# Debating Einstein's General Relativity

**EDITORIAL NOTE**

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*The Editorial Team*

#### Open Debate

## Debating Einstein's General Relativity

**EDITORIAL NOTE**

*This dialogus solely admits technical comments by specialists in Einstein and Santilli studies when expressed in due scientific language. We discourage the submission of arrogant and offensive comments frequently used to dismiss dissident view on EGR. Posts should be short and to the point with a maximum of five lines; they should identify the intended section from 1 to 15; and they should carry at the end, the selected User Name. Unless otherwise specified, all quoted equations and references refer to those of the above paper. Posters should allow time for the technical review of their proposed comments. The editorial rules of this Dialogus are those used by Wikipedia.*

*The Editorial Team*

**Paper to be debated**

Ruggero Maria Santilli

**RUDIMENTS OF ISOGRAVITATION FOR MATTER AND ITS ISODUAL FOR ANTIMATTER**

American Journal of Modern Physics 2015; Vol. 4(5): pages 59-7

Available for free pdf download from the link:

http://www.santilli-foundation.org/docs/10.11648.j.ajmp.s.2015040501.18.pdf

**ABSTRACT**

In this paper, we hope to initiate a due scientific process on some of the historical criticisms of Einstein gravitation by Einstein himself as well as by others, that have been widely ignored for about one century, with particular reference to: the apparent lack of actual, physical curvature of space due to the refraction of star-light within the Sun chromosphere; the absence of a source in the field equations due to the electromagnetic origin of gravitational masses; and the lack of clear compatibility of general relativity with special relativity, the interior gravitational problem, electrodynamics, quantum mechanics and grand unifications. We show that a resolution of the historical doubts can be apparently achieved via the use of the novel isomathematics and related isogeometries. We then show that the resulting theory of gravitation, known as isogravitation, allows a unified treatment of generally inhomogeneous and anisotropic, exterior and interior gravitational problems by jointly achieving a clear compatibility with 20th century sciences, thanks to the verification of the Lorentz-Poincar-Santilli isosymmetry, as well as the replacement of the Riemannian curvature with the covering notion of isoflatness. We then present, apparently for the first time, the isogravitational isoaxioms characterized by the infinite family of isotopies of Einstein axioms for special relativity, which are applicable to both exterior and interior isogravitational problems. We finally show, also for the first time, the apparent compatibility of the isogravitational; isoaxioms with current knowledge on black holes and other gravitational conditions in the expectation of due scientific process for the final resolution of the historical doubts on general relativity.

Keywords: special relativity, general relativity, isorelativity

**TABLE OF CONTENTS**

**1. Introduction**

**2. Historical Insufficiency of General Relativity**.

2.1. First historical insufficiency of general relativity:

Ignoring the refraction of star light passing through the Sun chromosphere, with consequential lack of evidence that space is curved.

2.2. Second historical insufficiency of general relativity:

Ignoring the electromagnetic origin of the mass, with consequential invalidation of Einstein's reduction of gravitation to pure curvature without sources.

2.3. Third historical insufficiency of general relativity:

Abandoning the majestic Lorentz and Poincar\'e "invariance" of special relativity in favor of the "covariance" of general relativity with consequential lack of prediction of the same numerical values under the same conditions at different times.

2.4. Consequences of the historical insufficiencies of general relativity:

Incompatibility of gravitation with special relativity, interior gravitational problems, electrodynamics, quantum mechanics, and grand unifications.

2.5. Problems to be solved for an axiomatically consistent grand unification.

**3. Rudiments of IsoMathematics.**

**4. Rudiments of IsoMechanics.**

**5. Rudiments of IsoGravitation for Matter**

5.1. Elementary Formulation of IsoGravitation

5.2. Minkowski-Santilli IsoSpace

5.3. Minkowski-Santilli IsoGeometry

5.4. Lorentz-Santilli IsoSymmetry

5.5. IsoGravitational IsoEquations

5.6. Operator IsoGravitation

5.7. Compatibility of IsoGravitation with 20th Century Theories

5.8. IsoGravitational IsoAxioms

5.9. Verification of IsoGravitation for Exterior Problems without Source

5.10. Verification of IsoGravitation for Exterior Problems with Source

5.11. Verification of IsoGravitation for the Interior Problem

**6. Rudiments of IsoDual IsoGravitation for AntiMatter**

**7. Rudiments of IsoGrandUnification**

**Acknowledgments**

The author would like to thank the organizers of the Eight Marcel Grossmann Meeting in Gravitation, held at the Hebrew University, Jerusalem, June 22 to 27, 1997, for having my talk presented by the session chairman and publishing my paper [34] in the proceedings despite my being incapacitated to attend.

**Figures**

Figure 1. According to the first and perhaps most important unresolved historical criticism of Einstein gravitation, Sunset is a visual evidence of the lack of actual, physical, curvature of space because we still see the Sun at the horizon, while in reality it is already below the horizon due to the refraction of light passing through our atmosphere. Exactly the same refraction without curvature of space occurs for star-light passing through the Sun chromosphere, in which case the only "bending of light" is that due to Newton's gravitation in a flat space (see Section 2). Note that Einstein gravitation cannot represent light refraction because it requires a locally varying speed of light within a medium, first with increasing and then decreasing density. Hence, the representation of refraction via the curvature of space violates visual evidence, physical laws and experimental data [111-15]. To achieve a credible proof that the bending of Star-light passing near the Sun is "evidence" of the curvature of space, Einstein supporters have to prove that star-light passing through the Sun chromosphere does not experience refraction. The impossible existence of such a proof is readily seen from the fact that Einstein gravitation was solely aimed at a description of "exterior gravitational problems in vacuum," while the propagation of star-light within the Sun chromosphere is strictly an "interior gravitational problem" treated later on in Section 5. Its description via the Riemannian geometry is beyond any realistic possibilities due to the need for a metric possessing a dependence on coordinates , as well as density , temperature , frequency , etc. (see Sections 5-11 below).

