Thursday, June 22, 2017

Constituent Models - Useful Supersets of the mnp Model

Abstract

The term Constituent Model is explained as an attempt to model fermions and fields as made up of constituent(s) moving at c. Interpreting momentum, movement, and mass in a Constituent Model with constituent(s) moving at c is seen as leading directly to the familiar concepts of rest mass, gamma, and relativistic mass. Added: 2017-06-24

The author believes Constituent Model is a new term, though great minds may be working in the same direction.

The author recognizes a potential naming conflict; the term constituent is also used for constituent quarks, which are current quarks along with (some of) their associated virtual quarks and gluons. Constituent quarks are NOT directly related to Constituent Models, though the mnp Model sees quarks as intrinsically recruiting and keeping what QCD calls gluons.

The term Constituent Model is chosen intentionally, since particles are seen as more or less cohesive collections of participants in a given region. Net movement is the net of each contribution. Fields are seen not as specific motions but the result of imbalances in the random potential offered by constituent(s) moving at c. Field-particle interactions may be as dependent on the particle constituent(s) as on the field constituent(s). The word Constituent is specifically intended as an analogue to politics. Particle and field behavior is seen as rather like voting; individuals have their own paths but the net or average of a vote determines an issue. The plural of constituent is shown here as constituent(s) to indicate that constituent(s) may be either discrete tiny entities as posited by the mnp Model, in which case the "plural" would be constituents or may be continuous, in which case the "plural" would be constituent.

Interpreting the Ψ function of a particle as the particle is not far removed from a Constituent Model. If influences on the electron are seen as influences on the Ψ function itself, this picture is even closer to being a Constituent Model. Add an expectation that influences on a Ψ function and changes in the Ψ function travel at most at the speed of light, and the interpretation has become a Constituent Model. This necessitates seeing the Ψ function as representing both the particle, our incomplete knowledge of the location and movement of that particle, and accumulated inaccuracies due to the mathematical formulation. The author suggests the Ψ function has infinite tails only as a way to make the mathematics tractable. So "finding" an electron at a location does not require infinite time in a Constituent Model based on the speed of light.

The mnp Model is an example to a Constituent Model.

Introduction

Seeing fermions as made up of charge structure and mediators traveling at c is, the author suggests, useful in particle dynamics. Remaining stationary requires that the constituent(s) be rotating internally in a mostly symmetric fashion. Movement involves a net direction to that internal movement. Slight asymmetries may lead to spin and chirality.

Seeing quarks, electrons, and positrons as having charge structure in six parts, is useful for understanding nucleons, weak interactions, high energy collisions, and Quantum Chromo Dynamics. This is one level of greater specificity in the mnp Model.

Seeing the charge structure of leptons as consisting of coiled loops, may be useful in explaining spin, strong nuclear force, van der Waals forces and Casimir effects, Abraham-Lorentz forces, and the quantization of charge. This is another level of even greater specificity in the mnp Model.

Seeing fields made up of mediators and, in the case of electrostatic fields, charged mediators, will be useful for dealing with fields and offers hope of integration with gravity.

Seeing photons and neutrinos as bundles of energy may be useful for handling a puzzle of how constituent(s) traveling at c, traditionally seen as perpendicular, could possibly yield entities traveling at c again in a perpendicular direction. This is a different level of specificity in the mnp Model.

Seeing gravitational fields as made up of gravitons or diffuse field effects moving at c allows gravity to be integrated into a Constituent Model. Seeing gravity as resulting from gravity fields/gravitons recruited and acting both approaching and leaving the mass allows conservation of mass. If the recruitment is in proportion to the directionality of a mass, then the field varies with the mass's movement and rotation. Seeing gravitons as moving at c and having a span of effect allows small scale effects and short term effect limits without concern for singularities. This is yet a different level of specificity in the mnp Model.

Seeing gravitational fields as made up of gravitons which are the same as the mediators that make up neutrinos, photons, and "gluons" traveling both directions toward and from the mass allows simplification of a model and perhaps more confidence that recruiting for all fields will be possible. This is a greater level of specificity in the mnp Model view of gravity which has led to a great deal of integration with matter and the other fields in the mnp Model.

Constituent Models are physical. Resorting to extra dimensions can be useful during model and mathematical development and useful as an investigation of limits, but the author would prefer to minimize hiding wherever possible.

