When you have a lecture on Navier Stokes, they immediately explain that in order to solve for NS, you then have to solve for the x,y,z vector directions, you look at the planes, look at mass and Energy conservations, and momentum. Ultimately what you're looking for is which way is the particle or the fluid moving?
...with reference to a frictional or pressure gradient, just as Relativity as it went down this track and converted ALL mass and Matter to energy and then described it as a pressure gradient in order to describe gravity as the 'supposedly' - 'bent rubber sheet' of curved space-time...Useful as it allowed us to solve problems and solve things, at the same time it was an explanation without and explanation.
It gave us a way to get an answer without really understanding what is going on. This is what happened in "Quantum Cosmology" when Abraham rationalized and unified....
By the time Abraham rationalized, unified and explained Newton and Coulombs similarities, and then how they related to Einsteins field equations, merged the whole lot to give the unified gravitational field, the answer to Navier Stokes was staring him in the face.
Non-linear simultaneous equations, and field tensors are mathematically complicated...
What Tetryonics does is give us a model that covers it all-at-once in one image...
Space, Time, Energy, momentum, mass and Matter.
This gives us all the forces, everything physical and everything immaterial so in that respect, the one simple basic foundational geometry of Tetryonics can therefor explain this work.
Rather than focusing upon the differential equations, focus on the picture. An image is worth more than a 1000 math words...its the key.
Physics is completely missing what is going on here. What is measured as a sin wave of electric fields or magnetic fields, is in fact the result of a 2[pi] equilateral geometry. As they move past the point, any person or detector won't measure the geometries exactly, but rather they will measure the strengths of the E or M field position with respect to one another.
It's the actual motion of the diamond shaped 2[pi] arrangement of photons of energy passing the detectors that resolve to sin waves in this way. You'll notice the 90 degree phase relationship between the E-Field and M-field components.
First, we must wrap our heads around this 2 quanta EM field that is creating these changing values in the sin waves. It's not just wave mechanics, it's actually the measure of the triangles in relationship with one another.
The alternating diamond shape electric fields in the upper left...and the oscillating magnetic dipole fields shown in the upper right.
Traditionally drawn as circles, are really the passing equilateral triangles passing a point. The upper left maps the E-field max, and the upper right shows the M-Field max oscillations.
Tetryonics simply says that -- Scalar energy that makes a force is an Equilateral Triangle... The square root of that triangle represents the linear momentum as indicated by the pink color running up the height of the triangle.
Euler's equations have been known since the 17th century. It combines trig, exponential features, the square root of negative one, basically all the features of mathematics rolled into once equation, and now we have THE understanding that brings all this to life.
We are working to show that the square root of a negative number is not irrational, it's simply the heights of the Negative charged fields of the Triangle...it's a very real value of the negative charge.
e^i[pi] + 1 = 0
Can be rearranged...
e^i[pi] = -1
If this is the case, you have the square root of negative one being expressed, and mathematicians scratch their head at this...Tetryonics simplifies the issue and just says that the Square root is the height of a negatively charged equilateral triangle.
We have this quadrature wave made from the geometric photons and EM wave. The measurement past a point will produce the complex wave form that sinusoidally varies with time, and the 90 degree phase relationship can be easily understood.
We're not saying that the mathematics is wrong, rather that the mechanism/geometry at work has never been identified before. The concept as understood using a 'concentric pattern of radiating ripples' of electromagnetic energy that overlap to give us complex interference patterns and complex interactions of force, is the basis of field mechanics that led to the Navier Stokes solution.
Rather than radiating concentric rings and spherical point particles as the map, we are looking toward the tessellated Planck Quanta back of all the equations.
Tetryonics is a bottom up approach, given the geometry, the math comes out.
Mathematics (top-down) is simply pattern recognition looking down from our perspective down, and our human minds have found it difficult to interpret the math correctly.
There is a misconception to the underlying geometry, and as a species we've missed the equilateral geometry as being of vast important. The Relativity equations as written by Einstein are all the same as Navier Stokes, as in they are all non-linear simultaneous equations.
Relativity was based on Lorentz corrections ( as the velocity increases, wavelengths get shorter ), but was applied incorrectly. Lorentz corrections only apply to the secondary KEM ( Kinetic ElectroMagnetic Fields) that result from Matter in motion. It's not Matter itself that Lorentz contracts, but rather this secondary KEM fields alone!
The energy stored in the KEM fields, which have a kinetic component and a magnetic moment, and any Material object moving at any velocity will have mv^2 quanta in a secondary KEM field. All the Relativistic corrections, the Lorentz, transforms, Special Relativity and General Relative relates to the contraction and motion and geometry of Equilateral Fields of mass-energy.
Matter itself is NOT Lorentz variable. Matter Topology is not affected by the speed, velocity changes or application of force in any way shape or form. All the extra energy of the force goes into these secondary KEM fields. This applies to Navier Stokes. These KEM fields are fields of mass-energy momenta - Fields of Motion - or Kinetic Fields.
