WHAT CAUSES THE GRAVITATIONAL DEFLECTION OF LIGHT AND THE ANOMALOUS PERIHELION SHIFT OF MERCURY ?

by Mark J. Lofts

Abstract

E stablished tradition asserts that Einstein’s explain s Mercury’s anomalous perihelion shift and the doubled Newtonian d eflection of light by gravity . The se claims are in turn used to justify the theoretical concept of spacetime , a mathematically - based ‘fusion’ of space and time and the key concept underpinni ng General Relativity Theory . However, both of these very real phenomena readily reveal alternative explanations, these either partly unknown or unappreciated before the 1920s. A third observation attributed to General Relativity, the of light , does not alone provide justification for spacetime. The theoretical predictions of Joachim von Soldner and of Paul Gerber , while significantly incomplete or incorrect, help to reveal the alternative and correct explan ations for the gravitational d eflection of light and the anomalous perihelion shift respectively , without requiring General Relativity and therefore without spacetime - based explanat ions either . The doubled Newtonian d eflection of light is explained by qua ntum theory while the anomalous perihelion shift of Mercury is explained primarily by the rotation of the Sun.

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Keywords : Einstein, Gehrcke, Gerber, Goudsmit, Kragh, Lenard, Seeliger, Soldner, Sommerfeld, Uhlenbeck, Mercury, Vulcan, general relativity, fine - structure constant, quantum spin, prograde, spacetime, blueshift, wave - p article dualism, gravitational deflection, perihelion shift, equivalence principle

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Contents

1. The Equivalence Principle and the Gravitational Redshift 2. ‘Forbidden’ Reasoning from the Gravitational Redshift 3. Sommerfeld’s Quantum Theory. 4. Quantum Spin and the ‘Factor of 2’ Confusion. 5. The Doubled Deflection of Light by Gravity 6. The Perihelion Shift of Mercury 7. and the ‘Transmission’ of Gravitational Impulses 8. Professor Einstein and Senile Science 9. The Primary Cau se for Mercury’s Anomalous Perihelion Shift Conclusion

For over a century the received dogma has been that Einstein’s General Relativity explains both Mercury’s anomalous perihelion shift and the doubled Newtonian deflection of light by gravity, in turn evoking the central teaching of General Relativity (GR): spacetime ! This in turn invok es the concept of curved space – a manifestation of curved spaceti me – a teaching that necessarily implies that the universe is spatially finite, if not temporally finite too. This is because a curved spacetime (or space) will ultimately curve back upon itself. While more criticism and disbelief has been levelled at GR than at Einstein’s Special Relativity (SR), mere criticism has not led to consistent alternative explanations for the two phenomena supposedly explained by GR. Closer investigation of the steps leading to GR however reveals the inconsistencies and gaps in knowledge which permitted GR to be accepted prematurely as part of a widely held but ideolog icall y - driven agenda, even when these gaps in knowledge were subsequently filled. Although it is easy enough to criticize Einstein’s claims for GR, the problem has been to make the criticism effective so as to show that what it lays claim to actually has very different explanations. We begin from Einstein’s side of the debate to establish GR, passing through quantum theory then onto a detailed description of the tw o contested phenomena, finishing with the explanation for Mercury’s perihelion shift.

1. The Equivalence Principle and the Gravitational Redshift

Explained as a ‘generalization’ of Einstein’s Special Relativity (SR) to wider natural phenomena, GR began from the analogy between inertial forces and gravitation, comparing the two using the principles of SR, Einstein predicting a phenomenon later proven by experiment. Th is phenomenon, the gravitational redshift , occur s when light is emitt ed from a body at a lower gravitational potential (i.e. in a stronger gravitational field) to a detector in a region of higher gravitational potential ( lower gravitatio nal force ) i.e. the light is projected upward from the gravitating body . Conversely, when light moves downward , i.e. into a region of higher gravitational force , a corresponding blueshift of the light occurs. The phenomenon is essentially a linear one, unrelated to the concept of spacetime – but this is not how Einstein presents the otherwise straightforward issue . His relevant article dates from 1911: “On the Influence of Gravitation on the Propagat ion of Light”. In §2 of this text, Einstein imagine d two systems . One, K, is at rest in a homo - genous gravitational field ; the other, L , 1 is instead to be uniformly accelerated. He now consider s two homologous and mutually stationary points in each syste m : the first, S 1 where the attracting body K and/or accelerating observer L is found. The second, S 2 is separated from S 1 by distance H , and comprises the site where light beams are emitted towards both the gravitating body ( at point K a djacent to S 1 in the diag ram below ) and the accelerating body ( at point L , adjacent to S 1 but be neath K in the diagram below ). His diagram has the z - axis vertical, but the issue is treated horizontally below. The point K 0 is at position S 2 where the light is emitted towards K and L; point K 0 (at S 2 ) has a higher gravitational potential than S 1 since the latter is located at K’s gravitational source where instead the gravitational pull is greater. In other words, ‘upwards is to the right’!

