Cause of the origin of gravity and space-time curvature discovered

The general theory of relativity describes the attraction of masses through the curvature of space-time. But how can masses cause spacetime curvature? Is there a physically tangible background for this, a process or phenomenon that takes place in masses and which they themselves cause, beyond the mathematically abstract energy-momentum tensor established by Albert Einstein?

So far, all attempts to prove the existence of dark matter have failed. No conclusive physical background has yet been found for dark energy either. If gravity were not infinite but finite, as it appears in various quantum gravity theories, this would explain dark energy and matter as resolved gravitational energy in the growing universe and thus one of the greatest mysteries of physics. But how can gravity be finite? Previous gravitational theories with an arbitrarily large but finite range either violate fundamental physical requirements, are not limited to the general theory of relativity or both.

The mass of a body, according to PD Dr. Melissa Blau from the University of Tübingen, the author of the publication published in _Science Advance_, all consists of nucleons that have angular momentum. If quantum mechanical calculation models are applied to nucleons, it becomes clear that the angular momentum mvr in a nucleon does not fulfill the Heisenberg inequality because mvr is too small. The inequality would also not be fulfilled if v were zero or undefined. This is even more obvious for even smaller particles. However, since the spin of such particles is a very relevant parameter, it follows that the radius of this particle would have to be quantized, i.e. effectively much larger. However, if this were the case, mass up to this radius R (for a single proton R is 5.757 m, for galaxies in the order of 8*10^22 m) would be attracted inwards like mass points inside the particle, which corresponds to gravity.

Formally, a nucleon would then be R in size. G is the constant that holds the formal, oversized nucleon together. Since a nucleon has several relative speeds as it rotates in the universe around itself, around the earth, around the sun, around the center of the Milky Way, etc., different gravitational ranges come into play according to the formula R=c/8πf.

With the construct of the effective radius, there would be a force that attracts other masses within this radius R with mg=mMG/r2, i.e. the Newtonian gravitational force. This gravitational force is proportional to the square of the distance, which follows directly from the fact that the density gradient in a nucleon is dρ = m/r2. The formula dρ=ω2r/ß in the density gradient centrifugation gives exactly the value mG/r for this gravitational potential.

Even if a proton rotation cannot be described in the classical sense, the other rotational motions in the universe can certainly be included in the calculations in the classical sense. The gravitational range for the rotation within a galaxy, for example, is calculated to be approximately 10^22 to 10^23 m.

Does the new theory contradict the theory of relativity?

This theory does not contradict the general theory of relativity; on the contrary, it supports the idea of spacetime curvature, since the effective, enlarged space R^3 itself exerts a force (apparent force) on masses. The geometric mean value of the maximum range R is the square root of R multiplied by the smallest length, the Planck length lp. The mean gravitational force (inside and outside the nucleon) is inversely proportional to the square of this mean value, which interestingly corresponds to the right-hand side of Einstein's field equation.

After transformation, the spatially limited gravitational energy per volume Fg looks like the cosmological constant lambda from Einstein's field equations: Λ=Eg/F. F=mcf is a force which, multiplied by 8πR, corresponds to the energy mc2 of matter. From this, Ω, the proportion of dark energy, can be calculated as 0.7 under the above assumption of limited gravity: From a number of different observations, the value of the cosmological constant today is actually estimated to be ΩΛ ≈ 0.7, which means that around 70% of the energy density in the universe is in the form of dark energy.

The general theory of relativity postulates a hypothetical particle with spin number 2 that mediates the gravitational force: the graviton. This is massless by definition, but there is now also a consistent field-theoretical description of a massive spin-2 particle. The corresponding theory is an extension of the general theory of relativity with a very special mathematical structure, called Ghost-Free Bimetric Theory (Bimetric Theory for short). This is because its special structure avoids a mathematical inconsistency, a so-called ghost, which was a problem in earlier proposed theories. Bimetric theory describes both a massive and a massless spin-2 particle interacting with each other.

