Gravitational Field - Science topic

Synergy has to do with obtaining a total greater than the sum of its parts, but this seems not to be a logical thing if we think just in terms a real numbers in which 1+1 = 2.

In fact in my book

today available in researchGate:

and published in Amazon in 1999, there is a proposal how the Principle of Synergy can be applied not only to the physical, but to other areas of human thought, and how based on the most beautiful equation of mathematics, I mean Euler’s relation, it is possible to obtain a sum greater that the sum of its part, so that mathematically Synergy can be represented.

A whole greater than the sum of its parts is a concept that has been considered metaphysical, but that most prolific mathematician of all times, in his work with infinite series in 1745, found that relationship that was described as the most beautiful relationship in mathematics in a 1998 competition held by Intelligencer, called Euler's relation. This relationship in fact includes all numbers: one, zero, the equals sign, but also the square root of minus one, as well as infinity, of course, since it is an infinite series. It is this concept the one then that permits to describe mathematical the concept of Synergy and that has permitted to deduce all fundamental equation of physics in a unified framework of reference:

* that of the pendulum a real harmonic oscillator

* that of the gravitational field including that of the planet mercury obtained by Einstein, but in this case obtained with a mathematical tool not so much complicated as was done with Tensor Analysis

* those of SR in another approach, in which linear moving is just a special case of the more general solution obtained with the BSU concept in which covariance is included as it is a consequence of the isomorphic property of Euler’s relation mentioned above and finally the

* Schrödinger’s wave equation

and most probably it will serve even for that new field of physics called Quantum Field Theory, as in fact it is a real harmonic oscillator, that vector in the complex plane, that remains invariant in spite of change, as Euler’s relation remains the same with those mathematical operations that represent change: integration and derivation.

Edgar Paternina

retired electrical engineer

Soumendra Nath Thakur

February 15, 2025

The concept of "wrapping of space" is often interpreted as the wrapping of spacetime, forming the basis for the relativistic explanation of gravitational lensing and the Einstein Ring. This interpretation attributes the bending of light to spacetime curvature, yet an alternative perspective grounded in classical gravitational fields offers a more consistent explanation.

Observational evidence of light bending around massive objects is frequently cited as confirmation of relativistic spacetime curvature. However, gravitational fields themselves, as described in classical mechanics, inherently account for the deflection of light. If light bending were solely a consequence of spacetime curvature, the massive object generating the curvature should obstruct the bent light from reaching an observer. In contrast, considering light bending within a gravitational field avoids this inconsistency and remains aligned with empirical observations.

This raises a fundamental question: If a curved gravitational field around a massive body can provide a consistent and empirically supported explanation for the bending of light, why should these observations be interpreted as evidence of relativistic spacetime curvature? A reconsideration of the classical gravitational framework may offer a more precise understanding of light deflection phenomena, challenging the prevailing relativistic interpretation.

I've read the Einstein digital papers, and note that Einstein referred to a gravitational field as a pace where space was "neither homogeneous nor isotropic". He also referred to a varying speed of light, and light refracting downward like any wave moving through a medium where there's an orthogonal gradient in wave speed.

Other old papers make me think that an electromagnetic field is a place where space is curved, or twisted if you prefer, electromagnetism being associated with twist and turn. I can find old references to eg Maxwell talking about a transverse undulations and a screw mechanism, but I can't find any contemporary references. Can anybody point to any?

Well actual physics, can be represented mathematically with the Basic Systemic Unit, based on Euler’s relation with its most remarkable property of remaining the same in spite of change, that permits to deduce the fundamental equations of physics such as :

* that of the pendulum a real harmonic oscillator

* that of the gravitational field including that of the planet mercury obtained by Einstein, but in this case obtained with a mathematical tool no so much complicated as was done with Tensor Analysis

* those of SR in another approach, in which linear moving is just a special case of the more general solution obtained with the BSU concept in which covariance is included as it is a consequence of the isomorphic property of Euler’s relation mentioned above and finally the

* Schrödinger’s wave equation

For those interested in the way all this is obtained you can see my papers:

https://www.researchgate.net/publication/384190006_Quantum_Physics (https://www.researchgate.net/publication/384190006_Quantum_Physics)

https://www.researchgate.net/publication/385592651_A_Quantum_Theory_of_GravitationNewpdf (https://www.researchgate.net/publication/385592651_A_Quantum_Theory_of_GravitationNewpdf)

https://www.researchgate.net/publication/382357270_Special_Relativity_Another_Approach (https://www.researchgate.net/publication/382357270_Special_Relativity_Another_Approach)

that I really hope will contribute to overcome the great crisis of physics, because the great incompatibility between QM and GR.

So yes, actual physics, can be represented mathematically in a real coherent way, but for it is necessary to make a real paradigm shift.

Edgar Paternina

retired electrical engineer

In electromagnetism the Coulomb force F=q1q2/r^2, the Lorentz force F=q(E+νxB), are computed treating spacetime as flat, and we are measuring what is actually a macroscopic phenomenon, not at the microscopic level. But this does not mean that the principle fails completely at the microscopic level.

Consider particles with mass such as electrons, which should have both electromagnetic and gravitational forces (we cannot rule out the validity of GR at tiny masses). Looking at an electron from the outside, it expresses electric field, magnetic moment, and mass. The Stern-Gerlach experiment fully expressed these covariates [1]. The electron involves only 4 factors, time t, space x, electric field E, and magnetic field H. We express the electron in the set e={Δt, Δx, ΔE, ΔH}, where the elements are all variables. This then implies that the external electromagnetic force, gravitational force, and mass, should all be able to be described by these components, since we can only act on the electron through these components.

Mass then could be exclusively electromagnetic mass [2][3], me={Δt, Δx, ΔE, ΔH}, regardless of the mechanism by which it is produced [4]. The electric field force can likewise be expressed only in terms of Fe=α{Δt, Δx, ΔE, ΔH}, and the gravitational force in terms of the set Fg=G{Δt, Δx}. Obviously, this is their simplest expression.

We need not consider what the electron is. It can be inferred from the set that its electric and gravitational forces overlap, since they share the same part of spacetime expression. This can also be seen by comparing Coulomb's law with Newton's law of gravity. As for neutral massive particles, they can be regarded as cancelling out the electromagnetic field [5] leaving only the Fg = G{Δt, Δx} part. In this way, the gravitational force is naturally unified to the electromagnetic force, and they are coupled together by the spacetime {Δt, Δx}, and automatically incorporated into the gauge field theory; the 'graviton' can be regarded as the spacetime product of the 'photon'. As for gravitational waves, they can be regarded as a part of space-time detached from accelerated motion, like electromagnetic waves radiated by accelerated electrons. This is exactly what Poincaré envisaged [6].

"After Einstein developed his theory of general relativity, in which a dynamical role was given to geometry, Herman Weyl conjectured that perhaps the scale of length would also be dynamical. He imagined a theory in which the scale of length, indeed the scale of all dimensional quantities, would vary from point to point in space and in time. His motivation was to unify gravity and electromagnetism, to find a geometrical origin for electrodynamics. [7, 8]" Wouldn't Weyl have been right if, instead of searching for a geometrical origin of electromagnetism, he had searched for an electromagnetic origin of gravity? Wouldn't electromagnetism be equally geometrical if one considered that the electromagnetic force Fe = α{Δt, Δx, E, H} is essentially the same as that resulting from variations of {Δt, Δx} therein?

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References

[1] Schmidt-Böcking, H., Schmidt, L., Lüdde, H. J., Trageser, W., Templeton, A., & Sauer, T. (2016). The Stern-Gerlach experiment revisited. The European Physical Journal H, 41(4), 327-364. https://doi.org/10.1140/epjh/e2016-70053-2

[2] Thomson, J. J. (1881). XXXIII. On the electric and magnetic effects produced by the motion of electrified bodies. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 11(68), 229-249.

[3] What is Mass? Must the Hierarchy of Mass be Determined Simultaneously by the Origin of Mass? https://www.researchgate.net/post/NO45_What_is_Mass_Must_the_Hierarchy_of_Mass_be_Determined_Simultaneously_by_the_Origin_of_Mass

[4] Higgs, P. W. (2014). Nobel lecture: evading the Goldstone theorem. Reviews of Modern Physics, 86(3), 851.

[5] The Relation Between Mathematics and Physics (2) - Is the Meaning of Zero Unified in Different Situations in Physics? https://www.researchgate.net/post/NO26The_Relation_Between_Mathematics_and_Physics_2-Is_the_Meaning_of_Zero_Unified_in_Different_Situations_in_Physics

[6] H. Poincaré

[7] Straub, W. O. (2009). Weyl's 1918 Theory Revisited. Pasadena, California. Disponível em: http://www. weylmann. com/revisited. pdf.

[8] Gross, D. J. (1992). Gauge theory-past, present, and future? Chinese Journal of Physics, 30(7), 955-972.

The equation F = −Mᵃᵖᵖ·aᵉᶠᶠ:

The concept explores how photons interact with gravitational fields and the forces acting upon them. When emitted from a gravitational source, a photon experiences a unique interplay between its effective mass and acceleration. This results in a consistent, negative force propelling the photon away from the gravitational well. Essentially, the photon accelerates from rest to its characteristic speed of light almost instantaneously, driven by this force. This behavior reflects the dynamic properties of the photon’s effective mass, which differs from conventional mass. It explains why photons can escape strong gravitational fields and maintain their speed regardless of external conditions. The analysis provides insights into how photons respond to gravitational influences, offering explanations for phenomena like redshift and energy conservation in gravitational systems, while hinting at deeper connections with cosmic behaviors, such as dark energy-like effects.

This is a coherent presentation. It effectively summarizes the key aspects of the concept in an accessible manner while maintaining scientific rigor. It describes the dynamic relationship between the photon's effective mass and acceleration, emphasizing the resulting force that enables the photon to escape gravitational wells and reach the speed of light. The inclusion of broader implications, such as redshift and energy conservation, as well as a connection to cosmic phenomena like dark energy, ties the explanation to both local and universal contexts. The presentation balances technical accuracy with a quasi-layman approach, making it suitable for diverse audiences.

Consideration 1: The Photon’s Initial Straight-Line Trajectory

The photon begins its journey from the source along a straight-line trajectory with velocity c. Here, an initial redshift occurs as the photon loses a slight amount of energy due to gravitational interaction with the source’s gravitational well, resulting in a corresponding increase in wavelength (Δλ>0). This change follows the relationship E = hf = hc/λ, where the energy E and frequency f are inherent to the photon and directly proportional to the wavelength.

Consideration 2: Arc Path and Energy Exchange During Gravitational Bypassing

As the photon approaches and passes an external massive body, it undergoes a temporary arc-shaped deviation in its trajectory due to the external gravitational influence. This interaction involves two phases:

First Half-Arc: A blueshift occurs, corresponding to a wavelength decrease (Δλ<0) as the photon gains energy due to gravitational influence while approaching the massive body.

Second Half-Arc: As the photon moves away, a redshift (Δλ>0) occurs, returning the photon’s wavelength to its original state as it completes the arc and leaves the gravitational field. This reversible shift is due to energy exchange within the field, summarized by E + Eg= E + 0, where Eg represents the energy gained and then lost by the photon within the gravitational arc path.

Consideration 3: Return to Original Straight-Line Trajectory

After exiting the gravitational field, the photon resumes its original straight-line path. At this point, it retains its inherent energy, with any additional energy or momentum imparted by the gravitational field removed. Its wavelength also remains as it was upon entry into the gravitational encounter, indicating no net change in wavelength (Δλ=0) beyond that caused by its initial emission.

Initial Straight-Line Trajectory: The photon starts along a straight path from the source, traveling at speed c. As it moves away from the gravitational well of the source, a slight redshift occurs, indicating a small increase in wavelength (Δλ > 0).

Interaction with External Massive Body: As the photon approaches an external massive body, it undergoes a temporary blueshift (Δλ < 0) while moving toward the body. Once the photon passes the body and begins to move away, it experiences a redshift (Δλ > 0), returning to its original wavelength. This reversible shift reflects the energy gained and lost by the photon in response to the external gravitational field. The photon’s inherent energy drives its straight-line path, but the external field temporarily adds energy, altering its trajectory in an arc-like fashion. After completing this interaction, the photon resumes its original straight path, with no net change in wavelength (Δλ = 0).

Return to Original Trajectory: After passing the gravitational influence of the external body, the photon’s trajectory returns to its original straight-line path, maintaining its inherent energy and wavelength. The photon’s wavelength remains unchanged beyond the initial shift caused by the source’s gravitational well.

A photon, representing light, carries inherent energy denoted as E. As the photon ascends from the gravitational well of its emission source, it loses part of this energy, resulting in a redshift (increase in wavelength, Δλ>0). However, the photon’s behaviour changes significantly when it encounters a strong external gravitational field.