))))) K (gravitatio nal attractor) ……… …. <<<<<< S 2 (K 0 ) ------S 1 ------S 2 ------z - axis >>> L ( begins accelerating to the right) … <<<<<< S 2

Einstein writes that “we judge the process of the transference of energy by radiation from S 2 to S 1 from a system K 0 which is to be free from acceleration.” This means that S 2 is an inertial system and thus , ideally, is not subject to gravity (as is K) n or to acceleration (as is L). System K is at relative rest to S 2 (K 0 ). Equally importantly, system L too is initially at rest relative to S 2 and begins to move only when the light beam is emitted from S 2 . In this way, the measured change in energy (i.e. wavelength or frequency) of the light received by L is thus only from the effect of the acceleration of L, not from any initial motion of L relative to S 2 . Only in this way , as stipulated by Einstein too , can a separate Doppler Effect due to velocity – in this case a blueshift due to any initial motion of L toward S 2 – be exclud ed . (This is an important but seemingly trivial point, as we need to distinguish between any effects by SR and by GR, something not done by many investigators) . Thus the light received at both L and K will be blueshifted, i.e. there will be an increase in energy observed (and thus a decrease in wavelength), this blueshift being by an equal amount in both cases if the accelerational force at L is e qual to the force of gravity at K. Einstein however prefers the term frequency to that of its reciprocal term: wavelength! Einstein’s insight here is genuine since the blueshifting of light falling in a gravitational field is experimentally attested by e. g. the Mossbauer Effect. Conversely, a light beam escaping a gravitational field will be proportionately redshifted. However, in quantifying the energy changes by using the energy - mass relation (E = mc 2 ) Einstein is also trying to attach the situation to his SR theorizing, since it is wrongly believed that the energy - mass relation is either part of Einstein’s relativity or proves Einstein’s relativity to be correct . Rather, the energy - mass relation had not only been demonstrated already by Friedrich Hasenöhrl 2 a year before Einstein, but is also well - known to be implicit in and deriving from the concept and formula for kinetic energy, as shown even in popular literatu re by Einsteinians such as George Gamow. 3 The important insight of Einstein’s 1911 paper is the demonstration that g ravity and acceleration exert equivalent effects upon light beams traveling linearly away from and towards both gravitating and accelerating bodies. From this derives the Principle of Equivalence i.e. th e otherwise trivial observation that gravitational mass and inertial mass are always equal – Einstein noting correctly in passing that weight cannot be treated in the same way : i.e. gravitational weight is not equivalent to ‘inertial weight , ’ the latter concept hardly developed either by Einstein or anyone else! 4 However, these same insights are combined with tendentious reasoning about the accelerate d L system . Thus the Doppler blueshift c an be interpreted as merely from the mutual velocity of L and S 2 (the SR inference) rather than the acceleration of L from zero velocity, from relative rest (the inference leading to GR). Such a situation could eve n be interpreted to mean that the acceleration and the speed of L may independently contribute to the resultant blueshift. Einstein does not clarify the situation by arguing that further comments on the details are “impossible” and “forbidden”, writing: …we assume that systems K and L are physically exactly equivalent, i.e. if we assume that we may just as well regard the system K as being in a space free from gravitational fields, if we then regard K as uniformly accelerated. This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of re lativity forbids us to talk of the absolute velocity of a system. 5 This ambiguity particularly emerges above where the word ‘absolute’ is being used in two entirely different senses – in reference to acceleration and to velocity – serving to obscure and se cure the underlying issues as ‘forbidden’! Nor can s ystems K and L ever be exactly equivalent since gravity and acceleration are not one and the same. Nevertheless, their physical effect upon incoming radiation is the same, being proportional to the force exerted by either gravity or acceleration . F ortunately, through the equations, E instein at last reveal s that this blueshifting acceleration - effect on radiation is the same thing as the resultant velocity – only the description being different ! The equation s (1 & 1a ) supplied in his text indicate that the speed and acceleration contri butions to the blueshift (E 1 ) are actually the same thing , the equations combined below to enhance clarity . In the equation the initial light energy emitted at S 2 is labelled E 2 whereas the blueshift ed (E 1 ) light , of greater energy, is detected at S 1 . The velocity of L at detection is v , and the acceleration of L is represented by a . 6 Hence the blueshift is represented first by a velocity term addition (analogy to SR) , then in the second component by an acceleration term add ed to the initial E 2 energy (analogy to GR) .

= ( 1 + / ) = 1 + ≡ 1 +

The equivalence ( ≡ ) of acceleration and gravity is shown in the third component where the gravitational potential between S 1 and S 2 is marked by Φ , replacing the acceleration - dependent component and height. The sequence of equations above is here termed the ‘triple - component’ equation, which, while it shows insight into nature can also be mis interpret ed too easily , especially in wo rking from the reduced form below i.e.:

= ≡

The reduced form a ssert s not only an equivalence between gravity (3 rd component ) and acceleration (2 nd component ) , but also with velocity (1 st component ), as v here represents a blueshift or redshift of the light beam , a measurement depending entirely up on the mutual velocity ( v ) of the emitter and receiver. The problem is that the reasoning here can lead to confusion of the attributed causation between SR (the 1 st component using velocity alone) and GR (the 2 nd and 3 rd components embodying the analogy of acceleration and gravitation). Einstein also indicate s that the gravi tational potential (Φ) could be negative, just as velocity ( v ) can be too. So w e begin t o see that despite Einstein’s delving into times measured by clocks in different gravitational fields, what is really being d ealt with is the nature of light itself . If however this is not adequately understood, it readily leads to fatal confusion.

