I have been looking at describing our universe in terms of wave functions. These 3 functions seem to give a theory of the universe. \(\displaystyle \sum_{n=1}^4 \left( \sum_{m=1}^n \left( \frac {a \cos \left( {3^{( m+(n^2-n)/2)}} \theta / b \right) }{3^{(m+(n^2-n)/2)}} \right) \right)\) \(\displaystyle \sum_{n=1}^{40} \left( \sum_{m=1}^n \left( \frac {a \sin \left( {3^{( m+(n^2-n)/2)}} \theta / b + l \times (\frac {2 \pi}{3}) \right) }{3^{(m+(n^2-n)/2)}} \right) \right) , \ l=-1,0,1 \) \(\displaystyle \sum_{n=1}^8 \left( \sum_{m=1}^n \left( \frac {a \left( \sin \left( {3^{( m+(n^2-n)/2)}} \theta / b + k \times (\frac {\pi}{3} ) \right) + \cos \left( {3^{( m+(n^2-n)/2)}} \theta / b + k \times (\frac { \pi}{3} ) \right) \right) }{2 \times 3^{(m+(n^2-n)/2)}} \right) \right) , \ k=-1,1\) where a and b are constants and \(- \frac {\pi b}{3^{(n^2 - n)/2}} \leq \theta \leq \frac {\pi b}{3^{(n^2 – n)/2}}\) I am uncertain if this is the correct formula for the third wave function, but it should be something similar to this. The second wave function would give the strings in our universe for every value of l. The first wave function gives us the 10 dimensions of string theory and the third function gives the fields in string theory. When n = 2, this gives gravity as the 4 values of the third wave function becomes 1 + 2 + 1. When n = 3, this gives electromagnetism as the 8 values of the third wave function becomes 1 + 3 + 3 + 1. When n = 4, this gives the nuclear fields from 1 + 4 + 6 + 4 + 1. When n = 5, 6, 7 and 8, it gives the properties to the Strings with it having 26 dimensions as again in String theory. Our universe would have the l values like [0], [0, 0], [0, 1, -1], [1, 0, -1, 0]. Particle nature would emerge for n = 2, 3 and 4. When n= 1, the waves from each string where n > 4 would mingle and 3 waves at 120 apart will give a sum of 0. When n = 2, the strings are sufficiently distant that the waves from region 28 to 40 are not interacting. When n = 3, the strings are sufficiently distant that the waves from region 24 to 40 are not interacting. When n = 4, the strings are sufficiently distant that the waves from region 23 to 40 are not interacting. Any thoughts?
A pity. 99.99999% of idea people come to science fora with lots of ideas but little or no math. And they get lambasted for it. One guy comes with actual math, and he's told he won't be taken seriously? As physicists are wont to point out: all descriptive models are necessarily faulty (because they're words). Only math can accurately describe a model. The math IS the model. I'll be the first one to admit it: that math is beyond me. And that means I find zero fault with it. mathman, if you find fault with the math, you should lead with that.
The first formula describes a single structure of 10 waveforms where the frequency is increased by 3. The second formula describes waveforms as a tree structure where each branch produces 3 waveforms that have a phase difference of \(120^o\) and the frequency is increased by 3. There would be \(3^{820}\) leaves resulting and each leaf would be unique. The third formula describes waveforms as a tree structure where each branch produces 2 waveforms. This produces \(2^{36}\) unique wave structures. n=1 has the quanta without any particle nature The wave from 1st formula and 2nd formula (l = 0) forms a circle, with l = -1 or 1 it forms ellipsoids. This gives the dimension as the periphery of a circle or ellipsoid. This dimension of our universe contains \(3^{819}\) strings and the waves of these strings will overlap each other and because the 2nd formula has 3 waves that have their phase offset by \(120^o\) the waves tend to cancel out any effects that they may have in this dimension. Every string in our universe has 820 waves with it, and to be in our universe, the wave in this dimension is the same. To be in our universe, the first 4 realms (10 waves) of a string have be the same. The influence of the 3rd formula is to give 2 field properties. One has a dimension in the 1 dimensional space and a zero dimension for the string which is the point of its position. The other has zero dimensions in the 1 dimensional space which emerges as Time and has 1 dimension for the string.