The mnp Model sees the constituent(s) as discrete and equal effect and range of influence and therefore the same "size" and "mass." None of the Constituent Models need to adopt this view. In fact, the author could see a useful Constituent Model CMp just addressing particles, energy, mass, and particle interactions.

The mnp Model makes a number of interesting but unsubstantiated claims and speculations that a Constituent Model might well eschew. An example is the explanation of galactic dynamics and the Pioneer gravitational anomaly as gravitons recruiting each other when spaced far apart between masses that have been closer at a previous time in their history. The explanation of particle spin as resulting from coiled loop dynamics and chirality from the stranding of 6 coiled loops could be ignored even by a coiled loop Constituent Model CMcl.

So for now, the author has seven categories for specialization and is looking for further differentiation between the mnp Model and generic Constituent Models. The criteria for separation are fault lines in understanding and acceptance. If some physicists find A easier to accept than B, then separating the two concepts into separate categories or sub-categories of the Constituent Model is appropriate.

Table of Contents

Edit history: 2017-06-24 minor changes to Abstract and Conclusion, major rewrite of Momentum in Constituent Models and addition of Minor Comments.

Constituent Models - Specialization for Branches of Physics

Constituent Model Types
TypeModel Name
Particles have constituent(s) traveling at cCMp
Fermion charge comes in 6 parts, resulting in charges -1 -2/3 -1/3 0 1/3 2/3 and 1CM6
Fermion charge structure is 6 coiled loops of quantized length and "mass"CMcl
Fields have constituent(s) traveling at cCMf
Photons and neutrinos are particlesCMpp
Gravitational fields have constituent(s) traveling at cCMg
Gravitational fields share constituent types with other fieldsCMg1

Should Constituent Models and CM types ever warrant verbal discussion in public, the pronunciation "c Model" would also be reasonable.

Beyond Constituent Models

The mnp Model has been developed assuming discrete basic entities and makes a number of claims consistent with discrete basic entities, but a useful Constituent Model need not follow that path. Some of the claims made by the mnp Model include:

Beyond Constituent Models
Issue(s)Model
Gravitons attract oncoming gravitons, leading to greater coherence of gravitational fields in galactic arms at extremes of low gravity and greater attraction of between the sun and spacecraft leaving the solar systemmnp Model
Photons do not carry spin, but affect particle constituent(s) in ways that measure as spinmnp Model
A very small number of constituent(s) could explain all phenomenamnp Model
Space is not expandingmnp Model at its most extreme

Constituent Model - Particles

The constituent(s) of a particle at rest would be moving at c within the particle, logically moving perpendicular to any axis through the particle. If the particle could be destroyed, the momentum of the constituent(s) would total mc, the momentum squared m2 c2 and the energy mc2. The constituent(s) of a particle in motion would have net forward velocity v, with the rest of the motion logically perpendicular to v. If all constituent(s) of particle are moving at c and a constituent of a particle is moving at the average velocity v of that particle, then a component c*sqrt(1-v2/c2) of that constituent's movement must be moving within the particle logically perpendicular to the particle motion or at least in some circular fashion. In the limit, as the particle dimension goes to 0, constituent(s) must all be making progress at the same speed in the direction of the velocity. The larger the region in which the particle exists, the greater variation in the constituent(s)' vector at a given time and the greater the variation in forward component. Momentum of the bundle is the (only) way to talk about movement of the bundle. See Momentum in Constituent Models - Proof #1 and #2. In 3 space, if the constituent(s) in a cohesive region (called here a bundle) have a mass m and a net momentum mv-> then the bundle velocity is v-> Therefore the square of the total internal momentum not involved in bundle movement is m2(c2-v2) and the total internal momentum perpendicular to the direction of travel is m sqrt(c2-v2) and the net momentum perpendicular to the direction of travel is 0.

CMp sees the energy involved in movement as part of the particle, so acceleration can be seen as adding or subtracting energy to change the net velocity, applied to the totality of the particle at that particular velocity. That change in energy/mass must be applied to the entire particle.

Relativistic expressions become the only expressions for the m in F=ma. A Constituent Model for particles seems to fit well with the use of relativistic momentum in high energy particle physics.