As the photon approaches a strong gravitational body, it undergoes a blueshift (decrease in wavelength, Δλ<0) due to its interaction with the external gravitational field. This shift occurs as a result of electromagnetic-gravitational interaction, causing the photon to follow an arc-shaped trajectory. During this process, the photon’s momentum increases, described by the relation Δρ = h/Δλ, where h is Planck’s constant. This momentum gain reflects the gravitational influence on the photon's trajectory.

Completing half of the arc path (1/2 arc) around the gravitational body, the blueshift transitions into a redshift (Δλ>0) as the photon begins to lose momentum (Δρ=h/Δλ). This process indicates a symmetrical momentum exchange, where the photon experiences a balanced gain and loss of external energy (Eg), preserving symmetry in its overall energy behaviour.

Importantly, while the photon undergoes these external changes in wavelength, momentum, and energy during its trajectory around the gravitational body, it retains its inherent energy (E). The only exception occurs when the photon loses energy (ΔE) while escaping the gravitational well of its source. Thus, despite these external interactions, the photon’s inherent energy remains conserved, except for the loss associated with its initial emission.

After bypassing the gravitational field, the photon resumes its original trajectory, maintaining its inherent energy (E) and continuing unaffected by further gravitational influences.

The Schwarzschild metric describes the gravitational field of a spherical body. The special theory of relativity, based on Lorentz transformations, has a number of experimental confirmations. Is it possible to apply Lorentz transformations to the Schwarzschild metric? This was done

for the linearized isotropic Schwarzschild metric and the geodesic equations for the resulting metric were found. When using them to analyze the frequency shift data of the Pioneer 10 signal, it is concluded that the annual frequency variations are caused by a change in the velocity of the time flow on the apparatus from the point of view of an observer on Earth.

The resulting metric is used to determine the active gravitational mass of a cloud of rarefied gas of relativistic particles.

As the velocity of particles approaches the light velocity, this mass increases indefinitely compared to their total relativistic mass. This result can be extended to relic neutrinos. Since the minimum rest mass of neutrinos is not found, this leaves open the possibility that they may make up a most of dark energy.

The standard way to calculate the energy density of an electric field is to equate the work required to two change the separation of two charged sheets of infinite extent by a given amount, to the energy stored in the field between (or outside of) the plates.  This yields a positive-definite energy density proportional to the square of the electric field.  Doing the same for the gravitational field yields an energy density proportional to the negative of the square of the gravitational field.  Yet, it seems to be accepted that the energy density of the gravitational field is positive.  Can anyone explain this to me?

This mathematical presentation explores the behaviour of photons in strong gravitational fields, revealing a symmetrical relationship between photon energy changes and gravitational fields. The equations:

E = hf; ρ = h/λ; ℓₚ/tₚ (Equation 1)

Eg = E + ΔE = E − ΔE; E = Eg (Equation 2)

Eg = E + Δρ = E − Δρ = E; h/Δλ = h/−Δλ (Equation 3)

Eg = E; Δρ =−Δρ; ℓₚ/tₚ (Equation 4)

demonstrate the consistency of photon energy in gravitational fields, highlighting the symmetrical effects of wavelength changes due to gravity. This symmetry contradicts general relativity's predictions, suggesting that the theory might be incomplete or incorrect in this context. By engaging with alternative perspectives and addressing the contradictions raised by these equations, we can foster a deeper understanding of the universe and its underlying laws, ultimately working towards a more complete and accurate description of reality.

The pursuit of knowledge in science is exemplified by valid and established lines of inquiry that challenge the concept of curvature in general relativity. This ongoing refinement of our understanding of the universe is a testament to the dynamic nature of scientific inquiry. Researchers and theorists have proposed alternative perspectives on spacetime, gravity, and reality, aiming to address general relativity's limitations and inconsistencies.

The observed symmetry, where photons gain energy approaching a gravitational well and lose energy leaving it, may hold the key to refining our understanding of spacetime and gravity. This phenomenon, described by the equations Eg = E + ΔE = E - ΔE (Equation 2) and h/Δλ = h/-Δλ (Equation 3), contradicts general relativity's predictions and aligns with other scientific disciplines and mathematical frameworks.

This discrepancy suggests that general relativity might be incomplete or incorrect in this context, warranting further exploration and refinement. Alternative theories, such as quantum gravity and flat spacetime theories, may offer a more comprehensive explanation for this phenomenon. By engaging with these diverse perspectives and addressing the contradictions raised by the equations, we can foster a deeper understanding of the universe and its underlying laws, ultimately working towards a more complete and accurate description of reality.

For relativists, fiber optic gyroscopes are fatal.

Fiber optic gyroscopes have been widely used, which proves that the view that the basic theory of relativity "in any inertial system, the speed of light is constant" is wrong!

It proves that light is pulled by the gravitational field, and the speed of light on the earth will be superimposed on the moving speed of the earth! This is also the fundamental reason why the Michelson-Morley experiment cannot measure interference fringe movement.

When the fiber optic gyroscope is stationary relative to the ground, it cannot measure the rotation speed of the earth.

If the light on the earth is not superimposed on the moving speed of the earth (that is, the moving speed of the earth's gravitational field), then the fiber optic gyroscope cannot accurately measure it.

Everyone, physicist or not, seems to know what forces are, at least for mechanical, gravitational, and electromagnetic forces. And, even physicists take this sense of forces deeper into physics to recognise other forces, even those that may exist. So, what exactly are forces? How many kinds are there? Do we classify forces by their 'strength'? by their 'distance'? by their 'position'? by the 'object'? by their 'roles'? by their 'origin' ? Are forces and matter separate entities? Are force and energy separate entities?

In physics, there are many kinds of mass [1], all of which are called 'mass'; there are many kinds of energy, all of which are called 'energy' [2]; and similarly, physics suggests that there are four basic forces, electromagnetic, weak, strong, and gravitational, all of which are called 'force'. We have been accustomed to treating these things with the same dimension as if they were different, and no longer bother to find out whether the differences are essential or not.

The classical concept of force, with direction, magnitude and point of action, obeys the principle of vector superposition, but there is no concept of propagation and field. Obviously, this force is only a macroscopic equivalence.

The concept of force in QED and QCD is propagation and exchange of 'virtual particles'. The electromagnetic force is an 'virtual photon', the weak force is an 'virtual W boson', the strong force is an 'virtual gluon', and the gravitational force is an ( virtual) 'graviton'. The definition of force chooses to exchange discrete 'virtual particles' with no definite parameters, rather than the real continuous, intersecting 'field' of matter itself.

QFT argues that 'symmetry dictates interaction (force)' [3][11], Symmetry Create a Force [4]. Invariance, symmetry, and conservation are associated and even identical concepts [5][11]. QFT believes that the first three forces have already achieved 'unification', gauge fields based on different Lie groups, and that the current focus of theoretical physics is on quantum gravity. Is this ‘unification’ what we really understand? Can symmetry be understood as field exchange?

I have tried many ways to find an acceptable description of the weak force, but without success. Most physicists simply say that the weak force is a special kind of force^①. It is not attraction or repulsion, it is transformation. Can a transformation that be described by symmetry cannot be described by an intuitive force? It should not. Any transformation must involve a spatio-temporal change between interacting fields, and that should characterise the action of the force field^②. It is just that we are not yet able to specify it.

It is generally assumed that the 'unification' of forces would be at a very high energy level [8], and at the time of the Big Bang, the forces were unified. We think of the Big Bang as the starting point because we are currently in a state that is midway from the Big Bang. But shouldn't the so-called ‘singularity’ of the Big Bang be a result in the first place? There is no reason to deny that it is the end of a previous state of the universe. It should then be assumed that forces are uniform at any stage of the evolution of the universe, and that what is not uniform is only the way they are expressed. Shouldn't the unity here be the same as the unity of QFT?

Is there a process by which force fields are generated? Observe the annihilation process, e+ e- → γ+γ. Does the attraction between the electrons 'disappear' at the end of the reaction? Where does the accompanying force field go? In turn, γ+γ → e+ e-, the photons transform themselves into electron pairs with the help of the field inside the atom^③. The electromagnetic field is not newborn in this process, but has always been there, only transformed in form. Physics considers the nuclear force as the strong force ^④ that maintains the stability of the nuclear structure. According to the cosmic evolutionary process, there is a period of nucleosynthesis [9]. Where is the strong force when there is no nucleus formation? Waiting in the void? Obviously it is impossible. The only force at this time is the force of the quark (assuming it has been created) itself under extreme space-time conditions. The nuclear structure can only be produced by it and maintained by it. Therefore, force must be united with matter [7]; we cannot separate force from matter. All matter is a form of energy-momentum, therefore without energy-momentum there is no force^⑤ . The force field is the expression of the energy field and the matter field when they interact with each other, and there is only the difference between equilibrium and non-equilibrium.

With this line of thought can we answer the following question:

1) Is inertia a force? Are Newton's first, second, and third laws unified? Should all motions, including motion 'at rest' with zero velocity, and the fastest motion, the speed of light, be interpreted in the same way? Isn't light the baseline of inertia? shouldn't the baseline of relativity be equally the baseline of the forces?

2) Is gravitational redshift a 'force'? Is cosmological redshift a 'force'? Is the Doppler effect a 'force'? Aren't they all interacting processes? Aren't they all processes that exchange energy and momentum? If all redshifts are forces, does that mean that gravitational and expanding spacetime are associated with electromagnetic fields?

3) Interference is an interaction, but is interference a force, either in free space or on an interferometer?

4) Is vacuum excitation, if any, a force? Is there a force in the 'probabilistic interpretation' of the wave function? Is there a force in the 'Uncertainty Principle'? Is there a 'force' in the 'fluctuation' of a quantum field? Is 'coupling' a force? They are all manifestations of interaction, how can they be unified?

5) Are the four interacting forces independent of each other? The electromagnetic force is independent of the gravitational force, and there is no interaction between the strong force and the weak force. ......? If they are completely different things, why do we define them all as 'forces'? If there is a commonality, why are they independent of each other? Wouldn't they be the same force in different situations?

6) Forces have always been there, with or without them. If they have an 'origin', what is the 'force' that produces them?

7) Electromagnetic potentials, gravitational potentials, Yukawa potentials, Higgs potentials, are they all expressions of forces? Are they entities [10][12][13][14] or are they distributional 'parameters' of the field? Is the unity of 'force' the unity of potential?

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^① “The weak interactions have even a very much shorter range and, so far as we know, are not responsible for holding anything together. They are, however, responsible for nuclear beta decay." Weinberg also said that the weak force is a strange force because it is not described in electrodynamics. It occurs slowly, but causes atomic nuclei to decay. It is hoped that a new and similar theory will be developed to explain it.

^② There is no need to be confused about the fact that the weak force is able to effect a transition within the nucleus, rather than causing a split, simply because it is not strong enough; the ‘transition’ is still in fact a process of splitting to the nearest state. This process maintains the overall structure of the nucleus, but not the state of the nucleus.

^③ Physics considers vacuum excitation.

^④ "But the known forces, gravity and electromagnetism, were insufficient to bind protons and neutrons tightly together into objects as small as the observed nuclei. Physicists were confronted with a new force, the most powerful in nature. "[6]

^⑤ If conservation of energy and momentum is the first principle, the exchange and conservation of energy and momentum is the source of 'force'.

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[1] https://www.researchgate.net/post/NO45_What_is_Mass_Must_the_Hierarchy_of_Mass_be_Determined_Simultaneously_by_the_Origin_of_Mass?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSIsInByZXZpb3VzUGFnZSI6InByb2ZpbGUiLCJwb3NpdGlvbiI6InBhZ2VDb250ZW50In19

[2] https://www.researchgate.net/post/NO10_Can_different_forms_of_energy_be_unified2?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSIsInByZXZpb3VzUGFnZSI6InByb2ZpbGUiLCJwb3NpdGlvbiI6InBhZ2VDb250ZW50In19

[3] Yang, C. N. (1980). Einstein's impact on theoretical physics. Physics Today, 33(6), 42-49.

[4] Schmitz, W. (2019). Particles, Fields and Forces. Springer.

[5] https://www.researchgate.net/post/NO20Symmetry_Invariance_and_Conservation_1-Who_is_the_Primary?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSIsInBvc2l0aW9uIjoicGFnZUNvbnRlbnQifX0

[6] Wilczek, F. (2005). "Nobel Lecture: Asymptotic freedom: From paradox to paradigm." Reviews of Modern Physics 77(3): 857.

[7] Wilczek, F. (2016). Unification of force and substance. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374(2075), 20150257.

[8] Dienes, K. R., Dudas, E., & Gherghetta, T. (1999). Grand unification at intermediate mass scales through extra dimensions. Nuclear Physics B, 537(1), 47-108. https://doi.org/https://doi.org/10.1016/S0550-3213(98)00669-5

[9] Allahverdi, R., Amin, M. A., Berlin, A., & etl. (2020). The first three seconds: a review of possible expansion histories of the early universe. arXiv preprint arXiv:2006.16182.

Fields, B. D., Olive, K. A., Yeh, T.-H., & Young, C. (2020). Big-bang nucleosynthesis after Planck. Journal of Cosmology and Astroparticle Physics, 2020(03), 010.