Quantum gravity

In both Newtonian and Einsteinian theories, gravity is not limited in its range; it merely becomes significantly weaker with increasing distance. Nevertheless, there are considerations and quantum gravity theories in which gravity would be a quantized quantity, i.e. it could only assume a multiple of a certain value. In this case, it would be quite possible that a limited range would be an accurate description, because from a certain distance, it would fall below a multiple of this value and thus remain zero times the elementary gravity. However, such quantum gravity theories are currently still the subject of research.

Effective radius can explain a lot

The construct of the effective radius, which is created by Heisenberg's principle, can be used to explain not only gravity itself, but also the non-quantizability of ART, dark matter and dark energy, the unification of the four fundamental forces and even the Hubble tension. It would also explain why only Andromeda and the Milky Way attract each other and other more distant galaxies in our Local Group do not. In the broadest sense, dark matter would be the graviton energy within galaxies (massive gravitons) and dark energy would be free energy, both of which have arisen from gravitational energy that has dissipated due to the limited range of the expansion of the universe. One would also understand physically why masses ultimately bend space-time. The causal process in masses that causes space curvature and gravity would therefore be the fact that one or many nucleons, due to Heisenberg's principle and their rotation (in space), not only attract mass inside the nucleons, but also mass outside the nucleons in the same way, up to a maximum radius of about 8*10^22 meters. The space-time outside would be bent by this process. Since the gravitational force is based on Heisenberg's inequality, a fundamental principle of quantum theory, this may open up new ways of describing gravity in terms of quantum theory.


Proofs

Twelve trans-Neptunian objects orbiting the Sun beyond 240 AU (large semi-major axis) have very similar orbital directions, which cannot be a coincidence and why a ninth planet of 5 Earth masses in size is suspected beyond Neptune, which influences the orbit of these planets. However, the search for this planet has so far been unsuccessful. The protons, which cause the gravitational field of the sun and whose radial field ends at c/8πf = 240 AU according to this theory, still rotate relative to the galactic center at a speed of 220 km/s. In this direction, the field has a greater range due to the very low rotation frequency of c/8πf, so that these objects are still attracted to the Sun, but in orbital planes that are arranged towards the galactic center. The fact that the similar orbital planes of objects beyond 240 AU point exactly in this direction underpins the radially limited gravity, which is not infinite as Newton's theory states. This theory can be proven by demonstrating a rotation of the orbital plane of these objects by 1.29 arc seconds per year or 129 arc seconds per century, as according to the theory the orbital plane should always point exactly in the direction of the center of the galaxy.

A further indication of the correctness of limited gravitation is a publication by Nhat-Minh Nguyen, Dragan Huterer and Yuewei Wen, who report that they have found evidence of suppression of structural growth in the cosmological model, i.e. that large structures in the universe do not condense in accordance with the theory of relativity. This publication appeared in Physikcal Review Letters and was published on September 11, 2023. Due to the fact that gravity is limited, denser structures cannot form at a galaxy distance > 10^23 m, as there is no gravity between the galaxies that would promote densification.

Finally, the observed proportion of visible (4.9%) and dark matter (26.7%) can be determined exactly from this theory if massive gravitons are assumed as dark matter, while the dark, free energy (68.5%) can be calculated from the quotient R/Dg (Dg = diameter of an average-sized galaxy, R = range of gravitation) and the proportion of dark matter if it is assumed that both quantities have arisen from the dissolved gravitational energy in the expanding universe. In a galaxy cluster with an average of n = 500 galaxies, the typical distance between the galaxies is rg = 1 mpc. If we assume that today, due to the limited gravitational range, a galaxy is gravitationally bound to only 10 other galaxies in the immediate vicinity, we obtain a gravitational force that is 20.4 times smaller than the gravitational force in the earlier smaller cluster in the young universe, in which all the galaxies in the cluster were still gravitationally bound to each other (R=c/8πf=8 million Lj). This means that today there is 20.4-1=19.4 times more dark energy and dark matter than visible matter, which is also observed (68.4%+26.7%)/4.9% = 19.4).

