The complex description of gravity

The complex description of gravity - like the complex description of time, is a part of our Concept – ToE–Quantum Space. Can gravity have its Imaginary part and its Real part? The concept of Imaginary Gravity has its justification according to our concept of Quantum Space. So the Complex description of gravity is a kind of consequence of our interpretation of “time”. As in the case of Imaginary Time, our Concept also assumes the existence of imaginary gravity. Maybe Dark Gravity?

Among other things, our Universe is made of Matter. Matter is composed of elementary particles. Each mass/matter interacts gravitationally according to our Laws of Physics. The basic law describing gravity is the Law of Universal Gravitation. This law describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass.

This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica (Latin for 'Mathematical Principles of Natural Philosophy' (the Principia)), first published on 5 July 1687.

The equation for universal gravitation thus takes the form:

where F is the gravitational force acting between two objects, m₁ and m₂ are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.

History

Before Newton's law of gravity, there were many theories explaining gravity. Philoshophers made observations about things falling down − and developed theories why they do – as early as Aristotle who thought that rocks fall to the ground because seeking the ground was an essential part of their nature.

Around 1600, the scientific method began to take root. René Descartes started over with a more fundamental view, developing ideas of matter and action independent of theology. Galileo Galilei wrote about experimental measurements of falling and rolling objects. Johannes Kepler's laws of planetary motion summarized Tycho Brahe's astronomical observations.

Around 1666 Isaac Newton developed the idea that Kepler's laws must also apply to the orbit of the Moon around the Earth and then to all objects on Earth. The analysis required assuming that the gravitation force acted as if all of the mass of the Earth were concentrated at its center, an unproven conjecture at that time. His calculations of the Moon orbit time was within 16% of the known value. By 1680, new values for the diameter of the Earth improved his orbit time to within 1.6%, but more importantly Newton had found a proof of his earlier conjecture.

In 1687 Newton published his Principia which combined his laws of motion with new mathematical analysis to explain Kepler's empirical results. His explanation was in the form of a law of universal gravitation: any two bodies are attracted by a force proportional to their mass and inversely proportional to their separation squared. Newton's original formula was:

where the symbol  means "is proportional to". To make this into an equal-sided formula or equation, there needed to be a multiplying factor or constant that would give the correct force of gravity no matter the value of the masses or distance between them (the gravitational constant). Newton would need an accurate measure of this constant to prove his inverse-square law. When Newton presented Book 1 of the unpublished text in April 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him, ultimately a frivolous accusation.

Modern form

Every point mass attracts every single other point mass by a force acting along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them:

where

• r is the distance between the centers of the masses.
• F is the force between the masses;
• G is the Newtonian constant of gravitation (6.674×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²);
• m₁ is the first mass;
• m₂ is the second mass;

This diagram describes the mechanisms of Newton's law of universal gravitation; A point mass m₁ attracts another point mass m₂ by a force F₂ pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance (r) between the point masses. Regardless of masses or distance, the magnitudes of the two forces, |F₁| and |F₂| (absolute values), will always be equal. G is the gravitational constant; G ≈ 6.67428(67)×10⁻¹¹ m³/(kg·s²). Sourse: User:Dna-Dennis

Assuming SI units, F is measured in newtons (N), m₁ and m₂ in kilograms (kg), r in meters (m), and the constant G is 6.67430(15)×10⁻¹¹ m³⋅kg⁻¹⋅s⁻². The value of the constant G was first accurately determined from the results of the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798, although Cavendish did not himself calculate a numerical value for G.

Gravity field

The gravitational field is a vector field that describes the gravitational force that would be applied on an object in any given point in space, per unit mass. It is actually equal to the gravitational acceleration at that point.

It is a generalisation of the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon). For two objects (e.g. object 2 is a rocket, object 1 the Earth), we simply write r instead of r₁₂ and m instead of m₂ and define the gravitational field g(r) as:

so that we can write:

This formulation is dependent on the objects causing the field. The field has units of acceleration; in SI, this is m/s².