[10] Aharonov, Y., & Bohm, D. (1959). Significance of electromagnetic potentials in the quantum theory. Physical Review, 115(3), 485.

[11] Wu, A., & Yang, C. N. (2006). Evolution of the concept of the vector potential in the description of fundamental interactions. International Journal of Modern Physics A, 21(16), 3235-3277.

[12] Yukawa, H. (1935). On the interaction of elementary particles. I. Proceedings of the Physico-Mathematical Society of Japan. 3rd Series, 17, 48-57.

[13] Agrawal, P., Saha, D., Xu, L.-X., Yu, J.-H., & Yuan, C.-P. (2020). Determining the shape of the Higgs potential at future colliders. Physical Review D, 101(7), 075023.

The lack of experimental data, the ambiguous representation of the real picture of the world in most models, theories, and hypotheses about the Universe, and the huge scale factor of the issues under study, have led to the fact that many problems have arisen in modern physics, astrophysics, and cosmology. Among this set, the most relevant and debatable are the following problems:

- the optimal choice of the metric tensor for solving the Einstein equation of the General Theory of Relativity, which most fully corresponds to modern experimental data. As a consequence of this optimal choice, there is a need to correct the basic equations of cosmology, which is also due to new experimental measurements of the Hubble constant;

- an ambiguous experimental estimate of the Hubble constant;

- stability of constants, the maximum transmission rate of physical interaction;

- dark energy and dark matter;

- correct choice of the coordinate system in cosmological studies;

- the physical nature of the cosmological constant;

- representations of the general structure of the Universe;

- concepts of the Big Bang, singularity point, initial conditions, and limitations;

- connections of the Standard Model of physics with gravitational interaction;

- understanding the features of the quantum-wave nature of the gravitational field;

- the physical nature of time and its relationship with real space;

- the optimal choice of the quantum-wave model of the gravitational field of the observable Universe and the development on this basis of its physical and mathematical description, which corresponds to the modern set of experimental data in astrophysics and cosmology;

- estimates of the scale factor between the microcosm and the macrocosm of the observable Universe; - estimates of the mass of distant objects of the observable Universe;

- carriers of the gravitational field and dark matter.

With the term “gravity”, we refer to the phenomenon of the gravitational interaction between material bodies.

How that phenomenon manifests itself in the case of the interaction of two mass particles at rest relative to an inertial reference frame (IRF) has, in the framework of classical physics, mathematically been described by Isaac Newton. And Oliver Heaviside, Oleg Jefimenko and others did the same in the case of bodies moving relative to an IRF. They described the effects of the kinematics of the gravitating objects assuming that the interaction between massive objects in space is possible through the mediation of “the gravitational field”.

In that context, the gravitational field is defined as a vector field having a field- and an induction-component (E_g and B_g) simultaneously created by their common sources: time-variable masses and mass flows. This vector-field (a mathematical construction) is an essential element of the mathematical description of the gravitational phenomena, and as such an element of our thinking about nature.

One cannot avoid the question of whether or not a physical entity is being described by the vector field (E_g, B_g) and what, if any, is the nature of that entity.

In the framework of “the theory of informatons”^[1],[2],[3], the substance of the gravitational field – that in that context is considered as a substantial element of nature - is identified as “gravitational information” or g-information” i.e. information carried by informatons. The term “informaton” refers to the constituent element of g-information. It is a mass and energy less granular entity rushing through space at the speed of light and carrying information about the position and the velocity of its source, a mass-element of a material body.

[1] Acke, A. (2024) Newtons Law of Universal Gravitation Explained by the Theory of Informatons. https://doi.org/10.4236/jhepgc.2024.103056

[2] Acke, A. (2024) The Gravitational Interaction between Moving Mass Particles Explained by the Theory of Informatons. https://doi.org/10.4236/jhepgc.2024.103060

[3] Acke, A. (2024) The Maxwell-Heaviside Equations Explained by the Theory of Informatons. https://doi.org/10.4236/jhepgc.2024.103061

Free spacetime contains no energy-momentum^*, so when objects m are travelling at constant velocity in it, they do not exchange energy-momentum. Non-free spacetime contains energy-momentum. The Einstein field equation of general relativity,

Rµν - (1/2)gµνR = G*Tµν,

expresses the relationship between the energy-momentum (mass) and the structure of spacetime ( metric) at a point (region) in spacetime^**. Usually we think that "Gravity couples universally to all forms of energy" [1]. Then, we need to ask three basic questions:

1) What is the best way to express the energy-momentum of the gravitational field? or how are the "long-standing problems about energy-momentum localisation in GR" [2][3][4] addressed? The energy-momentum of the gravitational field is the energy-momentum of the spacetime field, which must be localizable. The energy-momentum of the spacetime field must involve only the spacetime parameter xi(i=0,1,2,3), because the independent spacetime field has no other parameter (or it has some other hidden parameter that does not play an explicit role). But it cannot be expressed directly in terms of spatio-temporal coordinates (t,x,y,z) because they must be background independent, nor can it be expressed in terms of time lengths T and space lengths L because we have no way of determining the measurement boundaries. So what are the remaining covariates? The rates of measure change, curvature, and deflection, etc.. which are the most appropriate? Even if we consider space-time as a "medium", what are the properties of the medium? Density, elasticity? What density? What elasticity?

2) By what means are gravitational fields and other forms of energy-momentum exchanged with each other? Obviously it must be through a common covariate, and then the only option available is the spacetime covariate. Does this qualify that all other forms of energy-momentum must contain spacetime covariates? Includes energy-momentum of dark matter (no dark energy involved). And more critically, the form of these spacetime Attributes and the form in which the spacetime energy-momentum is expressed should be the same, i.e., if the energy-momentum of spacetime is expressed in terms of a change of metric, the other forms of energy-momentum must be related to a change in the spacetime metric; and if it is expressed in terms of a curvature, the other forms must be related to a change in the curvature.

3) Is the energy-momentum of the gravitational field conserved[5]? If the energy-momentum of the gravitational field is not conserved, what will become of the gravitation dominated evolution of galaxies?

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^* We need to distinguish between the concepts of space-time and vacuum.“Are Vacuum and Space Two Separate Things?”，https://www.researchgate.net/post/NO34How_the_View_of_Space-Time_is_Unified_6-Are_Vacuum_and_Space_Two_Separate_Things；

^** The concept of a strict "point" interaction does not really exist in physics.

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[1] Kiefer, C. (2006). Quantum gravity: general introduction and recent developments. Annalen der Physik, 518(1-2), 129-148.

[2] Einstein Ann. d. Phys. 49, 769 (1916).

[3] Hestenes, D. (2021). Energy-Momentum Complex in General Relativity and Gauge Theory. Advances in Applied Clifford Algebras, 31(3), 51.

[4] Møller, C. (1958). On the localization of the energy of a physical system in the general theory of relativity. Annals of Physics, 4(4), 347-371.

[5] Szabados, L. B. (2009). Quasi-local energy-momentum and angular momentum in general relativity. Living Reviews in Relativity, 12(1), 1-163.

Force fields, including the gravitational field, contain an energy density. We therefor can exclude that a field source, moving with constant velocity, does permanently emit its static field. Providing the field energy content again and again would exhaust the field source.

We therefor must conclude that force fields are co-moving with its source as long as the source is not accelerated. But according to the co-movement, any local field strength value is instantaneously valid without any retarded transmission from the field source.

In cosmic distances it makes a tremendous difference if the proposed field retardation is real or not.

The consequence is that all calculations of galaxy dynamics are wrong, if they are based on that alleged retardations. Only the impact of accelerated movements is retarded.

The severe problem is that an absolute negative energy density of gravitational fields is not possible, because then a field source could not adapt its field via aperiodic radiation to a modified velocity.

Therefor we need a cosmic dark energy field with an extremely high energy density, sufficient to compensate for the negative energy density of gravitational fields around neutron stars.

If we consider that the gravitational field strength around neutron stars is about a factor 2.0E+11 stronger as the earth field, the omnipresent dark energy field must have a giant energy density.

The presence of such a strong field turns cosmology inside out. It even adds a new player to the theory of elementary particles. Such a strong field of gravitational nature could stabilize quarks and electrons.

The discussion should be about the pros and cons of the existence of such an omnipresent dark energy field and about the consequences, if such a field exists.

In standard physics and standard cosmology such a field is not considered.

Conventional physics emphasizes experiments verifying objective reality but both quantum mechanics (QM) and originator of the multiverse hypothesis Hugh Everett suggest there's no such thing as objective reality.

Regarding QM - if quantum superposition is taken to its logical extreme, everything in the universe would affect everything else. Regarding Everett - his idea of the universal wavefunction says the observed and observer are all mixed together. These two references mean an experimenter's consciousness can never avoid influencing (technically, biasing) an experiment.

Physicists would be aware of these QM/Everett things but they seem to be unconsciously reverting to a classical view in which objective reality exists in all space-time, and not just in the limited perceptions of humans or animals. Our restricted senses (along with the limited technology and mathematics developed by humans to date) might view a quantum superposition where everything, including consciousness, fills all space and time very differently. For example - instead of occupying the whole of spacetime, a subatomic particle could be interpreted as being in more than one place simultaneously.

Another instance of quantum mechanics being re-interpreted: The ones and zeros of binary digits are compatible with quantum mechanics and may be referred to as the Hidden Variables which Albert Einstein advocated to complete quantum physics, and to give its calculations an exactness which would bring a hidden order to its chaotic randomness and superficial uncertainty. If the universe can be quantized and viewed as comprised of infinitesimal ones and zeros, how could it not obey quantum physics? And if those ones and zeros are all ultimately connected by Quantum Gravity to make everything in space and time parts of a unification, waves and particles could never be separated but wave-particle duality would rule.

The precise, merely superficially probabilistic Quantum Mechanics proposed here unites each quantum object in space, and in every period of time. Macroscopic objects are composed of quantum ones and the two scales should be unified by a QM that produces exact results and is as applicable to the micro as much as it is to the macro. Unification of the microscopic and macroscopic in all of space and time can be regarded as only one point ever existing (a state reminiscent of John Wheeler and Richard Feynman speculating that the universe consists of a single electron zigzagging through time). This might be termed unipositional quantum mechanics in which transmissions throughout spacetime are instantaneous. If signaling can be instant, distance may be an illusion, making intergalactic travel feasible and eliminating all “distance” between past/present/future periods of time).

It's plausible that quantum entanglement by "advanced" and "retarded" components of electromagnetic and gravitational waves will play a role in this UQM. In 2008's "Physics of the Impossible", Michio Kaku writes -

"When we solve (19th-century Scottish physicist James Clerk) Maxwell's equations for light, we find not one but two solutions: a 'retarded' wave, which represents the standard motion of light from one point to another; but also an 'advanced' wave, where the light beam goes backward in time.”

(In 1925's "Electrodynamics in the general relativity theory", George Yuri Rainich discovered that Einstein's equations state gravitational fields possess enough data about electromagnetism to allow Maxwell's equations to be restated in terms of them. Therefore, gravitational waves may likewise have retarded and advanced portions.) Advanced waves were much loved by Richard Feynman. They travel back in time and when combined with the retarded waves which go forwards in time, their entanglement would result in an "eternal present" necessary for time travel.

John G. Cramer wrote in his 2022 article "Advanced Waves Detected" - “In summary, it appears that advanced waves do exist and have been detected. Much more work must be done to ensure that this effect is real and can be extended, but the physics implications are gigantic.”

Gravitational waves are ripples of spacetime propagating at the speed of light [1]. A gravitational wave can be described as a small perturbation h_μν on a flat spacetime metric η_μν [2]:

g_μν = η_μν + h_μν ....... (Eq.1)

1) Cosmological observations prove that the speed of gravitational waves and the speed of light are identical [3]. In the absence of any third party or any law constraints, if the speeds of gravitational waves and light are exactly the same, they cannot be independently unrelated to each other, so what should be the relationship between them?

2) "The energy associated with gravitational waves is a second-order effect, and so its justification goes beyond the linearised approximation considered so far. ...... Aside from energy, GWs may also carry angular momentum and linear momentum" [1]. Gravitational waves undoubtedly contain energy, and when it travels at the speed of light, it means that the energy spreads at the speed of light and that there is momentum, not that there may be momentum. It does not make sense that energy travelling at the speed of light is not light and is not directly related to light. Light itself contains defined energy and momentum, why wouldn't a gravitational wave contain both defined energy and momentum? How is it best defined if its energy and momentum are defined with only the spacetime parameter?

3) We usually interpret gravity as a geometrical effect of spacetime, and also as an exchange of "gravitons", what is the relationship between these two interpretations, and are gravitons embodied by spacetime parameters? Is there local gravity inside a gravitational wave? What is its relation to the "graviton"?

