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Read book (about science and math)

See new book by m concoyle at scribd.com put m concoyle into the scribd-website's search-bar

The new book is:

Describing physical stability: The differential equation vs. New containment constructs

It has about 370 pages
See new book by m concoyle at scribd.com put m concoyle into the scribd-website's search-bar

The new book is:

Describing physical stability: The differential equation vs. New containment constructs

It has about 370 pages

The title at Scribd,com is: Describing stability: The differential equation vs. New containment constructs, this is a result of their poorly designed mechanisms for editing (if there is any mechanism at all)



Introduce the need for the book, "Describing physical stability:"

Issues in regard to "What is real?" and "How to describe observed physical properties?" should have a deep affect on science and physics and mathematics.
The point is that modern physics (and its math constructs) cannot describe, to sufficient precision, the stable spectral properties of the general many-(but-few)-component physical systems so that these descriptions are based on the, so called, "accepted laws-of-physics." Thus, one needs to re-consider the more difficult question as to "What is real?" and, "Is the idea of materialism valid?"

Consider that:
1. Materialism identifies an open-closed topology, upon which the (partial)-differential-equation-models for the "laws of physics" are defined. But these laws cannot be used to identify (to sufficient precision) either "the cause" or "the structure" of the observed spectral-orbital properties of fundamental physical systems which exist at all size-scales, eg nuclei, solar-system, etc. Neither... the laws based on models of local measuring of physical properties (as originated by Newton), Nor... laws based on the combination of "function-space and sets of operators," which are models of both randomness and (supposedly, the stable) spectra of quantum physics
... , can provide these needed descriptions.
That is, in regard to both quantum techniques and particle-collision techniques; the stable spectra of general fundamental physical systems do not emerge as descriptive properties which possess sufficient precision, in regard to either the algebra-operator-structures applied to function-spaces or when non-linear operators are applied to internal particle-states which are attached to the functions of the function-space, where, supposedly, the particle-states are supposed to perturb the wave-functions of the quantum techniques so as to make the calculations more precise.
2. The claim to be able to describe reality, based on the idea of materialism and sets of differential equations, seems to be "doubtful at best," especially, since, after nearly one-hundred years of trying to use function-spaces as the basis for these types of descriptions (of the observed stable spectral properties), and, essentially, coming-up empty, in regard to being able to "sufficiently precisely" describe the spectral properties of general quantum-systems.
Furthermore, in regard to macroscopic physical systems, the non-linearity of general relativity means that it mostly describes chaotic patterns (ie unstable patterns), and this means that general relativity is not capable of describing the observed stability of the solar-system. This has resulted in applying... general relativity... "only to cosmology," where the assumptions about the uniform properties of space and that physical law, as defined by differential equations, are applicable everywhere, cannot be verified (within the context of materialism), by all the measurements which are, in fact, needed "in order for these assumptions to be considered valid" so that these speculative descriptions can be considered to be science. Rather, it is speculation, and the data is interpreted through physical theories, which might not be applicable. Thus, cosmology is a mostly irrelevant discussion.
Quantum physics cannot solve the difficult problems and general relativity is irrelevant.
Thus, one can conclude that, it is... worse to follow the ideas of the modern (overly dogmatic) physics... than it is to follow new ideas.
3. One way, in which to extend beyond the construct of materialism, is for one to find a math model which possesses "more dimensions" than "the idea of materialism allows," and yet "the properties of materialism" form a subset within that new descriptive context.
The new definition of a many-dimensional model of existence requires that the different dimensional-levels be stable shapes, and the models of material components are also stable shapes, but the stable shapes which are material-components are one-dimension less than the dimension of the stable metric-space shapes within which the material components are contained, so that all of these shapes (both material-components and metric-space shapes) have an open-closed topology, so that the dimensional levels are discretely discontinuous (or boundaries are defined) when one changes dimensional-levels, and there are many different possible size-relations which can exist between different dimensional levels (yet the set of different sizes, for these shapes, is a finite set). This is a new model of existence, within which materialism is a subset, and within which the stable spectral-orbital properties of the general many-(but-few)-component physical systems can be described to sufficient precision.
4. The new context is a math model which has surprising implications, but these, apparently, strange implications, are "strange," because of the limitations of language... {where our language is a language which has been built more on "faith in materialism," than it was built, so as, to determine a hidden physical reality}. A hidden physical reality, which exists beyond the idea of materialism, can be described when that "hidden structure of reality" is mathematically modeled.