2. ‘Forbidden’ Reasoning from the Gravitational Redshift At this point we can see the mathematical representation for a light beam moving down into a gravitational field, yielding a blueshift . T he gravitational redshift is merely the opposite situation where a light beam moves upward, away from a gravi tating body. This is experimentally proven, justifying Einstein’s insight here, at least qualitatively, since this redshift was denied by some of his contemporaries. However, the same mathemat ics above reveals that the gravitational redshift is also an inference based entirely upon analogy from acceleration, this giving the misleading impression that GR is not funda - mentally a development of SR but is instead based solely upon other reasonings and observations. Einstein develop s the argument in §3 , elaborat i ng the gravitational redshift by placing the S 2 emitter on the Sun and the S 1 (= K) receiver on planet Earth. He even relabels the energy symbols (E 1 and E 2 ) ν 1 and ν 2 , the Greek ν symbol being that of the frequency of light , not the velocity ( v ) of system L referred to earlier. Having now established the gravitational redshift as an authentic inference – since experiment s subsequently revealed at least its qualitative reality – he b egins to lure the reader into an alternative ‘explanation’. He start s by writing of the changed frequency of photons of light undergoing this phenomenon using a different terminology , relabel ling frequency as a “vibration - number” from an “ elementary ligh t generator ” , a s well as the “number of periods per second.” These words change the understanding of light - energy , re ducing it to mere waves measured by mere numbers , in effect rendering light - energy as an abstract train of points for mathematical ‘treatment’ – each point or period marking a wave - crest (or wave - trough) . He now highlights what he calls a seemingly superficial absurdity in the equations.

If there is constant transmission of light from S 2 to S 1 , how can any other num ber of periods per second arrive at S 1 than is emitted in S 2 ? But the answer is simple. 7 The italicized section shows that he is asking why the number of periods (= wave crests) between S 1 and S 2 is not fixed, not constant , since the variation in frequency is actually the Doppler shift in wavelength. This issue – which could alternative ly be described in quantum terminology as “the non - conservation of wave - crest numbers” – becomes more pressing in that we have to consider b oth upward and downward motion of light in a gravitational field. His supposedly simple answer ignores th is deeper question entirely . Rather than seeing the issue as one concerning a gravitational influence upon the Doppler Effect – and thus the nature of light itself – he instead introduces Special Relativity ( SR ) and its claims for time dilation , i.e. the dependence of time upon linear unaccelerated motion, his answer being:

We cannot regard ν 2 or respectively ν 1 simply as frequencies (as the number of periods per second) since we have not yet determined the time in system K [= S 1 = the Earth]. This last phrase reveals that Einstein is introducing SR’s time dilation as part of his explanation for the gravitation al redshift – rather than consider ing the observed Doppler changes for light rays moving vertically within a gravitational field , coupled to the Newtonian principle that time flows constantly and uniformly all through out the universe . Thus h e is presuming that time flows at different rates depending on the gravitational field strength present , a central claim of GR but based upon reasoning from SR . So for Einstein the rate of passage of time for the Sun is presumed to be different from that on Ea rth, these differences to be measured by non - malfunction ing clocks located at those places . Hence he follows with the SR - based rigmarole about different clocks at different locations in any gravitational field , eventual ly even asserting that “we must use clocks of unlike constitution for measuring time at places with differing gravitational potential , ” 8 the context indicating that he is not referring to heat - resistance or other potentially damaging physical effects on clock function . From all this rea soning, in §4 he infers the slowing of light waves as a beam of light passes by at right angles to the gravitational force of a massive object. From the proposition which has just been proved, that the velocity of light in the gravitational field is a func tion of the place, we may easily infer, by means of Huyghens’ principle, that light - rays propagated across a gravitational field undergo deflection. By ‘place’ he means the relative position of the light beam and gravitational source , since the further awa y the light passes by the less will be the deflection . Logically, he now use s Huyghens’ Principle of wavefronts rather than Newtonian reasoning but still c o me s up with a deviation of 0.8 3 ʺ of arc (i.e. 0.83 seconds of arc) for light passing by the rim of the Sun . The result was that from 1911 onward he was looking forward to an opportunity for his prediction to be tested during a solar eclipse. While Einstein was waiting for a suitable solar eclipse to test the G R - based deflection of light , both he and others had applied Special Relativity (SR) to the atomic scale – as we saw above with Einstein’s discussion of the gravitational blueshifts, redsh ifts and “periods per second” of light beam s. Max Planck, discoverer of quantum theory, championed SR over and above even his own discovery, popularizing it among the whole physics community – and not just in the realm of German - speaking science. 9 Hence the combination of Einstein’s relativity with quantum theory from the latter’s very roots in the first decade of the 20 th century. The main focus of study then was spectro - scopy, a significant advance made by Niels Bohr, who realized that the spectral lines in hydrogen (H) represented electrons emitting light as they transitioned from one atomic orbit to a less ene rgetic one.