4) One can think of hμν as the coefficients of the spacetime metrics <Δt, Δx, Δy, Δz>, which, if combined, can express this ripple wave packet in terms of the variable metrics <Δt', Δx', Δy', Δz'> (there is a Locked Relationship between the space and time metrics). Then, in such a spacetime, let us assume that there is a light that is fully accompanied by gravitational wave propagation, i.e. they have a common source:

4.1) How do we define the speed of propagation of light when light itself is in <Δt', Δx', Δy', Δz'>? Defined as c=Δs' /Δt', Δs' = √(Δx'² + Δy'² + Δz'²), it means that light is a synchronised ripple like gravitational waves.

4.2) How do we define the speed of gravitational waves themselves? Gravitational waves are the propagation speed of their own spacetime fluctuations <Δt', Δx', Δy', Δz'>. That is, how do we define the speed of propagation of this <Δt', Δx', Δy', Δz'>? How much distance Δs it travelled in what time Δt?

4.3) LIGO directly measures the length contraction of space, not "bending". "Gravitational waves change the metric describing the spacetime between two freely falling test masses" [1]. "strain-to-length relation used in GW detection based on Michelson interferometers is h+=ΔL/L" [2]; if we consider the geometrical nature of Space-Time Curvature. Can we design a direct measurement of Space-Time Curvature?

4.4）“If light waves are stretched by gravitational waves, how can we use light as a ruler to detect gravitational waves?” This is explained in the literature [4]; is it sufficiently rational?

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[1] Bambi, C., Katsanevas, S., & Kokkotas, K. D. (2022). Handbook of Gravitational Wave Astronomy. Springer Nature.

[2] Cahillane, C., & Mansell, G. (2022). Review of the Advanced LIGO gravitational wave observatories leading to observing run four. Galaxies, 10(1), 36.

[3] Abbott, B. P., Abbott, R., Abbott, T., Acernese, F., & etal. (2017). Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A. The Astrophysical Journal Letters, 848(2), L13.

[4] Saulson, P. R. (1997). If light waves are stretched by gravitational waves, how can we use light as a ruler to detect gravitational waves? American Journal of Physics, 65(6), 501-505.

Let ε_g be the energy of the gravitational field;

ε_s is the energy of the substance.

if both quantities are positive conservation law:

δ ε_s + δ ε_g = 0

But the energy of a stationary gravitational field is negative!

Does this mean that as the energy of matter decreases, the absolute value of the field energy also decreases? Those. in this case, part of both energies disappears?

Or in this case

δ ε_s - δ ε_g = 0 ?

General Relativity field equations [1]:

G_µν = G*T_µν...... (EQ.1).

It is a relation between the matter field (energy-momentum field) T_µν and the spacetime field G_µν, where the gravitational constant G is the conversion factor between the dimensions [2].Einstein constructed this relation without explaining why the spacetime field and the matter field are in such a way, but rather assumed that nine times out of ten, they would be in such a way. He also did not explain why the spacetime field G_µν is described by curvature and not by some other parameter. Obviously, we must find the exact physical relationship between them, i.e., why T_µν must correspond to G_µν, in order to ensure that the field equations are ultimately correct.

We know that matter cannot be a point particle, it must have a scale, and matter cannot be a solid particle, it must be some kind of field. The fact that matter has a scale means that it has to occupy space-time; the fact that matter is a field means that it is mixed with space-time, i.e., matter contains space-time. So, when applying Einstein's field equations, how is matter's own spacetime defined? Does it change its own spacetime? If its own energy-momentum and structure have already determined its own spacetime, should the way it determines its own spacetime be the same as the way it determines the external spacetime? If it is the same, does it mean that the spacetime field is actually a concomitant of the matter field?

If one were to consider a gravitational wave, one could think of it as a fluctuating spacetime field that propagates independently of the material source after it has been disconnected from it. They have decoupled from each other and no longer continue to conform to the field equations (EQ.1). Although gravitational waves are the product of a source, the loss of that source prevents us from finding another specific source for it to match it through the equation (EQ.1). Just as after an electron accelerates, the relationship between the radiated electromagnetic wave and the electron is no longer maintained. Does this indicate the independence of spacetime field energies?

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♛ “Does the Energy Tensor T_µν in the Field Equations Contain the Energy-momentum of the Spacetime Field?”：https://www.researchgate.net/post/NO37Doubts_about_General_Relativity_2-Does_the_Energy_Tensor_Tmn_in_the_Field_Equations_Contain_the_Energy-momentum_of_the_Spacetime_Field

♛ “Is the Geometry Interpretation of Gravity a Paradox?”：https://www.researchgate.net/post/NO36_Doubts_about_General_Relativity_1-Is_the_Geometry_Interpretation_of_Gravity_a_Paradox

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[1] Grøn, Ø., & Hervik, S. (2007). Einstein's Field Equations. In Einstein's General Theory of Relativity: With Modern Applications in Cosmology (pp. 179-194). Springer New York. https://doi.org/10.1007/978-0-387-69200-5_8

[2] “The Relationship Between the Theory of Everything and the Constants of Nature”：https://www.researchgate.net/publication/377566579_The_Relationship_Between_the_Theory_of_Everything_and_the_Constants_of_Nature_English_Version

The idea is based on these observations:

•Maxwell I, derived from Biot Savard law and divergece math identities is an analoque to the Einstein field equation relating curvature to mass-energy, i.e they both quantify the magnitude of force/force effect

• Einstein equations hypothesize an underlying gravitational field from which equations of motion detive. Same with Maxwell but with photons

•They both predict ot have plane wave solutions (EM waves and gravitational waves).

Note: While EM waves have been a basis fr commercial implementation, GR grav waves have only bern proposed for scientific utility and canot be produced in the lab.

But is this a final remark or can it be researched more to provide a valid answer?

Response to the You Tube video https://www.youtube.com/watch?v=-HHv3T4UHec

Albert could teach Dr Oppenheim a thing or two. The need by the doctor to introduce randomness into spacetime suggests spacetime already has the properties of quantum particles. Therefore, quantum gravity is the way to go. A paper by Albert asked if gravity plays a role in the composition of elementary particles. This has the potential to unite gravity - the curvature of spacetime - with quantum particles. A particle in the slit experiment would be the result of the one gravitational field composing the universe. The field can't split in two. So, the particle's seeming appearance in two places at once is the result of our limited understanding plus the restrictions of the limited technology we build and use for experiments.

The motivation comes from the following common observation. Blocks of stone with large dimensions (say of the order of three meters or larger) can be easily fractured into two pieces. First, cylindrical holes are introduced at top surface using drills. Second, fracture is initiated from the holes with the help of sledgehammers and wedges. Without any additional action, the crack will move with time downward other very large distance and separate the block of stone into two parts. The fracture surface is perfectly flat. What is the reason?

How do you see this gravitational field equation? Can it replace Albert Einstein's theory of relativity? I found the "repulsion force", the opposite of Newton's gravity. With this force, with this change, Oliver.Heaviside's gravitational magnetic equations are not contradictory.I added a negative sign to the gravity acceleration formula, that is: f= -mg, and then I derived a Poisson equation with a negative sign:Δ^2φ=-4Gρπ

This hypothesis has an aim to originate two manifolds which are dark energy field and gravitational field and these both fields can go singularity related with Poincare Conjecture. If you would like to see more details about this subject which is mentioned above, you can look at the pdf below.

Comparing gravitational field to electromagnetic field, the charge has the same sex and the opposite sex, but there are two kinds of "force"? Is there any gravity and any repulsion? What if Newton's second law was the repulsive force?

If I elevate a mass in a gravitational field, I have given the mass gravitational potential energy. This gravitational potential energy is usually presumed to be stored in the gravitational field between the two objects.” This implies a gravitational field has quantifiable energy density that increases when two gravitationally bound masses are separated.

This logical problem is “solved” by declaring the zero-reference point for gravitational potential energy is at infinite distance. This makes gravitational potential energy a form of negative energy and implies a gravitational field has negative energy density. The positive energy exerted to elevate a mass has reduced the amount of negative energy in the universe.

Does any gravitational field have quantifiable negative energy density? Does negative energy produce positive gravitational effects? The most extreme example of a gravitational field is a black hole. Does the event horizon of a black hole have infinite negative energy density? Does negative energy exist?

Dear Wolfgang Konle

You asked: Do you think that it is by accident that the integral (12) ∆Wfield just has the same value if you insert -1/(8πG) for alpha?

YES. It is a Fallacy.

The point where you created your fallacy is equation 12. That is when you put together three divergent integrals into a single integral and postulate a single r_0, later to be conflated with the r in the Potential Energy calculation.

Self-Energy of Coulomb or Gravitational forces are infinite (cannot be calculated). The example of a "Gravitational Capacitor" is contrived and can only be calculated in the case of electrostatics, where the field goes to zero on the conducting plates and is considered constant between the plates. The energy in the electrostatic capacitor is not being mapped to the self-energy of the EXTRA electrons in the plate, but they should. What you calculate there is the energy of the setup. That always fails when you consider a Coulomb potential.

Even there, if you allow for the existence of charges, the self-energy would become infinite.

So, by accident and carelessness, the difference in "Gravitational Field Energy" becomes "similar" to Potential Energy.

Of course, in the case of potential energy, the value of r is defined by the distance between the centers of mass of the two bodies.

In your case, r_0 has no meaning since, in your case, you are changing the mass of one of the bodies to become M+m. There is no physical process of moving masses or anything defining a geometry.

That is when the Fallacy was born.

From that, you started believing in the existence of a Gravitational Field Energy that is pervasive and not connected to the capacity of producing work (as it is in the definition of Potential Energy).

Since you started believing in your mistake, you conjured up a POSITIVE COSMIC GRAVITATIONAL FIELD ENERGY...

Since the positive energy nature of our Universe is already an unsurmountable problem in Physics (for the garden-variety scientists), adding more positive energy makes NO SENSE.

If Gravitational Field Energy is a real Physics construct, it should be well-defined irrespective of the interacting masses. For example, Newton's Gravitational force is GMm/r^2 irrespective of the interacting masses.

This means that one should be able to define it for each mass (M, m, and M+m). So, one should be able to calculate them independently and then calculate the difference.

Separate the integral into three integrals. One for M, another for m, and another for M+m. This should be done because U_g(M) is a concept that is defined for a mass M, so it shouldn't be dependent upon the other masses.

Call the smallest radii r_0, r_1, and r_2.

Now explain to us why r_0 should be equal to r_1, and r_2?

This is important because only when they are identical, is that one recover Newtonian Dynamics. Would would the radius used to calculate the Field Energy of a hydrogen atom be the same as the radius used to calculate the Gravitational Field Energy of TON618?

The point here is that you forced them to be equal to recover the value of Potential Energy, and that is where your sleight of hand took place.

There is no justification for it.

This is my full argument. Below is a rebuttal to a counterargument.

"Gedanken Experiment" is not an explanation since another "Gedanken Experiment" where the two masses join without just touching each other would give a distinct result. In other words, the Gravitational Energy Field definition should not depend on how the masses joined.

Marco Pereira

The only real theory of gravity is Einstein's General Theory of Relativity. The object of this theory is Einstein's physical space. This object has mass density, momentum and stress. However, the speed of the physical vacuum does not make sense. The same feature is inherent in the electromagnetic field. This property of the gravitational field (4-space) is equivalent to the requirement that there is no absolute coordinate system.

Thus, it is pointless to try to give meaning to the gravitational field to fields that have a certain speed. However, most hypothetical alternatives to general relativity have precisely this property, for example by incorporating such matter fields into the operation of classical general relativity.

It is this “extension” of the general theory of relativity that most researchers are engaged in. It is clear that this activity has nothing to do with gravity. Moreover, an adequate Einsteinian theory of gravity already exists.

Perhaps the only weak point of the general theory of relativity is the absence of a full-fledged conservation law. However, the introduction of the gravitational field energy-momentum tensor into the theory eliminates this drawback. More precisely, the field energy-momentum tensor is introduced into Einstein's gravitational field equation.

The updated theory has acquired the law of conservation of energy. In addition, the previously meaningless part of the Schwarzschild solution g_{00} became a finite continuous positive function.

In Special Relativity, a photon of frequency f is considered as a particle of mass m=h f/c2 with zero proper mass. It is experimentally verified that the photon carries momentum and exerts radiation pressure on the targets it impacts.

On the other hand, in General Relativity, it is proposed that the gravitational interaction between massive objects is due to the fact that gravitational field curves space-time. It has been verified that a massive body alters the trajectory and velocity of a beam of light that interacts with its gravitational field (Shapiro effect and gravitational lens effect). Within the frame of General Relativity, these effects are explained by proposing that photons follow geodesic trajectories within curved spaces. Obviously in this framework the mass of the photons can be considered negligible. But, in General Relativity, is the photon a massless particle?

According to the principle that force is an exchange of "virtual particles", the "graviton" appears only when an object enters the gravitational field, how does it appear? Where is the "graviton" when only isolated matter carries its own gravitational field?

