Categorical analysis

Oct 3, 2022
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In this paper there will be discussed a re-imagination of logical categorization, based on modern data from quantum physics for the reason of obviating the limitations, paradoxes, and arbitrary parameters found to characterize a said physical reality. If you are unfamiliar with categories: category, in logic, is a term used to denote the several most general, or highest types of thought forms or entities, or to denote any distinction such that, if a form or entity belonging to one category is substituted into a statement in place of one belonging to another, a nonsensical assertion must result.
Categorization shaped classical logic, which shaped mathematical logic, which shaped the scientific method, which in turn shaped the development of classical and quantum mechanics.
The discourse is developed into a new form of mathematical logic, and form of set theory that is corrective of the shortfalls above-mentioned.
This reconceptualization will be called compositive logic.
The theory proposes that reality is an ob-reciprocal reference.
In the most general sense, that means that reality is of no reciprocal condition, or put in other terms- reality does not compartmentally express itself, and thus elements, making the substantive aspect of reality an indicative relation, and not absolute.
Reality as a totality in itself cannot have a precursor nor any external initiative, or initiation, because it itself encapsulates everythingness, thus objective reality shouldn't have specified characteristics, which are delimitations, suggestive of an external entity, or pre-generative entity, or inexplicable spontaneous internal function.
It will be demonstrated that the foundation of formal, and informal logic has a categorizational incompleteness, and issues of contradictions and paradoxes, consequently arising in the theories of math, classical, and quantum mechanics.
Not being privied to the now standard quantum mechanical data is being proposed as a fundamental negation that blocked pre-classical thinkers from forming sufficiently complex general parameters for the construction of the sentient reciprocal order, or in other terms- an accurate definition of categories that requires experimentally testable findings about the Planck scales of the universe and Planck epoch to be a part of the perspective.




The following three excerpts that are cited from the website Wikipedia.org contain information that has been externally fact checked:

" the Planck scale is an energy scale around 1.22×1019 GeV (the Planck energy, corresponding to the energy equivalent of the Planck mass, 2.17645×10−8 kg) at which quantum effects of gravity become strong. At this scale, present descriptions and theories of sub-atomic particle interactions in terms of quantum field theory break down and become inadequate, due to the impact of the apparent non-renormalizability of gravity within current theories."

Excerpt 2:

"At the Planck length scale, the strength of gravity is expected to become comparable with the other forces, and it is theorized that all the fundamental forces are unified at that scale, but the exact mechanism of this unification remains unknown. The Planck scale is therefore the point where the effects of quantum gravity can no longer be ignored in other fundamental interactions, where current calculations and approaches begin to break down, and a means to take account of its impact is necessary. On these grounds, it has been speculated that it may be an approximate lower limit at which a black hole could be formed by collapse. While physicists have a fairly good understanding of the other fundamental interactions of forces on the quantum level, gravity is problematic, and cannot be integrated with quantum mechanics at very high energies using the usual framework of quantum field theory. At lesser energy levels it is usually ignored, while for energies approaching or exceeding the Planck scale, a new theory of quantum gravity is necessary. Approaches to this problem include string theory and M-theory, loop quantum gravity, noncommutative geometry, and causal set theory."

Excerpt 3:

"In Big Bang cosmology, the Planck epoch or Planck era is the earliest stage of the Big Bang, before the time passed was equal to the Planck time, tP, or approximately 10 to the negative 43 seconds. There is no currently available physical theory to describe such short times, and it is not clear in what sense the concept of time is meaningful for values smaller than the Planck time. It is generally assumed that quantum effects of gravity dominate physical interactions at this time scale. At this scale, the unified force of the Standard Model is assumed to be unified with gravitation."

Here we have a synopsis of two universal extremes
and not merely the quantum universe, as the largest scales of the universe is where the universe from the Planck time is said to be right now, demarking physically in consistent examples, where our physical premises break down because of our physical incapacity, whether as measurement, or experiential incapacity in the case of the Planck epoch, where light (an aspect of physical reality described by theories invariably stemming from the faux categorizations of classical logic), from that early in the universe's so-called emergence will never reach us.
If we look at the universe from the perspective of its demonstrated structural limits, physical reality is assertable as a literal finite domain, containing all the physical outcomes possible.
However, where there are definable limits demarking where the dynamics of physical reality no longer apply, it does not explicate an imperative of negation of other possible domains, as physical reality, as a domain, contains strictly physical outcomes in accordance with the exclusive categorization.

Let x=x be equivalent to a domain characterized by the totality of all possible functions and transformations categorizable as physical: with our assertion of x=x being true, we discover that the domain x=x does not express that x=p.
The fact that x=x does not express x=p, for no aspect of x=p is containing in domain x=x, does not mean that x=p does not exist, in fact, as x=x can be defined as finite under the above-mentioned definition, there is no account for the structural exclusion of x=p that is consisting as domain x=x, for domain x=x is inherently and absolutely expressing domain x=x only ( as far as quantum mechanics go there has never been a non-physical outcome and will never be a non-physical outcome), which is a different categorical imperative from the exclusion of potential domain x=p, thus the non-existence of x=p as a domain is not proven by the expressions of x=x.
It has been established that x=x represents the consisting potential of physical reality; and it has been established also that the domain of x=x is both noninclusional and nonnegational of a domain x=p, which represents a single consisting potential other than x=x. There is also a noninclusion of x=o, =t, =5, x=s,.....n.

X=x and x=p are non-interdependent imperatives, based on the fact that x=x intrinsically excludes x=p, and x=p intrinsically excludes x=x, and that the intrinsic exclusion is not specific to x=p, or x=x but to all potential domains .
From the definition above we can assert a structural continuum that is not defined in the conditions of the superimposed domains, as they are superimpositions that are in themselves fine-tuned, thus demonstrating an adherence to a specifying context.
Ultimate reality cannot be an element, or a set type of universality as any such specification requires a specifier.
Reality, in its absolutely logical form, cannot be an expression of any kind, as this is fine-tuning, that domains the expression as a categorical domain that does not actively exclude the existence of external domains.



