metacogitans

What are the algorithms for the series, sums, and/or triple integrals for the structure of quarks and their probable location relative to one another?

(∫∫∫∑Wavefront Surface Area_a - ∫∫∫∑Wavefront Surface Area_b ) / ∫∫∫ Volume Designated

This is a simple metric for wave density of a given volume for two given wave fronts within it, which can be used as a value for mass-energy and mass-volume.

As the number of separate wave fronts can be infinite within a given volume, a method for describing wave density is useful, and can also be used to distinguish between the presence of different massive particles - the changing volumes between the surface areas of wave fronts indicates both particle type and  number.

2 hours ago, mathematic said:

I will try to answer your first question with a general observation.  When doing mathematics,the names of the variables (time, distance, etc.) don't matter.  For your first question t is a variable to be treated like any other.

Right that works just fine for Quadratic equations but what about an equation for two semi-circles when the radius is increasing over time? I guess I'm not sure if it would still be called a quadratic formula, but what I'm looking for is a formula that gives intersection coordinates.

How would one use a quadratic formula with time as a variable? For example, what the intersections between two circular functions would be when T=0 compared to T=5 if the radius of the functions increases over time? 

Also, is there a general equivalent of the quadratic formula for circles?

I would like to basically have a simple equation that gives me the coordinates of an intersection (x, y, z) for a given value of x, y, and time. 

After that, the derivative of an intersecting function is going to be treated as an axis for a change in slope of the other function over time (the slope will 'reverse' over the perpendicular line to the other function's derivative at the point of intersection).

The equations would be for wave equations when interactions between infinitesimally thin waves are involved.

Right now I have written the equations for this type of wave interaction, but only if I can make up a value for the other function's origin for every single intersection I am evaluating. I can't yet use them to determine what each secessive point of intersection will be without having to change the radius and origin of one of the functions for each intersection I calculate.

I am not sure if the term would be 'implicit', but with circular and spheroid functions I think what I am looking for would be called a "Implicit Quadratic Formula", as they involve variables paired with a constant together as a square root, which of course don't have a simple algebraic way of being determined. Rediscovering a proof for those types of intersections would take me weeks/months/years, and I have already tried and failed numerous times. 

With graphing algorithms, I could approximate the change in intersections over time to  a certain number of decimal places accurately through repeatedly estimating factors and adjusting them based on the range of difference, but this is labor intensive even for a computer. It'd be a lot easier if there was a more general formula like the Quadratic formula; does anyone know if it exists?

I couldn't just find the intersection between one function and the line equation perpendicular to the other's derivative, because this does not tell me what the first point of intersection would be for that perpindicular - there must be an equal increase in each function's radius over time.

This is something I have been building on for about 3 years or so now, originally as a part of a proof for a solution to the Navier-Stokes Equations and Smoothness problem; to give a simple summary, deflections between ray instances in wave fronts must fall into a specific category based on ray-to-ray angle for a ray deflection instance, simply assuming 3-dimensional Euclidean space with time, and would include (and from what I understand, can only include):

Front to Front Wave Deflection Instances:

- Shared Linear Trajectory Infinitesimal Wave Front Section

- Acute

- Obtuse

- Near Shared Angle Infinitesimal Ray Pair

- Acute Ray Deflection Off Rear of Ray

And then a corresponding set of deflection instance types for Front to Rear Wave Deflections.

These deflection instance type result geometrically when we hypothetically assume a repulsion-exlusive model of physics, charge, and particle interactions - where, basically, whenever 'attraction' occurs between charged particles, it is actually manifesting geometrically from what are fundamentally repulsing deflections between wave fronts, and clockwise or counter-clockwise intrinsic coiling of wave fronts is responsible for charge.

I'll add more to this later, ran out of time to be able to finish the rest of this post right now

 

 

Why not present your proof and let people here (not me!) review it. That seems like a good way of making sure it is valid.

 

You know me. I am just sceptical that someone who is not familiar with a concept could produce a proof related to it.

 

"I have a proof that Pi is normal but I just need to know what 'normal' means..."

I was familiar with smoothness - I just needed a more concise definition for it.

As soon as I am closer to a final edit of the solution, I will post it here along with having submitted it to a peer reviewed journal of physics/mathematics.

I'd really like to talk about my idea for the solution, but I guess this is actually something that if I think I have it, I should publish it first (and make sure the proof is kosher).