So, why not follow math constructs which actually solve the most difficult problems... , ie being able to describe (or determine from a math model) the stable spectral-orbital properties of the general (many-(but-few)-component) physical systems... , facing physical description, rather than following those (math-physics) ideas which do not solve these difficult problems?





Foreword

Stability and set-containment need to be considered in new ways.
One's model of existence needs to extend beyond (or transcend) the idea of materialism.
The open-closed topologies of metric-spaces which possess shapes is one of the sources for the idea of materialism, but it also fits into the new constructs for the containment sets for existence. The metric-spaces have shapes and they fit, as shapes, into a higher-dimensional containment-set, so that each subspace of each dimensional level is modeled as a stable shape [except for the highest-dimensional level which is an 11-dimensional hyperbolic metric-space, where a hyperbolic metric-space is equivalent to a space-time metric-space]. These shapes (especially, of different dimensions) are discontinuously related to one another, and each possess an open-closed topology, ie the properties of higher-dimensional-shapes are difficult to encounter, and each shape can contain lower-dimensional material components (except a 1-dimensional shape), and differential equations can be defined, in regard to each independent shape's material-components, which can exist within each of these metric-space shapes.
A stable-system which is modeled as a "3-dimensional hyperbolic metric-space shape" is contained in a 4-dimensional containing metric-space (a space which contains, amongst other things, eg ourselves), this 4-dimensional metric-space is our external structure... , the idea about which we view an external-set of properties is in a context of materialism... ., and the internal-structures of our being, are not so well divided from ourselves "as distinctive material objects," which is the sense we have in our 3-dimensional material containing (and what is often believed to be) an all-inclusive containing space.
Furthermore, since we are contained in a metric-space, which also contains "the solar-system as a stable 3-dimensional-shape," we, ourselves, since we are a higher-dimension than a 3-dimensional shape, and we are a part of the solar-system, then we would be bigger than the solar-system (if we are represented as a higher than 3-dimensional stable shape) and thus, we our 3-space-shape in the 4-space... , which represents our 4-dimensional subspace shape... , is quite large. However, this would also mean that we are related to the same mythology of the, so called, "giant Gods" and their associated mythological "descent to earth" (or singular, God, if one wants)" so that, in this case (ie since our 3-shape contained in 4-space would be very large, ie bigger than the solar-system) the sense of our "correct-size" would be (is) in opposition to our idea of materialism, and this is because we pay-attention to "our 2-shape size," which is contained in 3-space, and we think of as being a material object on the earth's surface.
Our sense of being, as well as our sense of perceiving an "external existence" is made difficult in a 3-dimensional metric-space, which is the shape which defines the earth's stable planetary-orbit... ,
{ie the metric-space where our notions of materialism are formed, and the space where an external existence (ie external to-ourselves) is well defined}
... , so that the idea of materialism is difficult to transcend, within pour own minds, because of the open-closed topology of the 3-dimensional metric-space, where we identify spatial position and relative size of material components contained in 3-space, and within which we define the differential equations of our material-based ideas about physics.
Thus, within the context of materialism, and this materialism being associated to an open-closed topology, it is not possible to identify the source of stability for the observed (stable) properties of material systems based on an open-closed topology related to a model of material interactions based on (partial) differential equations.
That is, the stable properties of material systems come from the stable circle-space shapes, which, in turn, can have many different dimensional-values, as well as being shapes which have many different sizes associated to themselves, so that existence is contained in a many-dimensional context and is associated with many different set-containment constructs.
Note: Since we do not think of ourselves as having a shape which is 4-dimensional, then "How can one discount these (above) ideas?" One can only discount them if one has complete faith in the idea of materialism, but materialism is not a logical necessity, and it fails to describe the stable properties which (it is observed that) material-systems possess.

