Structured Spacetime, Is there a limiting geometry...

If I good understand, whose circles and 3D particles don't mean real particles, but abstract understanding of plank lenght?

Good day everyone!
Troc posted a link that showed a pattern of relationships and that relationship revealed beautifull spirals that made the math easier to understand.
http://www.numberspiral.com/index.html

Why would you refuse to look into the relationship that could be revealed by applying minimum length to a quantum structure?

That is why we need the table of diameter, surface area, and number of nodes/particles.
http://www.rkm.com.au/CALCULATORS/CALCULAT...cle-sphere.html
GEOMETRY: CIRCLE & SPHERE
How to use the program.
Enter an even number for the surface area and it gives you the diameter (planck length = minimum length)
Diameter ……………….surface area … # of nodes

0.7978845608028654 …………. 2 ………………1
0.9772050238058398 …………. 3 ………………1
----------------------------------------------------
This is the first thing that becomes obvious. A surface area of less than 4 units produces a diameter that is less than the minimum length.
1.1283791670955125 …………. 4 ………………1
The smallest diameter that a sphere can have is 1.1283791670955125 planck length and with a node/particle that is a planck length in size.
The smallest surface area that a sphere can have is 4 planck length.

1. This is the first mistery that is resolved.
You cannot have a structure that is made up of minimum length and have all of the mesurements equal to minimum length.

2. The second mistery that is resolved is
Why is entropy = information = A/4
There is a total area of 4 and only one node/particle that can exist to transmit information.

Why is there only one node/particle on that surface?
There is room for another planck size node/particle at the other pole (other side of the sphere).
Okay! Let’s occupy/fill that position with a node/particle.

3. Third mistery solved.
By filling the second position with a node/particle you are preventing any kind of motion.
(Explain how those two nodes/particles can move without violation the minimum length.)
Until we get to doing dynamics (how things can move) with a model, we must stay with 4 planck lengths for every node/particle on the sphere.
Therefore, for every node/particles we need to have 3 empty nodes (planck lengths)
You have also, discovered another relationship.

4. The reason for uncertainty at the quantum level.
The node/particle can occupy either one of those two position and there is no way of being able to determine which of those two position that the node/particle happens to be occupying.

Do you want to continue with the table and discover more relationships?


We know that we need 3 empty nodes for every node/particle but I will do the table for every unit increase of surface area up to 13.

We will need a model that we can use/analyze when we explore the transfer of information.

Diameter ……………….surface area … # of nodes/particles
0.7978845608028654 …………. 2 ………………1
0.9772050238058398 …………. 3 ………………1
1.1283791670955125 ………. 4 ……………1
1.2615662610100801 …………. 5 ……………… ?
1.381976597885342 …………… 6 ……………. ?
1.4927053303604616 …………. 7 ……………. ?
1.5957691216057308 ……. 8 ……………. 2
1.692568750643269 ………….. 9 ……………. ?
1.7841241161527712 ………… 10 …………… ?
1.8712051592547776 ………… 11 …………… ?
1.9544100476116797 …… 12 …………… 3
2.0342144725641096 ………… 13 …………… ?
and here is
2.763953195770684 ………….. 24 ……………. 6
3.9088200952233594 ……….. 48 …………… 12

5. Mystery solved. Did you know that when studying black holes that the number of nodes/particles that are used is 6 and that represent 3d?
6. The minimums for a black hole are 2.763953195770684 ………….. 24 ……………. 6
7. Did you know that when they study the big bang that they have discovered that there is no singularity? There is a bounce. the bounce occures at 24 planck units. This just happens to be the surface area of a 2d sphere that contains 6 nodes/particles.

8. minimum length give a cut off for the spectrum without doing anything.