That makes it hard for me to ask the questions I need to ask, but let me ask this:

If a function ends abruptly, or has any sudden increases/decreases or 'sharp angles', it ceases to be smooth, correct?

I've been working on a solution for one of the millennium prize problems (the Navier-Stokes Equations and Smoothness problem), but one of the finalizing things I need is a formal definition of 'smoothness'.

The problem asks for proof which involves a smooth, divergent free vector field, a smooth function for a force, and a smooth function for pressure.

No. Scopolamine is an anticholinergic, which is where it gets most of its psychological effects.

You could compare low doses of it to normal doses of doxylamine, but without being an H1 antagonist (an antihistamine).

The memory loss isn't that profound, and I don't know where you heard that it causes individuals to be unable to 'refuse commands', but that is simply false.

This post makes it sound like scopolamine isn't dangerous, and I just wanted to make it very clear that it is, in fact, poisonous and dangerous, especially when found in scopolamine-containing plants.

Safety is the most important thing; education on it shouldn't be a problem, as once educated, most people stay far, far away from it. If everyone was educated about it they would know how to avoid contact with it. I am of the opinion that plants containing it should be eradicated, except on preserved wildlands.

I agree with most points of the original post, except 5, 6, and 7.

5. The discoverer says a belief is credible because it has endured for centuries. There is a persistent myth that hundreds or even thousands of years ago, long before anyone knew that blood circulates throughout the body, or that germs cause disease, our ancestors possessed miraculous remedies that modern science cannot understand. Much of what is termed "alternative medicine" is part of that myth.

Ancient folk wisdom, rediscovered or repackaged, is unlikely to match the output of modern scientific laboratories.

6. The discoverer has worked in isolation. The image of a lone genius who struggles in secrecy in an attic laboratory and ends up making a revolutionary breakthrough is a staple of Hollywood's science-fiction films, but it is hard to find examples in real life. Scientific breakthroughs nowadays are almost always syntheses of the work of many scientists.

7. The discoverer must propose new laws of nature to explain an observation. A new law of nature, invoked to explain some extraordinary result, must not conflict with what is already known. If we must change existing laws of nature or propose new laws to account for an observation, it is almost certainly wrong.

If 5 is true, then Newton, Leibniz, the ancient Greek mathematicians, early 18th century chemistry, etc., would qualify as 'pseudoscience'.

As for 6, many great discoverers have worked in isolation: Newton, the photographer and pair of student biologists who discovered the structure of DNA, all the inventors throughout the 20th century who came up with something new in a shed or a garage - you can't discredit their works merely because they worked in isolation.

As for 7, what is a 'law of nature'? Maybe the original poster meant a physical law. Even many of the accepted physical laws have exceptions, like the law of thermodynamics for entropy (water, for example, can be separated into hydrogen and oxygen and recombined repeatedly, and repeatedly frozen/thawed without the entropy of the ice 'increasing' over time necessarily); the quark entropy might increase over time, but I don't think that's what the laws of thermodynamics were meant to describe.

How can long-term neuroleptic drug (not cannabis) usage trigger psychosis? Is it possible that atypical antipsychotics inverse chemical balance (dopamine/serotonin levels) in the brain? Can atypical antipsychotics cause dopamine hypersensitivity?

 

Thanks.

Psychosis from psychoactive substances is in almost all cases reversible and temporary, lasting 1-2 weeks at most.

Ah, now I see neuroleptic withdrawals are the cause. Yes, they are awful, and completely paradoxical - a leftover from old psychiatry when incapacitating a patient was the desired effect of medication.

Although I don't think psychosis from withdrawal should last very long, there are other serious neurological disorders that often come with long-term use of neuroleptics and cessation of taking them, such as psychomotor 'tics' (involuntary muscle movements, and inability to change thoughts or speech patterns, slightly resembling obsessive-compulsive disorder or tourette's syndrome).

Your excitatory neurotransmitters are likely out of whack as well, but really the best thing you can do is eat healthy, follow a schedule, and sleep at a scheduled time for no more and no less than 7-9 hours, and your central nervous system, if at all damaged, will repair itself given the chance to and with the resources needed to (nutritous food and a healthy amount of sleep).

Can atypical antipsychotics inverse dopamine sensitivity?

