THE GENERAL CLASSICAL-QUANTUM THEORY OF GRAVITATION.

Author: Marek Skowronski

all rights to the content of the article reserved

September 10, 2024

Many myths and many theories have grown up around gravity. Some fall by the wayside, others take hold at some point in scientific trends, and then these old models are revisited to… Well, that’s what they are. And this means that in science one can never say “never” and it is science that should be free from authority and from dogma – excluding truths so obvious that the sun rises over our heads every day.

            This article is an attempt to address the subject of gravity from a different angle than the previous one, and the author does not claim to consider his theory as the only and infallible one. Being aware that science is something that is subject to constant development, I would like to make my small and modest contribution to the great monuments of the real world of science.

Introduction

            Theoretical physics is a branch of physics that deals with the development of mathematical theories and models to describe and predict physical phenomena. Unlike experimental physics, which involves experiments and measurements, theoretical physics seeks to understand the laws of nature through mathematical equations and abstract concepts.

The goal of theoretical physics is to create coherent theories that explain observations and experiments and predict new phenomena. Well-known examples include quantum mechanics, Einstein’s theory of relativity or the standard model of elementary particles. Today, theoretical physics plays a key role in understanding both the micro-world (elementary particles) and the macro-world (cosmology).

Aims and methods: The purpose of this paper is to present an alternative theory of gravitation on the basis of a descriptive method, with the presentation of a mathematical formula.

1. GRAVITATION
   1. Gravitation in the classical approach

            In the classical view, gravity is an attractive force that acts between all objects that have mass. It is one of the four fundamental forces in nature, along with electromagnetism, the weak nuclear force and the strong nuclear force.

The best-known classical account of gravity comes from Isaac Newton, who formulated his law of universal gravity in his work “Philosophiæ Naturalis Principia Mathematica” (often shortened to “Principia”). First published in 1687,

Where:

m₁, m₂ – masses of gravitationally interacting bodies

r – the distance between the centers of the bodies

G – gravitational constant,  G = 6.67·10^-11Nm²/kg².

            The classical view in physics recognizes the universality of gravity, which means that it occurs and acts everywhere, between all bodies that have mass, no matter how far apart they are.

Gravity is always an attractive force, which means there is no “repulsive gravity.” In addition, the force of gravity is proportional to the mass of bodies, which means that it is mass-dependent, and the greater the mass of an object, the stronger its gravitational field. Another feature of gravity in classical terms is its action at a distance, which means that there does not have to be direct contact between objects for this force to act, but according to Newton’s law, the force of gravity (attraction) decreases with the square of the distance. And here are examples of the action of gravity in classical terms:

1. people, objects and other bodies on Earth are attracted to its surface and this force acts toward the center of the planet,
2. gravity is responsible for the planets orbiting the sun, where the attractive force between the sun and the planets makes them move in nearly circular orbits.

            While Newton’s law of gravity works great in most cases, it also has its limitations. Newton did not explain exactly how gravity works at a distance or what its origin is. Nor does Newton’s law deal well with very massive objects (like black holes) or with very fast motion. For these reasons, in the 20th century Albert Einstein

1. Gravity in terms of quantum physics

            Gravity in terms of quantum physics is a much more complex and not yet fully solved problem. Quantum physics describes three of the four fundamental forces in nature (electromagnetism, strong and weak nuclear forces) by means of quantum theory, but gravity has so far not been fully integrated into this theory. Trying to describe gravity at the quantum level leads to many challenges and new hypotheses, but there is no single, universally accepted theory of quantum gravity. Nevertheless, there are some approaches and concepts that attempt to combine gravity with quantum physics.

1. Gravity in classical quantum mechanics

            Quantum physics describes elementary particles and their interactions in a probabilistic (probabilistic) manner, based on the wave nature of matter. However, gravity, according to Einstein’s general theory of relativity, is explained as the curvature of space-time by masses. Trying to reconcile these two descriptions of reality – curved spacetime and the quantum description of forces – leads to some difficulties, especially at very small scales, such as the space around black holes or the early stages of the Universe (e.g., during the Big Bang).