Constituent(s) do not act like particles, they just move at c. Addition and averaging of constituent(s) do not require relativistic corrections, just as photons and neutrinos do not require velocity or mass corrections. Gravity to be treated later.

The author admits that seeing particles as made up of constituent(s) is probably the easiest concept to understand or accept. The going gets harder from here on.

Constituent Model - Charges Quantized at 1/6 Electron Charge

Experiment shows quite clearly that quarks have +-1/3 or +-2/3 of a full charge, electrons -1 and positrons +1, with no other possible values. The author proposes that the (only) uniform way to get this result is to have all possible combinations of 6 charges which can be positive or negative. This does result in the possibility of a 0 charge "small" lepton of 3 negative and 3 positive charges. The mnp Model calls this a z and suggests that z are involved in naked proton and nucleon decay and (paired) in spontaneous creation of electrons and positrons. The mnp Model has made no progress in suggesting the z's mass or masses.

Quantized charge can lead to understanding of nucleons, weak interactions (trading of charge material), high energy collisions (trading, rearranging, recruiting charge material), and Quantum Chromo Dynamics. Quarks are seen as attempting to trade charge material but unable to complete the interaction. For example, in a proton, two up quarks attempt to take the same positive charge material portion from a down quark and continue to do so as long as the charge material is quantized and moving at c.

Constituent Model - Coiled Loops as the Basis of Particles

Coiled loops are seen as useful in explaining

  • h/2 is the angular momentum in the one loop that must be present for the loops to complete and exist in real space
  • h is the angular momentum in two loops that must be removed if the electron is to expand into the simplest shells
  • spin results from coiled loops that can proceed either clockwise or counter clockwise in the direction of progress

At least in the mnp Model, if coils attract one another by the direction of their travel both in the direction and in the opposite direction as gravitons do, then explanations become possible for:

  • strong nuclear force
  • van der Waals forces and Casimir effects, Abraham-Lorentz forces
  • positrons and electrons interact if their spin is appropriate

Constituent Model - Fields

Electrostatic and gravitational fields have, classically, a logical point source and are linear in propagation and effect. Magnetic fields have a logical linear source and are planar in propagation and effect; they only redirect and do not change speeds in classical formulations.

Note that the words propagate and propagation are used as intransitive verb and noun form of movement respectively to describe the movement of constituent(s) at c in spreading and maintaining the field. This clearly contracts with the way quantum mechanics uses the different term propagator for the function or matrix that represents the probability amplitude of particle travel or travel with a particular energy and momentum.

Magnetic fields may be the easiest of the fields to be seen as made up of constituent(s). While charge is conserved, energy is used to create the field and affects the current. But first: Magnetic fields traditional description uses "Magnetic Lines of Force," which the author finds to be a terrible misnomer. "Magnetic Lines of Zero Force" seem much more appropriate. If the constituent(s) of the magnetic field are propagating from the line of current in all planes containing that line of current, the constituent(s) are able to affect moving charges in directions within that plane but not perpendicular to that plane. The author suggests that the difference between stationary charges and moving charges is that the constituent(s) of the moving charge have a net direction forward and that the magnetic field affects only this net direction, not the component of constituent movement rotating with the charge at c but net perpendicularly to the direction, and are unable to add energy to the particle.

Electrostatic fields do not diminish or increase charge over time, therefore the constituent(s) of the charge cannot provide the constituent(s) of the electrostatic field. The author suggests that potential for electrostatic fields must exist around the charge. The charge then recruits constituent(s) to form the field, in proportion to the magnitude of the charge. Since electrostatic fields have two directions, the field organized by a negative charge must point the opposite direction from that organized by a positive charge. The author also suggests that point charges are useful mathematical fictions and that recruitment may well require that charge has dimension.

Gravitational fields, which appear simple and uni-directional in concept and become complicated when interacting with matter, are treated separately below as CMg. The author suggests that mass concentrated at a point is a useful mathematical fiction, that recruitment requires dimension and surface area.

Electromagnetism is not easily treated as part of a Constituent Model without accepting photons and perhaps neutrinos as particles of energy, treated below as CMpp. The author admits he has not integrated the planar nature of magnetic fields back into his views of traditional electromagnetic radiation. He holds some small hope of headway in that direction.