According to the principle that space-time is "curved" by matter, and curved space-time is gravity, is the "graviton" a part of matter? Does it also participate in the bending of space-time? Or is it the bending of space-time that produces the "graviton", and must the graviton also propagate along the geodesic?

a) Space-time is a kinetic "background medium "* that we should consider as a universal energy-momentum form. It can be transferred and exchanged like any other form of energy-momentum, and thus has the ability to change, and to be changed. Any elementary particle possesses an intrinsic spacetime parameter, which is where SR's "Length Contraction and Time Dilation" manifests itself, and why GR matter is able to change spacetime. Any interaction must be transmitted and exchanged through spacetime.

b) Different forms of energy-momentum can cause spacetime "bending", which must reflect the unity of energy-momentum [1]. The only thing that can cause spacetime to bend is spacetime. That is to say, energy-momentum, matter can only rely on its own spacetime to change other spacetime. Therefore, one of the properties that matter carries is the "curved" state of spacetime around it [2].

c) The essence of the "curvature" of spacetime is the unequal change of the components of the four-dimensional spacetime intrinsic metric Δs={Δt,Δx,Δy,Δz}† . This can be expressed as (ds)^2=-(a0*dt)^2+(a1*dx1)^2+(a2*dx2)^2+(a3*dx3)^2, with a0~a3 unequal. Such a definition is concise and physically complete, and is able to unify all spacetime-related concepts under the Minkowski spacetime framework. Consider spacetime as consisting of arbitrarily small-sized elements ΔV, which are of the same size, but in which the metric components Δt,Δx,Δy,Δz can be different. This requires the existence of two different properties of spacetime, an absolute positional coordinate and a relative metric between positions. This is equivalent to giving spacetime the concept of "metric density". Obviously it presents the media role of spacetime in a more vivid way.

d) This kind of definition of curvature can bring many convenient and reasonable explanations:

It guarantees the continuity of the whole spacetime and the global orthogonality of the three-dimensional space; it perfectly matches the "Length Contraction and Time Dilation" effect of SR and the Riemannian spacetime concept of GR✧.

Light does not change spacetime in free space, but participates in energy momentum to change spacetime in curved spacetime. Light changes spacetime in the same way that it is changed, e.g. gravitational redshift [4], violet shift, cosmological redshift, what actually happens is that its spacetime metric {Δt,Δx,Δy,Δz} is changed.

According to GR's causality, and reversibility, the energy-momentum causes the spacetime {Δt,Δx,Δy,Δz} to change, and then the energy implied by spacetime itself should be a function of Δt, and the momentum a function of Δx,Δy,Δz. This is the most direct and final expression, and the only possible choice!

Since the "geodesic" is the shortest path caused by energy-momentum L=∫ds=∫√gμν-dxμ-dxν, it is of course equivalent to the expression of energy-momentum. Therefore, this metric expression of distance has only a nominal meaning. In reality it should be the lowest "metric density" (lowest energy) path.

It is commonly believed that gravity is not a real force [5][6]. Objects move instinctively along geodesics, just as force is not required for inertial motion in free space. This interpretation is not in place††. It is the maintenance of energy-momentum conservation of the interacting system in a changing spacetime metric {Δt,Δx,Δy,Δz} that is the root cause of the "gravitational force" that leads to accelerated motion!

Criterion: What can change spacetime can only be spacetime. To change Δs={Δt,Δx,Δy,Δz}, another Δs'={Δt',Δx',Δy',Δz'} must join it, whether it is carried by a mass or arrives by a gravitational wave [7].

e) If the force is still defined according to the concept of exchanging virtual particles [10], then such a "graviton" does not exist‡. We must find a direct correlation between the so-called exchange of virtual particles and the exchange of energy-momentum. A "graviton "** exists if one considers the smallest unit of spacetime metric change due to the smallest unit of energy-momentum to be a "graviton". It consists only of the smallest spacetime metric {Δt,Δx,Δy,Δz} and must be dispersive. This is unlike any other elementary particle.

f) One of the symmetry manifestations of gravity should be the existence of positive and negative. If the theory has only gravity and no repulsion, then it must be deficient. Even if the repulsive force does not normally exist, a reason for its absence should be given.

g) When an interaction occurs, the energy-momentum involved is strong, the force presented is strong. In contrast to the electromagnetic force, the gravitational force is weak because it is not the main body of energy-momentum, but rather a spatio-temporal concomitant of the energy-momentum of matter, or an " residual " ♬.

1) How to define the concept of orthogonality of " intrinsic curvature " of spacetime between three spatial dimensions? How to realize its rationality?

(2) In the "curved spacetime", the "geodesic" is the shortest path, is its metric process essentially different from the "Length Contraction and Time Dilation" of SR?

3) Is the "graviton" currently sought by physics a detectable entity with a fixed form?

4) Doesn't it make sense that the positive or negative spacetime metric gradient determines whether an "attractive" or "repulsive" force is generated?

4) Photons are quantized, mass is quantized, and mass-induced "spacetime bending" should certainly be quantized. "Space-time bending" is equivalent to gravity. Doesn't the cause of space-time bending tell us what a "graviton" is? Aren't gravitational waves a collection of gravitons? Why do we have to search for "quantum gravity" through various assumptions，structures that are more fundamental than elementary particles [11]? Why should GR match the quantum framework and not the other way around?

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* "The main insight of Einstein's general relativity was the change of the role of space and time from a passive 'arena', in which physics takes place, to an active dynamical entity that is shaped by matter and acts back on it; but space-time remained a sharply defined classical object"[9]. However, space-time is not the same as matter in many ways, for example, it is universal, flat free space-time contains no energy-momentum, it can only be modified by the addition of energy, it can change nothing else. g = g0 + h, g0 is background metric (coordinate spacetime), contains no energy-momentum; h is modulation metric (relative spacetime), with energy-momentum. Therefore, it is appropriate to call this view of spacetime an upgraded version of the "Aether" doctrine [3].

✧ Einstein never argues for the spacetime bending premise in GR, but takes Gaussian coordinates directly, which seems to be the only option. In fact, in SR, point-particle states vary equally in each component of the measure, g00 = g11 = g22 = g33, and the other gμν = 0; when there is a scale for the object, it changes only in the direction of motion. In GR the static Schwarzschild spacetime g00, g11, g22, g33 is not 0, and the other gμν = 0. Forcing the other gμν = 0 does not lead to complete failure of GR.

† Expressing spacetime bending in a deformed "3D mesh" animation [14], although more graphically expressing Δs={Δt,Δx,Δy,Δz}, may result in definitional conflicts: can spacetime be locally and infinitely stretched or extruded, resulting in spacetime tearing, or overlapping? Can the bending directions of neighboring spacetimes conflict? Does the endowed bending of spacetime conflict with the external bending of the overall spacetime? How is the orthogonality of the overall 3D spacetime manifested? How do field representations reflect spacetime curvature when other fields are in curved spacetime?

§ As when light passes through a medium with different refractive indices n, resulting in a decrease in the speed of light. This actually reflects the change in spacetime density in the path.

†† We need to focus on why there is motion, not whether there are "forces". An ant and a bee both know the shortest path to their nests, but if the ant loses its legs, it will not be able to return to its nest, and if the bee loses its wings, it will fall free along the geodesic and will not return to its nest.

‡ The essence of exchanging "virtual particles" is to exchange fields; the essence of exchanging fields is to maintain the conservation of energy-momentum; maintaining the conservation of energy-momentum is manifested as "force".

¶ The energy-momentum itself is a function of space-time and manifests itself internally. When energy-momentum is exchanged with the outside world, there must be external motion to balance the exchange. In fact, the relationship between energy-momentum and space-time is reflected in both rest and motion.

** Defined in this way, the essence of the graviton is the minimum spacetime metric. Because the constituents of matter and energy-momentum that lead to the curvature of spacetime are different, the metric of spacetime curvature they lead to is also different. We need to note one thing, energy quantization is derived from the theory of blackbody radiation. It is not correct to generalize that the photon is the smallest energy quantum, it is simply the smallest energy quantum at a particular frequency E=hν. the same is true of the graviton.

♬ Wilczek said, "The apparent feebleness of gravity results from our partiality toward the perspective supplied by matter made from protons and neutrons ." [13]. Concerning the question of the order of magnitude of forces, why don't we first see that different forces are located in different structures, and why don't we analyze them structurally?

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[1] https://www.researchgate.net/post/NO10_Can_different_forms_of_energy_be_unified;

[2] https://www.researchgate.net/post/NO5_How_Fermions_combine_four_properties_in_one;

[3] Whittaker, E. (1910). A History of the Theories of Aether and Electricity, Courier Dover Publications（1989）;

[4] Will, C. M. (2018). Theory and experiment in gravitational physics, Cambridge university press.

[5] Ashtekar said,“Gravity is a manifestation of spacetime geometry”：Ashtekar, A. and E. Bianchi (2021). "A short review of loop quantum gravity." Reports on Progress in Physics 84(4): 042001. “”

[6] Kiefer said,“All manifestations of the gravitational field known so far can be understood from a classical theory—Einstein's theory of general relativity (GR), also called geometrodynamics. It is defined by the Einstein–Hilbert action." Kiefer, C. (2007). Lecture Notes in Physics-Approaches to fundamental physics, Springer. Why quantum gravity?: 123-130.

[7] Abbott, B., S. Jawahar and etl. (2016). "LIGO scientific collaboration and virgo collaboration (2016) gw150914: first results from the search for binary black hole coalescence with Advanced LIGO." PHYSICAL REVIEW D Phys Rev D 93: 122003.

[8] Why Should We Study Quantum Gravity? What Are Prima Facie Questions? Isham, C. J. (1994). Prima facie questions in quantum gravity. Canonical gravity: From classical to quantum, Springer: 1-21.

[9] Kiefer, C. (2007). Lecture Notes in Physics-Approaches to fundamental physics, Springer. Why quantum gravity?: 123-130.

[10] Cowan, G. (2012). "Review of particle physics." Phys. Rev. D 86(010001): 390.

[11] Mielczarek, J. and T. Trześniewski (2018). "Towards the map of quantum gravity." General Relativity and Gravitation 50(6): 68.

[12] https://www.researchgate.net/publication/373877548_Convergent_and_Disperse_Cyclic_Multiverse_Model_CDCMM；

[13] Wilczek, F. (2005). "Nobel Lecture: Asymptotic freedom: From paradox to paradigm." Reviews of Modern Physics 77(3): 857.

[14] Schutz, B. (2009). A first course in general relativity. China, Cambridge university press.

How we know about the dimensions given in sensations? At the level of our feelings three dimensions are not more than orientation of body in respect to the local gravitational field. Take off the gravity the dimensions will disappear in our feelings, so that is not good source of knowledge about the world's dimensions. Then, as always, will turn to the physics experiments. From there we know that any quantum field (perhaps except scalar which we have no in a stable form in reality) are built in a way to respect the symmetry of the 3+1 dimensional world and does depend on the 4 coordinates (which are in general is simply human way to mark a point, there are no any coordinate as physical quantities in reality). Nevertheless, we need 4 coordinates for  fields  of 4 dimensional world  and that works absolutely perfect in any physical experiment description.  Now let's speculate. Let's assume that there is no such thing as spatial dimensions (will not talk about the time arrow right now) and the dimensions are simply a human way to handle a position of our bodies in an external gravitational fields. How it can work? First of all, what about the fields, why they respect a symmetries of 3+1 world? The answer can be simple in fact. These fields do respect the symmetry 0f 3+1 world but they are do not request an existence of 3+1 dimensions of Universe as a unique and only option. In some extend we talk about the 3+1 dimensions of whole Universe simply because the fields we explore have this structure. Namely, take a world without the gravity, make experiments, make conclusions about the structure of the world. The simplest conclusion will be that we can handle and feel only that kind of fields and corresponding matter, but  the conclusion that the whole Universe has that 3+1 structure is a kind of not necessary logical jump. We simply made of and observe that kind of matter that respect the symmetries of 3+1 physical bubble but nothing more. Now will consider a gravity field. First of all, classical gravity field has a form of metric of 3+1 manifold, so it must be a proof 3+1 world's structure for the first sight. But, quantum gravity is not a geometry as it seems right now. So, if we will consider a metric simply as a spin 2 quantum field  it will not be related to a geometry at all. We can replace all physical geometrical notions by the notions of interplay of quantum fields without introducing spatial dimensions, instead the dimensions we will have a number of components of the spin 2 field.  In this picture is assumed, we can imagine that we live in big something where each physical event we can observe is defined by particular matter fields and their mutual interactions. Namely, the law of physics we have are dictated by the fact that we and the world we explore are made of the same matter and we can feel, observe and handle only that particular reality made from the particular particles and fields. Of course, two questions remain then, what is time dimension and why we so perfectly isolated from other possible phenomena of possibly more complicated general Universe. I do not like an anthropic principle as an answer.

Until recently, practically no one was involved in the development of general relativity. Thousands of people are engaged in dead-end hypotheses. However, general relativity remains the only confirmed theory.