1. Quantum gravity

            Quantum gravity is the term used to describe theories that attempt to combine quantum mechanics with gravity. Although a full theory of quantum gravity does not yet exist, the following are some approaches that attempt to do so:

1. Gravitons: Analogous to particles mediating other interactions (such as the photon in the case of electromagnetism), quantum gravity assumes the existence of a hypothetical particle called a graviton. The graviton would be the particle that carries the gravitational interaction at the quantum level, just as photons carry the electromagnetic interaction. In the classical view of gravity, this force is continuous, but in the quantum one it would manifest itself as an exchange of these particles.
2. String theory: Is one of the most popular approaches to quantum gravity. In this theory, all elementary particles, including graviton, are treated as vibrations of one- or multi-dimensional strings. String theory suggests the existence of additional spatial dimensions (in addition to our three dimensions of space and one dimension of time), which are rolled up in microscopic scales. One of the main successes of string theory is that gravity can be incorporated into the model, although the theory is still being developed and is not fully experimentally verifiable.

1. The black hole paradox and information

            One of the key problems at the intersection of gravity and quantum physics is the problem of black holes, particularly the question of what happens to the information of matter falling into a black hole. Quantum mechanics suggests that information cannot be lost, while classical gravity, in the context of black holes, assumes that once an object crosses the event horizon, information about the object disappears. This problem leads to the so-called information paradox of black holes, which is one of the biggest challenges in modern physics.

1. Problems and challenges

            Quantum field theory describes electromagnetism and nuclear weak and strong forces well, but trying to apply it to gravity leads to infinity in equations that make no physical sense. The theory of gravity, which works on large scales (such as the classical general theory of relativity), is not compatible with quantum theories at the level of very small scales, leading to the need to develop more advanced models, such as the aforementioned string theory or loop quantum gravity.

1. FORCE

            When talking about gravity, both in the terms of classical physics and quantum physics, we move all the time around its key character, that is, force. This is because both of these approaches treat gravity as a force. Therefore, it is necessary to cite what force is as understood in physics, which is a field of science.

• Force as understood in classical physics

            In classical physics, a force is a vector quantity that causes a change in the motion of a body, or acceleration, according to Newton’s second principle of dynamics. The key principles describing the force are Isaac Newton’s second principle of dynamics and the interaction principle.

• Newton’s second principle of dynamics:

            The most basic definition of force in classical physics comes from Isaac Newton, who stated that the force acting on a body is equal to the product of the body’s mass and its acceleration, which is expressed in the following formula:

F = m · a

Where:

F – force,

m – body mass,

a – acceleration.

That is, in Newtonian terms, the force causes a change in the velocity of the body, or acceleration, and the greater the mass of the body, the greater the force needed to cause the same acceleration.

• Force as interaction:

            In classical mechanics, a force can act at a distance (e.g., gravitational force) or through contact (e.g., frictional force). There are different types of forces, such as:

gravitational force: attraction between two masses,

Electrostatic force: the interaction between electric charges,

frictional force: the resistance that bodies encounter in moving relative to each other.

• Force in quantum physics

            In quantum physics, the concept of force compared to classical physics is understood somewhat differently. Here, forces are the result of intermediate particle exchange between particles of matter. Instead of thinking of force as direct attraction or repulsion, in quantum field theory interactions are described by the exchange of so-called intermediary bosons.

• Quantum field theory

            In this theory, every force in nature is described through particles that carry a given interaction, in which:

• photon: is responsible for the electromagnetic interaction,
• gluon: is responsible for the strong nuclear interaction (binds quarks in hadrons),
• W and Z boson: responsible for the weak nuclear interaction (e.g. in radioactive decay processes),
• graviton (hypothetical): if it were possible to create a quantum theory of gravity would be its predicted carrier.

            Instead of the classical definition of force, quantum physics describes interactions through the exchange of those mediating particles that carry interactions between particles of matter.

• Forces under fundamental interactions

            In quantum physics, forces are interpreted as fundamental interactions, viz:

• electromagnetic interaction: described by quantum electrodynamics (QED), where photons carry the interaction between charged particles;
• strong interaction: described by quantum chromodynamics (QCD), where gluons carry the interaction between quarks;
• weak interaction: in the standard model, W and Z bosons carry this interaction, which is responsible for radioactivity, among other things.

These interactions are expressed mathematically through the exchange of intermediate particles, resulting in changes in the energy and momentum states of the particles. At the quantum level, the concept of the classical force as a vector acting on an object is replaced by a more abstract description through the exchange of field quanta.