3. Sommerfeld’s Q uantum T heory Great difficulty arose from attempting to interpret the major elemental spectral line changes induced by magnetic fields – the Zeeman effect – which comprises two separate effects from weak 10 magnetic fields. 1) The n ormal Zeeman effect comprises a triplet - splitting of spectral lines . 2) The a nomalous Zeeman effect comprises both the very prominent doublets of the alkali metals 1 1 and the fine structure doublet - splitting of the other elements’ spectral lines. The experimental key to sort out these phenomena came from one Johannes Stark who overcame the technical difficulties to pioneer the use of electric al fields for splitting spectral lines – the Stark effect – this in turn allowing the magnetic effects to be explained consistently. 12 Much was used in the theoretical interpretation of spectral lines, Arnold Sommer feld discovering the Fine Structure Constant (α) in 1916 as part of this increasing und erstand ing . At this stag e the accumulated and conflicting data meant that theoretical complexities came to the fore; this period is that of the Early or Sommerfeld Quantum Theory, ending ten years later with the discovery of quantum spin by George Uhlenbeck & Sam Goudsmit. Perhaps the key feature of the Sommerfeld Quantum Theory was its use of Einstein’s relativity, at first SR, then GR used to explain specific ally the fine structure features of the spectral lines . The exciting times were 1916 - 1920 , fading after 1923 as new and better evidence on hydrogen spectra demanded explanation. 13 However , from 1926 onward the fine structure differences in the energy levels between an electron oriented one way or the opposite way in externally imposed electro magnetic fields became the clear and obvious explanation for the anomalous Zeeman effect, i.e. quantum spin . Nevertheless, i n s ummarizing the earlier research in 1951 in his attempt to understand quantum theory better , David Bohm reproduced the standard t eaching concerning the doublet - splitting in that “the effects of spin and relativity also produce a small splitting of these [spectral line] levels, called the fine structure.” 14 In other words, in the Sommerfeld Quantum Theory it was the anomalous Zeeman effect, the fine structure, which Einstein’s relativity was being invoked to explain – until quantum spin was uncovered. Thus the belief in an SR and/or GR effect on the motion of subatomic particles manifested in spectroscopic differences wa s ultimately combined with the discovery of quantum spin into a dualistic explanation. So does this mean that spin and relativity combine together to create the fine structure ? O r are spin and Einstein’s relativity alternative but incommensurable expl anations for the fine structure , each designed to fit a different Kuhnian paradigm ? The official answer remains unclear , so, as Bohm reveals , modern physicists interpret it dualistically in the manner of Bohr’s complementarity, of wave - particle dualism, ‘flipping’ from one explanation to the other whenever it suits them . 15 The history of the Sommerfeld Quantum Theory has been outlined by Helge Kragh. Given Einstein’s 1911 paper detailed above it is hardly surprising that it was bel ieved that SR must be involved in atomic structure since redshifts and blueshifts are intimate questions in spectroscop ic analysis . Conversely, as GR became better known, it too was invoked from 1916 because gravity in some wider sense was considered to b e involved in the unknown nuclear processes of attraction, e.g. that protons are held together in a nucleus despite their mutually repulsive positive charges. Kragh labels Einstein’s opponents “right - wing physicists” yet Einstein’s comparatively left - wing supporters are instead called “progressive physicists.” 16 In 1915 Niels Bohr “became increasingly interested in the origin of the fine structure…. He now suggested that the doubling might be explained as a result of the relativistic mass variation of ele ctrons moving in elliptical orbits. He did not pursue this fruitful idea … ” 17 – due to the obvious incompleteness in the experimental findings. Two issues arise here: the first is the meaning of the vague term ‘relativistic’. Rather than necessarily implying the effects of SR or GR , ‘relativistic’ can merely mean “high - speed electromagnetic interactions”, referring e.g. to the momentum increase of el ectrons when accelerated by electromagnetism , a phenomenon misleadingly termed ‘electro magnetic mass’ . The second issue is the concept of point - particles. Point - particle electrons orbiting in circular and elliptical orbits mimicking planets in orbits wer e a favorite topic for investigators like Max Born who , writing to Einstein in 1922 , illustrates his claim with a diagram, stat ing that we “were able to confirm Bohr’s old claim that the inner electron moves around fast on an elliptical orbit whose major a xis always point ed towards the slowly moving outer electron.” 