The last significant result in the theory of gravity was obtained in 1918. Then it was understood that the elements of the pseudotensor are not densities of energy or momentum.

A significant result was obtained recently (2021):

I have experience in studying the impact of hydrogeology on catastrophic floods. An example would be the flooding in Europe in the summer of 2002. See my discussion "How is geodynamics and hydrogeology taken into account?". see my publication "Floods and droughts as a result of deformability of the geological environment" for details.

The water content of the rivers is formed by atmospheric precipitation and underground waters. Influence of underground waters on water content of the rivers cannot be measured. It is shown that the volume of underground water exchange is underestimated and can be commensurable with a volume of atmospheric precipitation. Change of level of underground waters is defined by changes of volume of the geological environment during geodeformations. It is offered to consider geodeformations as one of the reasons of floods and droughts. Studied the changes the gravitational field and geodeformations during droughts and floods in the Amazon in 2005-2006. Studied the hydrological regime of the River Nile. Shows the influence of geodeformation on the level of Danube and Dniester. Proposed detailed study the causes of floods in Europe in 2002. Influence of the Earth’s surface deformation on floods and droughts is very important and requires special detailed study. Changes in volume of rocks during Earth's surface deformation are accompanied by dilatancy which influence on the amount of drought and flooding has turned out to be significant. Study of the processes considered in the thesis gives grounds to expect that floods and droughts associated with deformations of the geological environment will be successfully predicted. Foto https://www.google.com/url?sa=i&url=https%3A%2F%2Fren.tv%2Fnews%2Fv-mire%2F1138805-v-chernomorskom-regione-turtsii-livni-vyzvali-navodneniia&psig=AOvVaw2SdhsJ2lm16vYlBvplRoZX&ust=1694020292799000&source=images&cd=vfe&opi=89978449&ved=2ahUKEwjyktC_-5OBAxWdEBAIHSPSCyEQr4kDegQIARBc

Light should be dispersion in the gravitational field:

Therefore, to have a right measurement of the numbers and spectrogram of the celestial objects and to have an accurate measurement of the size and distance of a celestial object, light dispersion in gravitational field need be considered.

For example, as one galaxy with multi-wavelengths was observed as several galaxies with one wavelength, it should result in that the numbers and spectrogram of the galaxy is wrong. Further, it should result in that the conclusion about the origin and the element making up of the galaxy is wrong.

And, the observed size and distance of the galaxy are not accurate.

Therefore, astronomical observation need be reconsidered as Light dispersion in gravitational field is known.

Greetings and courtesy

A feather and a ball fall with constant acceleration in the gravitational field.

According to the arrow of time, do they fall in the gravitational field or move in the time dimensional?

it's humorously, but it seems that we are all moving at the speed of light in the dimension of time. When we move in space, the speed of our movement in the dimension of time decreases (time dilation).

In the gravitational field, depending on the intensity of the gravitational field, the speed of our movement in time is less (Gravitational time dilation).

Do you think the object falls in the gravitational field?

The gravity of earth is always attracting all the things(including objects in motion) within the earth's gravitational field towards the center of earth.

Raphael Neelamkavil, Ph.D., Dr. phil.

Without the presence of existent gravitational propagation wavicles / particles, nothing physical can hold together. Additionally, there are electro-magnetic and other non-gravitational propagation wavicles / particles. Both are carriers of energy. Thus, there can be two kinds of force-carrier existents (energy wavicles / particles) which are forms of physical matter processes and hence irreducibly are matter:

(1) force-carrier existents that get propagated from existent physical processes and pull other objects a step backwards, thus attracting the object gradually into the graviton-issuing object, and

(2) force-carrier existents that get propagated from existent physical processes, do not pull other objects to the issuing object, and thus give a portion of themselves off to other objects.

Do these gravitational and non-gravitational (electromagnetic and other) wavicles exist? Before using them in physics, it must be determined whether they exist and how they may exist, for them to exert causally real physical effects. Existents cannot be vacua, and hence, they must exist, and hence they are:

(1) in Extension (each having a finite number of finite-content parts), because if not extended, EM quanta would be non-existent, and

(2) in Change (existents, which are always with parts, possessing parts which always exert finite impacts on a finite number of others, inclusive of exertion of finite impacts on some parts within), because anything that has no change is not in existence.

In short, any matter particle and any force-carrier wavicle can exist only Extension-Change-wise. Whether they really exist is clear enough: if they do not exist, then the matter particles that issue force-carrier existents (wavicles) too need not exist, since force-carrier wavicles are just another (relativistically, and not absolutistically, source-independent) form of existence of mater particles.

An existent without own parts and own exertion of impacts will be imaginable as existent. Anything that is not in Extension-Change is non-existent – a physical-ontological fact at the foundations of physics, which most physicists (and other scientists) forget while performing their statistical and other related miracles!

This much for an introduction. Now, what are the implications of such existence in the case of EM wavicles and gravitons?

If electromagnetic and gravitational wavicles are EXISTENT, then they possess also EXTENSION and CHANGE. They are not absolutely geometric particles, instead, they are elongated at various dimensions.

Let us assume the following as a general principle in physics: Anything physical issues gravitons, which are the basic attractive forces within physical existents.

If an existent energy wavicle is thus a matter wavicle with extension, it must also issue gravitons! In that case, the only stuff in the cosmos that cannot themselves issue further gravitons from within are gravitons themselves. What can this work to in physics and cosmology? I believe that we need a revolution from this viewpoint. This is a proposal that waits being tested by future physics and astrophysics.

Gravitons too are extended and changing wavicles. But they are themselves the wavicles possessing also their parts that attract each other, and are long-range in nature. If they issue sub-gravitons, they will naturally be kept attracted within the issuing sources, because the parts from which they are supposed to be issued are themselves attractive by nature and other matter and energy particles attract each other basically by means of issuing gravitons.

But naturally, gravitons too must be existent, and hence possess parts. What would be the sort of parts that gravitons can possess? Repulsons or Gravitons? Sub-repulsons or sub-gravitons? I think that they cannot themselves be repulsons and sub-repulsons, because repulsons and sub-repulsons without coherence will not stick together as parts of gravitons. Gravitons cannot issue gravitons themselves, since this is self-creation. But they can possess sub-gravitons as parts, but these need not be of the same power as their totality that each graviton is.

In any case, one thing should be accepted: BOTH ELECTROMAGNETIC AND GRAVITATIONAL QUANTA MUST ISSUE THEIR OWN WAVICLES OF ATTRACTION. IN THE CASE OF ELECTROMAGNETIC QUANTA, THE ISSE IS THAT OF GRAVITONS (and whatever other sub-wavicles that might be there for them to give rise to). IN THE CASE OF GRAVITONS, THE PARTS WILL HAVE TO BE SUB-GRAVITONS (plus whatever other sub-wavicles that might be there for them to give rise to).

The Extension-Change kind of existence is what we call Causation, and therefore, every existent is a causal Process in all parts. This is nothing but the Universal Law of Causality. That is, no more do we need to prove causation scientifically. This Law is a pre-scientific and hence physical-ontological Law, meant also for biological existents.

Hence, no quantum physics, statistical physics, or quantum cosmology can now declare that certain processes in nature are non-causal or acausal, after having admitted that these processes are in existence!

That is, existents at any level of formation are fully physical, possess at least a minimum of causal connection with others in its environment, are not merely virtual (nor fully modular / non-local / non-emergent / self-emergent / sui generis in a totally isolated manner). Therefore, any existent must have causal connections with its finitely reachable environment and within its inner parts.

Physical-ontologically real generalities must be about, or pertinent to, existents in groups, i.e., as parts of a type / natural kind. These generalities are not existents, but pure ontological universals in natural kinds. Extension and Change are purely ontological and absolutely basic characteristics of all existents. Hence, I have termed them Categories.

Space and time are just the measurement-based epistemic notions or versions of the more generally physical-ontological Extension and Change respectively. The latter two are ontological generalities of all existent processes, because nothing can exist without these two Categories.

Hence, space and time are not physical-ontological, not real about, not pertinent to, existents. In short, physical science working only on measuremental space-time cannot verify newly discovered energy wavicles and matter particles by use of the physical “properties” they are ascribed to.

The test criteria for the existence of any existent particles will be Extension (each having a finite number of finite-content parts) and Change (existents, which are always with parts, possessing parts which always exert finite impacts on others, inclusive of exertion of finite impacts on some parts within).

Bibliography

(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.

(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.

(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.

(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.

(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.

The unexploited unification of general relativity and quantum physics is a painstaking issue. Is it feasible to build a nonempty set, with a binary operation defined on it, that encompasses both the theories as subsets, making it possible to join together two of their most dissimilar marks, i.e., the commutativity detectable in our macroscopic relativistic world and the non-commutativity detectable in the quantum, microscopic world? Could the gravitational field be the physical counterpart able to throw a bridge between relativity and quantum mechanics? It is feasible that gravity stands for an operator able to reduce the countless orthonormal bases required by quantum mechanics to just one, i.e., the relativistic basis of an observer located in a single cosmic area?

What do you think?

Light(photons) can bend as it passes through a black hole. Because it is due to the intense gravitational field of the black hole.

A careful study of Einstein's works shows that the declared program of the general theory of relativity, contrary to popular belief, has not been fulfilled. Namely, Einstein put forward the principle that the energy of the gravitational field is the source of the gravitational field.

However, it was not possible to include the energy of the field (energy-momentum tensor of the field) in the Einstein equation, more precisely, it was not possible to find the field energy tensor. For two years, Einstein looked for a way out of this situation, and eventually abandoned this principle, since the equation without field energy explained the rotation of Mercury's perihelion.

As a result:

1. The momentum energy tensor of the gravitational field remained unknown.

2. The energy-momentum conservation law has disappeared from the theory.

3. As it turned out, this was the reason for the appearance of singularities in the theory.

I managed to fix it - find the energy-momentum tensor and include it in Einstein's equation.

Newtonian gravity works in the range of low gravitational field intensity. For strong gravitational field intensities, General Relativity is a better approximation.

Could Newtonian gravity not work as a good approximation in the very low gravitational field intensity regime, and a quantum theory of gravity be a better one just like General Relativity works better for strong gravitational field intensities?

There are macroscopic phenomena that cannot be explained without quantum mechanics, such as non-collapsing neutron stars due to degenerancy pressure. Maybe dark matter is another macroscopic phenoma due to quantum gravity.

A pendulum bob oscillates between potential energy maxima at the top of its swing through kinetic energy maxima at the bottom of its swing. The potential energy is given by the mass times the height of the arc times gravitational acceleration and the kinetic energy maximum is given by the mass times the maximum velocity times the average velocity. Energy may be treated as a scalar in many phenomena, but here both energies are products of two vectors, fall direction and gravitation for potential energy and momentum times average velocity for kinetic energy. This nature of the pendulum is important.

The potential energy of the pendulum is equal to the work it can do under gravitational acceleration until its string is vertical. That work accelerates the pendulum bob to its maximum velocity. The kinetic energy of the pendulum is equal to the work it can do against gravitation to bring the pendulum bob to the top of its arc. It is posited that the shape of the atoms and molecules in the bob is the cause of its acceleration in the refraction gradient of a gravitational field, like a light path bending when passing a star. When the bob is free to move, their asymmetrical oscillations change the position of the bob as the process of falling. The response of the atoms and molecules in the bob to motion is to adjust their shape in order to remain in harmony with themselves, that is they shorten to enable complete oscillations despite translation. These shape changes together transfer potential energy to kinetic energy in the bob which is then available for the work of lifting the bob by reversing the changes in shape while decelerating. The key to this speculation is that reversible refraction or translation compensation actually move the location of internal oscillations in matter.

In my monograph "Interaction in the lithosphere-hydrosphere system" a review of scientific articles on the topic of using the energy of earthquake preparation for the formation of cyclones was reviewed. This topic was studied in most detail in my article "Influence of the gas component of the fluid regime of the lithosphere in the water area on atmospheric processes". The article shows that the hydrogen and methane released from the lithosphere before an earthquake and the oxidation energy are sufficient to form a local cyclone.

I have proved that changes in the gravitational field are also able to form a local cyclone. Slide from the discussion "Is it possible to see how rapidly the Earth's gravitational field is changing by looking at how clouds move (with their help and without GRACE)?" attached.

In the discussion "The earthquake in Turkey is a consequence of planetary scale geodeformations. Is the concept of stress accumulation before an earthquake wrong?" I have shown the coincidence of the pleistoseist zone of the Turkish earthquake with the atmospheric pressure anomaly. Such an anomaly arises with an increase in air temperature and with a local decrease in gravity. Attached are the maps from the discussion.

Let's discuss some synoptic maps over the epicenter of the Turkish earthquake.

In my opinion, the rate of atmospheric pressure change over the epicenter is extremely (anomalously) high. 02/02/023 - 1005 hPa, 02/03/23 - 1025 hPa, 02/06/23 - 999 hPa. This is not typical for the physics of the atmosphere.