This is not about opinions... other than... interpretations of math patterns which are associated to the idea of measuring reliability and stable (math) patterns.
Measuring reliably requires that a stable uniform unit of measurement be defined and maintained, that is a unit of measuring must be identified with very stable patterns (or very stable properties). Since only the line and the circle can be made quantitatively consistent with one another, as has been demonstrated within the complex-numbers. Thus, the stable shapes are the circle-spaces, eg the tori (or doughnut-shapes) and shapes which are composed of toral-components (eg an n-holed-doughnut, ie an n-toral-component shape).

Furthermore, in regard to physical properties, they are identified with distinctly different metric-spaces, thus a description of systems which have several properties associated to themselves eg they possess the properties of position in space and the systems have stable energies associated to themselves, must be contained in several different metric-spaces, whose spatial-subspaces have the same dimension, at the same time, or a collection of different metric-space types are needed to contain the different properties which are associated to the system.
Note: These are the stable shapes identified by Thurston-Perlman in their geometrization theorem, but geometrization is only required by the math-community, since the above sentence proves geometrization based on elementary considerations about quantity and stable shapes.



preface
The new math context is much simpler and logically more consistent than today's vision of physical description, and yet the new description opens-up a descriptive context which is much more diverse, eg capable of describing living systems based on a (higher-dimensional) unifying-form (shape) associated with the living system.

To present the new math context of the new descriptive construct in few words (here it is in about 1 pages) and given in math words which are used within the range of their technical meaning (Also go to the figures provided in the back of the book):

In this new descriptive context the stable shapes (or stable patterns)... ,
{in a context where measuring is reliable (ie both linear and metric-invariant as well as continuously commutative almost everywhere (or except for one-point), [where continuously commutative everywhere, is a property which characterizes the circle-spaces, or the discrete isometry shapes which are of non-positive constant-curvature])},
... , are based on the discrete isometry (and associated unitary) subgroups (of various dimension metric-spaces with various signature metric-functions) so that the associated unitary groups (which are associated to isometry groups) are based on the pairs of opposite metric-space states,
and
where the metric-functions have constant coefficients, and the descriptive context is expanded to a set of properties of existence, ie physical properties... ,
{where new physical properties, which begin as 1-dimensional shapes (of either inertia-displacement or charge-energy properties), depend on both changing dimensional levels, and changing the metric-function signature, ie the various signature metric-functions of the various dimensional metric-spaces are associated to specific physical properties}
... , which are associated to each of the different metric-spaces (different spatial-dimensions and different metric-function signatures, especially, when the metric-spaces have the same spatial-dimension, then the different signatures represent different physical properties, all contained within the same spatial-dimension subspace, where these math properties (eg spatial-position or stable-(energy)-pattern) represent the possible physical properties of a system-defining shape, which is contained within the spatial subspace of the given dimension).
A physical system is a stable metric-space shape, which is in resonance with a finite spectral set (see below), and its (physical) properties require that its description by contained in "a mixture of different metric-spaces," which are related to either the same, or adjacent, spatial-dimension subspaces, where the relations are based on material interactions.
These physical properties are essentially defined by the physical symmetries identified by E Noether, eg invariant spatial-displacements are associated to inertia, invariant temporal-displacements are associated with energy, etc.
The changes between dimensional levels can define discontinuous discrete changes in open-closed topological metric-spaces, so the (local) operators which define the properties of local measuring (defined on metric-spaces) act in a discrete and discontinuous manner, and so that action-at-a-distance can be defined in the Euclidean part of the system's (interaction) properties (assuming that action-at-a-distance is the essence of Bell's non-locality property, a property which A Aspect measured, to confirm the property of non-locality in physical systems) in an inter-dimensional model of material interactions.
Furthermore, this context is contained in (or organized around) an 11-dimensional hyperbolic metric-space, due to properties about discrete hyperbolic shapes uncovered by D Coxeter, where the 11-dimensional hyperbolic metric-space, which is partitioned by discrete hyperbolic shapes... .,
{so that in each subspace of each dimensional level, there is a largest discrete hyperbolic shape, which is a part of the finite partition},
... , so that all discrete hyperbolic shapes in the 11-dimensional hyperbolic metric-space must be in resonance with (at least) one of these largest shapes (largest for each different dimensional level and defined for each such subspace of each given dimension) in the partition.
This causes the 11-dimensional hyperbolic metric-space to define a finite spectral set, to which all components of discrete hyperbolic shapes [and associated discrete Euclidean shapes which possess various set-containment relations, as well as discrete shapes of other metric-function signatures of other metric-spaces] are in resonance (ie with this finite spectral set).
In fact, the finite spectral set is defined on the set of 1-dimensional to 5-dimensional, bounded, discrete hyperbolic shapes which compose the partition, since, according to Coxeter, the 6-dimensional and higher-dimensional discrete hyperbolic shapes are all unbounded.
Furthermore, discrete Weyl-angles can be used to fold the discrete hyperbolic shapes in a natural way, where Weyl-angles are a part of properties which distinguish the different conjugation classes of the maximal tori of the fiber Lie groups, ie the classical Lie groups, eg the finite dimensional isometry and unitary groups. There is a finite set of discretely defined Weyl-angles. That is, any element of a Lie group can be conjugated to be in one of the Lie group's maximal tori, where the matrix elements of a maximal torus are all diagonal, ie linear and always (or continuously) locally orthogonal, as long as (or when) the local coordinates transformations (defined by the Lie group elements) stay within the given maximal tori.
A word about containment: If there are a set of 3-cubes of various sizes, each defining a different 3-subspace, then each 3-cube has a choice of being in any of (11-3) = 8 different 4-cubes (or 4-subspaces), but some of these 4-subspaces will be excluded due to size restrictions required on the size of the 4-subspace cubes, so as to be able to contain the size of the 3-cubes. This construct allows for trees-of-containment which can have various types of branching structures.
Partial differential equations and material interactions are re-defined as discrete, discontinuous operators, defined for small discrete time-intervals, in turn, the time-intervals are defined by (time) periods of spin-rotations of metric-space states. These new models of material interactions are similar to the classical model of local measuring of physical properties, and second-order 2-body classical problems are used to adjust the (orbital) properties of the stable spectral-orbital constructs, where these very stable constructs for material systems are the main result of this new description.