From what I've read and heard 10+ years ago and haven't heard anything different, they cause pre-synaptic dopamine vesicles to 'pre-load' with dopamine, to be released more frequently than normal, which is likely the cause of 'tics' after a person quits taking anti-psychotics, as the dopamine antagonist is no longer there to dampen dopaminergic activity, and excessive and/or unnecessary action potentials result.

They really are unpleasant and terrible medicines; they end up producing neurological and psychological disturbances and long-lasting disorders (I've heard some people say that their 'tics' never went away after being prescribed certain antipsychotics).

The 3 types of schizophrenia diagnosed (paranoid type, disorganized thinking, and catatonic type) are mistakable for behavior caused by stress or trauma. Pronounced symptoms such as 'clanging' / word salad mentioned in literature from the past seems to indicate exposure to neurotoxic compounds (lead, volatile solvents, paints, glue, etc.) which were more common in past decades, rather than wholly attributable to psychosis. Supporting this is the fact that diagnosis of schizophrenia has dropped sharply in modern times, and used to serve as a 'one disorder to lump all cognitive disorders under.

Reading skills have never been better than they are right now. Everyone owning handheld devices with internet access which they are reading on primarily while using is the main reason I can think of for that.

People are very educated on topics which used to otherwise be somewhat privileged information back before an internet age.

To be honest, the decades when television had complete grip over the lives of everyone was when humanity was at its dumbest.

As for when we were smartest, the first half of the 20th century is when problem solving skills were strongest, especially for westerners and Europeans; the knowledge and education people had then was also more applicable in the real world, especially when it comes to understanding machinery and physics; most significant inventions came from that time period.

 

 

What particles make up the electron?

You might call me crazy but I don't think electrons are particles at all; I think they are stowed kinetic potential.

Leptons have always been considered slightly removed from traditionally defined particles such as a hadrons, haven't they?

I suspect that electrons can form sporadically/spontaneously when an interaction occurs with high enough energy (basically, if you imagine waves of energy, forces, or what have you, interacting with matter with enough energy, it will get caught in the jumbling between the electrons already present in the matter, and residual kinetic fluctuations within the matter after the interaction may actually be new free electrons; although presumably with no positive charge to pair with, they would quickly go to wherever it is excess electrons usually go (into the ground, making a material negative ionic, etc).

Every elementary particle discovered is later found to consist of additional constituent particles, and there has never been a way for us to determine whether or not that continues indefinitely with particles being perpetually divisible.

For a particle to always consist of another tier of constituent particles at a smaller scale would be tantamount to there not being such thing as 'particles', only waves and energy -- and matter could be described more generally as an elemental material 'essence' or cloud, with indefinite form.

Chemistry, as a science, accurately and consistently describes interactions of elements; it does not detail a science for particles like theoretical physics often will. The periodic table is structured to describe patterns in behavior of material elements and how they are organized relative to one another -- what it is, and how it was discovered and assembled, never required, necessitated, or implied the existence of particles, or that a given body of matter is made up of a discrete number of particles.

Avogadro's number has no role or application outside of offering a possible explanation to give us some kind of perspective when considering the neutronic ratios of different bodies of mass.

Every experiment said to prove the existence of particles has an alternative explanation:

- electron microscopes are structured to emit similar-portion bursts in discrete intervals -- in this case, the electron's mass can only be measured in terms of energy, and vice versa.

- 'detector plates' and other apparatus for determining the presence of a particle are, by design, going to relay that every interaction within certain parameters was a 'particle'.

- experiments showing the conservation of mass pertains to mass, not particles.

- experiements where a body off mass is repeatedly divided into smaller and smaller amounts down to individual particles when they can no longer be split are actually limited by the apparatus which does the 'splitting', and can only be divided to the extent which the apparatus allows.

- Since all fine measurements are made with equipment following the same standard and definitions, inconsistencies in 'particle numbers' are difficult to notice.

I like referencing this 'missing piece' puzzle to show how greatly error can appear in such a small area, making measurements unreliable:

And that is error present in only a 13x5 section of a grid; when dealing with scales exponentially removed from our own, how much certainty can we really have for any measurement?

I like to think that other instances of the 'missing piece' puzzle can be found all around us, and one of the rarest things to actually exist is certainty.

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(Added with Edit)

Even if we try to assume the existence of discrete particles, we are forced to begin making exceptions on just how 'particle-like' in nature they really are, due to various physical laws and principles:

- The relative nature of time and space has the implication at microcosmic scales that our metrics of measurements for various properties begin to cross over and meld together, meaning that the criteria of 'structure' for a particle has to be broadened to allow for particles being amorphous chaotic blobs rather than possessing a distinct structure...