Reality is logically non-referential, and the tangibility that we associate with physical reality is not "in the expression of" a beingness
(beingness is defined by physical reality's quantitative standards when we see it as a domain that simply just is, without proper categorization).

We can find non-referentiality by reduction of the quantum mechanic relativism that we experience in physical reality.
In the overarching domain that contains all superimpositions such as x=x, is characterized the non-interdependency of x=x and any given other domain such as x=p.
Superimpositionality is not describable within the local frameworks of finite domains themselves: they are not expressing of overarching dynamics in themselves. They seem absolutely local
Invariation of external domains, both in themselves as superimpositions, and as naturally extenuating domains, indicate a relativism that does not express the structural limitation of locality, just universalism, which without the usual physical reference of locality is something quite different from solely physical interpretations of an empty set.
The reduction of superimpositionality to non-referentiality sees the non-locality in superimpositionality prevariated by further non-localizational relativism, where now universality goes, the basic reference of quantitative coherence in relation to context excluding the opposite, is the said nonreferentiality that reality can be logical. It's not nothingness, however it's not as irrational as existency.
So we can see where non-referentiality covers all truly realistic outcomes and demonstrates through a determined reduction of Relativistic structural ethos, not only explication of all realistic participles, but also the de-relativistic subjectivization of all realistic participles, making the non-referentiality actual, in not being objectively expressing of intrinsic, or perturbed fine-tuning.


We can establish that applying substantive, elementary metrics to non-referentiality, basically making reality a materially existing location, must have the metrics somehow amount to a non-referentiality being true.

The elementary metrics being proposed must then be categorizable as basally referential, however, maintaining of non-referentiality.
The application of element metrics to nonreferentiality creates the least relativistic relationship.
The active de-gradualization from physical reality to nonreferentiality as a base logic system is the affirmation of nonreferentiality itself as a non-expression, as all extents involved are categorized within reality.
The most basic relativism is singularly universal, where elements are intrinsic property, thus of no particular demarcation. This is superimpositionality. Giving metrication to nonreferentiality equals to the sphere of superimpositionality, which, further metricated, results in local superimpositions, of all possible typologies, non-interdependent in nature on a level that represents a specific prevarication.
Further metrication invariates elements of superimposed domains, for instance, in physical reality, planets, space, time, forces, etc.
If we choose to element nonreferentiality like this we become capable of any typology of transformation graphed within the framework of a field theory.
The proposed field, consisting of these levels of relativism as sub-fields, hold all objects as defined with 4 basic values from the sub-fields:
1. Non-referentiality
2. Superimpositionality
3. Domains
4. Elements of domains

These values are of course general. They are simply significant points on a spectrum.
 
Jan 27, 2020
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The following might interest The Logical Arc:

An Introduction to the Theory of Gravity at the Planck Scale

January 2020


Authors:
Aloysius Sebastian at Aloys
Aloysius Sebastian


This is a theory which explains the basic nature of energy at the Planck scale. By starting from the very smallest possible units, we can have the fundamental nature of energy. Here I am considering Planck volume as the smallest space, which a unit Planck energy can accommodate perfectly. This system will not allow any empty space in it. So basically we can consider Planck energy and Planck volume as the same, with different units. With this concept we can relate the fundamental units of mass, time and length with the dimensional units of length, breadth and height. At this stage we can see that the gravity as the result of the work done by unit Planck energy in a unit Planck volume. This allows the system to spread its effects into outer space, and which will cause the curvature of spacetime.

This theory allows an object to obtain different strengths in its gravitational fields. It states that a gravitational system can have only a limited range. At a certain level, the distribution of its gravitational field will be zero. The curved spacetime of a gravitational system has a fixed volume. Increasing volume will decrease the strength of the field. By starting from the very smallest units, this theory allows to explain the nature of larger masses by adding energy in a system on the Planck scale. By considering mass as just a dimension of the energy, it says mass is one of the reasons for gravity.

This theory allows the quantization of length and time inside the Planck volume. So the total energy of the system will determine the gravity of a system. The volume of a system is not interfere directly with gravity, but it's Planck scale volume will determine the gravity of this system. It allows us to learn more about the dark energy and dark matter.

By quantizing time and length, this theory suggests the possibility of changing the dimensional arrangements of the system. Different dimensional configurations of a system will allow the system to show different properties. The character of a system will be determined by its dimensional configurations. So a system can obtain one of its many dimensional configurations at a time. This concept will allow the energy to be self consistent and conscious inside the Planck volume. Energy itself act as the source of life. So the probability of the existence of life on any part of our universe is very high.

As we know, matter (Energy) can exist in different sizes. It can be existing in an extremely small size and at a very large size. Here I am trying to know more about the properties of the extremely smallest possible forms of energy. In physics we are using the plank units to represent the smallest measurements. We can theoretically say that Planck Energy is the smallest form of energy present in the
universe.

Similarly, in particle physics we can see that particles exhibit different properties such as spin, charge, and everything. I am curious to know about the reasons of all these properties.

Here I would like to summarize the facts, which I have realized from such thoughts, about the physical world surrounding me. It is an introduction to my understandings about my surroundings. In physics, we are dividing the
concepts about our universe into two different fields, like microscopic and macroscopic and both of them explain us the incredible nature of our universe. The more we know about the universe, the more we can see new questions arise. This is just the beginning of my journey, to discover the secrets that the universe hides in its beauty.