0. Preface

One must always identify the exact problem which physics and physical science is trying to deal. This is because the media and journalists are indoctrinated to believe that the truth is difficult to identify, but really the truth, which the media represents, is adjusted to fit the interests of those who control creative actions within society by their investments, and that only a few people have the capability to discern truth, namely, those scientists indoctrinated by... and competing within... an institutional vision of truth and its relation to creative actions (ie adjusting the complicated instruments owned and controlled by the very wealthy)... and to deal with the range of language which is needed to find the truth, where it is this limited and narrowly defined "truth," which the journalists find from the experts, and then the journalists present this "expert truth" to the public.
Thus, the journalist is all about the institutional truths of the age, and this truth must be associated with the documentation and quotes from the experts, so as to prove the point about the truth which the journalist is making within the media.
This is all nonsense, truth is about the language developed around the principles upon which one is claiming to base:
1. society's organization, and behavior within society, or
2. thoughts, in regard to discerning a truth, and in regard to a context for creative actions, about
evidence and its interpretation, and subsequently organized in a descriptive context associated to a simple principle (simple stable pattern) which allows one to find hidden information which is both accurate (to sufficient precision) and is practically useful, either as information or in relation to controlling the properties which exist in a practically creative context of action, which, in turn, exists in a context of reliable and repeatable measured properties, which are within the context of one's stable thought patterns, in regard to creative efforts.

There are many ways in which this can be done, and given the failures of the current way in which this is being done now (2013), and presented in very narrow contexts by the propaganda system, this should be a prevalent activity for rational thought, which is trying to identify a "precisely described truth" which is accurate and possesses practically useful capabilities.

While journalists are all about elitism and inequality, and narrow expressions of truth.
Publication controlled by journalists and editors (or based on peer-review, remember peer-review cannot review new ideas) is all about indoctrinated people who express the institutional elitism, which is defined by the powerful, where elitism defined within the narrow context determined by the blinders which they (ie those serving the powerful as wage-slaves) have had fixed to their eyes, or to their vision, which requires that they see a narrow institutional truth.