Figure 2. The "blood red moon" (top view) during a Lunar eclipse is an additional visual evidence of the lack of curvature of space because Sunlight reaches the Moon even when it should be in total darkness (bottom view). Note that for both Sunsets and Lunar eclipses the entire spectrum of Sunlight is redshifted without relative motion, merely due to loss of energy by light to a cold medium (IsoRedShift). Note also that we are dealing with "direct Sunlight" traveling in empty space for which scattering and other interpretations have been dismissed in peer refereed journals [11-15]. Note finally that the "blood red moon" confirms the view by Einstein, Hubble, Fermi, Zwicky, Hoyle, de Broglie and others on the lack of expansion of the universe because, when our Sun is seen millions of light years away, we merely have the replacement of Earth's atmosphere with very cold intergalactic gases under which the entire spectrum of visible Sunlight will appear redshifted without any relative motion [11-15].

Figure 3. A view of a Solar eclipse showing no "bending of light" because the Newtonian attraction of light by the moon is extremely small and there is no refraction due to the lack of lunar atmosphere. The faint luminescence at sea level is due to the diffraction of light in our atmosphere. In conclusion, final claims of "bending of light due to curvature of space" must be based on star light passing tangentially on a body without atmosphere or chromosphere and be proved to be greater than the Newtonian attraction.

Figure 4. A typical representation of the claimed curvature of space caused by the gravitational field of a mass, which representation has been adopted for one full century. The historical, yet unresolved criticism is that the notion of physical curvature in one dimension requires a bigger dimension for its identification. In fact, the physical interpretation of the mathematical Riemannian curvature in two dimension can only be identified in three dimension as clearly illustrated by the above figure. Therefore, the additional historical criticism of Einstein gravitation that needs to be addressed is that the physical identification of the mathematical Riemannian curvature in three dimensions, as needed for realistic models of gravitations, requires four space dimensions that do not exist, thus confirming the lack of physical evidence for the actual physical curvature of space depicted in Figure 1, 2, 3. In any case, Einstein supporters are requested to illustrate with concrete geometric example the physical curvature needed for realistic models, not in two dimensions as done for one century, but in three dimensions.

Figure 5. Another illustration of the insufficiencies of the one century old assumption that planets moving around the Sun in our Solar system actually move along a real, physical curvature of space. The historical criticism is that the above representation is purely mathematical because, to actually sense curvature in a three-dimensional space, the planet should move in a fort space dimension that does not exist.

# COMMENTS

**DEBATING EINSTEIN'S GENERAL RELATIVITY (EGR) VS SANTILLI'S ISORELATIVITY (SIR)**

**1. Visual, geometric and experimental evidence on the lack of g curvature of space or of spacetime**

*Einstein EGR represents exactly the 1.75 arc-seconds for the bending of light passing near the Sun. Hence, I cannot accept Santilli IR. Zeus*

Yes, but visual evidence of the Sun at Sunset establishes the historical objection that 50% of the bending is due to refraction of light in the Sun chromosphere (Fig. 1). The remaining 50% is known to be due to Newton's gravitation. Hence, the representation of the bending of light via EGR is purely mathematical without any physical content. ZeusSon

I have been convinced on the lack of curvature of space and of the purely mathematical character of EGR by the geometric evidence (Figs. 4 and 5) that the representation of curvature in three space dimensions requires a fourth space dimension that does not exist. KsyPtrtrtCsfd

The curvature of space has been independently established by astrophysical evidence achieved by the European Space Agency on light bending in deep space, including gravitational lenses, thus confirming the invalidity of SIR. Zeus

I disagree. Astrophysical evidence on the bending of light has been proven to be equal due to the refraction of light within hot plasma near galactic centers and not to curvature. Gravitational lenses are known to be due to Newton gravitational attraction. The interpretation of gravitational lenses being due to curvature of space is known to be political. ZeusSon

EGR has established that the curvature golds for space time, further than space, thus invalidating the argument of Fig. 1 as being due to refraction within a chromosphere, Jupiter

The "curvature of time" has no physical value whatsoever. Additionally, the time lapsed for light passing near the Sun is too short to produce the gravitational deflection needed to represent experimental values. For these and other reasons, Einstein clearly spoke of the "curvature of space" and not the "curvature of space=time." JupiterSon

Santilli's numerous experiments on IsoRedShifts (Refs. [11,1,15] (see also the vast literature in http://www.santilli-foundation.org/docs/No-universe-expans.pdf) have established the refractive origin of the bending of light in the Sun chromosphere beyond any possible scientific doubt. The extrapolation of the experimental angle of light bending in our atmosphere (Fig. 1) to the Sun chromosphere represent 50% of the 1.75 arc seconds exactly and invariantly. To have any credibility, "Einstein supporters" (Figs.1-5) should dismiss Refs. [11-15] via counter-experiments. JupiterSon

The curvature of space can be proven to exist from the Equivalence Principle (EP) and other EGR laws, thus disproving Santilli's argument. Poseidon3

I have strong objections again the rather widespread use of the words "Santilli argument" since the argument on the lack of curvature of space is historical. Santilli merely halted its suppression by Einstein fanatics for about one century. 153527e457

The use of the theoretical EP to claim the physical existence of the dismissed in numerous refereed papers, as well as by the recent detection of antimatter galaxies by Santilli and various independent scholars. Poseidon 333

I fully accept the additional historical criticisms of EGR resuscitated by Santilli according to which curvature cannot credibly represent the free fall of bodies along a radial line, due to the lack of any curvature along a straight line, while said free fall is consistently represented by Santilli SIR. ZakuPuleTi

The central assumption of EGR is the representation of gravitational attraction with the curvature of space. Therefore, the lack of curvature in free fall is evidence that space cannot be curved. I consider offensive the usual arguments via geodesics, the EP etc. because they try to bypass physical evidence via ad hoc mathematics under the expectation that I agree. ZicZac

The refraction of light within the Sun chromosphere is a strictly interior dynamical problem that cannot be even formulated in EGR, let alone treated, while Santilli SIR was constructed, firstly, for interior problems, and secondly, for exterior problems in vacuum. ZeusGrandSon

Santilli is right in stating that no deflection of light beyond the chromosphere of the Sun has ever been observed, thus confirming that the deflection in the Sun chromosphere is due to refraction and not to curvature of space. According to Einstein, the deflection is inversely proportional to the Sun radius R. If Einstein's gravitational lensing is real, gravitational lensing should be observed all over the sky, but it is not observed. Ergo, space is not curved and, without curvature, EGR is empty.