18 The elaboration of pointillistic electrons in elliptical orbits strongly suggest s Einsteinian relativity , the historian Kragh even label ling this a fruitful idea . However , given that the idea was subsequently discarded for quantum spin , perhaps he means that it is only fruitful in the sense of being the primary subject for him to write about – so benefitting us all . For Sommerfeld and others, the fast moving, i.e. relativistic, electron ac quires not momentum but “electromagnetic mass”, this being equated with SR - based notions of mass increase for non - electrically charged bodies, the latter actually just increases in momentum ( mv ) and kinetic energy ( mv 2 /2) , echoing the triple - component equa tion given here in the previous section. In 1916, Sommerfeld attempted to create a theory from incomplete data, Bohr calling it “a beautiful application of relativity theory” ; Einstein call ed it “a revelation. … Only through it do Bohr’s ideas become comp letely convincing.” 19 Yet “while some physicists saw in Sommerfeld’s theory a reason to accept the quantum theory of atoms, others regarded it as a conf i rmation of the theory of relativity.” Thus we find that “to some still reluctant to accept Einsteinian relativity, Sommerfeld’s theory of the fine structure was still considered controversial by several physicists, in as well as abroad. … The classical alternatives to Einsteinian relativit y had not completely disappeared and many conservative physicists longed for the day when Einstein’s theory would be replaced by a more comprehensible theory based upon the concept of ether.” 20 Without venturing into the dualistic swamp of what is meant by ‘ether’, the result of the widespread acceptance of Sommerfeld Theory’s led not to any general under - standing of the situation – since the experimental evidence was incomplete at this stage – b ut rather to a Mexican standoff in the theoretical interpretation of spectral lines and subatomic particle interactions , particularly as attitudes towards both Einstein’s relativity and quantum mechanics correlated very poorly with one’s background or poli tical affiliation. There was Max Abraham (Jewish) who defended a classical stagnant ether against both SR and GR – and the aptly - named Karl Glitscher who applied Abraham’s mass formula to Sommerfeld’s Theory to vindicate Einstein! 21 Attacks on Sommerfeld’s Theory began in 1920 logically with Johannes Stark who had pioneered many of the experiments ; likewise with the spectroscopist , both p referring “to do without refined theories at all . ” 22 Nevertheless, Stark accepted SR but not GR, whereas , the other Nobel - Prizewinning future Nazi, rejected Einstein’s relativity comprehensively. 23 Another spectroscopist - turned - Nazi was Pa scual Jordan – colleague of Heisenberg and Max Born – who nevertheless supported relativity theory but not under Einstein’s name, like Sommerfeld himself. 24 The standoff was entrenched by the fact that it could not even be decided whether the ‘relativistic ’ fine structure changes , notably in hydrogen, were to be attributed to SR or GR – not a surprise in the light of the triple - component equation above. One G. Jaffé used GR to bolster Sommerfeld’s theory; his work was adopted by Gerold von Gleich who treat ed electrons like planets around an atomic nucleus via a “non - Einsteinian version of general relativity” and so decided that “Sommerfeld’s quantum theory contradicted general relativity!” 25 Lenard saw that any “experimental confirmation of Sommerfeld’s theory does not imply the confirmation of relativity theory but rather confirms any theory that leads to the mass formula of Lorentz & Einstein,” as he realized that the mathematics was being misinterpreted. Nevertheless, t he opposition to Einstein’s relativity became “scattered and ineffective” due to no common position nor consistent alternative theory. 26 Th e situat ion climaxed with the theory of M. Sandoval Vallarta who “supported von Glei ch’s idea of fine structure as a general relativistic effect.” So “his aim was to show that Sommerfeld’s equations of motion can be derived from the general theory of relativity too , ” his “confirmation of Sommerfeld’s result” supporting “the applicability of GR to problems of atomic structure.” Hence by elaborate theor izing without new data, Vallarta merely underscored both the situation and his own nationality : Mexican! 27