- Particle's having a set geometric structure would violate the speed of light, as one section of a particle's structure accelerating could not cause the rest of the structure to accelerate with instantaneity and unison without having been transferred throughout the structure faster than the speed of light. If, however, the intrinsic structure of particles is dynamic, then it would imply there are more constituent particles -- at what point would we actually have a particle by definition?

If we lump this particle paradox as belonging to the standard model, we may owe it several other known 'problems' in physics as well, such as the presence of dark matter, and the anomalous abundance of leptons (why don't we ever 'run out' of electrons? Wouldn't bodies of mass eventually lose most of their electrons to the expanse of space? If we leave 'particle' out of the definition of an electron, they could be thought of as forming spontaneously with high enough energy.

 

The very first thing you need is to decide what sort of wave you mean and how to describe it.

 

By what sort I don't mean sound or light or gravity, I mean its geometric distribution in space, in short its 'shape'.

Is it 1D, 2D or 3D?

Is it plane spherical or what?

Clearly (to you I hope) it is a travelling wave since you say it is reflected.

I was initially thinking of the wave as an infinitely thin sphere propagating out in all directions from its center, and following the inverse square law having a diminishing intensity with distance.

I was trying to figure out if perhaps the degree of curvature of the wave (being 'flatter' the further the wave propagates), proportional to the curvature of the spherical object/particle, would determine its intensity.

As for the type of wave, a force-carrying wave in its simplest form (if there is such a thing), traveling at the speed of light. Or it could just be considered light, or some other simple electromagnetic wave that transfers inertia.

I'm trying to figure out how to describe the geometrical coordinates of a wave contacting and reflecting off the surface area of a spherical object/particle; specifically waves traveling at the speed of light.

My goal is to be able to explain the torsion in a region of surface area over time making contact with a wave reflecting off it, considering how the velocity of the object/particle changes as well, and how the geometry of the reflecting wave changes too.

I have a good picture in my head of how it all comes together geometrically, but I don't know how to go about writing it down with tensor geometry on paper.

I'm still very new to using tensor calculus; I would be very excited to be able finally to actually write out the math of a concept I'm thinking about instead of hitting a roadblock at tensor calculus every time and not being able to do anything after that - so, teachers are welcome =)

I know calculus up to about what a second year student would know, and understand the FToC, how differentiation and integration are inversely related, etc.. I even know 3-coordinate volume integrals and planar derivatives, as long as its not too complex of a problem. So, it seems to me like learning tensor geometry and calculus in physics is right where I should be in looking for what to tackle next.

So would this go faster than light, or just be an alternative way of space travel? Is there also something that can back this up, I'm not an expert in any of this so if there is I'd be happy to know. Thanks

Alternative to space travel that would be virtually fuel-less; I'm not sure how fast it would go but if it can accelerate without fuel then I'm guessing it could go as fast as the structure of the ship could handle - maybe even getting up into relativistic speeds; 10-25%, maybe even 30-40% the speed of light. At those speeds though, it would have to emit strong magnetic fields ahead of its path to keep debris out of the way.

I just thought of some more key parts of the design I mentioned earlier:

So in the rear of the craft is a solar sail with a sort of twisting, winged screwdriver shape (sort of like an ice auger ). The solar sail spins faster the more it is accelerated by solar radiation.

Now, this is the smart part: an electrical current is running through the solar sail. Once the solar sail is spinning fast enough, the electrons in the current would interact with their own electromagnetic field which they had produced earlier (similar to how electrons interact with their own field to form interference fringes after passing through a double slit),

This means thrust is being produced by motion which the ship had already made.

Then, you're asking "what do I do about all that pesky 'space-time' in front of the ship", right? Well, since the structure of space-time is simply its contents, then displacing them aerodynamically is what is needed, but why just displace space-time when it could be harnessed for more thrust? Matter in front of the ship is diverted into 4 or more cylindrical drive chambers with electromagnet coils inside the wall of the cylinder, hooked up to the same circuit as the electrical current running through the solar sail, but in the opposite direction to complete the circuit! The wire coiling through the walls of the cylinder generates a current from passing space debris going through the drive; the electromagnet coiling also accelerates debris, creating a vacuum effect which pulls in even more debris faster.