Cosmologists invoke gravitational forces when they speak of gravitation in terms of EGR. However, gravitational forces do not exist in EGR because according to Einstein, gravity is spacetime curvature, not force. But we have seen in this section the lack of existence of actual curvature of space. Hence, EGR is mathematically nice, but physical vacuous.

EGR is correct.

Since you support EGR without resolving the litany of inconsistencies treated in Sections 1 to 15 of this blog, you are Einstein fanatic, thus being an enemy of serious science.

The experimental results have, thus far, all been entirely within and interpretable in the context of EGR. This includes the usual culprits of frame-dragging, gyroscope precession, precession of planetary orbits, the slow-down of at least two binary pulsar's at a rate predicted by EGR from energy loss due to Gravitational wave radiation, the direct detection of said gravity waves at least twice now, Gravitational red-shift from a variety of stars, gravitational lensing from numerous galaxies..my favorite is the quasar who's image is split into four by the lensing effect of a closer galaxy..but this is just one of many instances. I am sure other frameworks might exist to explain ALL of these measured effects, but the fact that, thus far, EGR has predicted about 1/2 of them correctly prior to their measurement and explains all of the others is just too powerful to ignore. Indeed, I am not yet aware of a single test that EGR has failed. At best a rival to EGR can only compete on equal ground until quite a number of experimental tests are shown to be incompatible with EGR. Oh and by the way, I saw a reference above to faster-than-light neutrinos. An experimental mistake was found in that apparatus and so that report from OPERA has been retracted. Experimentally we have NO, I repeat, NO evidence for any "faster-than-light" particle of any kind. afsfsewew43435465

The statement by afsfsewew43435465 is essentially correct. However, in my view, the following comments are in order: A) The representation of experimental data via EGR is purely mathematical since all treatment are crucially dependent on the curvature of space, while we have incontrovertible visual, geometric, and experimental evidence that space is not curved. Hence, the indicated representations are physically vacuous. B) All indicated representations are a kind of "Polaroid picture" of gravity at a frozen point in time. It is easy to prove from the covariance of the theory that numerical values change under the same conditions at different times. C) The indicated representations are not unique since there are several possible linearizations of the field equations leaving to different numerical results. More insidiously for the physical content, the indicated representations are done via generally different linearizations, thus suggesting that EGR is the perfect mathematical theory allowing the tailoring of the representation to the data at hand. Therefore,afsfsewew43435465's argument, even though deserving respect, is far from establishing EGR as the final theory of gravitation. What would really help science would be that afsfsewew43435465 achieves the representations of exactly the same experimental data via SIR and compare the two results. The advantages of DIR over EGR are crushing primarily because of the universal Lorentz-Poincare'-Santilli isoinvariance from which all advantages follow as discussed in these comments. Adf3547d835dgsg

It seems to me that "curvature of space" is a contradiction in terms, because once 'space' or 'reference frame' is bend, then we have created a primary unbend 'space' from which to define the bending in the secondary 'space.' The conclusion is then that 'space' is not bend (primary space here), but something now left undefined and unproven is supposedly bend. All of this questionable and unproven theorizing seems to be irregular in the field of science. Regards J.Boersema

I agree with Boersema's view. I believe I am far from being alone. ZeusSon

When Einstein needed proof of his concept of general relativity he could not point to any Earthly based proof. The Sun was used as a massive object that because of its mass was supposed to bend light passing near it. In 1909 Eddington using a 4.5 inch telescope during a solar eclipse, claimed starlight near the Sun was bending. This made Einstein instantly world famous and he claimed that this proved his general relativity theory. A 4.5-inch telescope is hardly adequate for this research. Einstein, also changed his figures to match the recorder measurements. The very hot Corona refraction properties were not taken into consideration. In other measurements taken after that time, they were just observing the Newtonian Re fractions. Recent information scientifically states that Einstein's general relativity does not bend light about the Sun. It is totally Newtonian Refraction that is responsible for this. See: OBSCURANTISM ON EINSTEIN GRAVITATION? http://www.santilli-foundation.org/inconsistencies-gravitation.php

Serious scholars in gravitation should take the above comments seriously. ZeusSon

**2. Riemannian Geometry (RG) vs Santilli IsoGeometry (SIG)**

*What is SIG? Zeus*

If you do not know what is SIG, you do not belong in this debate. ZeusSon

I greatly support this debate because the visual, geometric and experimental evidence on the lack of curvature of space establishes the need to replace the RG with a more adequate geometry. ZeusGrandSon

Thank you ZeusGrandSon. In my view, Santilli's first main achievement in gravitation has been the discovery of a basically new geometry [29], http://www.santilli-

The RG represents all experimental evidence on EGR. Hence, I do not see the need for a new geometry. Jupiter

I disagree with your personal opinion. Physics is expected to be a representation of physical reality. The vast evidence on the lack of curvature of space eliminates the RG as a credible geometry for gravitation. ZeusGrandSon

I see no need for a new geometry since the RG beautifully characterizes the universe. ZurlicZac

This view should not be admitted in this blog because it's not technical. (Galaxies are at such a large mutual distances to prevent any credible use of the RG since gravitation is null.) Hence is RG has no technical sense at a large cosmological scale, while fully admitting SIG due to its isoflatness. Inner-galactic dynamics is fully represented by Newton's gravitation (including black holes as well known!) plus Santilli IsoRed and IsoBlue shifts. PirlivSpark

The position by Jupiter, ZurlicSpac et al is political because the RG can only represent matter, while the evidence on antimatter galaxies is increasing. Only SIG can jointly represent matter and antimatter galaxies via its anti isomorphism, besides representing gravity without curvature, and achieving consistency with 20th century theories, including grand unification. 35472920497362

I believe that Santilli's views in gravitation are wrong.