Gravitational fields are also conservative; that is, the work done by gravity from one position to another is path-independent. This has the consequence that there exists a gravitational potential field V(r) such that

If m₁ is a point mass or the mass of a sphere with homogeneous mass distribution, the force field g(r) outside the sphere is isotropic, i.e., depends only on the distance r from the center of the sphere. In that case

As per Gauss's law, field in a symmetric body can be found by the mathematical equation:

where  is a closed surface and  is the mass enclosed by the surface.

Hence, for a hollow sphere of radius  and total mass ,

For a uniform solid sphere of radius  and total mass ,

Limitations

Newton's description of gravity is sufficiently accurate for many practical purposes and is therefore widely used. Deviations from it are small when the dimensionless quantities  and  are both much less than one, where  is the gravitational potential,  is the velocity of the objects being studied, and  is the speed of light in vacuum. For example, Newtonian gravity provides an accurate description of the Earth/Sun system, since

where  is the radius of the Earth's orbit around the Sun.

In situations where either dimensionless parameter is large, then general relativity must be used to describe the system. General relativity reduces to Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity.

Observations conflicting with Newton's formula

Newton's theory does not fully explain the precession of the perihelion of the orbits of the planets, especially that of Mercury, which was detected long after the life of Newton. There is a 43 arcsecond per century discrepancy between the Newtonian calculation, which arises only from the gravitational attractions from the other planets, and the observed precession, made with advanced telescopes during the 19th century.

The predicted angular deflection of light rays by gravity (treated as particles travelling at the expected speed) that is calculated by using Newton's theory is only one-half of the deflection that is observed by astronomers. Calculations using general relativity are in much closer agreement with the astronomical observations.

In spiral galaxies, the orbiting of stars around their centers seems to strongly disobey both Newton's law of universal gravitation and general relativity. Astrophysicists, however, explain this marked phenomenon by assuming the presence of large amounts of dark matter.

Einstein's solution

The first two conflicts with observations above were explained by Einstein's theory of general relativity, in which gravitation is a manifestation of curved spacetime instead of being due to a force propagated between bodies. In Einstein's theory, energy and momentum distort spacetime in their vicinity, and other particles move in trajectories determined by the geometry of spacetime. This allowed a description of the motions of light and mass that was consistent with all available observations. In general relativity, the gravitational force is a fictitious force resulting from the curvature of spacetime, because the gravitational acceleration of a body in free fall is due to its world line being a geodesic of spacetime.

Source: https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation

The gravitational interaction at the subatomic level seems negligible. However, in the micro-world, elementary particles live by different laws. At the subatomic level, the micro-world is described by the Standard Model. The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles. As can be seen, the problem is gravity.

Can imaginary gravity exist in the micro world? Before we try to answer this question, we must first focus on the combination of micro and macro world phenomena. If gravity depends on mass/matter, then such mass/matter must be stable. And if such mass/matter is not stable, does such mass/matter not exist? How does the instability of mass/matter with its existence? The concept of Imaginary Gravity, therefore, is based on the existence of unstable mass/matter. If mass/matter is stable only in our Here and our Now, then mass/matter instability takes place in the other moments of our “time” - Of course, from our point of view.

A complex description of gravity. If gravity is linked to time, then can there be a Gravitational Interaction from our “Past” or a Gravitational Interaction from our “Future”? So, if Gravitational Interaction exists for our unstable mass/matter from either our “Past” or our “Future”, then our Gravity outside of our present moment has an imaginary form. This could therefore mean that if our Imaginary Gravity can exist, then there should also be an Ensemble description of Gravity. Our Concept of Gravity (ToE-Gravity Concept) should therefore be extended. The Gravity of our “Past” and the Gravity of our “Future” can be interpreted as an Imaginary part of our Gravity.

The complex description of gravity is done both at the macro level and at the micro level. This can be interpreted for oneself by examining the illustrations above and below, which present the idea of the Complex Description of Gravity. From the point of view of macro phenomena - gravity from the “Past” does not exist for us. From the point of view of micro phenomena - we do not have access to other locations of elementary particles that are in different places at the same time.

A complex description of Gravity must also take into account the interconnectedness of phenomena that occur in both the micro-world and the macro-world. From our point of view, we are only able to experience Reality for the present moment in time. This means that a stable image of matter can only exist for our Here and our Now. However, in order to stabilize such a image of matter for our present Reality, phenomena must take place at the micro level - in the world of elementary particles.