• Comparison of force in classical and quantum physics

            As mentioned above, in classical physics, force is a vector quantity that causes a change in the motion of a body, it is a simple mechanism that depends on mass and acceleration, acting on objects mechanically or through fields (such as gravitational). It is directly related to mass and acceleration (Newton’s second law of dynamics). The classical theory of gravitation and electromagnetism describes forces as acting at a distance. In quantum physics, on the other hand, force is not interpreted as a vector, but as the result of quantum interaction, described by the exchange of mediating particles. Forces are the result of quantum fluctuations and the exchange of intermediate bosons, which is more abstract and more difficult to understand intuitively, but gives a more accurate description of fundamental processes occurring at the microscale.

1. Gravity as a dimension
   1. Definition of the term “dimension”

            The definition of the term “dimension” in physics and mathematics is multi-layered, depending on the context in which we use it. In its simplest form, dimension refers to the minimum number of coordinates needed to uniquely determine the position of a point in a given space. Let’s look at this concept at different levels:

1. Dimension in classical space (Euclidean geometry).
2. One-dimensional space: A line on which a point can be defined by a single coordinate (e.g., a straight line);
3. Two-dimensional space: A plane where a point needs two coordinates to define its position (e.g., a sheet of paper, where we use X and Y coordinates);
4. Three-dimensional space: A space where we need three coordinates (X, Y, Z) to determine the location of a point (e.g., our daily experience in space);
5. Four-dimensional space: In the general theory of relativity, space-time is four-dimensional because we add time as a fourth dimension to the three spatial dimensions.

• Dimension in physics
• Classical mechanics: Dimension refers to the number of independent directions in which objects can move. For example, motion in 3D includes displacement along the X, Y and Z axes;
• Time as a dimension: In relativity theory, time is treated as the fourth dimension, creating what is known as space-time. Spatial dimensions define the position of an object, while time indicates the moment at which that object is located;
• Additional dimensions: In some theories (like string theory), additional spatial dimensions are postulated to be “collapsed” and invisible to our senses. In such theories, there may be more than four dimensions (e.g., 10, 11 or more).

• Dimension in mathematics:
• Vector spaces: In vector theory, dimension is the number of independent basis vectors needed to describe a space. For example, in a three-dimensional space, we have three independent vectors that can be used to define the position of each point.
• Fractal dimension: In the context of fractal geometry, there is a concept of dimension that may not be integer, such as fractal dimension. It describes how the detail of a fractal varies with scale.

• Dimensionality in the context of gravitational theory and quantum physics:
• The general theory of relativity: Gravity arises from the curvature of four-dimensional spacetime, which suggests that dimension is crucial to understanding how gravity works. Rather than being a force, gravity is a property of the dimensions of space-time.
• String theory: Postulates the existence of more than four dimensions. The extra dimensions are invisible because they are rolled up into very small spaces (compact dimensions). This theory attempts to link gravity with quantum physics, suggesting that gravity may be related to hidden dimensions.

• Dimension in philosophical and metaphysical context:

            In various philosophical and metaphysical systems, dimension can refer not only to physical space, but also to other aspects of reality, such as different levels of existence (tangible and intangible), which can be seen as “dimensions” of some reality.

            To summarize the issue, a dimension can be defined as the number of coordinates needed to determine the position of a point in space. Usually we speak of three spatial dimensions and one temporal dimension, but in more advanced theories (like string theory) additional spatial dimensions appear. In the case of gravity, in terms of the general theory of relativity, the space-time dimension is a key concept, since gravity results from the curvature of this multidimensional structure.