You disqualify yourself by referring to "Santilli;s views," while Santilli studies "historical" objections whose treatment had been suppressed by Einstein fanatics like yourself for one century. To see how political is your position, you should search and study the 1020 objections against EGR by Ludwik Silberstein who is essentially the originator among many others of Santilli Historical Objection 2.1.

Following the seminal 1974 paper at MIT Annals of Physics [16], Santilli's best presentation of the physical (not mathematical) inconsistencies of EGR was provided in the 1984 book Il Grande Grido http://www.scientificethics.org/IlGrandeGrido.htm , see Chapter 1 and Section 1.5 in particular. It appears that in his 2015 paper herein reviewed, Santilli has achieved a quantitative treatment of all preceding criticisms with no credible dismissal published in refereed journals.

**3. Einstein-Hilbert field equations (EHFE) vs Santilli isofield isoequation (SIFE)**

*SIR is wrong because it abandons Einstein's field equations. Zeus*

In my view, Santilli's second main achievement in gravitation has been that of "preserving" rather than abandoning, EHFE, thanks to the admission in Santilli flat geometry of the Riemannian machinery. ZeusSon

But Santilli introduces an external source in the field equations I cannot accept. Zeus

This view is due to lack of study of SIG. A first order source is necessary to represent the elm origin of mass is, as well as to prevent the prediction by EGR that one black hole swallows the entire universe (Section 5.11). ZeusSon

A complete replacement of EGR is out of the question for me, Jupiter

SIG merely reformulates EGR via a new geometry allowing a resolution of the historical objections. Besides, you can project Santilli reformulation of the field equations on an ordinary Riemannian space and you recover the field equation you so much love, but then you have a plethora of inconsistencies. JupiterSon

I accept SIG primarily because it reformulates Einstein's conception of gravitation in a form admitting a universal symmetry, the Lorentz-Poincare'-Santilli isosymmetry, which I consider to be Santilli's third main achievement in gravitation." 35472920497362

I see no main difference between Santilli basic equations (35) and the conventional ones, except for a simple hat in the symbol. Zeus

That hat indicates an entire new math, from new numbers to new typologies. You are ignoring it to your peril. ZeusSon

**4. Gravitational waves**

*Santilli dismisses gravitational waves. Therefore, their recent experimental verification in PRL 1061102 (2016) dismisses SIR. Zeus*

Dear Zeus, this is an additional political statement ventured without technical knowledge of SIR. As commonly understood, "waves" cannot be even defined in the RG. By contrast, SIG admits a fully consistent formulation of Maxwell's equations due to the isomorphism of SIG with the conventional Minkowski geometry. Hence, in case confirmed, gravitational waves confirm SIR much more than EGR. ZeusSon

SIR is inconsistent because Santilli rejects gravitational waves. Jupiter

That's not true. Santilli rejects the popular belief that the gravitational force is propagated or mediated by waves because, under grand unification, that belief would require the assumption that electric and magnetic forces and also propagated or mediated by far fetched "electric and magnetic waves". JupiterSon

Besides the fanfare by Einstein's followers, the experimental data mentioned by Zeus and Jupiter indicate the apparent existence of "gravitational bursts" caused by the sudden release of large masses in black holes collisions. The claim that these data establish "waves" is political. 35472920497362

I am disturbed by the use of apparent gravitational waves to dismiss SIR because Einstein essentially threw the idea of the gravitational waves out of the blue sky. By contrast, in the 1974 paper [6] at MIT Annals of Physics, http://www.santilli-foundation.org/docs/Santilli-14.pdf. Santilli achieved a unification of gravitation and electromagnetism. Consequently, elm waves implies the existence of gravitational waves. Zuckie

I regret to state that, following the affair on the superluminal neutrinos and so many others, PR excessively biased on Einstein and consequently, it is no longer a credible scientific journal when dealing with Einstein theories, as I am sure the majority of physicists would agree. Antares321

EGR cannot localize the gravitational energy. Consequently, Einstein's gravitational waves cannot exist when formulated on the Riemannian geometry as technically explained by Santilli . Moreover, Einstein's gravitational waves do not have a unique speed of propagation because said speed is coordinate dependent, thus admitting superluminal values. Santilli is correct in the main geometric point: gravitational waves cannot be even defined on a Riemannian space in a physically meaningful way, although they can be consistently formulated on Santilli's isominkowskian space [29] due to its isomorphism with the conventional Minkowski space.

**5. Einstein covariance vs Santilli invariance**

*I do not accept SIR because it eliminates Einstein's principle of covariance, thus destroying the geometric beautifies of GR. Zeus*

In my view, Santilli's fourth main achievement in gravitation has been the discovery of a universal variance of all infinitely possible, non-singular, Riemannian separations. which was first achieved by Santilli the 1993 paper [32] written while visiting Moscow State University, http://www.santilli-

I definitely do not see the need for an invariance since covariance is verified by the experimental verifications of EGR. Jupiter

I definitely disagree with your personal opinion. As clearly shown by Santilli in Section 2.2 and Ref. [7], www.santilli-foundation.org/

I believe that the real most serious problems of covariance emergence when studying the compatibility of EGR with 20th century theories. 35472920497362

I still do not see the argument of this section, because Wikipedia speaks of "Lorentz covariance," and not "Lorentz invariance," or "symmetry", see the Wikipedia Article https://en.wikipedia.org/wiki/Lorentz_covariance. Zeus

It is unfortunate that the Editors of this scientific blog have allowed the quotation of the politics at Wikipedia. The universally known name of "Lorentz invariance" has been turned by known Einstein fanatics at Wikipedia into "Lorentz covariance" for political alignment with the "covariance of EGR". In short, the unfortunate editors of Wikipedia know well that Einstein's variance is grossly flawed. Therefore, they manipulate science by dreaming to achieve credibility by turning the beautiful Lorentz invariance into the flawed covariance. Wikipedia is totally disqualified for any statement pertaining to Einstein because the "universal constancy of the speed of light" in vacuum can only be proved on serious scientific grounds outside politics via the Lorentz "invariance." ZeusSon