The General Theory of Relativity is the best for understanding the visible universe. And it is explains the mysterious phenomenon which we call gravity. The General Theory of Relativity can accurately describe all the fascinating puzzles hiding in the visible universe. Albert Einstein presented his theory with all its charms. He revealed to us a series of realities that were never intended to correspond to common sense, and which would change our imaginations. Still we are searching for a theory of gravity, concerning on the microscopic universe, which can describe the entire properties of energy and by the whole universe, by itself. Thus, our knowledge of the phenomenon of gravity is incomplete. Einstein's theory deals with the large scales yet are unable to find a way to import this theory to the increasingly smaller scales. That is why we need to think about Quantum gravity. Science has been searching for a Theory of Quantum Gravity for a long time.

In my opinion, such a theory should be based on plank units. It is best to formulate an idea from the smallest possible scenario. In this situation, an object can show its fundamental properties only. If we were to understand the nature of energy at the Planck level, it would contain the basic properties of energy under any conditions. All the theories we have today, support the idea that gravity is due to the mass of an object. Yet, by the equivalency principle, we know that mass is also a form of energy. We do not consider that a photon has mass, but it does interact with gravity. In my opinion, the gravity of an object is not dependent on its mass, it is dependent on its energy.

My theory is based on a geometrical structure, and how the dimensions are play in it to change the nature of the system.

This paper is an introduction of my ideas about our universe in both microscopic and macroscopic scales. So it can explain the quantum world and visible universe at the same time, because I am starting to elaborate my ideas from the very smallest scales. (grammar corrected by Hartmann352)

See: https://www.researchgate.net/publication/338595047_An_Introduction_to_the_Theory_of_Gravity_at_the_Planck_Scale

Planck Gravitation Theory
October 2019
DOI:10.31219/osf.io/6zxq2
Planck gravity theory
Authors: Li Xiao Lin

The author proposes a new gravitation theory, the Planck gravitation theory. The theoretical name is in honor of Planck proposing the Planck Length. Gravitation is a force in 4-dimensional space, or a force in 5-dimensional space-time. Every quantum particle produces gravitation.

Gravitation is not actually related to the mass of particles. Every quantum particle produces the same gravitation, regardless of the type of particle. The origin of gravitation is quantum, and gravitation is a quantum force. In 4-dimensional space, gravitation is inversely proportional to the cubic of distance, not square of distance.

The strength of gravitation is entirely determined by the Planck Length. The Planck Length is the identification constant of gravitation. The author's earlier projection gravitation theory is only a derivation of the Planck gravitation theory. From the theory, we deduce the gravitation of photons.

Planck gravitation is separated into two different patterns in 3-simensional space. For particles with rest mass, Planck gravitation translates into projection gravitation, which is inversely proportional to the square of distance. For particles with zero rest mass, gravitation is inversely proportional to the cubic of distance. Every quantum particle is an empty hole in space, the radius of empty hole is Planck Length. This brings the effect of the quantization of space-time.

Planck gravitation theory can solve the problem of ultraviolet divergence in quantum field theory without the need for renormalization. If the Planck gravitation theory is true, human need to rethink the gravitation, and need to rethink the way of gravitation quantization. The author finally discusses the projection action, it is the key to human understanding of the truth about gravitation.

From the projection gravitation theory, we can derive a lot of meaningful results. The projection gravitation theory is an independent and rational theory of gravity. More importantly, the principle of projection gravity theory is
fully consistent with quantum mechanics, and the derivation of black hole entropy is based on quantum mechanics. There is no contradiction between projection gravitation theory and quantum mechanics. The projection gravitation theory is a self-contained theory of quantum gravity.

However, in projection gravitation theory, there are two
big problems that have not been solved.

(1). Since gravitation is a projection force from 4-
dimensional space into 3-dimensional space, so what
properties does gravitation have in 4-dimensional space?

(2). In the projection gravitation theory, the author
thinks that only rest mass can produce gravitation, and
particles without rest mass do not produce gravitation.
Photons do not produce gravitation, not a source of
gravity. Is this conclusion correct? What is the gravity
produced by photons?

In the study of these two problems, the authors propose
a more basic theory of gravitation. The authors find that
gravitation exists in 4-dimensional space. Gravitation is
purely a quantum effect. Gravitation itself actually comes
from quantum. The projection gravitation theory is also
the result of this new gravitation theory. This new
gravitation theory is the real basic theory of gravitation.
And this new gravitation theory provides a clear answer to
these two questions.

See: https://www.researchgate.net/publication/336860748_Planck_Gravitation_Theory

Planck gravitation theory has a special property similar to the quantization of space. A Planck gravitation theory can give a maximum momentum, can solve the problem of ultraviolet divergence in quantum field theory from the principle without the need for artificial renormalization. Planck gravitation theory may, therefore, lead to the black hole entropy formula.
Hartmann352




 
Mar 4, 2020
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Reality involves much more than physicality. In truth, reality is a common ignorance, composed of individually created ignorance's. This is so because no one has ever had a clue of what physicality really is, and therefore, the concept is individual. It starts in infancy and stops when you do.

No one can prove what mass is, not yet. Not even a narrative. We only measure how it reacts to stimulus, not determine what mass is. Present physical reality, physicality, is the only common reality.

Particle energy is in quantum steps. This means particle mass is in quantum steps. Mass, what ever it is, can be added and subtracted. This means physical size changes, in quantum steps. We are not use to this dynamic in our macro-world. And that the amount of E field density changes in quantum steps, while maintaining a constant amount of E field. Also the spin RPM of the particle changes in quantum steps.....while maintaining a constant angular velocity......we are not use to that either.

Almost everything about mass, remains unknown.

