Energy does not have a Gravitational Mass (Flaw of the Einstein’s gravitational theory)
Takaaki Musha
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In one page
Takaaki Musha opens with a problem every physicist agrees is real. Take the zero-point energy of the vacuum literally, cut it off at the Planck frequency, and Einstein’s field equation says the universe should have curled up into a ball smaller than an atomic nucleus. Something in that accounting is wrong. Most physicists look for the mistake in the vacuum energy; Musha looks for it in the equation. Building on Sakharov’s and Puthoff’s idea that gravity is induced rather than fundamental, he models attraction as a momentum exchange — virtual particles boiling out of the zero-point field push on matter, and two masses shield each other from part of that push. Worked through, the exchange returns Newton’s inverse-square law with no curvature of space at all, and hands the gravitational constant a recipe: the vacuum’s own density and a retardation time. From that he draws his title. Energy as such does not gravitate, only matter does, and G should move when the vacuum around it is changed.
Why it matters hereChapter 3 holds that inertia and gravity are effects of the zero-point field rather than fundamental forces, and Musha pushes that idea to its sharpest edge — if gravity is a vacuum effect, the vacuum’s own energy need not weigh anything. Chapter 11 cares because the proposal comes with a handle: a gravitational constant that shifts when the field’s cut-off frequency or retardation time is driven.
What it claims
01If the zero-point field is real and its cut-off sits at the Planck frequency, about 3 times 10 to the 43rd per second, then Einstein’s field equation puts the radius of curvature of the universe orders of magnitude below the size of an atomic nucleus — the paradox the paper is written to resolve.Curvature of the universe due to the ZPF field, Eqs. 3 to 5
What to watch02Musha models gravity as a momentum exchange in which virtual particles created from the zero-point field push on matter, adapting Jordan-Mbeutchou’s ether-fluid analogy with the vacuum field in place of the fluid.Gravity generated by an interaction between the mass and the ZPF field, Eqs. 6 to 9
Published and peer-reviewed03Carrying that exchange through returns the Newtonian inverse-square force between two masses without any curvature of space, with the gravitational constant given by G equal to c squared divided by three times the equivalent mass density of the field times the square of a retardation time.Gravity generated by an interaction between the mass and the ZPF field, Eq. 10
Published and peer-reviewed04The same equation predicts that the gravitational constant itself changes when the cut-off frequency of the zero-point field or the retardation time is changed — the paper’s testable hook, developed in the author’s 2022 paper on the gravitational constant under a strong electromagnetic field.Gravity generated by an interaction between the mass and the ZPF field, paragraph after Eq. 10, citing reference 5
What to watch05Musha argues the equivalence principle is not fundamental, pointing to the long-standing puzzle that a uniformly accelerated charge radiates while a charge at rest in a uniform gravitational field does not; his ZPF gravity does not need the principle, because the force is built from the momentum exchange of Eq. 6.Other problem of Einstein’s gravitational theory
What to watch06Two consequences follow from the proposal: there is no graviton to find, and negative gravity from tachyons inside the zero-point vacuum of a collapsing star would stop matter short of a singularity, so black holes as usually described would not form.Other problem of Einstein’s gravitational theory, closing paragraphs; Conclusion
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Abstract
According to the Einstein's gravitational theory, the zero-point energy in the vacuum will collapse the universe into a gravitational singularity if the cut-off frequency of the zero-point field is the Planck frequency. But, according to the ZPF gravity theory proposed by the author, the energy does not have a gravitational mass as claimed by the Einstein's gravitational theory. From which, it is considered that Einstein's gravitational theory is not correct.
Keywords: Einstein's gravitational theory; equivalence principle; gravitational mass; zero-point energy; ZPF gravity
Author. Takaaki Musha, Advanced Science-Technology Research Organization, Yokohama, Japan; Foundation of Physics Research Center (FoPRC), Cosenza, Italy.
Introduction
The mass of an object determines its acceleration in the presence of an applied force. The inertia and the inertial mass describe this property of physical bodies at the qualitative and quantitative level respectively. According to Newton's second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A body's mass also determines the degree to which it generates and is affected by a gravitational field. This is sometimes referred to as gravitational mass. Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are identical; since 1915, this observation has been incorporated a priori in the equivalence principle of general relativity.
According to the Einstein's relativity theory, an energy has an equivalent mass and it has a gravitational mass as shown Einstein's gravitational equation.
Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle (i.e., the ZPF field). If the cut-off frequency of zero-point energy is equal to the Planck frequency, the radius of curvature of the universe would be expected to be orders of magnitude smaller than an atomic nucleus, which means the universe will collapse into a singularity if the zero-point fluctuation of energy (ZPF) were real. This is a paradox of ZPF energy field of the universe. Based on Sakharov's idea, Puthoff proposed a gravitation mechanism by an interaction between elementary particles and the ZPF field. According to his idea, the author proposed the ZPF gravity theory [1] and it shows that an energy does not have an equivalent gravitational mass.
