User:Quantim/Process Physics

(Extracted from http://wiki.mindcloud.org/wiki/Quantim/Process_Physics ;-D)

here are some papers bout this:
[Quantum Cosmology: No Dark Matter, Dark Energy nor Accelerating Universe] [3-Space: A Review]

now here's me wanking on about it

This here is an iterative equation that generates a 3-dimensional structure over repeated time-like iterations:
$\mathbf{B}_{ij}\rightarrow \mathbf{B}_{ij} -\alpha (\mathbf{B} + \mathbf{B}^{-1})_{ij} + \omega_{ij},\quad i,j = 1,2\dots,2N;N\rightarrow \infty$

the $\mathbf{B}_{ij}$ represents the ith row and jth column of a matrix $\mathbf{B}$ , $α$ is a constant, and $ω$ is a wiener random variable. This model for how reality evolves is a hell of a lot like the math used to model Neural Networks. Essentially this equations is modelling the universe as information. Conceptually each element $\mathbf{B}_{ij}$ represents the strength of a connection between two nodes i and j of this network - a connection that is relational information in nature and a strength of correlation need not be determined by the distance between - ala quantum teleportation & the instantaneous transfer of information.

When run with a computer, this program successfully models time with a

finite past - the program will only remember some of its past iterations
present moment effect - whatever the current time-like iteration is
a future that is stochastically modelled - both a perfectly deterministic term & a random term

There's a bunch of philosophical wank underpinning the motivation to bother generating a 3-D space and an iterative time, to do with [[Wikipedia:Gödel's_incompleteness_theorems#Second_incompleteness_theorem | Goedel's incompleteness theorem] and the inherently geometric nature of modelling time as a line, among other things.

3-Space Velocity Field Formalism of Gravity

It is possible to demonstrates Process Physics' velocity field formalism of gravity without referring to the underlying theoretical arguments which gave rise to the formalism. However, one must invoke the idea of a 'fluid' that flows - this is akin to many pre-Einsteinian physicists conception of gravity - i believe even of Newton himself. This fluid is similar conceptually to the old 'aether' theories, however there is a subtle but by no means trivial difference between them. Rather than an 'aether' being a fluid flowing through space, we say space itself has a structure which can be modelled as a 3-dimensional fluid. Conceptually this is quite similar to MODELLING space & time as a combined construct known as space-time which itself has internal structure. No accuracy of the ontology of either of these points of view is necessary when introducing the mathematics. The trick is whether it works.

One starts with this equation for the newtonian gravitational field (i.e. 'acceleration field') equation, a vector calculus (i.e. fancy) form of Newton's inverse square law:
$\nabla.\vec{g}(\vec{r},t) = -4\pi G\rho$
This is known as the Gaussian form of Newton's so-called 'universal' law of gravitation. This $\vec{g}(\vec{r},t)$ is the gravitational acceleration, acceleration of course being the time derivative of a velocity, i.e.
$\vec{g}(\vec{r},t)=\frac{d\vec{v}}{dt}$
However, in fluids this description of acceleration is incomplete. so that:

$\frac{d\vec{v}}{dt} \rightarrow \frac{\partial\vec{v}}{\partial t}$

There is an additional term in total acceleration, namely $\vec{v}.\nabla.\vec{v}$ , which wikipedia notes as: the effect of time independent acceleration of a fluid with respect to space. This can easily be obtained from the definition of the derivative (ergh, limits), along with the knowledge that if a body is moving at velocity $\vec{v}(\vec{r},t)$ over a small time interval $d t$ then the distance travelled is $dr=\vec{v}(\vec{r},t).dt$ . The total time derivative of the velocity is then:
$\vec{g}(\vec{r},t) = \lim_{dt \rightarrow 0} \frac{\vec{v}(\vec{r}+\vec{v}(\vec{r},t)dt,t+dt)- \vec{v}(\vec{r},t)}{dt}$
which if you chug out the terms then we end up with what is known as convective derivative, amongst many other names.
$\frac{D\vec{v}}{Dt} = \frac{\partial \vec{v}}{\partial t} + \vec{v}\cdot\nabla \vec{v},$ so that
$\vec{g} (\vec{r},t)=\frac{D\vec{v}}{dt}\equiv \frac{\partial\vec{v}}{\partial t} + (\vec{v}.\nabla)\vec{v})$
and our original gaussian form for the
$\nabla.(\frac{\partial\vec{v}}{\partial t} + (\vec{v}.\nabla)\vec{v})=-4\pi G\rho$

Newton's theory is only correct for distributions of matter

Solving this equation for velocity is difficult in most situations. In the case of a spherically distribution of matter, OUTSIDE of this matter is the inverse square law, which in terms of velocity looks like EQUATION MISSING and if a time derivative is performed on this expression for $\vec{v}$ we get the familiar inverse square law for gravitational acceleration: EQUATION MISSING

so Newton's law is not so universal - and only applies to spherically symmetric system. The solar system is such a spherical system, but galaxies & binary star systems etc are not. Hence any theory that assumes Newtonian gravity to be correct, then extends that theory to other situations, will be fundamentally flawed i.e. the maths will be off. Einstein's General Relativity is such an extended theory of Newtonian Gravity - BUT each event in history that shows that the maths is off is ignored and instead a new concept is invented in order to force the math to fit observational data. In other words, whenever history has shown a flaw in einstein's theory, some new concept is introduced into the theory in order to "save" the theory. bleah. herein the author's bias is shown.

musings and conceptual holes

There are additional terms in the proper versions of the equations (which i WILL write in math font when i can be bothered). In the spherical case these disappear - two constants, call em A and B, are in front of two terms. These two terms amongst the other number filth produce the inverse square ONLY if A = -B - so in the spherical case they disappear. This is used to say "no wonder newton was so successful, our solar system is spherical and newton's stuff worked so well for so long" - then once A = -B then the next step is to determine the value of this constant A. Fitting to experimental data gives that this constant is the fine structure constant, implicitly suggesting that this model of gravity is inherently quantum in nature.

I personally don't yet understand why those 2 terms are invoked as the most 'general' terms for a bunch of scalars equal to 4 pi Gee times the matter density rho. Something to do with these particular scalars being the most general zero rank tensors or some shit. Should find out about that.

User:Quantim/Process Physics

3-Space Velocity Field Formalism of Gravity

Newton's theory is only correct for distributions of matter

musings and conceptual holes

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