**6. Field equations with or without a source**

I spent my research life by adopting Einstein's very elegant reduction of gravitation to pure curvature without any source, and do not plan to change my view. Wuckperpt

Yes, I admit that Einstein conception of gravitation is beautiful, but it is a dream.The pillar of serious physics is the admission of reality. The refereed paper [16] (at MIT Annals of Physics mind you) Annals of Physics, Vol. 83, 108-157 (1974), http://www.santilli-

But EGR is a classical theory while Ref. [16] deals with QED, I do not see the application of the latter to the former. Wuckperpt

You prove not to have studied Ref. [16] because, after QED calculations for the elm mass of the electron, positronium, and the pi-zero meson, the paper passes to a fully classical representation of the elm origin of macroscopic masses. 255390405873

Despite its beauty, I never accepted Einstein's reduction of gravitation to pure curvature because I could not identify in a clear way in a curved space or spacetime the 50% Newtonian contribution in the bending of light passing near the Sun, which is defined on a flat Euclidean space from the, from the remaining 50% contribution which is presumed to be due to curvature. QarBlarPirk

According to Einstein, spacetime and matter have no separate existence. This is confirmed by his field equations due to the lack of a source. If either the energy-momentum tensor or the Einstein tensor is zero, so is the other. Without a material source in Einstein's field equations, there is not only no gravitational field, but there is no universe. This illustrates the importance of Santilli 1974 paper, Ref. [16], on the need for a source representing the entire gravitational mass for gravitation to make physical sense.

**7. Compatibility with SR**

No contribution on supporting EGR has been received for this section to date (July 15, 2016). Editorial note

EGR cannot be compatible with SR because Einstein covariance can never be reduced to the Poincare' invariance, By contrast the Lorentz-Poincare'-Santilli isosymmetry of SIR trivially reduces to the conventional Lorentz-Poincare' invariance in the absence of gravitation. ZeusSon

EGR is incompatible with SR for numerous reasons treated in refereed publications. I mention here only the impossibility for EGR to produce the ten total conservation laws of SR. JupiterSon

I accepted SR because it is a covering of Galileo relativity. I never accepted EGR because it is not a covering of SR as shown by the lack of any physical meaning at null curvature. By contrast, Santilli SIR is a true covering of SR by recovering it uniquely and identically at the limit when the gravitational isotopic element becomes the identity. 255390405873

I never considered EGR a consistent description of gravitation because of its known series of incompatibilities with SR. By contrast, I accepted SIR because of its true covering character of SR in all its components, that is, SIG is a covering of the MH, the Lorentz-Poincare'-Santilli isosymmetry is a covering of the Lorentz-Poincare' symmetry, etc. The advantages of SIR over EGR are so crushing to disqualify their denial. AntiQuark

EGR violates the usual conservation of the energy and momentum for a closed system due to covariance, as explained by Santilli. EGR is thereby in conflict with a vast array of experiments.

I agree with Santilli (and many others) to the effect that EGR is incompatible with SR because the former has no means to model more than one mass, whereas the latter permits any number of masses.

The validity of the general covariance of EGR is established because of its compatibility with the EP.

There is no physical value in comparing an object in free fall with a mass experiencing gravitation when space is believed to be curved, because the latter is based on curvature while in the former there is no curvature whatsoever since the fall occurs along a "straight line." Of course you cannot connect these two irreconcilable conditions via any invariance and, therefore, you need a covariance, but that;s pure mathematics. Hence I believe that the EP is the biggest blunder in the history of gravitation because it has been used for one hundred years to maintain EGR (see, e.g., the 1917 criticism of Einstein's covariance by Erich Kretschmannn that remains fully valid to this day).

I accept SIR against ESR because Santilli achieved for the first time the "invariance" of line elements [12], thus terminating the physical inconsistent covariance. It should be noted that this clearly major result is due to the prior construction of isomathematics, in which absence Einstein had no other choice than go for general covariance with ensuing litany of inconsistencies.

**8. Compatibility with QM**

In my opinion, the construction of relativistic hadronic mechanics [23] is Santilli's fifth main achievement in gravitation and particle physics due to the encompassing of exterior and interior gravitation and particle problems, reversible and irreversible processes and so much more. AntiQuark

Santilli must be complimented for the clarity of his argument that the classical non-canonical character of EGR will never admit a consistent quantum image since the latter must be non-unitary with ensuing known solutions violating causality and other quantum laws. ZeusSon

I believe that the validity of SIR over EGR becomes compulsory when considering the compatibility with QM because Santilli merely embeds gravitation in the unit of QM, thus preserving its axioms and physical laws. JupiterSon

Since the field equations are the same for both EGR and SIR (except for the source), I do not see how their operator image can be different. Kubitswusza

That's because you do not have technical knowledge in Santilli isomathematics and isogravitation. Zazaczac

Tell me the gist. Kubitswusza

It's a beautiful construction which is all contained in the paper [26], (http://www.santilli-

Still, the operator images of the field equations an the isoequations should be non-unitary. Kubitswusza.

