1) The document proposes a theory of a quantized and finite reference frame based on the Quantized Universe Theory and Grid Extra Dimensions Theory. 2) It suggests that space is made up of discrete 3D elements the size of the Planck length, with extra dimensions between them allowing for quantum nonlocal behavior. 3) Velocities, masses, and momenta are proposed to have discrete quantized values depending on factors like the particle's wavelength and Planck's constant, with a minimum time between movements of a particle equal to the Planck time.

1. Yoav Weinstein – yoavw@dir-technologies.com ; Eran Sinbar – erans@dir-technologies.com
Quantized and finite reference of frame
Based on Quantized Universe Theory (QUT)
And
The Grid Extra Dimensions Theory
4 February 2016
Please review for back ground :
http://www.slideshare.net/eransinbar1/heuristic-approach-for-
quantized-space-time

2. The Grid extra dimensions theory (an illustration based on bubble images)
Illustration of
Quantized 3D
Space elements in the size of
About Planck length(each bubble illustration)
Each space element may move, rotate or vibrate
Keeping a uniform symmetric behavior.
The Grid extra dimensions
Between the quantized
3D space elements.
(between the bubbles illustration).
Each bubble represents the 3D quanta cells of space.
The void between the bubbles illustrates the “grid extra dimensions”
That connect between all the 3D quanta cells of space, enabling non locality quantum behavior .
http://www.superbwallpapers.com/abstract/bubbles-20111/

3. λ 𝑤𝑎𝑣𝑒 𝑙𝑒𝑛𝑔𝑡ℎ =
ℎ
𝑝
[𝑚]
ℎ is Planck constant [6.63 ∗ 10−34 𝑚2 ∗
kg
s
],
𝑝[momentum, kg ∗
m
sec
] = Mass ∗ 𝑣 [velocity ]
Based on the QUT theory ,space is built from quantized cells in the size of Planck’s length (ℎ∗)in each of its 3 dimensions.
ℎ∗
= 1.62 ∗ 10−35
m
Between them are the Grid Extra Dimensions .
The quantum of time is in the size of
ℎ∗
c
λ = ℎ/p
𝑝 =
ℎ
λ
=
ℎ
𝑁 ∗ ℎ∗
𝑁 𝑡ℎ𝑒 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠 𝑤𝑎𝑣𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑑𝑒𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑃𝑙𝑎𝑛𝑐𝑘′ 𝑠 𝑙𝑒𝑛𝑔𝑡ℎ
𝑁 =
λ
ℎ∗ = 1,2,3,4,5, … integer positive numbers
min λ = ℎ∗
one space quanta
C = speed of light [m/sec], m=meter sec=second s=second kg= kilogram
De Broglie wave length
𝑝 ≤
ℎ
ℎ∗
m ∗
kg
s
𝐴 =
ℎ
ℎ∗ ≈ 41
𝑝 ≤ 𝐴[𝑚 ∗
𝑘𝑔
𝑠
]
𝑝 𝑁 =
𝐴
𝑁
[𝑚 ∗
𝑘𝑔
𝑠
]

4. Quantized values for v(velocity) , mass & p(momentum)
Based on Einstein's relativity theory:
𝑐 = 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑚
𝑀𝑎𝑠𝑠 𝑑𝑖𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 = 𝑀𝑎𝑠𝑠0 ∗
𝑐2
𝑐2 − 𝑣2
𝑝 𝑁 = 𝑀𝑎𝑠𝑠0 ∗
𝑐2
𝑐2 − 𝑣2 ∗ v =
𝐴
𝑁
𝑀𝑎𝑠𝑠0 ∗ c ∗ v ∗ N = A ∗ 𝑐2 − 𝑣2
(𝑀𝑎𝑠𝑠0 ∗ c ∗ N)2
+𝐴2
∗ 𝑣2
= 𝐴2
∗ 𝑐2
𝑣2 =
A ∗ 𝑐2
(𝑀𝑎𝑠𝑠0 ∗ c ∗ N)2+𝐴2
𝑣 𝑁 =
𝐴2 ∗ 𝑐2
(𝑀𝑎𝑠𝑠0 ∗ c ∗ N)2+𝐴2
𝑀𝑎𝑠𝑠 𝑁 𝑞𝑢𝑎𝑛𝑡𝑖𝑧𝑒𝑑 𝑚𝑎𝑠𝑠 = 𝑀𝑎𝑠𝑠0 ∗
𝑐2
𝑐2 − 𝑣 𝑁
2
𝑝 𝑁(𝑞𝑢𝑎𝑛𝑡𝑖𝑧𝑒𝑑 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚) = 𝑀𝑎𝑠𝑠 𝑁 ∗ 𝑣 𝑁
𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 = 𝑀𝑎𝑠𝑠0 ∗ c
𝑣 𝑁(𝑞𝑢𝑛𝑡𝑖𝑧𝑒𝑑 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦) =
𝐴2 ∗ 𝑐2
(𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 𝑁)2+𝐴2
𝑁 =
λ
ℎ∗