A complex description of gravity. In order to merge Gravity (Real and Imaginary), a connection must be made between the phenomena that occur in the micro-world and the macro-world. The image of our present Reality is the end product of what takes place in our micro-world - the world of elementary particles. In order for our present Reality to stabilize for our Here and our Now, gravitational state changes must take place for the individual elementary particles that co-create our present Reality. In the micro-world, simultaneous phenomena are taking place due to quantum entanglement - from the point of view of our present moment.

Erwin Schrödinger mathematically wrote down the equation known from his name, as a wave function and a statistical function. This function is therefore determined by the equation, but already the determination of the position of the particle itself is undetermined. This means that an elementary particle can be in more than two places at the same time. Measurements of quantum systems show characteristics of both particles and waves (wave–particle duality).

Hugh Erevett, an American physicist, explained in his doctoral thesis in 1957 that BOTH possibilities occur, i.e., that the wave function collapses - Everett's theory dropped the wave function collapse postulate of quantum measurement theory, incorporating the observer in the same quantum state as the observation result. The quantum statistic becomes a measure of the branching of the universal wave function. The particle realizes both possibilities - wave function and position at a point.

Since elementary particles are in multiple places, it can therefore be assumed that they can co-create different parallel Realities. It remains to ponder the question: “Does quantum mechanics work on macro scales?” Even the physicists who influenced the creation of quantum mechanics did not believe in it. Erevett wrote down his theory mathematically - he created the so-called EREVETT ALGORITHM (Lagrange multipliers).

So, could the Law of Universal Gravitation take into account a different description of gravity - an Complex description of gravity? If elementary particles at the subatomic level can co-create matter at different locations at the same time, then perhaps they co-create stable forms of matter “shifted” relative to each other at imaginary times at those locations. Then this matter is stable only for particular imaginary times. If we were in these places in imaginary time, then our present Reality (our Here and our Now) would be an imaginary place in time.

This means that our Real Gravity could not affect this imaginary place. It would then become only an imaginary part of our Gravity. The micro-world realizes its basic phenomena in the imaginary part of our concept of “time”. Therefore, quantum mechanics from our point of view leaves a kind of understatement. This understatement is expressed through the Uncertainty principle proposed by Werner Heisenberg.

Heisenberg's Uncertainty principle It states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. In other words, the more accurately one property is measured, the less accurately the other property can be known. The act of measuring one quantity affects the system so that part of the information of the other quantity is lost. The Uncertainty principle is not due to imperfect methods or instruments of measurement, but to the very nature of reality.

This could mean that our Gravity becomes Imaginary due to the loss of some information. The loss of information occurs when mass/matter loses its stability relative to the present moment in time. Then we are dealing with mass/matter from our past moment in time. Lack of stability does not mean that mass/matter has stopped existing. It means that in our Here and our Now we have no access to it - that is why it is unstable. See more in Stabilization of matter part 1.

If there is a loss of information during the loss of stabilization of matter in time, it could mean that our Law of Universal Gravitation describes one special case - the case of gravitational interaction in our Here and our Now. In order to connect macro and micro phenomena, we need to use a different approach to the concept of “time.” This type of approach will allow us to interpret time in a different way and, consequently, to describe Gravity in a different way. Then our Gravity will gain a Complex description of Gravity. All for the preservation of information. Gravity for our present moment considers the case only for our present moment.

In order to generalize our Law of Universal Gravitation for all cases that include unstable mass/matter, we should extend our concept of Gravity and introduce another description of gravity. In other words, with reference to the Law of Universal Gravitation, our equation:

does not take into account the lost information by mass/matter from beyond our Here and our Now. Our above equation is dedicated only to the form of stable mass/matter in time - and only to our Here and our Now. Perhaps, in order for this equation to be extended to the totality of phenomena - occurring on both the macro and micro scales, a complex Description of Gravity would have to be introduced. Does this mean, then, that our Constant of Gravitation G would have to have a different form - a complex form?

for Agnieszka

Marek Ożarowski