I am surprised that the Editorial Team still allows you to post due to your lack of technical knowledge of relativistic hadronic mechanics I cannot possibly review here. Zazaczac

Is the map from the classical to the operator forms unique? Jupiter

Yes, because uniquely set by the 4x4 matrix T*(x, v, ... ...) containing gravitation. Zazaczac

What is the meaning of "operator isogravity"? Zeus

In the presence of gravitation, the conventional QM formalism is gone, although its axioms are preserved. Hence "Operator IsoGravity" is a nickname for relativistic hadronic mechanics. ZeusSon

I always considered quantum gravity an academic exercise due to a plethora of insufficiencies. The dramatic validity of Santilli operator SIR can be illustrated with one example, the Dirac-Schwartzchild equation allowing, for the first time, the study of an electron in the gravitational field of the Sun, and ensuing application to solar flares simply impossible with GR. 255390405873

The most compelling argument by Santilli the lack of curvature of space is his achievement of a consistent operator image of gravity since it is possible if and only if, the curvature is zero. JupiterSon

**9. Compatibility with QED.**

*No contribution on supporting EGR has been received for this section to date (July 15, 2016). Editorial note*

I believe that Santilli's argument (Section 2.2) on the elm origin of the mass for the electron, the positronium, the pi-0 and masses in general is simply incontrovertible, with ensuing incompatibility of EGR with QED. ZeusSon

The conclusion of Ref. [16] is very clear, either one accepts EGR, in which case QED has to be modified, or one accepts QED, in which case EGR must be modified. The evidence in favor of the latter case is out of question, JupiterSon

Santilli's remarkable achievement of a consistent operator image of gravitation resolves all objections against the compatibility of SIR with QED. AntiQuark

**10. Interior gravitation**

*How is it possible for the isometric of SIR to have an arbitrary functional dependence on local variables, as needed for interior gravitation? Zeus*

I am surprised again that the Editorial Team allowed this question since this blog is solely for experts in isomathematics, isomechanics and isogravitation. The sole restriction on the gravitational isotopic element T*(x, v, ...) is that of being positive-definite, thus illustrating the power of isomathematics and the consistency of SIR for interior problems. ZeusSon

Einstein followers believe that the interior gravitational problem does not exist because gravitational masses can be reduced to elementary particles and everything is recovered at that level. This piece of said posture is offensive for serious scholars, due to the never ending list of inconsistencies, such as the lack of a consistent quantum gravity. ZeusSon

Yes, ZeusSon, the indicated posture is offensive because everything compatible with Einstein, no matter how far fetched, is pretended to be accepted, otherwise Einstein followers will throw you out of academia. AntiQuark

The primary reason I accept SIR is that it achieved the first known geometrically consistent formulation of the interior gravitation, including the representation of locally varying speeds of light within physical media, although in a unified treatment with exterior gravitation. JupiterSon

Water is part of interior gravitation. I agree with ZeusSon that the reduction of masses to elementary constituents is offensive because gravitation is known to disappear at that reduction. Also, the reduction to particles will never represent the reduction of the speed of light in water by 100,000 km/s which event is beautifully represented by SIR due to the unrestricted functional dependence of the isometric on all needed local variables, including c/n. 255390405873

SIR claims that the gravitational mass is smaller than the inertial mass. Experimental knowledge (Eotvos, Krotkopv-Dicke, Brakinsly-Panov, disproves that. Zeus

The experiments you quote indicate that the possible difference between the gravitational and inertial mass is less than one part in 10^{12}. Santilli makes no quantitative claim on the indicated difference. Hence, your view is technically insufficient to rule out SIR. ZeusSon

I know the experiments quoted by Zeus, and can prove that they do not have actually measured the inertial mass, since they include it via the usual theoretical-mathematical assumptions via the use of the EP, covariance etc. True "experiments" on the gravitational and inertial mass require tests with and without accelerations that do not exist in serious scientific circles. AntiQuark

In view of its deep implications, I believe that the achievement of a consistent formulation of interior gravitational problems constitutes Santilli's sixth achievement in gravitation. ZeusSon

**11. Verification or violation of the Freud identity**

*It is my understanding that Santilli does not properly treats the Freud Identity (Section 1.1). Zeus*

The Freud identity requires "two" source terms for the r.h.s. of the field equation, thus being ideally suited for interior gravitational problems, since one term represents the elm origin of mass and the other the contribution due to internal short range interruptions. It is evident that, passing to the exterior problem, the internal term is inapplicable and we have only the elm source. ZeusSon

But then Santilli exterior gravitation violates the Freud identity.

No, because the Freud identity solely applies to the RG. Santilli's major effort is to replace the RG with a new one for which the Freud identity does not apply in its Riemannian form. ZeusSon

It can be proved that the new source suggested by the Freud identity is null in a Lorentzian frame and therefore, it must be null for all Riemannian coordinates. Jupiter.

By using the same argument, the curvature tensor is also null in a Lorentzian frame and consequently, the Riemannian geometry must be flat according to the tensor/pseudo-tensor semantic. ZeusSon

I disagree because Santilli does not properly identify tensors and pseudo tensors and consequently, Santilli's use of the Freud identity is wrong. Kupiter

This is pure semantic because the words "tensors" and "pseudotensors" do not exist in the paper precisely to prevent mathematical manipulations of the physics, which is the need for a first order "source" in the r.h.s. of the equations. JupiterSon.

Regrettably, the use of the Freud identity to appraise SIR, has no physical value, since the physics is established by two interactions, the long range exterior elm interactions and the additional short range interior interactions. The isotopic reformulation of the Freud identity and not the old identity, must be adapted to represent said reality. Period. 255390405873

**12. Black holes vs brown isoholes**

*No contribution on supporting EGR has been received for this section to date (July 15, 2016). Editorial note*

I cannot accept EGR because it predicts that one single black hole should have swallowed the entire universe billions of years ago because the rotational motion of stars around galactic center is too slow to counter large gravitational attractions. Hence, a black hole at the center of a galaxy should swallow first all galactic stars and then pass to swallow under a sufficiently long lapse of time all of the remaining galaxies. ZeusSon

Yes, I agree. That's one of many reason I accept SIR since it predicts a limit on the value of the mass in the interior of black holes (Section 5.11) thus preventing the destruction of the universe. JupiterSon.