Curvature of the universe due to the ZPF field
Einstein's gravitational equation can be given by [2]
R(μν) = − κ (T(μν) − (1/2) g(μν) T), (1)
where R(μν) is a Ricci tensor, T(μν) is an energy-momentum tensor and κ is the Einstein's gravitational constant.
Then we have [2]
R(44) = − κ (T(44) − (1/2) g(44) T), (2)
where T(44) = − ρ c² = − ε and ε is an energy density.
As we can write R(44) ≅ (1/2) g(44) / ℛ², then Eq. (2) becomes
g(44) / ℛ² ≅ 2 κ [ ε + (1/2) g(44) T ], (3)
Quantum physics shows that the vacuum is filled with zero-point fluctuation of energy. The total, frequency integrating energy density of the ZPF can be given by [3]
ε(E) = ( ħ / 8 π² c³ ) ω(c)⁴, (4)
where ω(c) is a cut-off frequency of the zero-point field in the vacuum.
Since it is assumed that ω(c) must actually be on the order of the Planck frequency given by
ω(p) = [ c⁵ / ħ G ]^(1/2) ≅ 3 × 10⁴³ /s, (5)
then the radius of curvature of the universe would be expected to be orders of magnitude smaller than an atomic nucleus, which means the universe will collapse into a singularity if the ZPF were real according to Eq. (3).
This is a great problem. Hence the author proposed another gravitational theory instead of the Einstein's gravitational theory.
Gravity generated by an interaction between the mass and the ZPF field
Jordan-Mbeutchou proposed a new model for Newtonian gravity by assuming space is filled with an ether (or aether) fluid [4]. He modeled gravity as an interaction between matter and ether fluid.
He assumed that matter can absorb ether fluid proportionally to its mass. Instead of an ether fluid, we assume that virtual particles (most of them are virtual photons) created from the ZPF field in a vacuum push matter, then the momentum flux density of virtual particles can be shown as
J = − ρ(m) / τ(0), (6)
where J = ε(E) / c ( ε(E): energy density of the ZPF energy), ρ(m) is an equivalent mass density of the ZPF field and τ(0) is a retardation time.
Figure 1. Two rest masses undergo the force generated the flow of ZPF energy.
For the ZPF field, we have the equation shown as [1]
dP/dt = − lim (r₁ → 0) ∫(S) ( p₁ + p₂ ) [ ( p₁ + p₂ ) · e₁ ] / ρ(m) dS, (7)
If ω is defined as ω = c k where k is a wave vector satisfying k = ω / c, we can write p = ħ ω / c and ρ(m) = ħ ω / c², the amount of momentum created by the ZPF field can be shown as
dP/dt = − lim (r₁ → 0) ∫(S) ( ħ / ω ) ( ω₁ + ω₂ ) [ ( ω₁ + ω₂ ) · e₁ ] dS, (8)
where ω₁ and ω₂ are vectors of the radial frequency of the ZPF field at the point e, as shown in Figure 1. According to the Jordan-Mbeutchou model, we have
( ω₁ + ω₂ ) · e₁ = ω₁(r₁) + ω₂(r₂) ( r₁ − r cos θ ) / √( r₁² + r² + 2 r r₁ cos θ ), (9)
where θ is the angle o₂ o₁ e and o₁e = r₁, o₂e = r₂ in Figure 1. When we let c ω₁ / ω → v₁ and c ω₂ / ω → v₂, then the force at the point o₁ in Fig. 1 becomes the equation, according to the Jordan-Mbeutchou model [4].
F = dP/dt = (1/3) ( c² / ρ(m) τ(0)² ) ( m₁ m₂ / r² ) e(z), (10)
where a gravitational constant is given by
G = (1/3) c² / ρ(m) τ(0)².
Figure 2. Generated force by the ZPF field.
The Equation (10) shows that the gravitational force can be generated by an interaction between matter and the ZPF field in a vacuum as shown in Fig. 2. According to this equation, the Newtonian gravitational law can be obtained without the curvature of space. Hence it is considered that the gravity is an electromagnetic phenomenon induced by the ZPF field in the vacuum and it is not due to the curvature of space as claimed by Einstein. Thus it is considered that the gravity is an electromagnetic phenomenon induced by the ZPF field in the vacuum and it is not due to the curvature of space as claimed by Einstein. This equation predicts that the gravitational constant can be changed when the cut-off frequency of the ZPF field or the retardation time will be changed [5]. Thus the ZPF gravity theory predicts that the overall ZPF energy does not gravitate and this means that the energy does not have an equivalent gravitational mass as shown by
m = E / c².