Though C Hedges is one of the more independent journalists, yet, he cannot see the failing of society as a failing of the experts, ie a failing due to the narrowness of the indoctrination and reward system of society. He essentially believes the "security argument," which is an argument for tradition, and established authority, and fixed ways of doing things, where if one does not follow such a conservative path then one will end-up with chaos and unnecessary destruction, a conservative path which acquiesces to wage-slavery and the attachment of blinders so as to keep our focus narrow and safe. That is, the great intellectual achievements of our society must be made secure.
Even seemingly courageous journalists, and, apparently, whistle-blowers too, are so well indoctrinated, so as to serve the failing (so called) "institutional truths" where these "unquestionable truths" are the, so called, "truths" expressed by the illusional-icons of the intellectual illuminati, ie the indoctrination (of those who serve the moneyed-interests) is a deep belief in inequality and a belief-in a rigged word-game, which is supposed to rigorously identify an absolute truth... , and one can be assured (as the propaganda system assures us all) it will be an authoritative truth.
There is a vague questioning of economics, politics, and the justice system but the illuminati, who express our deepest cultural truth, can not have their dogmatic truths or their intellectual capacities questioned.
Thus, the journalist is not assertive of their belief, rather they are authoritative in that they researched the established authorities so as to ascertain a truth about, which the sole voice of an authoritative truth of the media, is allowed to express, where that sole voice of truth is the propaganda system.
It is a "catch" in the endlessly repeating, and circularly-referential, propaganda system, which is allowed to trap what is supposed to be the voice of rationality... , but the well meaning journalist who seeks to provide truth... , instead espouses the greatest of illusions, where one of these illusions is a religiously-faithful belief in the authority of science.
Saying these words results in the readers "buttons being pushed," (this is a result of the deep control that the propaganda system has on everyone's ability to think) and as a result it needs to be stated that "this skepticism of science's authority is mainly because a better alternative 'mathematical model' is being presented," and it is not motivated so as to support either skepticism of global warming (the CO2 global-warming issue should have been settled back in 1900 with renewable energy sources) or to support creationism or creative-design ideas which are supported by groups of people who do not supply a valid alternative math model. Nonetheless Darwin's probability based model of evolution needs to be strongly criticized, since (1) the origins of life cannot be random, since life formed on earth almost as soon as the earth cooled, and (2) DNA cannot be put-together as hypothesized, apparently 90% of a living system's physical structure emerges (during embryonic development) from the properties of the epi-genome.
On the other hand these new math models provide a new context within which to view life and how the epi-genome might work.
The, so called, "truthful" journalist only supports (or reports on) institutional truths.
But institutions always (or also) provide, in hidden ways, red-herrings (deceptions) about the nature of their (the institutions'), so called, truths, so the focus becomes about the red-herrings, and not about the very questionable validity of institutional truths, which are provided by university departments of, so called, public institutions, whereas a university-department's "truth" serves the interests of the ruling-class, not the creative interests (or the creative capacities) of the public (where creative capacity is expanded by, equal free-inquiry).
Similarly, all ideas, associated to organizations, which are, identified as being against the interests of the ruling-class, are attacked by the justice department, and subsequently these attacks are legalized by the political structure, ie or equivalently the propaganda structure (that is, the social function of the political system is to serve as a well paid-cog in the propaganda system, and the function of journalism seems to be that of uncovering injustices so the politicians can re-write the law so as to make these injustices legal).

One cannot live in a sustainable manner where society is based on property rights and minority rule, this leads to selfishness, violence, and destruction
Rather
Law must be based on equality, where the context is each person is an equal creator.
That is, human-value is about creativity.
That is, value is not to be based on the ownership of material property, nor based on scarce material-types.
The material of the earth must be used in ways which are harmonious with the earth's structure.
The market is about the gifts which human creativity provides to society, and to the earth.
The market needs constraints in regard to advertising, and the large-scale of the creative efforts, and the subsequent over-use of certain types of material, ie it needs constraints based on curtailing domination and control. Etc.

But essentially "anything can be done to the public within today's society," as it is constantly demonstrated in the news, provided that one:
uses extreme violence, and
the media announces the changes and
the violent institutions of society enforce what is to be done (as it was announced, in a way which is consistent with the communication-political-propaganda channels of society).