Not too bad ...... 8 mysteries solved already.... and we have not even made a model.
Perhaps TRoc can develop the relationship that has been revealed in the growth of the diameter and the # of nodes/particles from a surface area of 4 to a surfacer area of 12 units.
(TRoc take sloooow steps. We got 12 year olds following this discussion)

Questions?
Discussion?
Don’t jump a step by saying that we can combine/fuse/reduce empty nodes if we join a lot of spheres together. We still do not have a model.
jal

This post has been edited by jal on Sep 12 2007, 04:01 PM

Darn I missed the edit time and missed the most obvious mystery that has been revealed.
9. Gravity cannot go to a minimum of one unit (planck length)

Hi all,



Jal,

If, as you suggest, there is a pattern that can describe the progression, how will we know which one is "more fundamental".


You have described a relationship with the "circle & sphere",

WN? has talked about the "hexagon" lattice.


Do we have a "fundamental shape", or geometry?



http://en.wikipedia.org/wiki/Directional_statistics

The thing about "vibrations" is, that each movement (off axis; or from center) happens only "1/2" of the time, and the other 1/2 of the time, is counter directional. We have not reached a "shape" yet, but it is easier to model with a circle, in the initial explanation.


However, even in the realm of the circle/sphere, we are not limited to only moving from the center, out. So, the relationship of the radius to the circumference may NOT be "fundamental".


What happens when "the node splits in 2"? Basically speaking, they "co-exist" while still in the realm of "one unit", or our original shape, or boundary. Actually, there would be a "slight bulge" in our original circle, of some "minimal increase" in size, or volume. This value could only be expressed as a ratio, of the fundamental unit (1) to said increase.


One only has to watch cellular division under a microscope to understand the "fundamental nature" of the method. It is the progression from "1 to 2"


The question of which is more fundamental, between the "loci" (the center of the circle) or its boundary, calculated by the constant ratio of pi, is also worth asking.


These loci, or nodes, I propose follow the Pauli principle, and are the fundamental process of "not sharing space", which runs as the inverse of superposition. This is called "anti-bunching" sometimes. The relationship between "anti-bunching and bunching" produces the general "Brownian motion", and "zwitterbewung", which is our general "oscillating phenomenon", measured by "vibrations", or "cycles".


They can not "follow" this principle, until they are "born", or fully created, "pinched off from the bubble", and actually measurably separate from each other, in which case, they are "thrust apart" at the speed of light. This is "aided" by the creation of our "other" fundamental component, the "anti-node", which will form AS SOON as geometrically possible.


Again, we are at the point where we ask, "what is this distance, or interval"?


In order to "volumize" the area surrounding a "node", we must give the boundary some LIMIT. It could be pi . This has worked for many different models, and each has brought understanding to us. With these "dualistic" properties of "phase", or the difference (in time and space) between nodes and anti-nodes, IF we use pi, we must admit an "anti-pi" sort of concept.


If we start from a circle, split it in half, and separate them by the diameter (the fundamental unit x2) then we arrive at the "sine wave". This is the "anti-pi", and it operates in "complex space" in order to measure the duality. The vibration is measured from -1 to zero to +1 , because, using pi, the loci has the value of "zero", because it was the "starting point" of the "radius" (1/2 diameter).


Even if we use angles, or degrees, we have to contend with "zero"; even worse, letting a position have "0, 360" shared relationship. This does nothing to measure "fundamental units", where we just need to get from "one", to "two" as our first step. The "first step" is primordial; it is "the urge" that is in all life. It is the oscillation that is in all energy, regardless of velocity, or other change in linear coordinates.


Note, that we have not even completed a "fundamental cycle", and we are already into complex mathematics, and "non-physical counting". Was that "large first step" really necessary?


Can we come up with a system, that will measure the "linear, unit (integer) progression" of the "radius becoming the diameter" AND the ratio of that radius to the circumference (pi)?


This system will have to be "compatible" with BOTH addition and multiplication. This sounds easy, and perhaps even "a bad question"; don't we always follow such a "cardinal rule"?


Can we follow that rule, if our increments are "-1, 0, +1 "? Not without "higher mathematics", which require a fantastic amount of complexity to "stay in step" with this progression. I'm not really going to comment more, and just be "negative". The point is, that we should at least explore the possibility of a different method, that stays with these "fundamental" principles.