And if gravity is a fundamental property, why do charge particles continuously accelerate for weeks at a time away from gravity wells, like stars? It seems that stars break down gravitational matter and emit non-gravitational matter. It seems that symmetrical inertia is immune to gravity.
 
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Hayseed

This might be of interest on explaining gravity wells...

earth's gravity well.png
Depiction of Earth’s Gravity Well

A gravity well is a term used metaphorically to describe the gravitational pull that a large body exerts in space. The more mass that the body has, the deeper the gravity well. For our solar system, this means the Sun has the deepest gravity well, followed by Jupiter, Saturn, etc. The term “well” is used to describe the shape of the curve created by the gravitational potential of a body (see above image). The deeper the well, the more energy that a mass must have in order to leave the gravitational pull of the large body.

One method to help visualize a gravity well is representing space as a stretched out mesh fabric. You can lay a heavy ball on the mesh (simulates large body in space) to stretch out the “fabric of space.” The mesh stretching represents your gravity well. The heavier the ball you place, the deeper the gravity well it produces. To visualize this concept further, you can place a smaller ball on the mesh, and it will roll to the larger mass, simulating the larger mass’ gravitational pull. If you give the smaller ball a push, the ball will simulate an orbit around the larger ball (eventually the smaller ball will drop to the larger ball due to friction).

By now, we know the depth of the well is determined by the amount of mass a body has, but how do we visualize the mesh stretching? The gravity well can be depicted by calculating the gravitational potential that the body has. The gravitational potential, V, of a body is defined as the gravitational potential energy, U, (from Newton’s law of gravitation) per unit mass. The gravitational potential is described by the following equation:



In this equation, M is the mass of the large body, m is the mass of a small body, G is the universal gravitational constant, and r is the distance from the center of the large body to the smaller body. The distance, r, determines the gravitational potential and, in turn, the gravitational potential energy that the smaller mass has. Using this equation for Earth, we get the following gravity well, which describes the amount of energy a mass must overcome to escape Earth at a certain distance away from the center of the Earth.

earth's potential gravity.png
Depiction of Earth’s Gravity Well

The black ring in this picture represents the surface of the Earth. Every point above the black ring is above the Earth’s surface. You might still be wondering how this diagram or gravitational potential is useful. Think about this. Let’s say you wanted to know how to leave the surface of a planet and fly into an orbit (something we do regularly) or you want to completely escape the pull of gravity of a planet or moon. The gravity well is an excellent visual of the energy required to pull it off. Consider the total energy (potential and kinetic energies combined) of a rocket with mass, m.



In order to determine what velocity is required to escape a planet’s gravitational pull, we can set the total energy equal to zero, or kinetic energy equal to the potential energy. By doing this, we can determine what kinetic energy is required to overcome the gravitational pull at a certain distance, r, from the larger mass’ center. Then, if we solve for the velocity, that will give us the required velocity to escape the gravitational pull of a body, or the escape velocity.



For example, if we were trying to escape Earth’s gravitational pull from the surface of the planet, we would calculate the escape velocity by using Earth’s mass and the radius of the Earth in the equation above.



From this result, it would take an object moving at about 11.18 km/s to escape Earth’s gravitational pull from Earth’s surface. The result does not take into consideration atmospheric drag, but the concept remains. If you were working to determine what kind of rocket you need to leave the Earth, you could start with this rough calculation to determine a target velocity required for such a mission.

Similar to the gravity well, an escape velocity mesh can be developed to show the velocity required to escape a planet’s gravitational pull given the distance from the planet. The mesh below represents the escape velocities required to leave Earth’s gravitational pull. Again, the black circle here represents the surface of the Earth. Every point below the black ring is above the Earth’s surface.


Depiction of Earth Escape Velocities

While gravitational wells are not actually shaped like a well, they are an interesting way to visualize the energy required to escape the pull of a planet, star, or even black hole. Using the potential energy, the required escape velocity can be calculated, giving you a rough estimate of the rocket size you need for a mission.

What the Hawking hypothesis postulates is that sometimes a massless particle-antiparticle pair (picture a photon/antiphoton pair) can spontaneously come into existence outside the event horizon of black hole due to local vacuum fluctuations.

What supposedly happens next is that the negatively charged antiparticle immediately falls into the black hole, while the positively charged particle is propelled away.

The fact of having absorbed a particle with negative charge lowers the total energy of the black hole. This in turn, through the equivalence of energy and mass, lowers the mass of the black hole as well.

You may already have noticed the key point here, which is that even if Hawking radiation does exist and works as predicted, it does not involve any matter or energy crossing the event horizon in an outward direction. Quite the opposite in fact: it is a prediction that something negative is crossing inward.

So to address this to the question, it means that no particle is escaping from inside the black hole’s event horizon. Even the positively charged half of the pair, which supposedly does escape, doesn’t do so from within the horizon, since it only sprang into existence outside and had never passed beyond the event horizon.

The Hawking hypothesis itself is built on a rather shaky foundation, scientifically speaking. For starters, in order to get the math to resolve at all, Hawking was forced to violate the Planck length in regards to the wavelength of the infalling antiparticle. In addition, Hawking himself could never decide firmly whether or not it violated causality. He reversed himself twice on that question before finally saying that he could not resolve the question, a rather courageous bit of intellectual honesty for a man speaking about perhaps the most famous piece of theoretical work he ever published.

The upshot of all this is that you should not act as if Hawking radiation, or energy escaping from a black hole via the negative impact of virtual particle energy, is real until some evidence comes in supporting its existence. Hypotheses are not something you want to use as the basis for any scientific conclusions. And in this case the hypothesis does not even imply what most people assume it does, i.e. that something can directly cross a black hole’s event horizon in an outward direction.

gravity wells 3.png
This doesn't take into account the energy imparted by orbital motion (or gravity assists or the Oberth effect), all of which can make it easier to reach outer planets.