However:

In science there is the need to develop (new) ideas in an intuitive manner (not in an overly authoritative, and overly formal axiomatic structure), and one wants many different ideas to be expressed, so that they are different, and they challenge the accepted dogma about science expressions, ie expressions which also have great limitations as to what patterns, the (given) language being used, can express.
That is, one wants new language to be built based on new: assumptions, contexts, interpretations, purposes, ways of organizing language, and new ways to identify a containment-set.
The versatility of language needs to be exploited in regard to seeking new realms of creative actions, and this exists in a context of identifying:
What is one trying to do (what purpose)?
In what context?
and
How is that context to be contained and organized (by words and relationships)?
What observed property is to be re-interpreted?
Etc etc.

In physics one sees the containment set defined in
either
In a very narrow vision such as Einstein who believes materialism, and one must define material and its containing space, ie the material is defining the containing space, and all of physics properties are to be contained in this metric-space with its open-closed topology and its metric-function signature being related to R(3,1), where 3 is the dimensional of the spatial subspace, and 1 is the dimension of the temporal subspace, so that R(3,1) is a (3 + 1) = 4 , ie a 4-dimensional metric-space. Furthermore, along with the measures for material quantities all the physical properties are related to local measures of the given property so as to be locally measured in the function's domain space, where the physical-property of the material system is represented as a function, and this is assumed to be able to identify and determine all of the system's physical properties if the local measured properties satisfy the physical laws, because the system is contained in the domain space where the domain space is a metric-space. Furthermore, Einstein wants to unify all the forces associated to the different materials into one expression for force so that this is based on covariant invariance for arbitrary changes in coordinate motions so that all force fields can be related to the distortion of the shape of space and the subsequent geodesic structures on this shape geodesics which are supposed to define inertial properties.
or
In a very broad vision about physics, expressed in quantum-physics and particle- physics, where the system is basically random (so it is modeled as a function-space of harmonic-functions oscillating about a geometric structure of a system's energy, ie the potential energy term) but the system defines a set of discrete spectral-values, where these values can be related to particular operators, and so that the system's properties are represented as a set of operators (a complete set of commutative Hermitian operators) which act on the quantum system's function-space of harmonic-functions, where the function-space is complex-valued, and "the" Hermitian-form-operator (defined on the function-space) is invariant to unitary operators, where for Hermitian operator, H, then e^iHt is a unitary operator, and where (so that) the Hermitian-form, along with commutativity, is used to separate (or identify) the spectral functions of the system's function-space, and thus, the unitary operators preserves the spectral-structure of the system's function-space, where completeness allows convergence to all spectral (or energy) states.
But then the quantum system (or any material system) is assumed to reduce to a finite-set of elementary-particles, which have internal particle-states associated to different energy-properties, so that wave-function is provided with an internal particle-state structure, and all quantum-material-interactions are modeled as particle-collisions, where the internal particle-states of the colliding particles are always changing, ie locally the particle-states are moving between different (particle) energy-values, apparently, due to the collisions. This is supposed to perturb the wave-function, which is a sum of the set of spectral-functions, where the particle-state operators (which change the internal-particle-states) are (non-linear) connections (or derivatives), which act on the particle-states of the quantum-system's wave-function, so that in the perturbation the wave-function is summed over all such particle-state changes, ie apparently for a lot of particle-collisions as a part of the material interactions.
But such a containment set has
1. many different local vector-space structures associated to the physical system in regard to the interaction fiber factor-group, U(1) x SU(2) x SU(3), and
2. the wave-function is no longer defined on a smooth containing metric-space, but space breaks-down around particle-collisions (apparently, allowing for all the different particle-collision adjustments in the perturbation sum) ie the continuum (upon which the wave-function's smooth structures depend) breaks-down, and
3. it is a random basis for the local particle-spectral events so the particle-collision geometry also breaks-down, eg due to an uncertainty principle which is always associated to a random basis for description.
That is there are several local space structures, not simply the metric-space, which is defined by materialism, and furthermore, the continuum loses its properties, so convergence loses its defining context, the geometry of a particle-collision cannot fit into a random context used for the descriptive basis, and there is not any notion that the interacting material quantum-system has any valid structure for containment, rather it is a set of different math constructs applied for the convenience of identifying certain math patterns (or to use certain math structures) and then abandoning these structures (in another stage or) in the next step of (in) the interaction descriptive sequence.
That is, in quantum description, there is a set of separate-islands of math structures, which apply when one is within any of the (different) particular island, but which are not relevant on the next island, in the, apparent, island-jumping sequence of descriptive constructs, which are associated to describing the quantum-model of material interactions.
Thus, it is incomprehensible.
But, apparently, the cohesion of this descriptive structure is claimed to be resulting from the "axiomatic formalism of mathematics," and thus, the patterns are not stable, eg non-linear changes of particle-states, and the quantitative structures are not consistent eg the smooth wave-function and the break-down of the continuum for point-particle collisions, but, it is claimed that this is OK, within each formalized context of math.
Furthermore, this is a perturbation process used to adjust, slightly, the energy-values of the system's spectrum. But, in regard to the wide array of many different quantum systems, the wave-function for general, many-but-few-component quantum systems cannot be found. Thus, this is all about completely indefinable randomness, and it simply does not work for a wide enough range of stable systems, which are observed.