n=2 has Gravity Field The second realm has 2 dimensions and is from the interaction between 1st formula and 2nd formula and is the surface of toroidal shapes. The first wave of this realm has its amplitude as a third of the amplitude of the waves of the first realm, and the second wave has its amplitude a third of the first wave. This realm has \(3^{817}\) strings and has more area than the first realm which leads to the emergence of a particle nature to the quanta. In a torus where the major radius is 3 times the minor radius (r), the surface area is \(12 \pi^2 r^2\) and distance around circumference of the first realm would be \(18 \pi r\). If the effective distance between strings in the first realm was 1 unit then r is \(3^{817}/2 \pi\). The surface area for the torus would be \(3^{1635}\) and it has \(3^{817}\) strings, so the effective width of a string in the second realm is \(3^{409}\) greater than the effective width in the first realm. This means that a considerable portion of the smaller realms (from the 28th realm to 40th realm) of a string do not overlap with other strings leading to the emergence of` a particle nature. Although this is based on a circular torus, ellipsoidal torii would not have significantly larger or smaller surface area. The interaction between the 1st formula, the 2nd formula and the third formula gives us gravity. The effect of the 2nd formula is to give us 4 possible fields in the surface of the torus. 2 of these fields are the same with 1 property to the string and a 1 dimensional field for the expression of that property. The field is the gravity field and it gives an acceleration on other quanta towards the originator of the field, so is considered a one dimensional force of attraction as having the locus of points that have equal force being a circle around the string. The property given to the string is mass. If all are at rest, then formula for this acceleration is Gm/d towards the originating string. A string can only influence the string that are immediately adjacent, so the field effect is from the adjacent string spreading it further and adding their own field. Another result gives a 2 dimensional field and the string having 0 dimensions which gives its position in this space. The third has 0 dimensions in its space and 2 dimensions in the string which should give the emergence of time. A string is affected by all of the gravity fields of those strings that are in its universe. This realm has the strings of 243 universes. There are 9 of these realms in each of the 3 first realms.
ArafuraOpal, May I ask how you discovered these functions? What thinking led to these? Can I see your derivations from first principles? What, exactly, is the independent variable \(\theta\)? And why is it constrained as it is? And what do the constants \(a\) and \(b\) actual represent in the theory? You say these are wave functions, but wave functions of what? Let's start with the first function, shall we, and then consider the others later. Can you please explain how it does that? n is constrained to take the values 1 to 4 in the first function, and there is a sum over those values. Explain how the function says anything about gravity. Can you derive any basic physical results using this function (or the other two, for that matter)? The first function doesn't allow n=5, 6, 7, 8. Is it a simplification of the other two functions? Please show how it emerges from function 1. n>4 isn't possible for the first function. Does this statement only apply to the other functions, then?
The frequency of what? There are 16 terms in the formula. How do you get 10 waveforms from this? The quanta of what? What do you mean by "without any particle nature"? How does particle nature or its lack manifest in your formula? Forms a circle where? So the formulae are not independent. What three quantities are they determining, exactly, when we carry out the summations?