Escaping a planet or moon's orbit requires enough energy (e.g. by walking, jumping, or rocket) to reach the top of either peak that defines the edge of the well. The peak to the left indicates the minimum energy required to exit orbit. The peak to the right indicates the maximum energy required to exit orbit. In order to exit orbit with the minimum amount of energy, you would have to travel towards the center of the solar system; to exit orbit with the maximum amount of energy, you would have to travel away from the center of the solar system (the Sun). In reality, the strength of gravity decreases with distance from the planet. However, a comparison of energy expended to escape the gravitational pull allows for a simpler comparison between the objects.

The height of the graph is scaled to kilometers via the gravitational potential an object has at the given height assuming at a constant acceleration due to Earth's surface gravity. The Sun's gravity well is not shown in its entirety, but is just indicated on the far left as "Very very far down". Had it been shown in its full extent it would have made the rest of the drawing so small in comparison that it would have been unreadable. As the gravitational potential increases with distance from the sun, the graph has a general upward slope. To rise out of each well on the diagram, and therefore escape the planet's gravity, it would require the same energy required to rise out of a physical well of that depth at Earth's surface gravity.

The length of each gravity well is scaled to the diameter of the planet and the spacing between the planets is not to scale with distance from the sun. This is necessary to make the graph readable. Because the distances between the planets are condensed, the gravitational potential - from the gravity pulling toward the sun - accumulates quicker. This is the reason for the large peaks between the planets. The moons shown in the chart are at the appropriate distance from their respective planets' gravity wells for their orbits.

Escaping a planet or moon's orbit requires enough energy (e.g. by walking, jumping, or rocket) to reach the top of either peak that defines the edge of the well. The peak to the left indicates the minimum energy required to exit orbit. The peak to the right indicates the maximum energy required to exit orbit. In order to exit orbit with the minimum amount of energy, you would have to travel towards the center of the solar system; to exit orbit with the maximum amount of energy, you would have to travel away from the center of the solar system (the Sun). In reality, the strength of gravity decreases with distance from the planet. However, a comparison of energy expended to escape the gravitational pull allows for a simpler comparison between the objects.

The height of the graph is scaled to kilometers via the gravitational potential an object has at the given height assuming at a constant acceleration due to Earth's surface gravity. The Sun's gravity well is not shown in its entirety, but is just indicated on the far left as "Very very far down". Had it been shown in its full extent it would have made the rest of the drawing so small in comparison that it would have been unreadable. As the gravitational potential increases with distance from the sun, the graph has a general upward slope. To rise out of each well on the diagram, and therefore escape the planet's gravity, it would require the same energy required to rise out of a physical well of that depth at Earth's surface gravity.

The length of each gravity well is scaled to the diameter of the planet and the spacing between the planets is not to scale with distance from the sun. This is necessary to make the graph readable. Because the distances between the planets are condensed, the gravitational potential - from the gravity pulling toward the sun - accumulates quicker. This is the reason for the large peaks between the planets. The moons shown in the chart are at the appropriate distance from their respective planets' gravity wells for their orbits.

See: https://medium.com/intuition/what-are-gravity-wells-3c1fb6d6d44c

See: https://www.quora.com/How-can-particles-escape-blackholes-gravity-after-escaping-it-through-Hawkings-radiation?share=1

See: https://www.explainxkcd.com/wiki/index.php/681:_Gravity_Wells

According to Diogo Ricardo da Costa,1 Carl P. Dettmann,2 and Edson D. Leonel
in their paper "Escape of particles in a time-dependent potential well":
The escape of an ensemble of noninteracting particles from inside an infinite potential box that contains a time-dependent potential well and the dynamics of each particle are described by a two-dimensional nonlinear area-preserving mapping for the variables energy and time, leading to a mixed phase space. The chaotic sea in the phase space surrounds periodic islands and is limited by a set of invariant spanning curves. When a hole is introduced in the energy axis, the histogram of frequency for the escape of particles, which we observe to be scaling invariant, grows rapidly until it reaches a maximum and then decreases toward zero at sufficiently long times. A plot of the survival probability of a particle in the dynamics as function of time is observed to be exponential for short times, reaching a crossover time and turning to a slower-decay regime, due to sticky graviton metric regions observed in the phase space.
Hartmann352
 
Mar 4, 2020
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No thanks Mr. Hartmann352, I have no interest in modern narratives. Gravity is not an interaction between mass and spacetime. Gravity is between the masses alone, and comes from an unstable inertia.....or an asymmetric inertia, might better describe it.

Gravity does not exist with symmetric inertias. Such as isolated charge.

It's amazing to me that science explains gravity........without explaining inertia. But again, it's typical.

For years we've heard how inertia and gravity are related........but I guess they dropped that aspect about gravity. Convenient.

I can't wait for the new narrative of inertia.
 
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Hayseed - here are a few ideas on inertia which you might find of interest.

in·er·tia
1a: a property of matter by which it remains at rest or in uniform motion in the same straight line unless acted upon by some external force

b: an analogous property of other physical quantities (such as electricity)

2: indisposition to motion, exertion, or change : INERTNESS

See: https://www.merriam-webster.com/dictionary/inertia

The term 'inertia' comes from the Latin word 'iners', which translates to lazy or idle. Johannes Kepler coined the term. The meaning of inertia is related to the fixed characteristic of an object made of matter. Inertia is a quality found in all things made of matter that have mass. An object made of matter keeps doing what it is doing until there is a force that changes its speed or direction. A ball on a table will not start rolling unless someone or something pushes it. It is noteworthy that if you toss a ball in a frictionless vacuum space, the ball will keep moving at the same speed and direction forever unless there is some action created by gravity or collision.