5. Quantum Mass
𝑣 𝑁 =
𝐴2 ∗ 𝑐2
(𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 𝑁)2+𝐴2
= 𝑐 ∗
𝐴2
𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 𝑁 2 + 𝐴2
= 𝑐 ∗ 𝑃𝑟
𝑃𝑟 = probability of the particle, for each quantized pulse of time
ℎ∗
𝑐
to move one 3D quanta of space ℎ∗
.
For each quantized pulse of time, a particle can either move one quanta of space or stay in its position.
The probability for movement is the value between 0 to 1 of 𝑃𝑟.
𝑖𝑓 𝑀𝑎𝑠𝑠0 increases, the curvature in space and time, caused by the particle, every where it moves around, increases,
and the probability for the particles movement , for each pulse of time 𝑃𝑟 , decreases.
𝑖𝑓𝑁 increases, the probability for the particles movement for each pulse of time 𝑃𝑟 , decreases.
𝑖𝑓𝑁 decreases, the probability for the particles movement for each pulse of time 𝑃𝑟 , increases.
if the particles wave function is spread in space larger N , its velocity will decrease .
if the particles wave function is squeezed into a small region in space smaller N , its velocity will increase .
Heisenberg un certainty principle

6. Maximum velocity
𝑓𝑜𝑟 𝑝ℎ𝑜𝑡𝑜𝑛 𝑃𝑟 = 1
𝑓𝑜𝑟 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑤𝑖𝑡ℎ 𝑚𝑎𝑠𝑠, 𝑃𝑟 ≤
𝐴2
𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 1 2 + 𝐴2
𝑓𝑜𝑟 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑤𝑖𝑡ℎ 𝑚𝑎𝑠𝑠, 𝑣 ≤ 𝑐 ∗
𝐴2
𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 2 + 𝐴2

7. 1
𝑣 𝑁+1
2
−
1
𝑣 𝑁
2
=
𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 𝑁 + 1
2
− 𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 𝑁 2
𝐴2 ∗ 𝑐2
= (2 ∗ N + 1) ∗
𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 2
𝐴2 ∗ 𝑐2
The velocities have discrete values meaning velocity can only “jump” from one discrete value to the next.
There are no values in between these discrete values (“jumps”)
The difference between 2 adjacent discrete velocity lines

8. 1
𝑣 𝑁+1
2
−
1
𝑣 𝑁
2
= 2 ∗ N + 1 ∗
𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 2
𝐴2 ∗ 𝑐2
= 2 ∗ N + 1 ∗
𝑚0
2
𝐴2
In extremely slow velocities of an element particle, (very large N) ,in a lab setup, this discrete pattern might be measured.
The difference between 2 adjacent velocity lines

