on practical application of metrology (the science of units), standards and procedure of measurement.

Let us suppose that by the existing level of technology we are able to measure the position of a very small object (particle) with an uncertainty or tolerance equal to one micron meter (1µm) or with a precision within ±0.5 µm for instance, that seems to be realistic. According to my interpretation of Quantum Mechanics described in the following articles, published in ToeQuest Research Library:

1- How Can the Photons Tolerate Each Other?
2- Double Slit Experiment and Quantum Mechanics,

by means of more advanced technology higher accuracy or smaller uncertainty in measurement is attainable which is differentiated from the preceding one by the coefficient 1/6. This means that if at present the uncertainty in measurement of dimensions could be 1µm, through the higher levels of technology it would be the same as (1/6), (1/6)^2, (1/6)^3,…,(1/6)^n µm respectively. This reminds us of quantum geometry which is founded on this true concept that the order of measurement is important.

I realized that when n=37, the uncertainty in measurement will turn into Planck Length which is believed to be the smallest fundamental length in physics:

Uncertainty (tolerance) =ΔL= (1/6)^37 µm =1.61586 ×10^-29 µm

Planck Length = LP ≈ 1.61624 ×10^-35 m = 1.61624 ×10^-29 µm

It appears that at Planck Length the uncertainty in Quantum Mechanics changes into virtual certainty which may have physical and philosophical significance.

In this hypothetical and random measurement it was our intention to identify the position of particle, but we reached to Planck Length as one of 3 dimensions of particle. Taking into consideration that we didn't specify which dimension is the subject of measurement, this virtual particle must have the same size in all directions and logically it cannot be something like a string, for example.

Questions:

- Why there exists such relation between uncertainty in measurement and Planck Length?
- Why the 37th order of measurement and what does it mean? Probably the roulette players know the answer!
- Is Planck Length the dimension of virtual point in nature?
- What is this virtual point particle and what are its characteristics?

[Hamid]

Ancient Millimeter-Precise Ruler Unearthed in the Burnt City
3200-2100 BC

”Recent excavations in the archeological site of the Burnt City led to the discovery of a ruler with millimeter measurement units. Experts believe now that the ancient residents of the city used precise units for measurements and was skilled in areas of mathematics and geometry."

http://www.payvand.com/news/05/jan/1296.html

[everymansmedium]

Hello Hamid:
I see you have been here at Toe Quest for quite a while. I have never run into any of your posts before this one. So I will say welcome to Toe Quest because I never got to before.

I find your material on this subject left me wanting more.
I would like to read this complete article. Where might I find a copy.
John.

[Hamid]

Hello John;
I admire your curiosity.
You can find my articles in <Forums→ Member Articles →TOE Overview Articles> and in < Forums→ Member Articles→Physics Articles>.
Anyhow, I encourage you to have a look also to all my articles published in <Theories→ Homepage>. These articles are interrelated.

[Hamid]

Misuse of words is one of the main reasons prevent us from uncovering the similarity between or equality of some concepts in different branches of science and technology which have their own terminology.
The following figures and table have been extracted from:

http://www.nationalaperture.com/slits.htm

in which you can find a kind of incorrect use of words.

The word Tolerance in the above table has been used improperly. The correct wording in this case is "Accuracy" or "Precision".
As an example, tolerance or uncertainty of slit width 2.5µm mentioned in the second row of above table is equal to (+1)-(-0.5)=1.5µm. Tolerance is always positive.

Tolerance = Upper Deviation - Lower Deviation