So I don't have much of a background in physics, since I haven't had the opportunity to take it yet, but I'm really interested in theoretical FTL methods.

 

So my question is- What would it take for some sort of spacecraft to accomplish the speed of light or faster. I understand and methods are probably theoretical I just don't understand the math involved just yet, so I'm hoping for some clarification.

The idea I had for this was to 'cheat' the geometry of how waves accelerate a particle by setting up an nano-apparatus which would distribute absorbed inertia such that the apparatus continuously accelerates into more waves of force.

If possible, the major drawback would be that it wouldn't be able to travel in a straight line, and how it would fit into designs above the nanoscale is a head-scratcher.

Another idea I had for long distance space travel (maybe not FTL, but relativistic speeds) would be to set up a solar-sail turbine with sort of a screw-like shape, which also has a strong electrical current running through it; as the solar sail reaches a relativistic threshold where it can no longer provide sufficient acceleration, the electrical current would be arranged such that the electrons end up interacting with their own electromagnetic field producing propulsion from the electrons accelerating themselves basically. Hitting the brakes would be as simple as flipping a switch to change which direction the electrical current flows through the solar turbine. It would definitely be cool to send a probe to Alpha Centauri with only a 6-7 year travel time.

Wouldn't a more practical question be "What slows down a particle"?

 

Ie mass=resistance to inertia. What interaction gives the gluons mass?

 

As far as your model idea goes Not enough detail to judge atm

Well, I was thinking of that same question earlier; Particles held together by an electron bond would inadvertently share inertia to some extent with the particles they are bound to. Another thought I had was that if mass is defined as a number of particles (and not in terms of energy or electron volts), density must play more of a role in resistance to inertia than mass or mass-energy.

As for gluons, for a while it has seemed to me that the binding of quarks forming a hadron has to be a mathematical and geometrical consequence of particles set within such close proximity to one other (basically, I think they are too close to be separated by everyday interactions, and a particle accelerator has to knock them loose).

It also seemed to me that the phenomenon of beta-decay supported a model/theory of charge being a geometrical phenomenon, as it involves charge switching after another charged particle comes within proximity of the quarks, changing not only the charge of one of the quarks, but its orientation, as though charge is simply geometrical and can be switched by another particle being forced within proximity of the quarks.

But it's all really beyond my knowledge; those are just thoughts/ideas.

How do the simplest constituent particles of matter (quarks and leptons) accelerate?

Basically where I'm stuck right now is, all the fundamental forces including gravity seem to fit together coherently if I can assume that particles are always accelerating.

The problem with that is that particles would have to be affected by multiple waves at once, and every wave affecting the particle would be a high number (somewhere between 10^80 and !(10^80) or something) simultaneously, every instant, which:
- is too demanding mathematically to work with in most applications, perhaps not though
- doesn't fit with the idea of there being discrete wave packets of inertia (photons) which wouldn't provide continuous acceleration

The alternative would seem to be that particles are accelerated by point surface contact with one wave at a time; are waves of force present at every point in space, or are there gaps/emptiness in-between?

This is what I'm trying to make work:

What causes particles to have an electric charge, and what causes opposite charges to exhibit attraction?

Simply put, the clockwise or counterclockwise orientation of a particle's path through space determines the charge of a particle.

Since particles are not only always in motion, but accelerating, and the sources of acceleration are themselves particles moving in a unique direction and also accelerating, the direction which a particle is accelerating in must always be changing, and therefore a particle's path is always curving.

Since the field of a particle will propagate out over an infinite distance (with diminishing intensity), and a particle produces a field whenever it is accelerated by a force, with the reflecting waves of force acting as the field, a particle must be producing a field constantly if the particle is always accelerating.

As a particle's path is always curving, the overall progression of the curvature is preserved due to inertia, and can not change abruptly -- the geometrical implication of this is that the particle's trajectory will maintain a clockwise or counterclockwise orientation in its curvature - and the field produced by the particle will also propagate with a distinct clockwise/counterclockwise orientation.

When plotted out, the trajectory of the particle and the field it produces would seem to take on a 'coiling' shape; viewing the clockwise or counterclockwise orientation of this coiling as being a positive or negative electric charge, attraction between opposites can be explained geometrically, similar to how gears spinning in opposite directions mesh together, while gears spinning in the same direction kick off each other and aren't mechanically compatible.