If we are going to model fluid dynamics and the pressures and velocities and how the 'wavefront' moves, we must first understand that any force applied to Matter is made up of Equilateral Planck energy momenta that is stored in these fields...not in the Matter itself. We are introducing a secondary component that has yet to be identified. Separate from the mass-Matter of the particle itself.
We can resolve away the mysteries of 'Wave-Particle duality' this with an analogy. If we think of the KEM wave as the wake of a boat in water. As you push the boat away from the dock, the boat does not contract, but the energy of your push goes into the creation of a wake. As the boat speeds up the wake gets bigger, and as the boat slow down (due to friction) the wake gets smaller. KEM waves work in exactly the same way. The stored energy of motion is in this field.
The Matter Topology of the boat does not change, but the energy of your push off the dock, sets up a secondary wake/wave is generated and the dynamics of the wave change as the boat increases it's speed. At no time does the actual Matter of the boat contract at, near or faster than light.
Whatever force you apply will be stored in the KEM field, in both a kinetic and magnetic moment. It will cause the Material particle or boat to move in the vector direction of it's Linear Momentum....(the square root of the energy supplied by that force). If you know the weight of the boat you can divide the momentum by the weight of the boat to derive how fast the boat is moving...and more importantly which direction!
This is the Gaussian Distribution from the Geometric perspective of Tetryonics.
Our next illustration gives you more information directly applicable to Navier Stokes.
If you look at the color coded Photons, they form a Normal/Gaussian Distribution pattern in Tetryonics, they go from, red, orange, yellow, green, aqua, blue, Indigo, violet, --going back down---, Indigo, blue, aqua, green, yellow, orange, and then red. themselves...(this is the color coding representing a 64 square unit Equilateral Triangle with 8 quantum steps...the second image below, shows a Pink Linear Momentum Vector going up the center and it represents 9 quantum levels of 81 Planck Quanta going up the apex of the tessellated triangle arrangement.)
Every Quantum Physicist on the planet is missing this point!
This is where the statistical probabilities come into quantum physics itself. It all comes from this field and this arrangement of energy momenta within a charged geometry. Whether you measure it as mass (energy per second) or if you measure it as an energy density (Tau-a-b as a stress–energy tensor) using General Relativity -- with it's associated square root vector velocity or linear momenta -- it makes no difference--, or you can even measure it as a function of time by watching the change of Equilateral Geometry (Quantised Angular Momentum) per second.
If you do the quick algebra on (Quantised Angular Momenta/per second) you get (square-meters-per-second/c^2).... Do the algebra on it and you get 'Seconds'...Any changing seconds -- or changing angular momenta per c^2 will give you TIME...because you get delta seconds.
Delta Seconds is TIME. Time itself is quantised. It's a measure of QAM (Quantised Angular Momenta) or energy geometries per spacial region...That's the simplest way to put it.
All these energy distributions of energy quanta, the scalar as well as the quantised Planck Quanta and their various aspects of Kinetic energy, linear momenta, magnetic moments, time... all these features including velocity, can only be done in mathematics at present as 'simultaneous non-linear equations' because they are a scalar function. The linear momentum and the vector remain linear, but the rest of them are SCALAR functions.
Even though we can now quantize them using Tetryonic geometry, they are still treated as scalar. You try to solve for them, ( x, y, z) each direction of motion has to be solved with a non-linear simultaneous equation.
Just like gravitational fields, the mathematician looks at it and either has a stroke or shrugs his shoulders. To try and calculate them is a nightmare, but to visualize them in Tetryonics is simple.
You can see the Electric and Magnetic Components, You can see the kinetic components...the entire field is kinetic. You can make out it's linear momentum by the pink diamonds running down the center forming the central height of the triangle. You can see the vector direction that the particle is moving. You can also see how many Planck Quanta are present.
More excitedly from Navier Stokes side of it...you can now bring in Relativity, because as we have stated that the kinetic field is fully relativistic and it's the part that is Lorentz corrected due to velocity changes, we have found that as you add more energy by applying more force, you will put more quanta into that field and those planck quanta being squeezed into the same geometric area, obviously their wavelengths are then contract. As the velocity increases the wavelength of each quanta contracts. The particle itself's wavelength DOES NOT contract, or change.
De Broglie, who extended this to the physical contraction of particles, and Einstein doing the same thing, was COMPLETELY inappropriate. It was a mis interpretation as to what Matter was as opposed to what mass-energy is.
That's where Relativity has erred in it's foundation. The Lorentz contractions, which gave birth to Relativity, DO NOT apply to Matter. They only apply to Matter in so far as the energy of the mass in the Tetrahedral Topologies have a specific Compton frequency and De Broglie wavelength. That part is correct, but it's not Lorentz contracted.
Then you can take it to the final step. The image showing Bosons and Photons...(EM waveforms) shows the Lorentz contractions of bosons, showing the associated energy levels of a photo-electron as it's accelerated.