Constituent Model - Photons and Neutrinos as Particles

The author suggests that if the constituent(s) act at c, that electrical and magnetic fields do not interact fast enough to create electromagnetic radiation propagating at c. The author suggests that as bundles of energy, they affect the field potential through which they travel to create attenuating oscillating fields. Non polarized particles such as neutrinos create deBroglie waves. In the case of photons which are polarized, this will lead to electrical and magnetic fields. Photons must be created by electron or positron shells and cannot be recruited by changing electrical fields, if the constituent(s) are traveling at c and not already formed. Diffraction and interference remains to be explained, but the current thought is that it occurs as electrons influenced by the coherent electromagnetic field redirect or absorb the photons.

Constituent Model - Gravitational Fields

If c is the maximum speed for everything, then models of gravitational fields fall into three categories: pure information, affective, and magic.

If gravity is pure information, then matter and electromagnetism "know what to do" when presented with gravitational information, as in General Relativity. If the model insists that matter does not have any part in responding to that information, then the author suggests the interpretation fits in the third realm, magic. Which is OK, magic is just that which we don't really understand yet. "It just works" is a powerful argument for any theory, and postponing investigation and decision is an effective and often appropriate strategy in science and in politics. If gravitational fields cause change in matter's clock, mass or apparent mass, and movement, then those gravitational fields have energy.

Pure information field models must offer some means for matter to affect the information, for information to affect matter, and either for information emanating from one mass to interact with that from other masses or for that information to propagate at c and superimpose perfectly without influence from other information and without its travel being influenced by gravity, which is in contrast to current theory that electromagnetic radiation and neutrinos are affected by gravity. Pure information models have the advantage of mass and energy conservation.

Affective models of gravity (for want of a better term and a better word than affective) see matter as creating gravitational fields to which matter then responds. These fields are seen as having energy that is provided to matter when affected by the field. Since conservation of mass and energy are experimental facts, four explanations can be enumerated.

Mass and time are "running out" at a universally coordinated rate so that the experience of mass and time remains constant Mass absorbs as much as it sends Mass sends only what it can recruit Mass recruits and responds to potential that exists independently and which recruits influence each other.

All possibilities other than the first see two way exchange, so that gravitational fields travel away from mass and toward mass so that masses are not reduced by emitting gravitons. The simplest explanation is that gravitons have the same effect whether they are moving toward or away from the nearest mass. An alternate, rejected by the mnp Model, is that gravitons are always assumed to be "pointing to where they came from." The difficulty with this directional model is that incoming gravitons must equal outgoing gravitons over a relatively short time since the masses are not emitting. The author suggests that gravitational fields are not recruited by static mass but by the directionality of that mass; if constituent(s) are moving more in one direction, that the gravitational field is skewed forward and backward based on the balance of constituent movement.

This constituent sub-model CMg is a different area of specificity in the mnp Model which sees gravitational fields as requiring recruitment rather than emission and as propagating at c. If that field is made up of basic entities, as suggested by the mnp Model, some string theories, and perhaps quantum loop gravity, those gravitons could be tiny, non polarized, and distinct from the basic entities that act as mediators of the other forces. The entities that constitute relativistic mass could be mediators, which could become photons when released by electron shells. Or relativistic mass could conceivably be the non polarized gravitons. The mnp Model posits a unification of gravitons and mediators, as follows.

Constituent Model - Gravitational Fields Unified with Other Mediators and Other Fields

Seeing gravitational fields as gravitons being mediators that have random orientation of polarity would seem to allow unification of mediators and gravitons. Simplicity, reduction in the need for the mass of two separate fields, and personal preference are the author's only reasons for preferring the reduction in mediator type count.

A challenge posed by this unification is that gravity works the same for all masses, where charges have sign electrostatic fields attract or repel. Therefore, the constituent(s) of a gravitational field are bi-directional while the constituent(s) of an electrostatic field are directional.

The mnp Model

The mnp Model can be seen as an extreme version of the seven (and counting) Constituent Models. The mnp Model attempts to radically simplify basic explanations. In doing so, it more than occasionally creates complicated three dimensional geometry. The mnp Model is NOT complete and NOT numerically satisfying at this time.

The mnp Model suggests that there are three basic entities, with two basic effects and one non-effect on overlap, that result in all particles and fields, that the basic entities that lead to charge bind tightly into stranded coils that provide the hidden structure for electrons, positrons, and quarks.