The measure of inertia is mass. Objects with a greater mass resist a change in their motion or rest more than objects with lower mass. For example, moving a truck will require more forceful pushes. On the contrary, moving a bike will require less aggressive impulses. This difference in force is because the truck and bike have different masses. A truck has more significant inertia than that of a motorcycle.

The law of inertia is also known as Newton's First Law, it forms the basis of physics, it postulates that if an object is at rest or moving at a constant speed in a straight line will keep remaining at rest or will keep moving at the same speed unless it is acted upon by a force. This object will keep moving and less force or friction causes it to come to rest. The Law of inertia is the first law of the three laws of motion. This law was first experimented by Galileo Galilei and was later deduced by René Descartes.

We can define inertia as the property of an object by which it cannot change its state of rest along a straight line on its own unless acted upon by an external force. Inertia increases with an increase in the mass of the body and vice-versa. We experience a jerk while suddenly using the brakes of a moving car because of inertia.

Sir Isaac Newton utilised and expanded the principles shown in Galileo's observations into his first law of motion. He gathered that it requires force for a moving ball to stop rolling once it is in motion. It takes force to change the ball's speed and direction. In Newton's Principia Mathematica, he defined the Law of Inertia as "the motion of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forwards in a straight line without circular motion."

Thus, Newton's First Law of Motion asserts that an object will continue to be in the state of rest or a state of motion unless an external force acts on it.

Newton's Second Law of Motion defines the relationship between acceleration, force, and mass.

Newton's Third Law of Motion states that an equal force acts back on the original object any time a force acts from one thing to another. This law means that every action has an equal and opposite reaction. If you pull on a rope, therefore, the rope is pulling back on you as well.

Then Einstein told us that gravity and inertia are identical. And from the fact that two different masses fall at the same rate, I believe we can say that gravity and inertia are equal (That is, the inertia of a dropped larger mass is exactly sufficient to slow it’s acceleration to the same level as a dropped smaller mass, regardless of them being dropped on the Earth or on the Moon).

Einstein’s equates gravitational mass with inertial mass (in his principle of equivalence), but mostly simply because gravity and acceleration look like different phenomenon.

You could say that gravity and inertia are identical, and that the gravitational field and acceleration are inductive pairs (similar to the electromagnetic field and electric current.) A gravitational field induces acceleration, and acceleration induces a gravitational field.

From Einstein’s 1918 paper: On the Foundations of the General Theory of Relativity…

See: http://einsteinpapers.press.princeton.edu/vol7-trans/49

“Inertia and gravity are phenomena identical in nature.” - Albert Einstein

In a letter Einstein wrote in reply to Reichenbacher...

See: http://einsteinpapers.press.princeton.edu/vol7-trans/220

“I now turn to the objections against the relativistic theory of the gravitational field. Here, Herr Reichenbacher first of all forgets the decisive argument, namely, that the numerical equality of inertial and gravitational mass must be traced to an equality of essence. It is well known that the principle of equivalence accomplishes just that. He (like Herr Kottler) raises the objection against the principle of equivalence that gravitational fields for finite space-time domains in general cannot be transformed away. He fails to see that this is of no importance whatsoever.

What is important is only that one is justified at any instant and at will (depending upon the choice of a system of reference) to explain the mechanical behavior of a material point either by gravitation or by inertia. More is not needed; to achieve the essential equivalence of inertia and gravitation it is not necessary that the mechanical behavior of two or more masses must be explainable as a mere effect of inertia by the same choice of coordinates. After all, nobody denies, for example, that the theory of special relativity does justice to the nature of uniform motion, even though it cannot transform all acceleration-free bodies together to a state of rest by one and the same choice of coordinates.” - Albert Einstein

From Albert Einstein’s book: The Meaning of Relativity, pg 58

“…In fact, through this conception we arrive at the unity of the nature of inertia and gravitation. According to our way of looking at it, the same masses may appear to be either under the action of inertia alone (with respect to K) or under the combined action of inertia and gravitation (with respect to K’). The possibility of explaining the numerical equality of inertia and gravitation by the unity of their nature gives to the general theory of relativity, according to my conviction, such a superiority over the conceptions of classical mechanics, that all the difficulties encountered must be considered as small in comparison with the progress.” - Albert Einstein

Here and in other places Einstein specifically emphasizes the equivalence of gravity and inertia, and not merely the equivalence of gravitational and inertial mass.
… But is this where we are left hanging: that gravity and inertia are both identical and equal? Is gravity inertia? Or is inertia gravity?
Yes, that is kind of where we are left hanging.
What is the next step beyond saying that gravity and inertia are both identical and equal?
The next step would be in solving in greater detail the physics of inertia.

There are two distinct characteristics of a body - gravitational mass and inertial mass. The former measure's a body's "coupling strength" to a gravitational field as Newton conceived it - it measures the how much force a "standardized" gravitational field exerts on a body. The latter measures a body's "resistance to shove"; it measures how much impulse you need to impart to a body to change its velocity by a standardized amount. In more experimental terms: the former measures how much a body will stretch a spring balance when hung from the balance in a standardized gravitational field. The latter is to do with how quickly a body moves after it is shoved by a given standardized impulse shoving machine. On the face of it, these are very different experiments and two very different properties. And yet, bodies of different inertias fall at the same acceleration in a gravitational field. If this really is true, then the only way that this can happen is if the two different properties - inertial mass and gravitational mass - are precisely proportional to one another. We can then arrange our definitions so that the proportionality constant is unity and call the two equal. But the key result that allows this equality is proportionality, and the demonstration of proportionality was the result confirmed by the Eötvös experiment*.