Meaningfulness of a quantum-theoretical description of gravity

Quantum mechanics is (only) a special description of the physics of subatomic particles. The only difference to classical physics is that Heisenberg's principle is more applicable here, as we are dealing with very small quantitative quantities for which Heisenberg's inequality is not always fulfilled. A particle is also predetermined by the ratio of its De Broglie wavelength and its radius as to whether it behaves more like a particle or more like a wave (particle-wave dualism of small particles, e.g. the probability of electrons residing in atoms). If the ratio is large, as with electrons and quarks, the particle will behave like a wave; if the ratio is small, as with protons, the particle will no longer exhibit wave properties. Therefore, proton-based processes such as gravitation cannot be captured by quantum theory or expressed as a wave function. However, if the wave properties play no role here, then Heisenberg's inequality will cause the mysterious gravitation and spacetime curvature. This is because all "mysterious" observations in quantum physics can be traced back either to Heisenberg's inequality or to this particle-wave duality. And this is indeed very probably the case with gravity. It has long been understood that electromagnetic energy is emitted in quanta (photons), but there are also forms of energy that are not quantized, such as dark energy. The hydrogen problem, for example, can be solved with the help of Heisenberg's inequality and wave equations. The GUT theory, a quantum-theoretical summary of the weak, electromagnetic interaction and nuclear force, has proven to be invalid, and the Planck scale is also not valid, as the four fundamental forces were never equal in the Big Bang, which is clear from the causes of gravity described here. Therefore, instead of trying to find a quantum theoretical description of gravitons, it only makes sense to combine the four fundamental forces in a different theoretical way into a TOE formula.

Heisenberg's inequality has several formulations and these must always be treated specifically, e.g. with a certain formulation (∆L∆φ >=h/2 according to Pierre A. Milette) the spin of particles can be calculated from the inequality. From this it can be seen that the spin measurement value only shows the value of the inequality divided by ∆φ =2π, while the real angular momentum and angular velocity are much lower. With this realization, one can rightly doubt the fact that nucleons, for example, do not actually rotate; this intrinsic rotation could then also be included in the calculation described above in a classical sense. The gravitational force from the general theory of relativity is also not sufficiently understood, as the background that leads to this force is not yet known. For example, the gravitational constant G is not constant and varies slightly with a variable Earth's magnetic field, as was shown by measurements in the GRACE mission, as according to this theory gravity is based on the rotation of protons and this can be influenced by magnetic fields. This can also be seen, for example, in the fact that the old primordial kilogram in Paris has been steadily losing weight for unknown reasons, while the Earth's magnetic field has been steadily decreasing for centuries. This can be explained by the fact that the proton rotation speed v decreases in the decreasing earth's magnetic field and the weight of a body mg = mMG/r also decreases due to the decrease in G = v2r/m. It is worth noting that this problem cannot be solved even by the new silicon sphere introduced in 2023. Dark matter and dark energy can also be explained by this gravitational model, namely that gravity ends at a certain distance and, as a result, free energy accumulates in the empty spaces and mass-laden gravitons within the galaxies as compensation during further expansion (law of conservation of energy), which corresponds to the calculated quantity of the observed quantity. Such a process is also known from electricity, for example, where photons are emitted to compensate for the loss of charges (e.g. when electrons are knocked out of a light bulb).

Blau M.B. The Heisenberg principle as the source of gravity and space-time curvature. Science Advance 2024. https://doi.org/10.59208/sa-2024-05-13-7

Melissa Blau
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https://www.melissa-blau.de

Frau Melissa Blau
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melissa.blau27@gmail.com

Author, member of the University of Tübingen, Privatdozentin

This release was published on openPR.