Yes, ZeusSon and JupiterSon, that's an additional reason I accept a first order source in the r.h.s. of the field equations since the limit in black holes interior masses originates precisely from that term. AntiQuark

The mathematics of black holes in EGR implies that the square of a real number must take on negative values and implies other occurrences that are mathematically impossible. Hence the black hole theory in EGR is mathematically inconsistent. Physically,m Santilli has shown that, in the event true, one black hole could swallow the entire universe since there is no limit in mass accretion which mass accretion, by contrast, exist in SIR. DLINFLO818

I accept Santilli's view to the effect that, being unidirectional in the absorption of masses, black holes should be irreversible over time, thus requiring Santilli' Lie-admissible covering of the Minkowski geometry [29]. By contrast, EGR is strictly reversible over tine and has no means to truly represent mass accretion. This point alone dismisses the validity of black hole theories in EGR. SCIFIFAN71919

**13. Antimatter**

I believe that the validity of SIR over EGR becomes overwhelming when passing to antimatter because EGR has no possibility whatsoever of representing the gravitation of antimatter, while SIR includes a full description of antimatter via an anti-isomorphism of SIG based on negative definite isounits and isotopic elements. ZeusSon

Another offensive posture of Einstein followers is that they oppose gravitational repulsion between matter and antimatter since, in their view, it would violate the EP. This posture implies the advance adaptation of a yet unknown physics to their preferred theory. JupiterSon

EGR was formulated for matter. The ongoing attempts at adapting antimatter to EGR are very damaging to Einstein followers. 255390405873

As shown by Santilli in monograph [40], gravitational repulsion between matter and antimatter is predicted at all levels of study, from Newtonian mechanics to particle physics and it is necessary for a serious representation of matter-antimatter annihilation. The oblivion by Einstein followers on all this is disturbing. AntiQuark

I believe an experiment using anti-neutrons has already indicated that they fall towards the centre of the earth with the same acceleration as neutrons. This indicates that "antimatter" does not have a negative "mass" and would be consistent with EGR which claims that bodies simply follow curvatures in space-time. fgfgerer34545465

The post by fgfgerer34545465 seems to be intended to criticize Santilli's isodual theory of antimatter via political means because done without any technical knowledge of the field. For the record, Dirac conceived antimatter as having negative mass and Santilli resolved its violation of causality thanks to the isodual mathematics for which negative energies are referred to negative units, thus being fully causal. ZeusSon

fgfgerer34545465 appears to ignore the entire content of this blog. He/she should at least glance at Comments 1 on the visual, geometric and experimental evidence on the lack of curvature of space-time. Equally political appears to be the claim of experiments on the gravity of anti-neutrons which experiments do not exist and, in the event done, they are themselves political due to the extreme sensitivity of the needed neutron interferometry. The political character of the view is also established by the fact that, an "anti-neutron" with positive mass and conventional gravity is known not to annihilate with neutrons, thus non being a true anti-neutron. This is another case of imposing EGR via the suppression of a serious scientific process. JupiterSon

**14. Grand Unification {GU}**

In my view, Santilli's seventh main achievement in gravitation has been the formulation of the first and only known axiomatically consistent grand unification inclusive of electroweak (EWI) and gravitational interactions (GI).

In a remarkable limpid fashion, Santilli has shown in monograph [40], http://www.santilli-

14.1. GI cannot be formulated on a curved space because their non-canonical structure would propagate under GUF to the EWI by destroying their consistency.

14.2. GI cannot admit a covariance because the latter would propagate under GUF to EWI by destroying their beauty.

14.3. GI must admit antimatter as a necessary condition to be compatible with EWI since the latter are a bona fide theory of particles and antiparticle.

Einstein's failed attempt and all other attempts to date worth mentioning here violate "all" the above requirement, thus having no change of being consistent.

Thanks to the achievement of the formulation of gravitation in a flat geometry, a universal invariance of GI isomorphic to that of EWI, and the first consistent representation of the gravity of antimatter, Santilli has definitely achieved in monograph [40] the most significant grand unification to date. ZeusSon

I wonder how many scientists today (mathematicians or physicists) can truly understand Santilli's Iso-Grand-Unification (Section 7 and monograph [40]), perhaps two? or three? or perhaps five? because its understanding requires a technical knowledge of: 1) Advanced 20th century mathematics; 2) Its isotopic covering, including Santilli isominkowskian geometry; 3) Advanced 20th century physics, including EGR and unified gauge theories; 4) The isotopies of 20th century physics; and, last but not least, 5) The isodual image of all the above for antimatter. Ruggero, congrats, you topped them all! GTKOLME4114

**15. Conclusions**

With the understanding that I respect different views when admitting clear physical realities, I believe that EGR is afflicted by an excessively long series of fundamental insufficiencies, such as:

15.1. The visual, geometric and experimental evidence on the lack of curvature of space is incontrovertible, thus ruling out the foundations of EGR.

15.2. Being based on covariance, EGR cannot produce a dynamics as conventionally understood since it cannot preserve the same numerical values over time.

15.3. EGR is incompatible with SR.

15.4. EGR is incompatible with QM.

15.5 EGR is incompatible with WED.

15.6. EGR cannot incorporate interior problems, thus being unable even to formulate the propagation of light within chromospheres.

15.7. EGR predicts that one single black hole should have swallowed the entire universe billions of years ago.

15.8. EGR cannot incorporate antimatter.

15.9. EGR is incompatible with GU on numerous individually excluding grounds.

By contrast, I must give credit to Santilli, firstly, because of the lucid identification of the above insufficiencies despite known obstructive oppositions and secondly, because of a new conception of gravitation that resolves all the above insufficiencies in a remarkably harmonious and all inclusive way. ZeusSon

I disagree with all criticisms of EGR presented in this blog because they were addressed by Wikipedia, e.g., in the Article https://en.wikipedia.org/wiki/Criticism_of_the_theory_of_relativity where all objections are resolved in favor of EGR. LIFROMA9091

As a contributor to this blog, I suggest that no quotation of Wikipedia should be allowed in this Dialogus to prevent its being turned into politics on Einstein. Wikipedia is totally disqualified for any serious treatment of Einstein's theories because of its known control by Einstein fanatics (see www.i-b-r.org). In the quoted "Article," Wikipedia editors studiously avoid treating any of the litany of inconsistencies presented in this blog, they solely treat tangential issues, by even interpreting criticisms on EGR as being due to antisemitism (!!!). and by resolving in any case all criticisms in favor of EGR without any true technical treatment or quotation of technical treatments in refereed journals. STTLOAT5140

**16. COLLATERAL ASPECTS**

*I have been disturbed for the hacking of this website by organized interest on Einstein from Tel Aviv, Israel, because in the event hackers had any technical argument dismissing the evidence on the lack of curvature of space (Section 1), they could have presented them in this blog. Therefor, the hacking appears to be a confirmation of the arguments presented in this blog dismissing EGR on numerous independent counts. STARS408*

Cosmologist does not invoke a force, that's all the point of expansion it cannot be modeled by a force in the Newton point of view.