The mnp Model could be consistent with expanding space, but since the speed limit c is built into the foundation of the Model, nothing will be seen as exceeding c in a local region. The author claims the Model has higher ambitions for explanation, so is not conceding the expansion of space. Yet.

The mnp Model's approach to providing directional information in electrostatic fields using a single mediator is complicated. The mnp Model posits that electrostatic fields propagate slower than c. The mediators propagate perpendicular to the line toward the charge, with their polarity information pointing toward the negative charge and away from a positive charge. The basic entities that form charge are oriented and travel in the field in the direction toward the opposite charge and then are sent off from the charged particle at more oblique angles.

Constituent Models - Roadblocks to Acceptance

Constituent Models, even the most general particle only model CMp, all suffer a powerful roadblock to acceptance. They do offer hope of integration between small scale effects at a quantum level and large scale effects up to galactic dynamics. But they offer no hope of going back to special or general relativity as "virtual" or "apparent" theories. They offer no hope of relying on frames of reference, in the author's estimation, though reconciliation and explanation of why existing theories work well in appropriate conditions will necessarily follow development and will probably precede acceptance for Constituent Models - edited 2017-06-24. Particles are not seen as the same when they are moving as when they are in the never seen state called stationary.

Constituent Models must offer alternate explanations for experiment:

  • inertia
  • the two-way speed of light
  • time dilation
  • length contraction
  • gravitational time dilation
  • lack of time dilation due to rotational acceleration

and of course the currently unexplained

  • diffraction and interference
  • galactic dynamics

The author has every faith in physicists' ability to consider the impossible. Examples include "the only possible other explanation is sub-structure," those Theories of Everything that depend on an absolute frame of reference, "God does not play dice with the universe," the multiple universe models initially rejected and later seen as saving some theories, dark matter. Scientists' and theoreticians' ability to be honest is impressive though not quite universal. Still, the author has every expectation that the mnp Model will benefit for now from further obscurity. With a readership now into the low two digits...

The author is preparing to revise the now ancient 2012 "treatise" on the mnp Model and plans to codify the level of Constituent Model involved in the various discussions. So far, Constituent Models enumerates 7 sub-scripts: p, f, 6, cl, pp, g and g1. The author seeks a complete list. He would eventually like the Model to resemble a menu; to get an explanation for ____, certain levels of a Constituent Model must be posited... Some explanations or ideas may remain idiosyncratic to the mnp Model, and would be labeled as such. For example, the mnp Model is looking for alternate explanations of the Cosmic Microwave Background Radiation and for the apparent expansion of space, but expect the Constituent Model to yield explanatory success in those areas.

Earth's Frame of Reference - For Reference

  • The Earth's gravity gives rise to the greatest component of the gravitational field experienced on earth.
  • The Earth is rotating on its axis, giving rise to the greatest component of angular momentum of large scale objects on earth.
  • The solar system is orbiting the galactic core, giving rise to 220 km/sec movement.
  • The solar system (not galaxy?) has a speed of 371 km/s in a co-moving reference frame toward Leo, somewhat near the plane of the ecliptic of the galaxy. This frame appears to be useful in studies of the Cosmic Microwave Background.

So, in models and theories that depend on an absolute frame of reference, Earth's labs have NEVER been stationary.

Singularities and Constituent Models

If a Constituent Model accepts that fermions and fields are made of constituent(s) traveling at c, the author suggests that no singularities can exist beyond perhaps the instant of initial creation of the universe. Any other local singularities have exceeding low probabilities and evaporate at, well, the speed of light.

The mnp Model and Natural Philosophy

This discussion of Constituent Models is part of an on-going attempt by the author to understand our understanding of natural phenomena, to examine the approaches to understanding, to understand where radical simplifications can take place and what the effects of those simplifications would be, and to provide ways to translate the experimental results and theoretical language of modern physics into a different Model.

It that translation is even moderately successful, explanations of why current theory works so well should prove interesting and even fruitful. Failure at that translation may still aid the understanding of physics and the universe.

Movement in Constituent Models - Proofs #1 and #2 - 2017-06-24

This development of a toy Constituent Model will address only movement of a "bundle" and the constituent(s) comprising said "bundle." It will not address charge or mechanisms for acceleration and will (usually) avoid the term particle for bundle.