I ask you to take part in the discussion of weather forecasters.

Quantum Field Theory is based on an assumption that all subatomic particles are made of the surges of fields. These fields are known as “Quantum Fields”. Like gravitational field, most scientists believe that quantum fields are long range forces over the entire universe. However, according to Yangton and Yington Theory, quantum fields are only short range fields with a normal distribution.

Scientists also believed that quantum fields preexist in the universe. This concept was first proposed to explain that the remote gravitational force derived from Newton’s Law of Universal Gravitation is preexisted instead of that produced by propagation. However, according to Yangton and Yington Theory, the remote gravitational force is caused by graviton flux which is generated through graviton propagation based on Graviton Radiation and Contact Interaction Theory. In fact, remote gravitational field obeys Inverse Square Law (1/r²) but quantum field follows a normal distribution.

In contrast, according to Yangton and Yington Theory, subatomic particles are made of a group of Wu’s Pairs with string structures and short range forces including String Force and Four Basic Forces in a normal distribution. Although, these short range forces are generated after the existence of the particles, they can be considered equivalent to the Quantum Fields in Quantum Field Theory.

Furthermore, based on Quantum Field Theory and Yang Mills Theory, Standard Model is a group of subatomic particles that is derived by a mathematical model of non-abelian symmetry with a quantum field in a normal distribution. As a result, considering that string structures and short range forces including string force and four basic forces in a normal distribution are equivalent to the quantum fields in Quantum Field Theory, Yangton and Yington Theory can serve as the backbones of Quantum Field Theory, as well as Quantum Gravity Theory and Standard Model.

My questions are:

1. Is it true that quantum fields in Quantum Field Theory have to be long range fields or even infinitive continuous fields?

2. Can it be short range fields? Any problems?

The earthquake in Turkey occurred on the date of the tide syzygy in the solid body of the Earth on February 6, 2023. On the dates of syzygy, the amplitude of geodeformations increases by no less than 20%. The first destructive earthquake occurred at 01:17 (M=7.8), the second at 10:24 (M=6.7). At this time, at the earthquake epicenter, the amplitude of the diurnal and semidiurnal tides in the solid body of the Earth reached positive extremes. In addition, due to the 14-day zonal tide in the solid body of the Earth, the conditions of stretching and compression of the Earth's crust were formed on the surface of the planet. The zonal tide in the solid body of the Earth is associated with the extrema of the angular velocity of the Earth's rotation. The data is available only for February 3. Attached the chart https://hpiers.obspm.fr/ . Stretch conditions on February 3 and February 10, 2023. On February 3, in accordance, rapid changes in the Earth's gravitational field on a planetary scale were recorded. Changes in the gravitational field recorded by our method, see satellite images https://meteologix.com/. Between the expansion phases, the compression phase is fixed. The compression occurred on February 6, 2023 and triggered an earthquake https://zn.ua/img/forall/u/14/8/photo_2023-02-06_15.16_.16_.jpeg . These are the facts of the formation of compression deformations on March 6. The scale is planetary.

Planetary-scale deformations (amplitude 30 cm) were blocked on February 6 in the epicentral zone of the future earthquake. The blocking of tidal waves in the solid body of the Earth is associated with the release of heat. In the atmosphere, the release of heat leads to a decrease in atmospheric pressure. Warm air weighs less. Look at the color map of atmospheric pressure and low pressure above the epicenter at the moment of maximum compression (map from Twitter https://twitter.com/BookofCrusty/status/1622643773900464128?t=Yy-KLEZn-FDuHvyIHh1y5w&s=09 ). The relapse occurred on February 20, 2023 after 14 days during the next cycle of the positive extremum of the angular velocity of the Earth's rotation associated with the repetition of the phase of the zonal tide in the solid body of the Earth.

What have you seen? Stresses do not accumulate over the years. The stress accumulation time does not exceed 3 days.

Could it be that there is a fifth fundamental force, a 'hypergravity' that only manifests (i.e. becomes physically significant) at a large cosmological scale ?

The gravitational field of a quark is negligible compared to their electric charge and strong charge (color). But when a sufficient amount of quarks in the form of atomic nuclei come together they produce powerful gravitational fields.

In the same way at the mass scale of planets and stars the 'hypergravitational' force

is negligible and ordinary gravity (as well as electromagnetism and other forces) plays the predominant role.

But at a cosmological scale (for mass, energy or distance, i.e. millions of solar masses) the hypergravitational force will come into the play and explain astrophysical (sp. galactic) and cosmological phenomena which seem to require 'dark matter'.

Another aproach could be through dynamical systems. The water of the ocean behaves very differently from the water in a bathtub. Ultimately this must be explained by a different scale (also different set of 'negligibles') and different values for physical and chemical parameters of the same model.

Some people believe that it is the end of physics laws. this question has taken around a century to be solved. But what are the problems? please inform them.

The discussion arose spontaneously within the framework of the discussion of the question “The Earth moves along the ecliptic. When the Earth crosses the Milky Way, weather anomalies occur. Does gravity affect the weather? I moved it to a separate question. correspondence on the topic of discussion: “Thanks to the diagram (see the answer of Janusz Pudykiewicz https://bigthink.com/starts-with-a-bang/earth-move-universe/), you can understand the reason for the same inclinations of the axes of rotation of Mars, Earth, Saturn and Neptune (https://kipmu.ru/pochemu-naklonena-os-zemli/). Are these planets (their gyroscopes) attracted (tilted) by the mass of the Milky Way? Mercury and Jupiter ignore this attraction? Does Venus have the “Dzhanibekov effect” (reverse rotation)? Uranus is not fully understood. I am an amateur in this matter. Maybe it's not scientific... "Boris." Once again I ask specialists in the field of astronomy to treat my questions with indulgence.

It is known to all that the propagation of gravitational field is not instant.

So for black holes, the gravitational field generated by the singularity of the black holes needs time to travel before exerting gravitational pulling forces on other celestial bodies.

According to gravitational time dilation, the time near black holes are extremely dilated to infinity.

This indicates, given the limited age of the universe, the gravitational field generated by the singularity of any black holes have NOT exert any pulling forces on any celestial bodies yet.

Thus, we can conclude, it is impossible for any current celestial body to be pulled by the gravity of any black hole and orbit around a black hole. actually there should be no celestial bodies now gravitationally pulled by any black holes at all.

But, this conclusion is apparently absurd.

Any professor can explain this please?

No, it is not. We found:

In any region of a space, the gravitational field cannot be eliminated. The speed of light in a vacuum has never been observed and cannot be observed with current technology. Till now, only the speed of light in a gravitational field has been observed. Here, it is presented that light could be dispersion in a gravitational field analogous to the dispersion of light in the Newtonian prism experiment.

This morning, I found a couple of paragraphs in a book I had published a year ago which made me wonder if the EmDrive, EM Drive or radio frequency (RF) resonant cavity thruster should be renamed the Possible Engine. I don't know if these are more deep thoughts or if it's just my subconscious telling me I have a secret crush on Supergirl 📷 but here are those 2 paragraphs -

"British engineer Roger Shawyer proposed the EmDrive, EM Drive or radio frequency (RF) resonant cavity thruster in 1999 and it's claimed to use patented microwave technology which converts electrical energy into thrust by amplification of the microwaves creating pressure which drives the vehicle's front forwards. Light is one form of electromagnetism – microwaves are another (so they also obey James Clerk Maxwell's electromagnetic laws and their solution for both retarded and advanced components of the waves).* So some of the microwaves are advanced, and travelling back in time.^  To this action, there is - agreeing with Isaac Newton's 3rd law of motion - an equal and opposing reaction i.e. a thrust forward in time. Since space can never be regarded separately from time, an object in space is affected and the forward thrust in time could power a spacecraft through the void via the EM Drive.

* Gravitational waves must also have advanced and retarded portions. Einstein's equations say gravitational fields carry enough information about electromagnetism to allow Maxwell's equations to be restated in terms of these gravitational fields. This was discovered by the mathematical physicist George Yuri Rainich. [George Yuri Rainich, Transactions of the American Mathematical Society, 27, 106 - Rainich, G. Y. (1925)]

^ The attached "Topological Propulsion Through Space-time" should explain how advanced waves are indeed possible.

"What are the consequences if gravitational fields play an essential role in the structure of elementary particles,** and if gravitational waves can travel back in time? Then the equal and opposite reaction providing the forward thrust in time could not only "power a spacecraft through the void", but it could power anything with gravitational waves in its composition. This includes giving controlled flight to Superman and Supergirl, without any jetpacks - acting in a manner similar to the proposed method of EmDrive, superbeings would be powered through the air."

** The section about vector-tensor-scalar geometry in "Topological Propulsion ..." explains the relation between gravitational fields and elementary particles.

"Out of Time - Predicting the Science of Future Centuries and Millennia (Edition 2)", 19 October 2021, Page 1-93 https://doi.org/10.9734/bpi/mono/978-93-5547-061-4

This question should have been asked by my graduate student Vadim Dolya, but he is busy now (he, as a senior officer, is fighting against Russia). I'm asking this question instead. In the autumn of 2005, we observed a whole chain of different contrasting natural anomalies not connected with each other, which were not synchronized with El Niño. These are the drying of the Amazon (#1), abnormal tropical cyclogenesis in the Caribbean, including Atlantic tropical cyclones in December and January (#2), unprecedented aseismic spreading in Ethiopia in the Afar Valley (#3), a fourfold increase in subduction of the Nazca Plate (# 4), an unprecedented avalanche of house collapses around the world (#5), a fourfold increase in the number of pipeline breaks #6. I have attached the "anomaly" slide. Perhaps I do not know everything that happened at that time. Vadim Dolya, in the manuscript of his thesis, studied the meteorological consequences of a short-term (48 hours) reverse vertical movement from a tectonic block measuring more than a million square kilometers with an amplitude of 150 cm, in the center of which was Great Britain. I have attached a map of this block ("Nord Sea" slide). This is exactly a tectonic block, since its spatial scale (1100x1100 km) and spatial orientation (35º and 305º) correspond to the theory. He described the formation of a mega cyclone associated with this process, which was generated by an anomaly in the gravitational field in this region. I have attached the "meteo" slide. Rapid changes in the Earth's gravitational field were manifested by a regional anomaly in the shape of the Earth's geoid on November 24-26, 2005. I have attached the "geoid anomaly" slide. For all this to happen, you need an external influence with great energy. This is the crux of the matter. The most important. Look at the change in the trajectory of the axis of the Earth's horoscope in 2005, in more detail in the fall of 2005, and in even more detail at the time of the change in the shape of the geoid in the UK region on 11/26/2005. It's on the Earth Gyro Axis slide. You and I perfectly understand that the nutation of the Earth's gyroscope axis does not occur so quickly. Certainly it is a different process. I'm wondering, is this all real?

The subject of discussion is on the "clouds" slide. Theory question on the slide "gravity". You can admire the rapid changes in the Earth's gravitational field in the region of Ukraine on the video (attached videos). GRACE does not provide such quality yet. Perhaps I am wrong?

We consider gravitational potentials, which let planets orbit around the sun. This view implies a remote non-local impact of the sun on the planets and vice versa.

But in fact, the gravitational fields have an energy density, which is present locally. The energy density E quadratically depends on the field strength and is given by E=-g²/(8πG), g=MG/r². G is the gravitational constant, r is the distance to the centre of mass M, which generates the gravitational acceleration g.

With the locally available energy density, the gravitational force also becomes a local force.

This force is an interaction between gravitational fields. The energy density of the gravitational field of the object decays with the distance d from the object to the fourth (~1/d⁴). The interaction of the local gravitational field of the object with the omnipresent background field, therefor is a local interaction.

The idea of a remote gravitational interaction on a distance is a blatant chimera!

The highlighted relation between energy density and force applies to all kinds of force fields.

In 1915, Einstein abandoned the energy-momentum tensor of the gravitational field in the theory of gravity. This ensured the general covariance of the gravitational field equation (Einstein's equation).

Gravitational fields slow clocks. For example, a clock located at the center of the Earth would be slowed by a factor of about 5.3X10^-10 compared to one on the surface, even though it would be weightless. Precise atomic clocks can measure elevation differences as small as one centimeter.

Is a similar effect associated with the electromagnetic force? If an atomic clock was placed inside a Faraday cage, and the cage was held at a constant voltage, would the clock’s rate change? Has anyone tested this?

Time varying gravity fields only differ from electromagnetic fields in that:

1, The forces are axial as opposed to the transverse forces of electro-magnetism.

2, Wavelengths and uncertainties in position, momentum and energy of gravitons must be very much larger. This due to the fact measured gravitational fields are mainly to to motion of large bodies and the size of the gravitational constant of force.

They are the same in that time varying fields of both have been clocked at the speed of light. Energy to move masses in both must be transferred by such time varying fields.