n = 3 has Electro-magnetic Fields The third realm has 3 dimensions and is from the interaction between 1st formula and 2nd formula and is the peripheral volume of 4 dimensional toroidal shapes. The first wave of this realm has its amplitude as 1/27 of the amplitude of the waves of the first realm, and the second wave has its amplitude a third of the first wave, and the third wave has its amplitude a third of the second wave. This realm has \(3^{814}\) strings and has more volume than the area of the second realm which leads to the emergence of more particle nature to the strings than in the second realm. In a 4 dimensional torus where the major radius is 3 times the minor radius (r), the surface volume is \(8 \times 27 \pi^3 r^3\) and distance around circumference of the first realm would be \(2 \times 3^{15} \pi r\). If the effective distance between strings in the first realm was 1 unit then r is \(3^{804}/2 \pi\). The surface volume for the 4d torus would be \(3^{2418}\) and it has \(3^{814}\) strings, so the effective width of a string in the third realm is \(3^{535}\) greater than the effective width in the first realm. This means that a considerable portion of the smaller realms (from the 24th realm to 40th realm) of a string do not overlap with other strings leading to them having a particle nature where the gravity field would have them as being waves. The interaction between all 3 formula gives us electro-magnetism. With there being 3 dimensions, we have the 3rd formula giving 4 different effects as 1 + 3 + 3 + 1. One has a field shape that is 2 dimensional (surface of a sphere), a simple vector force and a 1 dimensional particle nature called electric field and the other has a field shape that is 1 dimensional (periphery of a circle), a vector force and a turning moment, and a 2 dimensional particle nature of the North-South dipole called magnetic field. The electrical field has the string having 1 of 3 phase possibilities and the acceleration being directed to or from the string. The locus of points that have equivalent acceleration would be the surface of a sphere around the string. Thus the electrical field could be seen as having a 1 dimensional particle nature and a 2 dimensional field. The magnetic field has the string displaying 2 separate phases and this means that there is either no phase difference or \(120^o\) phase difference giving us the North-South dipole. This has 2 accelerations associated with it; the first is an attraction / repulsion and the other is a turning moment to re-align other string’s North-South dipole. The locus of points that have equivalent force would be a circle around the North-South axis. Thus the magnetic field could be seen as having a 2 dimensional particle nature and a 1 dimensional field. In current magnetism, scientists have been looking for monopoles unsuccessfully. The other 2 results from 3 formulae is to give our 3d space and the positions of the strings in it; and the inertia of the strings and time coming from the 0 dimensional field.
The formulae are not equations because they are representing objects. Particle nature would occur when a string has several waves that are not interacting with other strings. When 2 strings come into contact, the waves that were not interacting would repulse the waves of the other string as at least some of these waves would have different phases. If the strings had the same phases for all of the non-interacting waves in the string they would pass through each other, this would be very rare.
sum n = 1 to 4 for sum m = 1 to n gives us 10, 1 + 2 + 3 + 4. a circle of radius r is formed when \(r \sin \theta \) interacts with \(r \cos \theta \). These formulae are not independent.
n = 4 has Nuclear Fields The fourth realm has 4 dimensions and is from the interaction between the waves from the 1st and 2nd formulae. The first wave of this realm has its amplitude as 1/729 of the amplitude of the waves of the first realm, and the second wave has its amplitude a third of the first wave, the third wave has its amplitude a third of the second wave, and the fourth wave has its amplitude a third of the third wave. This realm has \(3^{810}\) strings and has more 4d volume than the volume of the third realm which leads to the emergence of more particle nature to the strings than in the third realm. In a 5 dimensional torus with the minor radius (r), the peripheral 4d volume is \(16 \times 3^{10} \pi^4 r^4\) and distance around circumference of the first realm would be \(2 \times 3^{55} \pi r\). If the effective distance between strings in the first realm was 1 unit then r is \(3^{764}/2 \pi\). The surface volume for the 5d torus would be \(3^{3066}\) and it has \(3^{810}\) strings, so the effective width of a string in the fourth realm is \(3^{564}\) greater than the effective width in the first realm. This means that a considerable portion of the smaller realms (from the 23rd realm to 40th realm) of a string do not overlap with other strings leading to them having the 23rd realm displaying particle nature where the electromagnetic field would have them as being waves. The interaction between the 3 formulae gives us the Nuclear Fields. With there being 4 dimensions, there are 3 fields emerging. One has a field shape that is 3 dimensional and a 1 dimensional particle nature, the second has a field shape that is 2 dimensional and a 2 dimensional particle nature of a dipole and the third would have a 1 dimensional field shape and a 3 dimensional particle nature arranged as a triangle. There are 81 of these 4 dimensional realms in each 3 dimensional spaces. This means that our universe occupies 1.234…% of our space which is consistent with dark energy.
ArafuraOpal: Oops. Of course. Sorry, my mistake. Where's the interaction in this theory? --- Are you going to answer the other questions I asked? Bear in mind that this is a discussion forum, not a blog.