Other problem of Einstein's gravitational theory
In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference. In 1907, physicist Albert Einstein devised what we now call the "elevator" thought experiment, in which he dreamed up the idea of having an entire physics laboratory inside an ascending elevator. The result of Einstein's experimental elevator experiment was nothing less than the principles underlying the General Theory of Relativity.
However, one difficulty in the Einstein's gravitational theory is known as the equivalent paradox. A uniformly accelerated charge is recognized to radiate electromagnetic wave. According to the equivalence principle, which is the basis of Einstein's gravitational theory, the charged particle will radiate electromagnetic wave, but a charge suspended at rest in a uniform gravitational field does not radiate electromagnetic wave.
According to general relativity, a uniformly accelerating system in free space should be equivalent to one at rest in a uniformly gravitational field. Thus, in this case the charged particle, the principle of equivalence seems to be violated. This problem has been discussed in some papers without adequate resolution [6-8]. Hence it is considered that the equivalence principle is not real, which is the basis of Einstein's gravity theory and Eq. (3) is not correct derived from the Einstein's gravity theory. But the ZPF gravity theory does not require the equivalence principle because the gravity is created as shown in Eq. (6).
According to the theory of the black hole proposed by the author [9], negative gravity due to tachyons created inside the ZPF vacuum in the star prevents all the star's matter to be completely crushed into a singularity.
Figure 3. Does the black hole really exist?
Thus there may be no black hole in the universe. From which, Einstein's gravitational theory is not correct and it is considered that the gravity must be reconsidered from the quantum electrodynamics theory.
Conclusion
According to the Einstein's gravitational theory, the ZPF energy in a vacuum will collapse the universe into singularity. Instead of Einstein's gravitational theory, the ZPF gravity theory is proposed and it shows that the energy field does not have an equivalent gravitational mass as claimed by the Einstein's gravitational theory. From this theory, it can be seen that there is no particle such as "graviton" predicted by Einstein's gravitational theory. Gravity is an electromagnetic phenomenon induced by the ZPF field in a vacuum.
References
[1] Musha, T. and Pinheiro, M. J. (2021) The Gravitational Force Generated by an Interaction between Matter and the ZPF field in the Vacuum, and the Property of a Superfluid Vacuum, Russian Journal of Astrophysical Research, 7(1), 20.
[2] Gotoh, K. (1977) Relativity Theory, Tokyo, Japan: Kyoritu Shuppan, Co. Ltd.
[3] Haisch, B., Rueda, A. and Puthoff, H. E. (1994) Inertia as a zero-point-field Lorentz force, Physical Review A, 4(2), 678.
[4] Jordan, Y-Mbeutchou, N. (2019) Analogies between Gravity and Fluid Dynamics, African Institute for Mathematical Sciences (AIMS), 1, https://researchgate.net/publication/334721090.
[5] Musha, T. (2022) Gravitational Constant under the Strong Electromagnetic Field, Russian Journal of Astrophysical Research, 8(1), 23.
[6] Atware, H. A. (1970) Radiation from a Uniformly Accelerated Charge, Am. J. Phys, 38(12), 1447.
[7] Ginzburg, V. L. (1970) Radiation and Radiation Friction Force in Uniformly Accelerated Motion of a Charge, Sov. Phys. Uspekhi, 12(4), 565.
[8] Boulware, D. G. (1980) Radiation from a Uniformly Accelerated Charge, Ann. Phys, 124(1), 169.
[9] Musha, T. (2020) Negative Gravity Force Created by Gravitational Collapse of the Star, Russian Journal of Astrophysical Research, 6(1), 7.
The way in
https://doi.org/10.51542/ijscia.v4i2.2TEXT. Full text below, abstract to conclusion, with the nine references. The article is a two-column PDF and the extraction flattened Greek letters, vector arrows, subscripts and superscripts, so the display equations are reset here. Restorations: the tensor indices in Eqs. 1 and 2; the radius-of-curvature symbol in Eq. 3, written ℛ, which the following sentence names in words; the standard zero-point energy density of Eq. 4 and the Planck frequency of Eq. 5, both of which lost ħ; the density and retardation-time symbols in Eq. 6; and the substitutions the author states in the text for Eqs. 7 to 9. Equation 10 is reproduced in the reduced final form the extraction preserved, together with the expression for G that follows it; its intermediate expression did not survive. The three figures are not reproduced; their captions are kept because they carry the argument. Obvious typographic slips in the printed text — ‘dose’ for ‘does’, ‘Plank’ for ‘Planck’, and the spelling of two section headings — are corrected; the duplicated sentence about gravity as an electromagnetic phenomenon is in the original and is kept.
How to cite it
Takaaki Musha (2023) Energy does not have a Gravitational Mass (Flaw of the Einstein’s gravitational theory). doi:10.51542/ijscia.v4i2.2
Where it sits in the curriculum
Inertia and gravity from the vacuumGravity control and superconductorsWhat the vacuum is