9. Time between movements - Discrete velocity
𝑃𝑙𝑎𝑛𝑐𝑘 𝑇𝑖𝑚𝑒/𝑃𝑟𝑁 = time between movements
𝑓𝑜𝑟 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑤𝑖𝑡ℎ 𝑚𝑎𝑠𝑠, 𝑃𝑟𝑁 =
𝐴2
𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 𝑁 2 + 𝐴2
0 ≤ 𝑃𝑟𝑁≤ 1
𝑓𝑜𝑟 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑤𝑖𝑡ℎ 𝑚𝑎𝑠𝑠 0 (𝑝ℎ𝑜𝑡𝑜𝑛), 𝑃𝑟0 =
𝐴2
𝐴2
= 1
𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑐𝑎𝑛 𝑟𝑒𝑎𝑐ℎ 𝑖𝑡′
𝑠 ℎ𝑖𝑔ℎ𝑒𝑠𝑡 𝑚𝑎𝑠𝑠 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑃 𝑀𝑎𝑥 = 𝑃𝑟1=
𝐴2
𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 1 2 + 𝐴2
𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑐𝑎𝑛 𝑟𝑒𝑎𝑐ℎ 𝑖𝑡′
𝑠 𝑆𝑙𝑜𝑤𝑒𝑠𝑡 𝑚𝑎𝑠𝑠 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑃 𝑚𝑖𝑛 = 𝑃𝑟𝑁=
𝐴2
𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 𝑁 2 + 𝐴2
Assuming N a huge number ≫ 1

10. How huge is N in order to get the slowest mass velocity
𝑃𝑙𝑎𝑛𝑐𝑘 𝑇𝑖𝑚𝑒/𝑃 𝑚𝑖𝑛 ≤ the age of the universe
𝑃𝑟𝑁= 𝑃 𝑚𝑖𝑛 =
𝐴2
𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 𝑁 2 + 𝐴2 ≥
𝑃𝑙𝑎𝑛𝑐𝑘 𝑇𝑖𝑚𝑒
𝑇ℎ𝑒 𝑎𝑔𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑒
𝑃𝑙𝑎𝑛𝑐𝑘 𝑇𝑖𝑚𝑒
𝑇ℎ𝑒 𝑎𝑔𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑒
= K
𝐾 ≪ 1
1 − 𝐾2
≈ 1
𝐴2
≥ 𝐾2
∗ Quantum Mass ∗ 𝑁2
+ 𝐾2
∗ 𝐴2
𝐴
𝐾 ∗ 𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠
≥ 𝑁

11. Quantized frame of reference
𝒗 𝑴𝒂𝒙 =
𝐴2 ∗ 𝑐2
(𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 1)2+𝐴2
𝒗 𝒎𝒊𝒏 =
𝐴2 ∗ 𝑐2
(𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 𝑁)2+𝐴2
𝐴
𝐾 ∗ 𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠
≥ 𝑁
Speed of light
Observers point of view
Illustration of the quantized frame of reference for every observer in the universe
(The observer is always at rest in its own frame of reference).
In this illustration the movement is just in one dimension and one direction (direction of movement).
Quanta of the
Frame of reference
Each quanta of the frame of reference
Has a different time frame and different spatial frame
Based on Einstein’s special theory of relativity
Each vertical line to the right ,represents the beginning of a higher
Quantized velocity and opens a new quanta of the frame of reference
𝑃𝑙𝑎𝑛𝑐𝑘 𝑇𝑖𝑚𝑒
𝑇ℎ𝑒 𝑎𝑔𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑒
= K

12. Summary
• Velocity is quantized from 1 to N
• There is minimum velocity for each basic particle (electron ,proton, etc.)
• There is maximum velocity for each basic particle (electron ,proton, etc.)
• The frame of reference (https://en.wikipedia.org/wiki/Frame_of_reference), is finite and quantized from 1 to N.
Velocity is defined only in these quantized values.
• It is not possible for a particle to accelerate above 𝒗 𝑴𝒂𝒙 .
when reaching 𝒗 𝑴𝒂𝒙 any added energy will transform to an increase in the 𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠
adding curves in time and space based on Einstein’s General Relativity.
𝒗 𝒎𝒊𝒏 =
𝐴2 ∗ 𝑐2
(𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 𝑁)2+𝐴2
𝐴
𝐾 ∗ 𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠
≥ 𝑁
𝒗 𝑴𝒂𝒙 =
𝐴2 ∗ 𝑐2
(𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑀𝑎𝑠𝑠 ∗ 1)2+𝐴2
𝑃𝑙𝑎𝑛𝑐𝑘 𝑇𝑖𝑚𝑒
𝑇ℎ𝑒 𝑎𝑔𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑒
= K