If we say that we MUST use multiplication, as part of the "tool kit" that we are assembling, because we want to use the "circle" as a model shape, and we are going to have to multiply r by 2pi , then we can NOT even use "one" as our starting point", because every # multiplied by 1, stays the same. Not a good way to measure change.


So, we set one of our initial parameters at >1 .


Next, we still need a "fundamental unit", and that needs to be "one", by definition. Sparing the full explanation of "why", let's continue from jal's example, and divide the fundamental unit up into 12 parts, separated by a common "multiplier", or "rate". If we ask the question, "what number, divided by a constant rate, in 12 steps or parts, will get us to "one"? , we are asking for the "12th sq rt of 2". This is the ONLY option. (a unique solution)


Parameter 2 becomes 1.05946..


Why would this work ( measure the "linear, unit (integer) progression" of the "radius becoming the diameter" AND the ratio of that radius to the circumference) ?


Because the "radius becoming the diameter" is "1 becoming 2", and it is never more than 1. However, from the previous discussion above, we remember that this is still happening WITHIN the circle, and is actually in the opposite phase space. This is a "simple" equivalent to measuring the complex space of -1.


This is because we decided that the radius is "first", then the other values (diameter, circumference), in order of importance. So, we are not going to move in the direction of expanding the circle, until we have completed the circle, from dualistic phase space.


Why am I doing this? Because we know that a wave has a rate that fluctuates. Whatever value we start with, has a peak on one side of a fundamental area, and then, in a separate moment in time, a peak on the "other side". The method I am using says that the "other side" is not "really imaginary", but also inverse or opposite.


The "opposite" of the radius would be a "counter radius". This simply completes the definition of the "diameter", which is the combination of the 2 values, "radius in our chosen direction", and a "radius in the opposite direction". However, we measure these with the same method; that is, the radius is "one" unit, and as we increase this value, in 12 steps, to get to the diameter, which is always 2x the radius.


The end result is that when we get to 2x our original radius, we still have to multiply by 2 pi. Now we have progressed one fundamental unit, and taken as a whole, have expanded our circle by 2. [2r x 2pi = 1r x 4pi = 4r x 1pi]


This means that if our nodes are separated by one unit, and that unit is our radius, then that unit has a constant ratio to the circumference (2pi). You are describing one circle, by this fundamental unit.


When this fundamental value is doubled to 2 units, you have the equivalent of 2 circles, of the original circumference, or 1 circle of double the circumference. This embodies Huygens' Principle. Drawing circles implies choices as to HOW MANY nodes are you counting? As long as the nodes are equally spaced, you can approximate the wavefront by finding the center of all of the nodes, and drawing a "greater" circle.


The wavefront is this expanding circumference then, and can be gaged with a constant rate, that also measure the linear expansion of the radius, by the same rate. If we increase the radius by 1/4, this will give a circumference that is 1/4 larger than the original circle, created from the fundamental unit.


When we reach a distance (in one linear direction) that is 2r , we have the option of interpreting this as a "new circle" of double size, and/or as 2 circles, of the original size.


Part of the decision as to how to interpret this comes from whether or not our "source" is moving. That is further along in the discussion, where we can discuss Doppler shift, which measures the "asymmetric" version that results from "not making the choice". In other words, keep our original circle, and move (and measure) the change in position of the loci, as if it was "on the way" to becoming "2 circles" (but never getting there).


The catch here, is that I have not expressed the interpretation of QM, which says that there is a minimum based on "harmonics", or a finite integer stack of nested curves, that will match our energy measurement. Nor have I expressed the limitation placed on this scale, that GR says exists due to gravitational redshift.


However, both of these interpretations say that at the center of the circle, we have "duality", or some bit of change in position (an average), that will effect our ultimate measurement, by a change in "expectation".


I just point these out, so that when making your decision, you are asking "from where (which parameter) do we derive a fundamental unit"? Something that is "ad hoc", and added to the "system", or something that can create the system on its own?



regards, (and sorry for the length of this post)


T.Roc

REASON # 10
10. Minimum length imposes a structure. The challenge is to find the model that is reflecting our observations. Remember, minimum length would apply to ALL models including models with extra dimensions and the structure inside those dimensions.
----------
I will try to examine your approach.
Eventhough I think that it is more of a "photon" approach it should give insight to all of the other reasons.
I'll be back with questions.
jal

Hi!