That is, consider the many fundamental and very stable quantum systems: nuclei, general atoms, molecules, molecular shapes, crystals, and then the macroscopic systems of classical physics or of general relativity, namely, the stable solar system, and then there are the very stable and highly controllable living systems. The properties of these systems are not being described to sufficient generality and with sufficient precision and to a level where this information has practically useful value, so as to be based on the, so called, laws of physics, as these, so called, laws are now being expressed in the propaganda based "set of institutional truths."

Perhaps, all material systems do not reduce to elementary-particles, and perhaps randomness is not the basic property upon which to base a description of material systems which possess stable properties.

Perhaps materialism is also wrong.

Perhaps the geometry of material systems defined within the assumed to be material containing metric-space is not capable of describing the observed order of the many-but-few-body solar-system, or the order and control which are possessed by living systems.

Perhaps it is not sets of operators which represent physical properties but rather it is sets of different dimension and different metric-function signature metric-spaces which represent the physical properties as well as the materials which exist and which are the parts of the properties of a stable system composed of different materials.


The containment space for existence is the main structure upon which the observed stable order of the most fundamental physical systems depend.
These fundamental stable systems are: charges, nuclei, general atoms, molecules, crystals, closed thermal systems solar-systems and apparently the closed stable motions of material within galaxies and the motions of entire galaxies.
The new containment set is characterized by:
1. its high-dimension, relative to the dimension defined by the idea of materialism,
and
2. by the different dimensional levels being determined by stable hyperbolic metric-space shapes (see below).
The observed order of material systems are derived from the set of stable shapes, which are a part of the containment space, and it is also based on these stable shapes being contained in a many-dimensional context.

The idea of materialism defines a topologically open-closed material containing metric-space (or metric-spaces), so as to be based on only one metric-space with a metric-function which has a particular signature, with one fixed dimension... , though there is some latitude in regard to the two metric-spaces R(3,0) 3-dimensional Euclidean space and R(3,1) where R(3,1) is a 4-dimensional space-time metric-space... , so that there are
either
force-fields based on material geometry
or
randomness modeled as complex-valued wave-functions, where these functions have a space-time domain space, ie materialism is maintained, so that the definite spectral-values for quantum systems are to be related to sets of operators, specifically the energy-operator... ,
where the assumption of randomness was a result of seeing the random events of particle-spectral values identified at single-points of such random events found in space-time
... , then it was believed that all of material systems could be reduced to elementary-particles.
Then, when trying to identify material interactions for quantum systems, based on the reduction of material to elementary-particles, the idea of "hidden" particle-state was developed, to be used to describe material interactions for quantum systems... ,
where it is assumed that the basic wave-function for the system can be found, ie harmonic waves oscillating about the system's locally measurable average energy-operator (or oscillating about the system's potential energy term).
Unfortunately, this is far from being true.
That is, these models of quantum interactions are defined in the random context of quantum descriptions, ie the uncertainty principle applies, but the model depends on point-particle collision geometry, a model which is incompatible with randomness.
Nonetheless, with each collision there is an associated set of changes of each particle's internal particle-state, which reflects the range of energy of the system and the energy of the particle-collisions, so that different internal particle-states are activated by different energy-ranges.
This is a model... ,
in which neither the geometry of particle-collisions, nor the discrete random energy changes of the internal particle-states, are consistent with the quantum system's smooth wave-function, which represents the random basis for quantum description, and an associated set of discrete energy (or spectral) values associated to the function-space's spectral decomposition by the set of operators, where these random, discrete energy-particle events are observed for the quantum system being described,
... , in which the notion of the containment of such a quantum system in a metric-space, which possesses the properties of a continuum, which, in turn, is needed to define its smooth wave-function, are obliterated.
That is,
either
(1) the construct of "randomness with the geometry of particle-collisions"
or
(2) the churning-energy-changes associated to changes of internal particle-states, and an apparently ever-present set of virtual particle-collisions associated to these changes in internal particle-states,
... , are two "math" constructs, which obliterate the continuum upon which the smooth structure of a quantum -system's wave-function depends. But, furthermore, it is the structure of the smooth wave-function upon which the assumed wave-function's internal particle-states act in a manner which is supposedly a set of perturbing agents.
Thus, it is very difficult to comprehend, or to see, any valid content in such a description of particle-physics, or likewise, it is difficult to conceive that any physical construct, which is derived from particle-physics, can possess any content... , such as string theory, etc.