• Definition of gravity as a dimension

            Let’s assume that gravity is a dimension that is also a force (specifically, an interaction) that is proportional to the mass of attracting objects to their density, the space in which they are located and their quantum potential, which we can express in the following formula:

Where:

• F – gravitational force between objects,
• G – gravity constant (may need to be modified to account for additional factors,
• m₁, m₂ – masses of objects,
• r – distance between objects,
• r1, r2 – density of objects (mass per unit volume),
• F – Quantum potential, which can depend on quantum effects such as the gravitational field at the quantum level,
• V – the volume of space in which the objects are located (this may be the volume of curved space-time or local curvature)

            The above concept or the idea of gravity as a dimension extends the classical concept of gravity with new elements, such as density, space and quantum potential, while the formula posted above would have to be verified experimentally, and parameters such as Φ Phi and volume V would require precise definitions that would make physical sense in the context of quantum gravity. Accordingly, the following variables are postulated to be included:

• Mass and density: According to the above idea, density would affect gravitational force, which would mean that objects with higher density (not just mass) would generate a stronger gravitational field. The formula takes into account both mass and density, through the product of these quantities.
• Space and volume: In classical physics, the gravitational force decreases with the square of the distance between objects. In the formula above, this could be extended to include the effect of the volume of the space in which the objects are located. This would assume that gravity could act differently in curved space, e.g. in smaller volumes it could be stronger.
• Quantum potential Φ\PhiΦ: This factor would be responsible for accounting for quantum effects, such as the potential existence of gravitons that carry gravitational force at the quantum level. This would be a new parameter that does not exist in classical theory, but would have to be developed based on the study of quantum gravity.
• New coefficients: The gravitational constant G could need to be adjusted to account for density, space and quantum potential. It is possible that in a hypothetical theory of quantum gravity, there would be another constant or a modification of an existing one that would include these additional factors.

            The above concept differs from the classical description of the phenomenon in question, which is based on Newton’s laws and Einstein’s general theory of relativity.

• Gravity vs. mass

            In classical mechanics, according to Newton’s law of universal gravitation, gravity is a force proportional to the mass of two objects and inversely proportional to the square of the distance between them. Density plays no direct role in this formula. In contrast, mass, which can be a function of density and volume, is crucial. In the general theory of relativity, gravity is the effect of curvature of space-time caused by mass and energy. Massive objects, such as stars or planets, curve space-time, and other objects move along curved paths, which is seen as the force of gravity. In this context, it can be said that the space in which objects are located influences their gravitational interactions, but the key factor is still their mass and energy.

• Quantum

            The quantum theory of gravity is still in a stage of development, and a full, coherent theory (such as quantum gravity or string theory) has not yet been accepted. At present, it is generally believed in theoretical physics that gravity at the quantum level probably involves very subtle effects and particles, such as the hypothetical graviton, but so far no universally accepted description has yet been made of how exactly it works at this level.

            A quantum is a basic unit that describes a minimal, indivisible portion of some physical quantity. The term comes from Latin (“quantus” – “how much”), and was introduced by German physicist Max Planck in 1900, who suggested that the energy of electromagnetic radiation is emitted and absorbed in specific, discrete portions, called quanta of energy.

In quantum mechanics, the concept of a quantum refers to a variety of physical quantities that are quantized, meaning that they occur at well-defined values, instead of continuously, such as:

• Quantum of energy: Energy in microscopic systems, such as atoms, is taken in discrete levels. For example, the energy of a photon (a quantum of light) is proportional to its frequency.
• Charge quantum: Electric charge is also quantized, and its smallest portion is the elementary charge (such as the charge of an electron).

The best-known examples of quanta are:

• Photon: The quantum of electromagnetic radiation, or light.
• Quanta of energy in atoms: Electrons in atoms can only take on specific energy levels, and transitions between these levels take place through the emission or absorption of energy quanta.

The phenomenon of quantization explains many phenomena in physics, such as the spectral lines of atoms and the photoelectric effect.

            Thus, referring to the concept of a quantum, it should be noted that each portion (each quantum) is characterized by a charge or energy, respectively, and each charge and each energy have a specific potential.

• Quantum potential

            Potential in physics is a scalar quantity that describes the energy state of a system at a certain point in space. It can take different forms, depending on the type of field we are dealing with. Potential determines how much energy a body at a given point in space has as a result of interactions with forces, such as electrical, gravitational or mechanical forces. In physics, the following types of potentials are distinguished:

• Gravitational potential: This is the potential associated with the gravitational field and it determines the potential energy of a mass placed at a given point in the gravitational field. For a point source of gravity, the gravitational potential V at a distance r from a mass M is given by the formula:

Where: G is a constant and M is the mass of the field source

• Electric potential: It is related to the electric field. The electric potential at a given point in space tells the potential energy of a unit charge placed at that point. For a point charge q, the electric potential V at a distance r from that charge is:

Where  e₀ is the electrical permeability of the vacuum

• Mechanical potential: A term used in classical mechanics, it most often refers to potential energy in a field of conservative forces, such as elasticity (spring potential) or gravity near the Earth’s surface (gravitational potential).