Meaning....The photon approach.

Meaning ... Trying to figure out where the nodes/particles are located.

Meaning ... We put all the nodes/particles on the surface of a sphere, (minimum length) and we do not need to concern ourselves with what is in the node/particle.


First job
We establish what is the minimum sphere with the minimum number of node/particles
Second job
We will realize that we need more than one sphere to be able to explain more than that minimum number of nodes/particles.
Third job
What patterns will we get
-------------
I do not disagree with what you said. I want to relate it to minimum length and find explanations for the differences that might exist.

Now, for a little bit of number crunching.
You get a different number .. Parameter 2 becomes 1.05946…
Which you derived from the speed of light.
Correct????
When I enter 14 for the surface area of a sphere I get a radius of 1.055502061411188 and a diameter of 2.111004122822376.
If I was to try to fill ALL of the positions (make a soliton) without violating minimum length I could have a maximum of 7 nodes/particles on the surface of that sphere. Since I want those nodes/particles to move around then I would limit the number of nodes/particles to something smaller (6,5,4,3,2).

I also like an even number. Also, the nodes can have a greater separation than one unit but never less than one unit.

If we assume that the radius obtained from the calculation (1.055502061411188) is not observed in experimental observations of the speed of light then there needs to be an explanation for the difference of those two radius
(1.05550… - 1.05946… = .00396…)
Would your number be the size of the nodes/particles as well as the separation (minimum distance) between the nodes/particles?
Have you got any suggestions/ideas?

Hummm…. When using the surface area of a sphere with whole numbers I only get 9 numbers between one and two that are smaller than two.
Do you have any idea how the two approaches can be reconciled?

I would think that if we could relate one of the minimum surface area of a sphere to agree with your starting number it would be sufficient.
We could then deal with the number of nodes on that surface that could be making a photon/soliton.
From what you have said, I think that you would want 2 nodes/particles on a sphere of 14 units.
Is that correct?
I think that when we get a diameter greater than 2 then the nodes/particles would no longer be on the surface of the sphere (1.9544100476116797 …… 12 …………… 3)
This is where we would need to limit the size of the sphere. (less than two)
( Hummm …This number could be related to QCD … 3 quarks/nodes/particles???)
If we had two or more spheres that did not have a diameter greater than 2 interacting with each other, maybe that would give use a solution.

(That is the part that Why Not? and I have as hex patterns.)
jal

Hi all,



Sometimes, when "editing", the first draft is better just "tossed", rather than trying to do a lot or "erasing". I can find no understanding of what happened in your last post. I'm sure that we lost our 12 year olds!


I thought we were going over the different "fuels" that we might use for a test flight , and you reached over and hit the "launch button"!




Let me restate the "question" that I think needs to be answered before the "test flight".


If space and time are related in the way that can be deemed "entwined", and they don't have a " 1:1 " ratio, then which number is "fundamental"? The value that is "one", or the value that is "<,>1"? Aren't BOTH required to give the "fundamental" answer?


I think that this is what WN? is saying about an "interval".


Since my method is "dimensionless", it can not answer this "choice" for us, we must interpret the whole picture, and decide whether space, or time gives us the answer we want. The one thing that I can say, is that if we want some KIND of number for an answer, like "integer numbers for units of distance" (like 1 meter), then our OTHER measurement can NOT be an integer, it "jumps" in an exponential way.


When you are "constructing" your "geometry", what is it that you are trying to model?



regards,

T.Roc

THE LAUNCHE HAS BEEN ABORTED.
We will need to come back after clearing up some communication problems.

Are you referring to philosophy or to fixed point and phase transition.