The Constituent Model's need to model action within a bundle/particle is different from the mathematical needs of basic physics (though the momentum term will be familiar), high energy particle physics (though the momentum squared term may be familiar), quantum mechanics (Ψ2), and mechanics and statistical mechanics. The use of a momentum term to apply to constituent(s) is as non-standard as the concept of constituent(s). The following development of constituent and bundle velocity and velocity squared may (nay should) be reminiscent of other developments in physics, but will attempt to refer for validation or permission to experience and experiment rather than to other branches of physics.

The first question of interest in a Constituent Model is "where are the constituent(s) going within the particle." Such a model sees even those particles considered to be points as merely having dimension too small to be seen by current experiments. Mass is seen as merely an ability to influence and to resist being influenced. No assumptions are made about mass, except that it does not change for a given tiny constituent or a differential volume of constituent(s) at a given time.

Three concepts are useful:

  • Where and how fast are the constituent(s) and the aggregate bundle going?
  • How much motion are the constituent(s) exhibiting?
  • How much of that constituent motion is in the axis of bundle travel?

Momentum, mv, is a good measurement for the where and how fast question. Aggregate motion is a volume integral of differential mass times velocity. Absolute value of constituent(s) motion times mass is a good measure for the how much questions, but the square root of dot products is computationally inconvenient so the expedient of squaring the integral will be used.

Givens and Nomenclature:

  • an inertial frame with no fields
  • constituent(s) in a cohesive region (reminiscent of a particle), called here bundle b
  • total mass of constituent(s) in the region, called here m
  • constituent(s) differential of mass, called here dm
  • velocity of the constituent(s) in dm, called here prog
  • all constituent(s) move at the speed of light, c
  • direction of travel of the cohesive region, called here the x axis with no loss of generality
Since Constituent Models look directly at the constituent(s), no complex numbers are required. Complex numbers are required when processes and progress within a particle are occurring but are not measured outside the particle.

  • The total mass of the bundle is a volume integral: b∰ dm = m
  • The total momentum of the bundle is a volume integral: b∰ progdm dm = mv
  • The velocity of the bundle is the momentum volume integral divided by mass: b∰ progdm dm / m = v
  • When the bundle is at rest in the inertial frame, velocity and momentum are 0.
  • When the bundle is at rest in the inertial frame, the author suggests the absolute quantity (integrated over the volume of the bundle) of constituent(s) progress (sometimes called here absolute progress or absolute momentum) is b∰ abs(progdm) dm -or-
  • b∰ sqrt(progdm) dm -or- Shown using the components of prog:
  • b∰ sqrt((progdmx2 + progdmy2 + progdmz2) dm
  • Working with square roots is a pain, so we will use the crude expedient of squaring the whole mess.
  • b∰ sqrt((progdmx2 + progdmy2 + progdmz2) dm b∰ sqrt((progdmx2 + progdmy2 + progdmz2) dm
  • Experimental results indicate moving particles such as electrons have no parts that are distinguishable. So recognize that m is independent of progress and progress does not depend on m so that the square roots can be gathered within one integral, leading to
  • b∰ (progdmx2 + progdmy2 + progdmz2) dm b∰ dm

The result should be mc2m or m2c2 since the constituent(s) are moving at c. Note that for continuous rather than discrete constituent(s), the integral also implies integrating over all directions present in the differential of volume, treating the constituent(s)' directions rather as a tensor. Constituent(s) absolute momentum would be the square root of the result, or mc. Note that we cannot add the squared results directly to represent a particle.

What happens if constituent(s) are added to the bundle at rest, moving at c along the x axis? Call the amount of constituent(s) added md. If this is added to the bundle (and integrated in somehow so that it does not just escape the other side), m for the total bundle (called bt here) would become m0 + md (called mt here). One might think that the momentum added would be md c and the resulting velocity of the bundle md c/mt, but to integrate the added constituent(s) into the bundle, the total movement of all the constituent(s) at c must be taken into account.