            Potential in physics tells how much energy a body has at a given point in space per unit mass (in the case of a gravitational field) or per unit charge (in the case of an electric field). Thus, the potential energy of an object at a given point is the product of its mass (or charge) and the potential at that point. In addition, potential allows you to simplify the analysis of the motion of bodies in force fields. Instead of analyzing the forces acting on a body at each point, one can use the concept of potential, which is directly related to the energy of the system.

In quantum physics and classical mechanics, the potential plays a key role in equations of motion, such as the Schrödinger equation for quantum particles.

            Gravity as currently understood is based primarily on mass and space-time curvature, and the concepts of density and quantum potential are not directly related to the classical approach. However, it is to be expected that in the near future, with the development of the theory of quantum gravity, there may be new explanations that incorporate other aspects, such as quantum potential. Quantum potential – according to the proposed understanding of gravity – is therefore a new quantity that has been taken as a hypothetical variable, referred to in the definition of gravity as a dimension and in the proposed formula.

Quantum potential is a concept that has no single standard definition in physics, but is associated with various quantum theories that attempt to describe the behavior of physical systems at the quantum level. The concept can be understood in several ways, depending on the context in which it is used.

In the so-called de Broglie-Bohm theory (also known as pilot wave mechanics or pilot wave theory), the quantum potential plays a key role in describing the motion of particles. In this interpretation of quantum mechanics, particles have a defined position and their motion is guided by a quantum wave, which is described by a wave function.

            The quantum potential is an additional force that results from the wave function and affects the particles in a non-classical way. It is the quantum potential that distinguishes dynamics in Bohm’s theory from classical Newtonian mechanics. Surprisingly, the quantum potential acts independently of the classical force that particles would feel in a given system, and its influence can extend over large distances. The quantum potential Q can be written as follows:

Where:

• ħ – Planck’s constant divided by 2π,
• m – mass of the particle,
• ψ – wave function,
• Ѳ – Laplace operator (second spatial derivative).

            Thus, the quantum potential is closely related to the local shape of the particle’s wave function and affects its motion in a way that has no equivalent in classical mechanics.

• Quantum potential in the context of quantum gravity

            In the context of attempts to unify quantum mechanics and the theory of gravity, quantum potential can refer to potential interactions arising from the quantum gravitational field. Although quantum gravity is not yet a fully developed theory, some models, such as quantum field theory, suggest that gravity could be carried by hypothetical particles called gravitons.

In that case, a quantum potential could describe how particles interact through gravitons at the quantum level, which would be a fundamental modification of Einstein’s classical theory of gravity.

In quantum chemistry, the quantum potential appears in the context of modeling interactions between electrons and atomic nuclei. Theories such as density functional theory (DFT) use various forms of quantum potentials to describe the energies of atomic, molecular and electron systems in a quantum way. Such potentials are used to predict molecular structures, chemical reactions and material properties.

            In general, a quantum potential can be understood as the effect of specifically quantum interactions that affect the behavior of particles in ways that are not predicted by classical mechanics. This potential often results from interference effects, quantum tunneling and other phenomena characteristic of quantum mechanics.

• The concept of gravity as a dimension vs. other modern concepts

            The concept presented in this article regarding gravity as a dimension rather than a force refers to modern physical theories that in some ways change the traditional understanding of gravity. There are such theories that, in the context of quantum physics, attempt to explain gravity as a result of space-time geometry, rather than as a force in the traditional sense.

The best-known theory that describes gravity as a geometric phenomenon is Albert Einstein’s general theory of relativity. In this theory, gravity is the effect of the curvature of space-time by mass and energy. In this sense, gravity is not a “force” like electromagnetism, but more of a property of the structure of reality itself, and therefore can also be a dimension in the concept proposed above and expressed accordingly in the formula.

            Quantum physics operating in a different, microscopic range and attempting to explain all forces, including gravity, by means of quantum particles (quanta of interactions), such as the previously mentioned hypothesis of the existence of putative particles called gravitons, which would carry gravity, just as photons carry electromagnetism, as well as the general theory of relativity – so far has not lived to see a coherent combination into the so-called quantum theory of gravity, still being the subject of research.