Can you link and explain what you mean from one of these links or some other.
http://en.wikipedia.org/wiki/Fixed_point_%28mathematics%29
Points which come back to the same value after a finite number of iterations of the function are known as periodic points; a fixed point is a periodic point with period equal to one.

http://en.wikipedia.org/wiki/Phase_transition
phase transition

http://en.wikipedia.org/wiki/Renormalization_group
As it was stated in the previous section, the most important information in the RG flow are its fixed points. The possible macroscopic states of the system, at a large scale, are given by this set of fixed points.
http://www.superkits.net/whitepapers/Fixed...onal%20Math.pdf
Fixed-Point Representation & Fractional Math
By Eric Oberstar
August 30 2007
---------
jal

Hey TRoc, Jal and all,

Maybe if I were 12 I would understand the last few posts! I believe I am in agreement with TRoc, we need to build the rocket first, so thank you Jal for aborting the launch.

I also think it may be a good idea to step back and examine why we think we need to define a minimum interval. (Maybe I am making assumptions, but to me, it requires space AND time to make an interval. Einstein showed that that the two are inexorably linked. It all comes down to "how long (time) does it take to travel distance (space).” So we should be giving equal consideration to time as to length. Agreed?)

I linked to Baez earlier and I will stick with dimensional analysis as a valid justification to suspect spacetime structure. The Compton wavelength and the Schwarzschild radius both have some experimental justifications. Combining the two and examining the result seem a pretty good place to start. My only contention with Baez is that the 2pi should not be ignored (at least until we are so mathematically sophisticated enough that such things can be ignored).

Best to all and Mahalo

Hi Why Not?TRoc, and all,
I am familiar with J. Baez and if memory serves (paraphrased) 2pi should not be ignored that it may be contain an unknown key.

Because if we go beyond/smaller than planck scale which was determined mathematically, (you posted a link before), then we cannot make any analysis or predictions.

Yes, QED for the Compton wavelength and minimum length for Schwarzschild radius.
There are a lot of links in my summary.
I think that we are saying the same thing but that the same words may have different meaning for each of us.

jal
TRoc, Just saw what I think is your answer in DSE thread.
http://forum.physorg.com/index.php?showtop...95&#entry260834
It will take time to read.

This post has been edited by jal on Sep 14 2007, 03:16 AM

Hi all,

Thanks Jal! I was going for General Relativity for the Schwarzschild, but, nonetheless,

The beauty of mathematics is that it is the Universal language.

So, if you will all induldge the question, is there a "maximal interval"?

Mahalo, ku`u hoa.

This post has been edited by Why Not? on Sep 14 2007, 03:25 AM

Yes... more than one.
It depends on the context. QED...QCD ... etc
jal

And they are what?!?

IMHO there is but one maximal interval...si? (bi-lingual pun intended )

In an ideal world, the maximal and the minimal should be scale invariant, no?

As always, Mahalo.

Hi Why Not?TRoc, and all,

Nobody knows the quantum maximum or minimum lengths but there are scientists who are doing experiments that can give us a better range of where are those distances.
Bookmark, Xiao-Gang Wen and do a search on the work that he is doing.
He is looking for the Quantum Minimum Length Structure.


http://dao.mit.edu/~wen/
Quantum field theory of many-body systems
Xiao-Gang Wen
Chapter 8
Topological and Quantum Order – Beyond Landau’s Theories
The concept of topological/quantum order allows us to have a new classification of orders. A quantum order is simply a non-symmetry breaking order in a quantum system, and a topological order is simply a quantum order with finite energy gap.

Look at his java dance of electrons. I don’t know how he set up his program. Set e to 12 and slow the speed and you will see that there is a preferred dance of triplet.
http://dao.mit.edu/~wen/java/dance/dance.html
-------------
You can do like me ... get ideas of where to look for information and pursue the trail. This forum will not give you the answers.
jal

Hey Jal, et al.

Thanks for offering up another great link. Regardless of speculation about what the minimum size might be and why , it would be nice to see some arguments against a minimum (length, time, or interval). To me, it seems "obvious" that there must be a minimum interval. A minimum interval implies a minimum distance and time. This, in turn, implies a spacetime structure. What are we missing that is "so obvious"? Or is everyone else just ignoring the "obvious"?

Mahalo