#### ArafuraOpal

**Registered Member**

$$\displaystyle \sum_{n=1}^4 \left( \sum_{m=1}^n \left( \frac {a \cos \left( {3^{( m+(n^2-n)/2)}} \theta / b \right) }{3^{(m+(n^2-n)/2)}} \right) \right)$$

$$\displaystyle \sum_{n=1}^{40} \left( \sum_{m=1}^n \left( \frac {a \sin \left( {3^{( m+(n^2-n)/2)}} \theta / b + l \times (\frac {2 \pi}{3}) \right) }{3^{(m+(n^2-n)/2)}} \right) \right) , \ l=-1,0,1 $$

$$\displaystyle \sum_{n=1}^8 \left( \sum_{m=1}^n \left( \frac {a \left( \sin \left( {3^{( m+(n^2-n)/2)}} \theta / b + k \times (\frac {\pi}{3} ) \right) + \cos \left( {3^{( m+(n^2-n)/2)}} \theta / b + k \times (\frac { \pi}{3} ) \right) \right) }{2 \times 3^{(m+(n^2-n)/2)}} \right) \right) , \ k=-1,1$$

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?