Regrettably, I do not see science in the above comments due to the political character of the never ending plethora of conjectures on the expansion of the universe intended to impose Einstein's theories to the large scale structure of the universe in oblivion of known inconsistencies and the ignorance of repeated experimental verifications of Zwicky's hypothesis of tired light, that is, experimental verifications on Earth that the universe is not expanding. Perhaps the author should study for his/her own sake at least some of the papers in the list http://www.santilli-foundation.org/docs/No-universe-expans.pdf. ZeusSon

There is no Einstein "space fabric" or "time space effects" that any general relativist can really prove its existence of. The Gravity B Probe detected no Einstein frame dragging data in Earth orbit. But after a year or more, they manipulated the non-data and claimed static electricity for an error. This was done to prevent total embarrassment to the general relativists for some billion dollars in funding wasted on this. Nikola Tesla expressed his sharp disagreement with the theories of Albert Einstein. He announced that the theory of relativity is "a mass of errors and deceptive ideas and opposed to common sense," and that "not a single one of the relativity propositions has been proved beyond doubt." Tesla said "Einstein's relativity for example, is not science, but some kind of metaphysics based on abstract mathematical principles and conceptions which will be forever incomprehensible to beings like ourselves whose entire knowledge is derived from a three-dimensional world." Tesla invented and developed many things, including AC electricity, long distance AC electricity transmission, induction motors, hydroelectric generators, wireless electricity, lasers, radar, x-rays, wireless communication, particle beam weaponry (star wars), electron microscopes, cellular technology, microwaves, fluorescent lights, neon lights, remote control, induction brush-less synchronous motors, turbine pumps, remote control systems, the Blackberry in 1909, and electron robotics. He had a total of 700 patents. How many did Einstein have? Please see: Einstein's Theory of Relativity versus Classical Mechanics http://www.newtonphysics.on.ca/einstein/index.html. SPCFCLL1957

EGR is flawed, and requires replacement. Why do photons from the Sun travel in directions not parallel to the direction of Earth's gravitational acceleration toward the Sun? Why do total eclipses of the Sun by the Moon reach maximum eclipse about 40 seconds before the Sun and Moon's gravitational forces align? How do binary pulsars anticipate each other's future position, velocity, and acceleration faster than the light time between them would allow? How can black holes have gravity when nothing can escape because escape speed is greater than the speed of light? The correct principle is refraction. Van Flandern, T. (1989) The speed of gravity what the experiments say. Physics Letters A 250: 1-11 http://www.sciencedirect.com/science/article/pii/S0375960198006501. sdds4342tyeg

Thank you sdds4342tyeg. The above quoted paper is a direct verification of SIR under the synonym of Lorentzian relativity. JupiterGrandSon

(Translated from French) Einstein had no formal training at all in physics and/or mathematics. His paper on SR of 1905 was primarily due to Einstein's first wife, Mileva Maric, who was indeed a trained physicist. Einstein's first marriage ended up in a divorce also because Einstein refused to accept Mileva as a co-author of the 1905 paper. It is known that, to tacitate Mileva, Einstein gave to her all the money received from his Nobel Prize. The paper of 1915 on GR is primarily due to Einstein;s second wife. his cousin Elsa Einstein, who was indeed a trained mathematician. Elsa brought to the attention of Einstein the Riemannian geometry (that was virtually unknown in mathematical circles, let alone to Einstein); pointed out to Einstein the application of the new geometry to represent gravitation; and made additional technical suggestions. This second marriage also ended up in a divorce also because Einstein refused, again, to accept Elsa as a co-author in his 1915 paper on GR. A documentation of Einstein's insufficient mathematical knowledge is provided by the Italian mathematician Tullio Levj-Civita who communicated to Einstein a number of errors in his mathematical treatment of GR, which errors and related corrections were admitted and acknowledged by Einstein. see, e.g., http://www.ilsole24ore.com/art/cultura/2016-11-18/il-matematico-che-corresse-einstein-163007.shtml?uuid=ADU3NSwB&cmpid=nl_domenica&refresh_ce=1 Very unfortunate for science is the century old politics on mc^2, which equation was first discovered (in its correct form) by Henri Poincare' and communicated via a letter to Einstein who abstained from quoting Poincare's communication in his papers where the equivalence law was originally presented in an erroneous form (incompatible with the Poincare' symmetry). A cover-up of the politics on mc^2 (among too many to review here) is given by the prohibition at CERN's library to read Poincare's works all the times I went there, eventually deciding not to return. ADSDE4355

Thank you ADSDE4355 for reporting documented facts on Einstein without political manipulations. In this optics, serious scholars should admit the existence of a century old obscurantism in gravitation implied by Santilli's paper at the heading of this post, and denounced in pages 130-135 of the memoir http://www.santilli-foundation.org/docs/new-sciences-new-era.pdf as well as in the recently quoted link in Comments 1 http://www.santilli-foundation.org/inconsistencies-gravitation.php Said obscurantism is also due to excessive propaganda on Einstein, rather than the aseptic report of documented facts as requested by serious science, which propaganda is then used to suppress due scientific process on gravitation. ZurbazCopt

The post by ADSDE4355 confirms Santilli's position of calling SR the Lorentz-Poincare'-Einstein (LPE) special relativity and then position by various scholars of calling its isotopic covering the Lorentz-Poincare'-Einstein-Santilli (LPES) isorelativity, of which isogravitation is a small particular case. ZAZAZA4343545

As a comment to ADSDE4355 and ZurbazCopt I want to say that the century old propaganda on Einstein keeps going because of supine acceptance, rather than denunciation, by individual physicists. QQQWW44