Where are the rigorous descriptions, based on the laws of physics, which describe to sufficient precision the spectra, of the entire range of all quantum systems in the following short list of: nuclei, general atoms, molecules etc?

The idea of defining a material-system's observed stable measurable patterns based on material interactions so as to be defined,
either
in a metric-space which possesses the properties of a continuum (either the wave-function, or classical material geometries),
or
(following quantum description) acting on energy-levels based on the collisions of elementary-particles,
... , is a description of particle-properties which defies attempts to make such an idea fit into a mathematical context.
Both of these math models of physical systems are ideas which "have not worked," based on either geometry or the pair of associated ideas of randomness and reduction to elementary-particle collisions, but where internal particle-states must conform to materialism, by requiring that particle-events stay inside an "assumed to exist" system-containing metric-space.
That is, it "has not worked," since the stable precise spectral-orbital properties of material-systems cannot be described (or identified) in a context of either geometry or random-waves (which have been reduced to particle-collision-determined particle-states).

Try some new ideas (let us have a scientific revolution, the very type of thinking which the public is indoctrinated against pursuing)

On the other hand partitioning an 11-dimensional hyperbolic metric-space by a dimensional-subspace-size determined partition, which is composed of stable shapes, where each dimensional level and each subspace (of any given dimensional level) has a largest shape, so that all the other shapes must be in resonance with the spectral values of some largest hyperbolic metric-space shape defined in the partition. In such a context there is, thus, a set of set-containment-trees, defined in the 11-dimensional hyperbolic metric-space, where these trees depend on the dimension-subspace-size properties of the shapes of the partition, which are associated to the spectra of the partition.
The order of material systems is
either
due to condensed material following the stable orbit structures defined by the shape of the material containing metric-space shape within which the condensed material is contained, but these orbits can be perturbed by the second order dynamics defined on the condensed material, which is contained in the metric-space, ie perturbed by the usual material-interaction models of classical physics (or by general relativity, but the context of general relativity is now contained in a linear, solvable shape).
or
are a result of component-collisions defined by second order dynamic equations, in turn, defined in the metric-space, but so that during such component collisions (which are also defined within a compatible energy-range, so that) there is defined a resonance between the colliding component-complex and the finite spectral-set defined by the spectrally partitioned 11-dimensional over-all containing metric-space, so that the colliding component complex re-forms into a new stable material component, which is in resonance with the finite-spectra of the over-all containing space.

The new model of material and of material interactions depends on new types of discretely defined operators, so as to be defined on discrete time-intervals (which separate opposite metric-space states) and discretely defined between different metric-space shapes, and between different dimensions (and/or dimensional levels), so this discrete-operator descriptive context has a mixture of:
1. metric-space states,
2. shapes,
3. discrete action-at-a-distance interaction geometric structures, and
4. there are also new physical properties and associated new materials,
where the basic physical properties are not operators, as in quantum physics, but rather the physical properties are determined by the presence of metric-space types, which, in turn, are determined by the metric-space's spatial-subspace dimension and the metric-space's metric-function signature, where the full identification of each different metric-space also determines different physical properties which can be associated to both physical systems and their interactions. Furthermore, the sets of opposite metric-space states (each defined by a metric-space's associated physical property) determine discrete time-intervals associated to the (new) discrete math structures of material interactions.