4. Quantum Spin and the ‘Factor of 2’ Confusion The standoff was broken from outside, by new experimental findings so that “by 1926 atomic physics had been drastically transformed and the new quantum theory made the debate over hydrogen’s fine structure obsolete . ” 28 Quantum spin explained the fine structure (and the alkali - metal do ublets) but the two discoverers were not awarded the Nobel Prize. The fundamental difficulty leading to Goudsmit & Uhlenbeck’s discovery of spin was to explain the half - integer spectral lines comprising the fine structure and alkali doublets , 29 Goudsmit e laborating the spectral arrangements and Uhlenbeck , who had a more classical physics education in Italy, 30 suggesting the spin concept to resolve them through explaining the 4 th quantum number . The 4 th quantum number tak es the value of either +½ or − ½ to indicate the atomic electron’s magnetic poles relative to the imposed electromagnetic field – right - side - up or upside - down – the rest of the atom , ‘the core’, being electrically and magnetically neutral. Hendrik Lorentz reacted negatively to t he concept as he realized that quantum spin meant that if an electron “rotated with an angular momentum of ħ /2 then the surface velocity would be about ten times the light velocity!” 31 Heisenberg welcomed the concept of spin, adding it to his matrix mechanics to make quantum theory workable mathematically – but he had no physical interpretation. P hysical meaning was only hinted at by Erwin Schrodinger when he subsequently treated quanta as “matte r waves” in opposition to point - particles , the Schrodinger wave equation nowadays being the usual form in which quantum theory is applied . 32 This did not render matrix mechanics an obsolete formulation however as spin is more easily represented this way, 3 3 especially as Schrodinger’s wave equation does not explain away ‘ quantum leap ’ phenomena central to the experimental findings. 34 Yet far from being immodest as he claims, 35 Goudsmit was peculiarly humble and deferential to the authorities even in older age: “…when anyone does something [ clever ] in physics [we say] ‘Yeah, he’s real smart.’ That’s true in some cases – with men like Heisenberg, Dirac and Einstein. There are a few such exceptions. B ut for most of us, who are not so exceptional, luck plays a major role, and that shouldn’t be forgotten.” 36 Heisenberg wondered how he and Uhlenbeck were able to “manage to get rid of the factor of 2” 37 in their spin paper, a problem that did not arise fo r them since their formula was derived from their own independent calculations. Bohr and Einstein met with Goudsmit and others to discuss their spin paper, nevertheless, “I never did quite understand the reasoning. When Bohr and Einstein were talking tog ether, when they discussed the electron spin at Ehrenfest’s place, I didn’t understand a word.” 38 The unsettling humility and deference of Goudsmit to established authority is a warning sign. It became a hallmark of modern physicists, their abstract math ematics without physical modelling, their loss of confidence in themselves and their intransigent defence of established patterns of thought, in Goudsmit’s case including those patterns established partly by himself! One Llewellyn Hilleth Thomas , then in C openhagen and “well up in relativity… figured out that Heisenberg’s missing factor of 2 was the relativistic factor, and that the whole thing was quite in order.” 39 Uhlenbeck gave more detail about this “…mysterious factor of two. It is now well known th at this difficulty was soon resolved by L. H. Thomas, who showed that it was a forgotten relativistic effect. I remember that when I first heard about it, it seemed unbelievable that a relativistic effect could give a factor of two instead of something of the order v/c . I will not try to explain it, so let me only say that even the cognoscenti of the relativity theory (Einstein included!) were quite surprised.” 40 So w ith the ‘factor of 2’ left in limbo after mathematical editing , Thomas enabled the continu ed invocation of Einstein’s relativity – whether SR or GR – within the new quantum theory’s explanations for subatomic physic s . Instead of a ny physical resolution the whole issue was quickly locked do wn mathematic ally by Paul Dirac, inserting SR & GR into the dualistic explanatory apparatus through the quantum formalism expressed particularly in Bohr’s Copenhagen Interpretation and its comple mentarity principle , this latter best expressed in wave - particle dualism. This dualistic conception studiously ignores the question of actual physical structures , even implying their nonexistence in favor of arbitrary acausal actions . The end result was the diktat of Max Bo rn in his 1954 Nobel Prize Lecture. This idea of complementarity is now regarded by most physicists as the key to the clear understanding of quantum processes. 41 Hence the complementarity (i.e. dialecticism) inherent in wave - particle dualism . The particle is but a point - particle without physical extent in any dimension. The wave is not physical either since: Again an idea of Einstein’s gave me the lead. He had tried to make the duality of particles – light quanta or photons – and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photon s. 42 Therefore i n quantum formalism there is no extended physical object, not even Erwin Schrodinger’s matter waves, just point - particles and mathematical “probability density.” So when David Bohm , invoking the standard dualism, describe d the fine structure as arising from “the effects of spin and relativity”, this explanation too refers not to a combined effect of two separ ate causes but is instead mere complementarity. Accord - ingly , it is quite clear from the above that the ‘factor of 2’ is but a mere mathematical error by Bohr, Heisenberg, Pauli & Co., an error that Goudsmit & Uhlenbeck had avoided by deriving their equations independently , due to their Dutch background and consequent separation from the main research institutes . Wolfgang Pauli in particular di slik ed the concept of quantum spin. Pauli remained intransigent , even after L. H. Thomas… found a surprising error in the relativistic calculation of the relative motion of the electron as it orbited the nucleus. Pauli and Heisenberg had simply erred. Thomas’s correction eliminated the obstinate two and with it any mathematical objection to the theory. Pauli , conceding the error but not electron spin, objected a while longer before “capitulating” with a “heavy heart” on March 12, 1926. 43 All very ironic in retrospect , given that Pauli’s ultimate claim to fame was his proven prediction of the neutrino to explain the mysterious loss of energy and of spin in β - radiation ! Nevertheless the implication is clear: the factor of 2, the so - called ‘Thomas Precession’ , is not a p hysical object or attribute but merely a mathematical adjustment to accommodate Einstein’s relativity with in quantum theory, rather than frankly admitting that quantum spin is the correct answer. Thus did Thomas’s work maintain doubt among the physics com munity towards quantum spin but indulgence towards Einstein’s relativity theory a s the explanation of the fine structure, Uhlenbeck already having noted Thomas’s super erogatory efforts in creating mathematical justification for Einstein’s theorizing . Sur ely Thomas is the English twin to his divinely acclaimed Swiss - German Relativitäts theorie m ei ster !