Experimental results indicate moving particles such as electrons have no parts that are distinguishable. So movement within the moving bundle that does not result in net bundle movement is represented by

  • sqrt[ bt∰ ( (progdmx - v)2 + progdmy2 + progdmz2) dm bt∰ dm] or
  • sqrt[ bt∰ ( (progdmx2 - 2 progdmxv + v2) + progdmy2 + progdmz2) dm bt∰ dm ]
  • Note that since bt∰ progdmx dm is mtv -and-
  • bt∰ -2 progdmx v dm is (-2 mtv2) -and-
  • the integral of v2 dm is (mtv2) -then-
  • the integral of what the constituent(s) are doing in the moving frame of reference is
  • sqrt[ (bt∰ (progdmx2 + progdmy2 + progdmz2) dm - bt∰ v2 dm ) bt∰ dm ]
  • The first integral is mtc2.
  • The second integral is mtv2.
  • So the resulting momentum is sqrt [ mt2(c2 - v2) ] -or-
  • mt sqrt (c2 - v2)

To express mt as a function of v and m0 requires some algebra and some physics (proto-physics? pseudo-physics?). The total (absolute) momentum of constituent(s) in the moving bundle is mt c, so the momentum seen outside the bundle is

  • mt( c - sqrt (c2 - v2 ))
  • The momentum imparted by md is mdc
  • which since md = mt - m0
  • can be written as (mt - m0)c.

The before and after momenta are equal. The results are very interesting:

  • mt( c - sqrt (c2 - v2 )) = (mt - m0)c
  • m0c = mt sqrt (c2 - v2 )
  • mt = m0 c / sqrt (c2 - v2 )
  • mt = m0 / sqrt (1 - v2 / c2 )

Surprise! Er, QED, though the author did not fess up to that intention to start. A Constituent Model where particles and energy are made up of constituent(s) moving at c yields the familiar gamma and familiar mass of a moving particle.

Let us look back at the (square of the) absolute momentum of the bundle in the moving frame:

  • sqrt[ (bt∰ (progdmx2 + progdmy2 + progdmz2) dm - bt∰ v2 dm ) bt∰ dm ] -or-
  • mt sqrt(c2 - v2) -or- written in terms of m0
  • [ m0 / sqrt (1 - v2 / c2) ] sqrt(c2 - v2) -or-
  • m0 c sqrt(1 - v2 / c2) / sqrt (1 - v2 / c2) -or-
  • m0c

So the absolute momentum of the constituent(s) of a moving particle within that moving frame is identical to the absolute momentum of the constituent(s) of a stationary particle within that stationary frame. Again, surprise. Er, QED.

The author humbly suggests that Constituent Models with all of the stationary or moving particle's constituent(s) moving at c is in fact viable and interesting.

Minor Comments After Momentous Conclusion - 2017-06-24

Apologies for the pun.

The author suggests that adding constituent(s) askew to the direction of travel might contribute to a new direction of travel, but only that portion aligned with the new direction of travel will be incorporated into the bundle with its new momentum.

If constituent(s)/energy could be directly "added" opposite the direction of the bundle's movement, the momentum will go down and the mass that can stay with the bundle goes down so the "added" energy plus that much again will be released probably in random directions unless the bundle is an electron shell. If the energy stayed with the bundle, experiment would show that bundles aka particles constantly gained mass. Experiment shows particles seem to be themselves and to be identical when traveling at the same speed in a frame of reference.

In like manner, if energy is added at an angle to the bundle's movement, the momentum will change in magnitude and direction and the total mass/energy of the bundle's constituent(s) will adjust for the magnitude of the new velocity.

Note that this discussion of bundles and internal momentum applies to particles and not to fields. Fields are seen as (except for electro-static fields) propagating at c, with none of the effectively circular motions required by particles to exist at sub-luminal velocities. So field constituent(s) interact only by affecting angles rather than conserving quantities in Cartesian components.

Conclusion - edited 2017-06-24

The author has submitted Constituent Model as a term for a set of generic approaches to modeling particles and fields and forces in physics, with a few specific sub-models.

With all constituent(s) moving at c, the concepts of rest mass and the gamma correction for moving mass are seen as growing organically out of the Model.

The author's mnp Model is an example of a specific Constituent Model using discrete tiny constituent(s) of three types interacting in three ways over very short distances. Whether "anyone else is thinking like this" remains to be determined, developed, and perhaps recruited. The author concedes Constituent Models are probably more interesting to many potential contributors.

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