Through the calculation of planetary orbital precession, the correctness of the gravity equation under the action of gravitational waves is verifified, indicating that the gravitational physical model has research value. From Newton to Pierre-Simon Laplace have realized that the speed of gravity on objects is very huge. But this view is not consistent with GR. I don’t know if GR is the only correct solution to gravity. If not, then the gravity model under the inflfluence of gravitational waves provides a new way for humans to study the universe.

Here we show that free fall in a gravitational field must be detectable by an experiment, while inertial motion is not detectable by any experiment. Since gravity is not annulled in free fall in a gravitational field, gravity is not rendered, somehow, shielded or immeasurable. This is contrary to electromagnetism, that can be shielded.

We are harmonizing "free fall" as defined under GR, with "inertial motion" as defined under SR, extended under GR, and even indepently from gravity, so it can apply to Cosmology, using the same notion of 4D spacetime but allowing the metric to be respectivelly different.

Free fall in a gravitational field is not inertial motion to an arbitrary observer, not even locally, only to comoving observers (note that, in SR and GR, comoving observers have identical velocity and position). But, even atomic clocks, by definition, or a person, cannot be entirely comoving, experimentally. In GR, it is the equivalence principle that does not let you feel it, IF you are entirely comoving with yourself, which no one, nor any clock, can, experimentally. This defect can be acceptable, while small, but the misconception remains. This means that one should NOT confuse free fall in a gravitational field with inertial motion, they also belong to different types, as shown.

FOREWORD

In this discussion, arguments are non-circular. This discussion does not suffer the linguistic and logic problems, noted by Einstein and others, in Newton's First Law -- what is the definition of a straight line, to be able to denote a straight line? A "traveling wave" is, indeed "a wave that travels" as the current, physics college textbook Serway says, but that does NOT convey any information ---- it is a circular definition. Physics is still full of those. It is also pointless to discuss about names, different national languages have different names for the same physical concept, for example. What is one to do?

Let us follow a semiotic road in logic, in recent advances in theory of types in mathematics and TCS (theoretical computer science), more basic than set theory, instead. Nothing is more fundamental than theory of types in maths, used in TCS. So, all circular references have no logical reason to exist, we just have to go deep enough to TCS and type theory, in this view. Not even "inertial motion" resists, as we shall see.

The term "inertial motion" is thereby treated as an arbitrary name, a reference, a truth value, and is considered not relevant here, could be "sdrufs". We discount the circular, logical problem, likewise, of defining a "straight line." But, how can we discuss, when a veritable Babel tower is in our discussions?

Simple, we do it intuitively everyday, in our laboratories of nature, and is explained in semiotics. If we were to talk about Bessie, we would not have to drag the cow from the barn, we just say "Bessie" -- the arbitrary name "inertial motion" links the truth-value to the exact referent, of many, the physical object in "Inertial motion" ---- which is what we talk about. What is also relevant here is the meaning, the sense, the truth-condition that the duple (reference, referent) denotes, forming a triple (reference, referent, sense).

This triple is further made unique, in semiotic considerations in the MCWG group, by adding trust:

trust: a non-localized "field" created by an intrinsic collective effect, that is directly and indirectly defined by knowledge (what you know you know, and know as to exemplify); that which is essential to a communication channel but cannot be transferred using that channel (Gerck, 1998).

Trust, as indicated above, binds all three elements together, within an extent, a measure. This forms a "hard" object, a "particle" of understanding -- not unlike a proton being studied as a set of three quarks and a confining field -- and this we study as "inertial motion", called by its quite arbitrary name, but a distinct physical object and a definite meaning, within a defined extent of trust in matters of physics.

Please feel free to, consistently, use any name you would like, physics is name-agnostic. The same phenomenon applies to any other name. Now, the language being clear and unique, in any language, we can go on to the physics.

If one is in free fall toward the Sun, the Sun gravity does not disappear! What it does happen, is that that, locally, one seems to experience no gravity -- but what does it mean, what is the truth-condition? Perhaps, gravity was somehow perfectly shielded, the Sun did disappear, the body is somehow suddenly at rest, the body is momentarily in inertial motion, or something else happens.

The entire Sun is still there, 100%, its gravity is still there, 100%, it was not shut-off, even the slightest, it is not negligible at all, spacetime is not even locally flat - someone else certainly experiences gravity at the same point if not in free fall; suppose one just passes by, when one is free falling, not anyone with a rocket, necessarily, but at the same point in spacetime, neglibly close in (t, x, y, z) -- just not exactly the same v.

Let us look at it another way, introducing consciousness, as often done in physics -- without naming the "demonology". The Sun does not know one is in free fall, neither the other planets and bodies. They don't go fly off because one is in free fall somewhere, gravity is neither negligible, nor disappears, not even momentarily, not even locally. Spacetime, curved, does not change because someone goes in free fall.

Also, regarding some differences ... when one is really in free fall, it is not only relative to the Sun. It is to every gravitational influence, even if the gravity field is dominated by the Sun.

Further, two satellites in orbit around the Earth must not be in free fall, they are just following a geodesic dominated by Earth. It is an extended Galileo's inertial principle, also called extended Newton's first law, valid for such non-inertial movement.

Another proof, if needed, is also that the satellites do go around, which is not a straight line, which free fall does not do.

Any satellite, also the Earth, is not in free fall -- just non-technically said to be in "free fall". This is demonstrated absolutely, in spacetime terms, not meaning that an absolute reference frame is to be used, by measuring the curvature of the worldline. No curvature means no acceleration, also in flat, Minkowski spacetime.

INERTIAL MOTION

Motion is not detectable if it is inertial. Inertial motion is a diagnosis of exclusion. Free fall qualifies as inertial motion to observers comoving with the free fall (note that, in SR and GR, comoving observers have identical velocity and position).

Therefore, one can say that motion is not detectable only if it is inertial.

There are no frames in inertial motion where the laws of physics are different to inertial observers. Free fall in a gravitational field is not inertial motion to an arbitrary observer, not even locally, only to comoving observers (note that, in SR and GR, comoving observers have identical velocity and position), thus it has two "strikes" and is detectable.

Also, one can use Newtonian physics arguments, with no maths, SR, or GR -- in Newtonian mechanics, any non-comoving inertial reference frame cannot be reached at constant velocity from a free fall body, as close as it may be (without being identical -- keeping the non-comoving condition). In other words, any non-comoving reference frame in free fall would be different in terms of laws of Newtonian physics, from any inertial reference frame, hence, it is not inertial. Let us look further at a Newtonian observer in free fall. The laws of Newtonian physics will be different, even locally, to any observer but at the same material point (i.e., same position, same velocity -- comoving).

Or, one can also use those consequences with students, and use for, hopefully, an illuminating discussion. There are the many other reasons, not all listed above, why free fall in a gravitational field is not undetectable, and the observer is not "at rest," even to the very observer falling, only to comoving observers.

Names seem to not matter, as expected, in physics. it would seem that it does not matter, then, if someone, for example, chooses a geodesic to extend Newton's First Law, overcome beautifully our limitation then (to define "straight line"), and designates it as an extended "inertial motion" -- the geometric basis is the same, the physics did not change. Or, like Mashhon, describe an infinte family of comoving observers, 3D, each one as a flash in time. One would seem to need less mathematics, it can all be solved in 3D +1D, even 3D, not needing 4D. But the context is just more limited, the region of validity is less, as we show next.

It is physically limiting to use names that do not distinguish curvature as stretching (as done in 4D spacetime), only considering curvature as bending. The spacetime that was being considered is flat, it can be seen in 3D like a stretched, flat pizza dough. The spacetime is flat but if the world trajectory is curved, it still fits with curvature as intrinsic, as stretching, so not just world straight lines "fit" in flat spacetime!

The 4D spacetime, in SR or GR, therefore, works for world-curves, as they may curve, in the world we see as flat spacetime, locally, as SR, or curved spacetime, as we see in GR. Only the 4D spacetime formulation of SR and GR can do that, we cannot use lesser dimensions, may be more.

The visible world, however, as viewed, is NOT 4D spacetime, it seems at first sight. The world is apppearing to us as 3D +1D, or 3D plus time as parameter. But, the world is governed in 4D spacetime, which manifests itself through laws that 3D or 3D+1D cannot represent, but we can see in everyday experience -- just like we do not see the Earth going around the Sun, we see the Sun going around the Earth, apparently, but we do have seasons, and the ancient Greeks measured the circumference of the Earth, with no rockets, quite correctly, through mathematics.

A clock, by definition, or a person, cannot be entirely comoving. It is the equivalence principle that does not let you feel it, IF you are entirely comoving with yourself, which no one, nor any clock, can. Thus, while inertial motion is not detectable by any experiment, free fall in a gravitational field must be.

Thus, as far as clocks are concerned, anything that is non-comoving with the central point of a free fall should be affected, including centripetal and coriolis forces, which are representable, therefore exist in the GR formalism. Any contrary result is to be understood as false under these definitions.

But human observations, as d'Espagnat agrees, must serve as criteria -- not as definitions of reality and truth.

The experimental difficulty to measure time at all, or to be be comoving, can be removed under the criteria that small defects are acceptable, vanishingly small to some, but still the main objection remains, as shown next.

A rock thrown on Earth, with a clock attached to it, will follow an accelerated motion, then decelerate to a stop. After the apex, the rock is in free fall in the gravitational field, including the Earth, the Moon, the Sun and other influences, here assumed as all just gravitational.

The trajectory can be calculated using SR in the 4D spacetime formulation, but not using the original SR formulation by Einstein. The original formulation, however, is still taught today in US colleges and Ivy League universities in undergraduate studies, for example using the physics textbook by Serway.

The clock, comoving with the rock, will measure the proper time, an invariant in 4D spacetime, calculated by the inverse function of the arc-length function, including any contributions, and the space coordinate will be zero, it does not travel in space. To an observer at rest in the ground frame, the rock does travel in space, space coordinates change, the time measured is dilated, and the rock, after the apex, is in free fall and not in inertial motion. The misconception, shown here, confuses free fall in a gravitational field with inertial motion.

Further, those concepts are not of the same type, in type theory in mathematical type theory and TCS terms, which are more fundamental than physics, and setting the very language of physics as truth-conditions, their meaning, and referent.

Physics cannot confuse these types, they are not just names, arbitrary. Whatever name we use, they must have the meaning and referent, in general, that the physics laws designates in nature, and they (not even the names, technically understood, in general) can be different.

CONCLUSION

There is no point in discussing only the names, free fall or inertial motion, different languages use different names, but we have tried to differentiate what they mean and point to, within the trust of the same physics, what we understand of nature. This is should not be fragmented, the names can.

Let us discuss the physics. The names change at will, physics can also change, but we need to ask what inertial motion means, what free fall means, in nature, and what they pont to. These are fundamental questions, and nature does not change, so our task is clear.

The author acknowledges contributions by Stefano Quattrini , Edgardo V. Gerck , and two anonymous reviewers.

NOTES

We are harmonizing "free fall" as defined under GR, with "inertial motion" as defined under SR, extended under GR, and even indepently from gravity, so it can apply to Cosmology, using the same notion of 4D spacetime but allowing the metric to be respectivelly different.

In SR and GR, accelerated motion is defined absolutely, for example, with no absolute reference system or geodesics, of course, by extrinsic and intrisic geometric properties of the curvature.

So, it does not matter if someone chooses a geodesic to extend Newton's First Law, overcome beautifully our limitation then (to define "straight line"), and designates it as an extended "inertial motion" -- the geometric basis is the same, the physics did not change, the context is just more limited.

It is limited to not distinguishing curvature as bending, only considering curvature as stretching, in spacetime -- the spacetime that was being considered is flat, like a stretched, flat pizza dough. The spacetime is still flat if the world trajectory is curved, not just world straight lines "fit" in flat spacetime!

It all works for geodesics, world-curved as they may in the world we see as flat spacetime, locally, which is NOT spacetime but governed by a flat spacetime, there is no ontological status anymore, and this is beautiful, not just right. This is also, perhaps, new to philosophers.

But... it does not work in GR, under free fall in a gravitational field, because the spacetime is curved under gravity, as bending. So, inertial motion must be redefined, not as a name, but as a truth-condition. This is how GR actually exists, we are NOT reinventing the wheel, just may be going a bit further into what GR means, not just what it says.

On the other hand, we are investigating what gravity, in nature, provides under the arbitrary human name "free fall". This is certainly fixed under the meaning of what we call "free fall", and the object. The same for the arbitrary name "Inertial motion" that we fixed under the meaning of what we call "free fall", and the object.

We also investigated if those are meanings that physics denote by its laws in nature, GR, SR, and others, no matter the name. It is a two-way process: is physics denoting the same as nature, under general assumptions, not casuistically, and vice-versa?

We have to resort to sense, referent, and trust (as a social construct, a collective effect of milions, that neither friend nor foe can change, not a perhaps misplaced confidence on any source or sources, nor perhaps hand-picked by one, nor bias), not names.

That means that what we call inertial motion, under any other name, or understanding, will behave (sense) and point to the same object (referent), as trusted in physics. The same for free fall. A rose, by any other name, would smell the same, is the gist as captured by the poet.