Explaining Gravity as a Result of Electromagnetism
Traditionally, space is thought of as an empty vacuum; however, quite the opposite is true, and space consists of a vast particle medium.
As our sun travels through space, it displaces matter in the interstellar medium, producing low pressure in its wake - as well as producing a repulsive effect on matter in front of its path.
The combination of these two effects is responsible for the gravitation of planets and other objects with the sun.

 

 

 

I don't think nonsensical word salad counts as a simple proof.

 

I asked about the nature of these waves of force, not a restatement of your claim. What exerts the force? What interaction is it?

 

 

How about answering my question? Show that these increments are quantized.

 

 

You also take the limit as h goes to zero. It is not an increment.

 

A point particle has no radius. A particle with a radius is not a point particle.

 

 

You also take the limit as h goes to zero. It is not an increment.

 

A point particle has no radius. A particle with a radius is not a point particle.

h is still non-zero. As part of a derivative, h can only be an increment; for example the derivative 2xh+h^2 / h simply means that for every increment of h, there is an increase by 2xh+h^2

Because a metric for distance can only be defined by a relation between particles, the radii of the simplest fundamental particle constituents of matter could only have a value described as non-zero.

I don't really feel like replying to the rest of your post

I think there may be a simple proof for this actually:

Because there is no objective passage of time apart from 'stuff happening', the only physical metric for time is the distance electromagnetic radiation travels proportional to other electromagnetic radiation.

An infinitesimal increment of time would be defined as all electromagnetic radiation traveling an infinitesimal distance. How particles react as a result has no discretion for time, and will continue reacting until no longer within a distance of electromagnetic waves to react with.

What is the nature of these waves of force?

 

If the particle takes an incremental step in one increment of time, how is it that it moved numerous steps (multiple waves of force) in that single increment of time. If it went 10 steps, that should be 10 time increments, since you have decreed that it moves one increment per increment of time.

 

I still think you don't understand what infinitesimal is. You are describing a quantization that has a discrete value (an increment). I can take a number and e.g. divide it by 2 and it will be half as large, and keep doing that. You apply the limit as the value becomes zero. You don't reach a limit where it can't get any smaller.

 

If these distances and times are quantized, show us the theory that predicts this quantization.

Waves of force reflect off the particle's surface on contact, transferring momentum to the particle.

If the particle travels through any waves, momentum has to transfer from them to the particle; the momentum can not be stored until the next increment of time.

Even though the momentum will only cause the particle to move an infinitesimal distance, this is still significant, as that is the particle's radius.

Since the increment of time is infinitesimal, both waves of force (which might be traveling at the speed of light) and particles can only travel an infinitesimal distance that is algebraically equivalent to the other.

It is paradoxical, but it would imply that during an infinitesimal increment of time, particles travel faster than light. However, because the only outcome is for the particle to travel back across a region it has already been through, it can't actually out-pace light, as the particle has to backtrack during subsequent infinitesimal increments of time.

 

I still think you don't understand what infinitesimal is. You are describing a quantization that has a discrete value (an increment). I can take a number and e.g. divide it by 2 and it will be half as large, and keep doing that. You apply the limit as the value becomes zero. You don't reach a limit where it can't get any smaller.

 

If these distances and times are quantized, show us the theory that predicts this quantization.

Infinitesimals in differential calculus are always over an increment, such as (x+h) - (x)

All that matters is that it is non-zero, so momentum transferred to the particle by waves of force has to move the particle by a non-zero distance, which is algebraically equivalent to the particle's radius if it is a point particle.

Alright you guys, I've made some pictures:

Well, that's about where I hit a speed bump, because much of the math needed after that is beyond me; to mathematically explain how point particles can demonstrate properties of mass and volume, a set of tensor equations and probability functions needs to be formulated for the wave dynamics of reflected waves off the surface of a sphere as they pertain to probable location and direction of waves of force and fluctuations over infinitesimal distances.

It'd probably have to translate existing energy-density wave equations so that wave intensity is expressed as the probable distribution of wave-fronts across the surface of a sphere, reducing to a single directional vector lacking magnitude. A tensor would be assigned at each wave front on the surface of the sphere, with a 2-dimensional directional value for what direction the wave-front is moving across the surface of the sphere, and magnitude values for wave angle, degree of bend, and redshift/blueshit to determine probability.