See: https://physics.stackexchange.com/questions/390540/what-is-the-relationship-between-gravity-and-inertia

See: https://www.vedantu.com/physics/inertial-force

* Eötvös experiment was a famous physics experiment that measured the correlation between inertial mass and gravitational mass, demonstrating that the two were one and the same, something that had long been suspected but never demonstrated with the same accuracy. The earliest experiments were done by Isaac Newton (1642–1727) and improved upon by Friedrich Wilhelm Bessel (1784–1846).

A much more accurate experiment using a torsion balance was carried out by Loránd Eötvös starting around 1885, with further improvements in a lengthy run between 1906 and 1909. Eötvös's team followed this with a series of similar but more accurate experiments, as well as experiments with different types of materials and in different locations around the Earth, all of which demonstrated the same equivalence in mass. In turn, these experiments led to the modern understanding of the equivalence principle encoded in general relativity, which states that the gravitational and inertial masses are the same.

It is sufficient for the inertial mass to be proportional to the gravitational mass. Any multiplicative constant will be absorbed in the definition of the unit of force.

See: https://www.detailedpedia.com/wiki-Eötvös_balance

In the 17th and 18th, and most of the 19th centuries, Newton’s view prevailed.

Einstein said that in any properly constituted theory of gravity, inertia would emerge as an “inductive” gravitational effect of cosmic matter since gravity was/is the only known long-range force that might cause such effects. His first explicit attempt in this direction appeared in his, “Is There a Gravitational Effect Which is Analogous to Electrodynamic Induction?” in 1912. Einstein noted that Newtonian gravity was not sufficient to correctly encompass the induction of inertia – that is, the generation of the mass of matter by the gravitational interaction with chiefly cosmological matter – and inertial reaction forces – that is, Newton’s third law forces on accelerating agents. Several years later, general relativity was Einstein’s theory that he was convinced accomplished this task. Indeed, that’s why he called it “general relativity” because he “unified” inertia and gravity by making inertia an inductive gravitational effect.

The effects singled out by Einstein – the contribution of gravitational potential energy to the rest mass of the test particle and the inductive action, a force, of accelerating masses – are the two features of gravity that would supposedly account for all of inertia – origin of mass and reaction forces – in a properly constituted cosmology.
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That's an awful lot of words and time, to define a simple property. Inertia is simply the resistance to acceleration. There are two types. Dipole inertia, which is asymmetric and monopole inertia, which is symmetric. Only asymmetric inertia generates and reacts to gravity. Symmetric inertia is immune to gravity.

Only an active counter acceleration can resist another acceleration. Einstein was right, but only for the asymmetric inertia, not the symmetric. I.E.......not for the majority of mass now in the universe. For the majority of mass now, is isolated charge. Which is why, during the lifetime of this cosmos....gravity itself has been decaying. Dipole inertia has been converted into symmetric monopole inertia. By the generation of solar and now cosmos wind.

And this is much more interesting.
 
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Of note, I received the following today:

Gravity and Inertia in General Relativity
James F. Woodward
Abstract

The relationship of gravity and inertia has been an issue in physics since Einstein, acting on an observation of Ernst Mach that rotations take place with respect to the “fixed stars”, advanced the Equivalence Principle (EP). The EP is the assertion that the forces that arise in proper accelerations are indistinguishable from gravitational forces unless one checks ones circumstances in relation to distant matter in the universe (the fixed stars). By 1912, Einstein had settled on the idea that inertial phenomena, in particular, inertial forces should be a consequence of inductive gravitational effects. About 1960, five years after Einstein’s death, Carl Brans pointed out that Einstein had been mistaken in his “spectator matter” argu- ment. He inferred that the EP prohibits the gravitational induction of inertia. I argue that while Brans’ argument is correct, the inference that inertia is not an inductive gravitational effect is not correct. If inertial forces are gravitationally induced, it should be possible to generate transient gravitational forces of practical levels in the laboratory. I present results of a experiment designed to produce such forces for propulsive purposes.

Keywords: gravity, inertia, general relativity, inertia as a gravitationally induced phenomenon, experimental test of inductive inertia

1. Introduction

Before Einstein’s creation of general relativity theory, the conception of inertia was that captured in Newton’s laws of mechanics, Newton’s elaboration of the idea of inertia, first introduced by Galileo some years earlier. Inertia, properly vis inertiae or inert force, was taken to be an inherent property of “matter” conferred on it by its existence in absolute space, that only ceases to be inert when external forces act on matter to produce proper accelerations, rising to produce the reaction force the matter exerts on the accelerating agent to resist the impressed force. Already in Newton’s day, this conception of inertia as due to absolute space was seriously called into question by, among others, Bishop Berkeley who argued that a body in an otherwise empty universe would have no inertia since there would be no other matter to refer motion of the body to. From this point of view, absolute space’s action on matter is not the origin of inertia, the action of other matter in space is the cause of inertia. In the 17th and 18th, and most of the 19th centuries, Newton’s view prevailed.

Berkeley’s conjecture was revisited in the late 19th century by Ernst Mach, who noted that local rotation coincided with rotation relative to the “fixed stars”,
suggesting that local inertial frames of reference were determined by some long-range action of matter at cosmological distances. Einstein took Mach’s insight to mean that in any properly constituted theory of gravity, inertia would emerge as an “inductive” gravitational effect of cosmic matter since gravity was/is the only known long-range force that might cause such effects. His first explicit attempt in this direction appeared in his, “Is There a Gravitational Effect Which is Analogous to Electrodynamic Induc- tion?” in 1912 [1]. Einstein noted that Newtonian gravity was not sufficient to cor- rectly encompass the induction of inertia – that is, the generation of the mass of matter by the gravitational interaction with chiefly cosmological matter – and inertial reaction forces – that is, Newton’s third law forces on accelerating agents. Induction requires vector or tensor interactions. Several years later, general relativity was Einstein’s theory that he was convinced accomplished this task. Indeed, that’s why he called it “general relativity” because he, as we would say today, “unified” inertia and gravity by making inertia an inductive gravitational effect. Analogous to Maxwell’s “unifica- tion” of electricity and magnetism in his electrodynamics.