At the same time, the author’s idea contained above, according to which gravity may be related to dimension rather than to the traditional “force,” is also reflected in some modern theories of physics, such as string theory and concepts related to extra dimensions. In these theories, space can have more dimensions than four (three spatial and time), and gravity can be a phenomenon resulting from how these extra dimensions interact with space-time.

It is worth noting that string theory and its expansions, such as M-theory, consider the possibility that there are many additional dimensions that are invisible in everyday life, and gravity could be a manifestation of these hidden dimensions in our reality.

Your concept is therefore in line with some modern attempts to explain gravity and deserves further exploration in the context of theoretical physics.

• Consequences of confirming the presented concept of gravity

            If the theory of gravity presented above, which takes into account mass, density, space and quantum potential, were to turn out to be true, it would have enormous consequences for both our understanding of the universe and the technologies that could result from it. Confirmation of the theory presented above could result in a new view of the structure of the universe. It would require modification of both Newton’s classical mechanics and Einstein’s general theory of relativity. It would mean that our existing models of gravity and space-time would be incomplete, and new equations and interpretations would have to be introduced.

Changing the way we view gravity would affect our understanding of such cosmological phenomena as the expansion of the universe, dark matter, dark energy and the formation of galactic structures. It could explain some cosmological puzzles that current theories cannot solve, such as the uneven distribution of matter in the universe.

A theory that assumes the influence of density and quantum potential on gravity could change our understanding of how black holes interact with their surroundings. It could lead to new insights into the event horizon, the information paradox and how black holes can interact with other objects. The theory above could also help in understanding hypothetical exotic objects, such as neutron stars and wormholes, which require new gravitational models. It is possible that the discovery of new properties of gravity would make it possible to detect these objects in a different way than before.

If we could understand how density, space and quantum potential affect gravity, perhaps we could develop technology that would allow us to manipulate the gravitational field. This type of technology could enable much faster space travel, potentially even making large-scale interstellar travel possible. Changing our understanding of gravity could also open the door to the theoretical possibility of traveling at superluminal speeds, or studying how curvature of space-time could affect time travel.

            If it turns out that density affects gravity, causing objects of different densities to attract each other differently than those of the same mass, this could change our understanding of interactions between planets, stars or even black holes.

The merger, the integration of quantum mechanics and gravity, could be a step toward the creation of a theory of quantum gravity that would unite quantum mechanics with the general theory of relativity. This is one of the most important challenges in modern physics. Such a development could lead to the discovery of gravitons (hypothetical particles responsible for transmitting the force of gravity), as well as to a better understanding of extreme phenomena such as black holes and the big bang. Further implications could also include a better understanding of the microstructure of space-time, since if gravity depended on quantum potentials, this could lead to a better understanding of the nature of space-time at the quantum level and shed new light on questions about the nature of singularities in black holes and the early universe.

            If the proposed theory were applicable in practical settings, it could lead to a revolution in technology, particularly in the field of extracting energy from gravity or the quantum nature of matter. A new approach to gravity could open the way to more efficient methods of manipulating the gravitational field. A pioneer in this approach to energy extraction was Serbian scientist Nikola Tesla. At the same time, confirmation of the existence of a quantum potential that affects gravity could accelerate the development of quantum technologies such as quantum computers and quantum teleportation. Understanding these processes could have direct applications in communications and computing.

            Considering the philosophical and social implications of confirming the concept of gravity presented in this article, it would mean highlighting that our reality at a fundamental level is more complex, and that gravity depends on the quantum properties of space and matter. This could change our understanding of the universe and our place in it. In addition, discoveries of this magnitude could spark tremendous interest in physics and science, which could advance education and research in these fields.

Summary

            Confirmation of the presented theory of gravity would require its development and detailed research. It is the fruit of many years of consideration of the nature of the Universe, its mechanics, its beginning and predicted end. Its confirmation would have revolutionary consequences for our understanding of physics, cosmology and technology, potentially leading to the discovery of new physical phenomena, the understanding of the quantum nature of gravity and the development of technologies to manipulate space-time, which in turn could revolutionize our research capabilities and even open the way to interstellar travel.

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