It shows the physical contraction or changing size of the quanta in the KEM field as the electron is accelerated. Again, a squared number for every KEM field as the energy is applied, so this is where we get Bohr's quantum jumps. Which cause all the problems with asking.
'How do we merge quantum theory in with Classical Mechanics and explain this contraction? How do we do all this in the case of Fluid Dynamics?'
All the particles that are in motion, in say a wavefront, a wave crashing on a beach, or a particle moving through a fluid situation, with resistance and things like that...In a macro scale model, we can do it mathematically, but how can we do it visually using a Macro scale model?
Tetryonics shows us the visual geometry at play, but it also shows exactly how the math was applied incorrectly.
The same KEM fields can be re-drawn showing the same fields, the same energy momenta, but this time we are focusing on the linear momenta, the vector direction created by the energy fields. The more quanta you have provided by the energy supplied by the force, the higher the value of the linear momenta and the higher the value of the associated velocity, in proportion to the mass-Matter, of the particle that that field is associated with.
mass is that lovely constant between force and acceleration. The heavier the particle, the slower the velocity b/c there's more inertia to get moving, so the force will not accelerate it to the same velocity of a lighter particle. mass acts as a fulcrum in the equation.
Any information about any particle in motion can be gleaned from the simple Equilateral geometries of Planck Quanta in a KEM field, as can ALL the information about the charged Matter Topology of any particle.
Using Tetryonics, if we had a computer big enough and coded correctly, we could physically describe each and every atom, all the spare electrons, the energy in the system, the complete makeup for ever type, whether it's a water molecule, or a metal bullet in a water solution, makes no difference, you can model all the physical particles along with their KEM fields for their directions of motion.
Now if it's random, obviously it makes it more complex, but we have super computers capable of meteorologica weather mapping...so why can't we do the same with the Quantum domain, once all these points are taken into account?
If you know enough information, you can predict, not only their exact outcome, but also their exact position, energy, and momenta, for any particle within the system that you are modeling.
What we have been lacking today, is the Equilateral Energy Momenta described as such, and to build the Topologies of the Matter while understanding the mechanics.
If you were to build a model of a one second snap shop of a system, you can put all the particles, with their KEM fields into the model and then progress that like a still shot for another second.
That's all the Navier Stokes equations are doing. They are trying to solve for one instant in time, and then a second later, you allow that system to evolve and take another snap shot. Calculate for their position, charge Topology and the KEM field of every particle in the experiment under question, and then a second later you allow that system to evolve and you take another snap shot with the geometry. Then place a series of 60 of these snap shots together and you have a movie.
Then you have gone from a Navier Stokes type situation, where it's just a black box, to a computer that is actually running the simulation. Then you can test it against physical models to validate Tetryonic Theory.
All the problems resolve down to people having Euler's formula and NS equations, but lack the underlying geometry. They still think of it as circular wavefronts creating interference patterns, when it is these Equilateral Geometries at work. If you shade these as 50% coloring, you can see the super-positioning of these equilateral KEM field overlays. This creates the the force between particles.
In the case of friction, all you have is a substance with it's KEM field that are super positioning with the KEM fields of the other particles in motion, and resisting it's motion, causing the particles to slow down and loose velocity.
Given enough time with these basic geometries that we now have via Tetryonics, we can do what Navier Stokes attempts to do mathematically, but can't do, and that is to solve for a 3D problem.
"Is it solvable?" -- Yes!
"Can any of the fields resolve back down to a singularity point?" -- Yes!
"Does it have the simultaneous equation component?" -- Yes, because there are scalar field geometries.
"Does it have conservation of energy mass and conservation of momentum?"
Yes, from which we can deduce geometrically/visually, the vector component of each particle. Then we just draw the situation, knowing the forces of motion with much greater detail than is possible with vector diagrams or with pure math. It then becomes a simple visual problem. If you want an exact answer you'll have to run the super computer for the length of time required. Allow the particle to interact and there's your solution.
You can prove for a 3D computational fluid dynamic example, an exact outcome for any particle or for the entire system.
You can't prove that using the math, because you can't solve the math. All you can do is manipulate the math and assume there is no vector rotation and that there are only linear motions, so then you can get rid of all your simultaneous scalar parts.
You can do both with Tetryonics. Where there is a vector straight line of linear momentum you know there is an associated Equilateral field of scalar energy surround it.
All these complex parts of the math, like curl, differentiation over time, just vanish and the solution becomes a simply slide show.
Whether the mathematician will accept this geometric approach will depend on how long it takes them to accept the logic behind it.
The complexity of the NS equations that we are so familiar with, simply disappear using the Tetryonic approach. The problem doesn't even exist as many believe that it does.
Tetryonics offers a strict differentiation between mass and Matter, and we offer clarity between the linear and the non-linear, and even P vs NP type problems that we also resolve using geometry alone.
KEM fields are electromagnetic fields that point in a vector direction. They have linear momentum - the square root - all this applies but Instead of 'circular spherical wave fronts,' we now have equilateral geometry as KING.