2. Einstein’s conception of gravity and inertia in general relativity

Einstein started talking about the gravitational induction of inertia as “Mach’s principle” shortly after mooting general relativity. Willem de Sitter quickly pointed out that the field equations of general relativity have solutions that are plainly incon- sistent with any reasonable interpretation of “Mach’s principle”. Einstein retreated from full-blown Mach’s principle, which seemed to require action at a distance, then deemed inconsistent with the conception of field theory as articulated by Faraday. But he did not abandon the gravitational induction of inertia which is consistent with the tenets of field theory. Einstein advanced his ideas first in an address at Leiden in 1920 where he analogized his evolving view of spacetime to the “aether” of the turn of the century theory of electrodynamics. That is, spacetime is not some pre-existing void in which matter, gravity and the other forces of nature exist. It is a real, substantial entity – not a void – which is the gravitational field of matter sources. And then he extended his view in remarks in a series of lectures at Princeton in 1921 [2]. He calculated the action of some nearby, “spectator” matter on a test particle of unit mass (at the origin of coordinates) in the weak field limit of GR. There he found for the equations of motion of the test particle (his Equations 118):


Screenshot 2022-11-20 at 13.49.38.png

The second and third of these equations are the expressions for the scalar (̄σÞ and vector (A) potentials of the gravitational action of the spectator masses with density σ on the test particle. l is coordinate time and v is coordinate velocity of the test particle. The first equation is just Newton’s second law. After writing down these equations, Einstein noted approvingly that,

The equations of motion, (118), show now, in fact, that.The inert mass [of the test particle of unit mass] is proportional to 1 +σ, and therefore increases when ponderable masses approach the test body.

Gravitational Field

There is an inductive action of accelerated masses, of the same sign, upon the test body. This is the term dA/dl... Although these effects are inaccessible to experiment, because κ [Newton's constant of universal gravitation] is so small, nevertheless they certainly exist according to the general theory of relativity. We must see in them strong support for Mach's ideas as to the relativity of all inertial interactions. If we think these ideas consistently through to the end we must expect the whole g μν -field, to be determined by thematter of the universe, and not mainly by the boundary conditions at infinity.

The equations of motion, show now, in fact, that.

The inert mass [of the test particle of unit mass] is proportional to 1 + σ, and therefore increases when ponderable masses approach the test body.

See: http://dx.doi.org/10.5772/intechopen.99760

There is an inductive action of accelerated masses, of the same sign, upon the test body. This is the term dA/dl ...

Although these effects are inaccessible to experiment, because κ [Newton’s constant of universal gravitation] is so small, nevertheless they certainly exist according to the general theory of relativity. We must see in them strong support for Mach’s ideas as to the relativity of all inertial interactions. If we think these ideas consistently through to the end we must expect the whole g matter of the universe, and not mainly by the boundary conditions at infinity.

Note that the small effects singled out by Einstein – the contribution of graviational potential energy to the rest mass of the test particle and the inductive action, a force, of accelerating masses – are the two features of gravity that would supposedly account for all of inertia – origin of mass and reaction forces – in a properly constituted cosmology.

The above quote was not Einstein’s last explicit word on gravity, inertia, and spacetime. In 1924, he again addressed these topics in a paper, “Concerning the Aether”. In it he quickly asserted that by “aether” he did not mean the material aether of turn of the century electromagnetism. Rather, he meant a real, substantial, but not material entity that is spacetime, and that spacetime is the gravitational field of material sources. No material sources, no spacetime. Why did he make this radical break with the conception if space as a pre-existing void in which nature plays out its events in time? Arguably, this was his way of getting rid of the Minkowski and other metrics that de Sitter had shown to be anti-Machian, delimiting acceptable solutions of his field equations to those consistent with inertia as a strictly gravitational interaction. As he put it toward the end of his article:

The general theory of relativity rectified a mischief of classical dynamics. According to the latter, inertia and gravity appear as quite different, mutually independent phenomena, even though they both depend on the same quantity, mass. The theory of relativity resolved this problem by establishing the behavior of the electrically neutral point-mass by the law of the geodetic line, according to which inertial and gravitational effects are no longer considered as separate. In doing so, it attached characteristics to the aether [Einstein's spacetime] which vary from point to point, determining the metric and the dynamical behaviour [sic.] of material points, and deter- mined, in their turn, by physical factors, namely the distribution of mass/energy.

That the aether of general relativity differs from those of classical mechanics and special relativity in that it is not “absolute” but determined, in its locally variable characteristics, by ponderable matter. This determination is a complete one if the universe is finite and closed ...

One may reasonably ask, if Einstein was convinced that general relativity, cor- rectly interpreted, encompassed the gravitational induction of inertia, why today is it widely believed in the community of relativists and beyond that inertia is not gravitationally induced? That inertia is no better understood now than it was in the absolute systems of Newton and Minkowski? See Carl Brans. and his “spectator matter” argument.

James F. Woodward 1,2
1 Space Studies Institute, USA
2 Department of Physics, California State University Fullerton, FullertoCalifornia,USA
Address all correspondence to: jwoodward@fullerton.edu

See: https://www.academia.edu/85519757/Gravity_and_Inertia_in_General_Relativity?email_work_card=view-paper

Objects capable of changing their internal energies simultaneously experience changing internal energy and proper acceleration, the action of the gravity/inertial field excited by the proper acceleration amplifies the rest mass fluctuation corresponding to the changing internal energy amplifies that rest mass fluctuation.
Hartmann352
 

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