5. The Doubled Deflection of Light by Gravity Now filled with the story of quantum half - integral spin and the missing factor(s) of 2, let us return to Einstein in mid - 1914. As the time for testing Einstein’s claim for the deflection of sunlight by gravity from total eclipse observation neared, Einstein d id not realize that his predicted value of 0.83 ʺ of arc was only half the value eventually observed – 1.7 ʺ of arc . Einstein was not properly aware of the risk to his credibility as he had still not worked out GR completely at the very time scientists were setting up their instruments ready for the solar eclipse of August 1914 over Crimea in Imperial Russia ! Just in time however Einstein was blessed with good fortune – the outbreak of World War One i n July ! T he scientists with the testing equipment were rounded up, imprisoned and handed over in civilian prisoner exchange s , providing Einstein with the extra time needed to complete his extended tensor - based 1916 article expounding the full theory of GR, predicting both the c orrect ‘doubled’ deflection of sunlight by gravity and laying claim to the anomalous perihelion shift of Mercury ! What Einstein also did not know was that his 1911 prediction of 0.83 ʺ of arc for light deflected at the solar rim had been calculated over a c entury before – by one Joachim von Soldner! Writing in 1801, Soldner worked entirely from Newtonian reasoning, extra polating from a slow object that would be heavily deflected by the solar gravity, to ever faster objects, culminating in a light beam graz ing the sun with minimal deflection , his paper now translated fully into English. 44 While Soldner predicted a deflection of starlight passing the solar rim by 0.84 ʺ of arc , 45 the predicted deflection is the same as Einstein’s, though the reasoning is different. Contra Soldner, the 19 th century stagnant ether theory was at that time under the influence of Thomas Young, so predicted no deflection of starlight by gravity, 46 the a nalogy from Fresnel interference patterns and the Arago spot not recognized until after 1815 . Soldner was inspired by Pierre Laplace’s speculations about a gravity so powerful it could prevent light emerging from an object – the basis of black hole theory . Soldner’s prediction however was far beyond the capacity of telescope technology in his era, so his work was forgotten until the 1919 solar eclipse photographs revealed that the deflection was twice Soldner’s Newtonian prediction. Philipp Lenard’s repub lication of part of Soldner’s paper did not include the most relevant section in the form of Soldner’s quote from Lucretius, Roman champion of the Greek materialist philosopher Epicurus. Besides, there is nothing which you can call distinct from body and separate from void [i.e. space] to be discovered as a kind of third nature. 47 The ancient Greeks had not invoked time as a separate all - containing ‘third nature’, hence Einstein’s ready invocation of spacetime as applicable in science so as to blur the distinction between matter, space and time! The relevance of these observations is that Einstein’s true genius is revealed – his genius at philosophy. 48 His physicist opponents were totally outclassed here, notably his principal opponent, Philipp Lenard , whose Great Men of Science reveals his philosophical naivete in the choice of ancient Greek thinkers. The issue does not blight Lenard alone but i s entrenched in the teaching traditions – apparently worldwide – at undergraduate university level, those st udying philosophy, modern or ancient, are studying for bachelor degrees in Arts, those studying physics for a degree in S cience . 49 Due to its cosmology the philosophical and emotional implications of GR stand foremost as Eric Lerner details . 50 These came to the fore particularly as Einstein’s GR - based explanation of the deflection of starlight was trumpeted to the world by the mass media in November 1919 – a vulnerable and depressed w orld rendered this way by World War One, the first anniversary of its end now approaching. Th us th is war benefitted Einstein yet again and even more in the form of a desperate populace yearning to believe in something after the bloodbath had weakened trad itional religious beliefs. “He fulfils two profound needs in man, the need to know and the need not to know but to believe … the divine man of the 20 th century . ” 51 Einstein was canonized a secular saint, his biographer assert ing : “I find the parallels to the rituals of beatification and canonization compelling even though they are applied to a living person. Note that a beatus may be honored with public cult… A canonized person is honored by unrestricted public cult.” 52 Thus the religious overtones of GR and Einstein himself are unmistakable, but the reason for this is not the discovery of the gravitational bending of starlight, but what GR implies for cosmology, its teaching of a finite universe. Given Einstein’s superlativ e expertise as a philosopher, the cosmological implication s can also be seen from Einstein’s overwhelming aversion to the philosopher Friedrich Nietzsche : e.g. Stanley Corngold’s biography of Walter Kaufmann reveals Einstein’s disgust 53 when Kaufmann revea ls to him his intention to writ e about Nietzsche. Einstein’s disgust is readily understandable because in Nietzsche’ s best - known work , dating from 1883, he had already intuited the resulting confusi on and disempower ment that would arise from yet - to - be - developed teachings like Einstein’s . Nietzsche’s mouthpiece, Zarathustra , is walking over the mountains , weighed down by a dwa rf sitting on his back. When finally the dwarf dismounts and verbal interaction begins, Zarathus tra asks the dwarf whether past and future stretch out eternally. The following sharp words ensue : DWARF: “All that is straight lies; all truth is crooked; time itself is a circle.” ZARATHUSTRA: “You spirit of gravity,” I said angrily, “do not make things too easy for yourself ! …” 54 The dwarf’s anti - Euclidean words have garnered no attention from commentators as they have backgrounds in Arts subjects rather than Science, while scientists do not read Nietzsche . H ence the deep philosophical implications of GR and its spacetime teaching remain unknown to even the educated public , Nietzsche’s words treated as mere metaphor . 55 While Einstein explains half t he observed deviation of starlight by Huyghens’ principle of wave - mechanics , Soldner explains the half - deviation by Newtonian reasoning , yet the two explanations amount to the same thing . However we m ust now expect detailed investigations aimed at combin ing the two explanations together – in an additive way, not via complemen tarity – to explain the full doubled deflection, in view of the clear refutation of the GR explanation given below. In his 1916 paper Einstein double s the predicted gravitational deflection of light compared to the Newtonian prediction and his own 1911 prediction. The reason is decidedly unclear since it is masked under formidable mathematical verbiage , 56 including the Riemann - Christoffel tensor . As however there is no concise non - mathematical statement as to why, physically , the original 1911 deflection prediction was to be doubled, the multitudinous equations can only be considered mathematical prestidigit - ation , since a physical answer corresponding to the GR mathematics is absent . 57 Remembering that relativity had been inserted into subatomic physics to explain the fine structure in place of what would be found to be due to quantum spin, we can now respond accordingly. I.e. that which GR claims for itself on the large scale, could in stead be explained by something established on the smallest scale : quantum theory , specifically quantum spin. Of the five fundamental stable particles, neutrons are stable only within atomic nuclei, the others stable everywhere in the cosmos unless transf ormed or destroyed by interactions. O nly after Goudsmit & Uhlenbeck’s work in 1926 did it become apparent that all o rdinary ponderous matter – atoms comprising protons, neutrons and electrons – consists only of spin - ½ particles, as shown in table 1. The spin of photons however is twice that of the other stable fundamental particles, spin - 1, a fact not really clear until 1926, GR having already been generally accepted as the cause for the doubled Newtonian deflection of light since 1919! Hence the cle ar inference: the doubled Newtonian deflection of light by gravity is simply due to quantum spin – but nobody considered this in 1926 since the GR ‘explanation’ was already set in stone by the propagandized scientific consensus. A case of propaganda - spin trumping quantum spin!

Table 1 Stable F undamental Quantum Particle s Spin Electron ½ Proton ½ Neutron ½ Neutrino ½ Photon 1

So where did Einstein get the idea to double the Newtonian gravitational deflection of light in the first place ? In fact Einstein had long been in written communi - cation with Sommerfeld before 1916 , implying that investigation of the anomalous Zeeman effect – the fine structure and the alkali doublets – by the latter triggered Einstein to double the Newtonian deflection, through some unconscious influence that he later justified through 40 pages of speculative mathematics. The result however is that if GR wishes a hearing at all, its advocates will have to follow table 1, to investigate the grav itational deflection properties of neutrinos . With future technology this could be achieved on the satellites of Jupiter, detecting solar neutrinos deflected in passing the edge of Jupiter. This would disprove the anti - GR claim made here only by a non - Newtonian deflection ; e.g. a doubled deflection or no deflection.

6. The Perihelion Shift of Mercury Given that GR has failed physically to explain the doubled deflection of light by gravity , in contrast to the clear combination of Newtonian physics and quantum theory, we now turn our attention to the other supposed proof of GR – Mercury’s anomalous perihelion shift. When researchers working independently come up with the same answers, apart from minor rivalry, it is a cause for celebration through greater understanding based on sound theory and experiment – which can be said of Einstein ’s earlier work when he came up with the same half - value for gravitational deflection as Soldner did a century earlier . There a re also many other examples in history e.g. in mathematics with the independent discovery of calculus by Newton and Leibniz. In physics, the strongest confirmation of all is found in the arrangement of the Periodic Table enabled through the combination of physical and chemical studies. The understanding of atomic spectroscopy confirmed the chemical studies through laying out the arrangement and number of shells of electrons and thus strengthening the prediction of unknown elements, later confirmed. A simi lar situation of independent discovery seems to occur with the Anomalous Perihelion Shift of Mercury, since the 1902 prediction of one Paul Gerber as to the degree of perihelion shift – unknown to Einstein in 1915 when he published on Mercury – invokes the same formula as Einstein to achieve the same answer . In turn, while their theoretical arguments differ, one might have thought that having two different theories predict the same answer would confirm and harmonize the two theoretical approaches , stre ngthening the proof overall – as with spectroscopy and chemical properties together confirming the veracity of the Periodic Table . This is not the case with Gerber and Einstein however, so we need to elucidate why. By convention the revolution of planets around the Sun is taken to be viewed from a point above the northern part of the sky. Hence the planets revolve around the sun anticlockwise, this planetary motion being termed ‘prograde’, the opposite circling motion of an object around the sun being ter med ‘retrograde’.

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Figure : Like the other planets, Mercury orbits the Sun prograde – in the direction of the red - headed arrow . It s elliptical orbit also moves around the Sun in the prograde direction , this being the perihelion shift, the resulting motion forming a complete rosette pattern as the orbital ellipse rotates a full 360° . ------

The ellipse of Mercury’s orbit r evolves in a circle once every 220,000 years , this motion being a precession ! 58 Like the motion of the other planets which create most of the perihelion shift, this precessionary orbital motion is prograde. This phenomenon is usually termed the Perihelion Shift of Mercury . D iscovered by Urbain Le Verrier in 1859, scientists were puzzled as to its cause. A planet’s orbit is like a spinning gyroscope. The position of its axis in space normally remains fixed relative to the cosmos (= fixed stars) , the process a kin to Foucault’s Pendulum whose plane of motion remains fixed relative to the cosmos , rather than follow the motion of the Earth . However, t he anomalous perihelion shif t of Mercury, attributed today to GR, comprises less than a tenth of the full perihelion shift. T his is because the main cause for the perihelion shift is the pull of the other planets, especially Venus and Jupiter. Bodies nearer Mercury have a dispropor tionate effect on Mercury’s perihelion shift, thus the hypothetical effect of the very distant Planet X – if it is finally proven to exist with a mass 3 - 10× that of Earth – would have an extremely small effect, much less than our Moon. The total perihelio n shift (  ) 59 of Mercury actually amounts to 574 ʺ of arc per century , the three largest contributors to its shift listed below . Venus accounts for 277 ʺ Jupiter accounts for 153 ʺ Earth accounts for 82 ʺ The Moon accounts for 1 ʺ In addition to the remaining planets, there are the se planets’ moons, the asteroids and the Zodiacal light particles. Yet even taking these into account there remains an anomaly of about 43 ʺ of arc. More exactly , by the 1990s the anomalous perihelion shift ( δ  ) wa s known to be: 60 δ  = 42.98 ʺ  0.04

For the proper measurement of the perihelion shift of Mercury we cannot use Earth - cent e red, Mercury - cent e red or even Sun - centered coordinates but instead require an external referent. We measure the shift from the sidereal reference frame i.e. relative to the cosmos, relative to the fixed stars. Only w ith this in mind can we consider and apply the mathematical formulas correctly. There were originally t wo leading suggestions to explain the anomalous perihelion shift . These were an intra - Mercurial planet called Vulcan and intra - Mercurial dust rings – these postulated as being of equal mass to V ulcan , but neither of them have ever been seen. The dust ring or rings were considered to be contiguous with the Zodiacal light particles, but asserted to be concentrated within Mercury’s orbit in order to be able to explain the perihelion shift. The Zod iacal light dust ring s concept was particularly associated with the astronomer Hugo Seeliger – and are not to be confused with modern notions of ‘dark matter’ pervading all sorts of corners in the universe. As neither Vulcan nor the dust rings were eve r se en, Einstein claimed that the anomalous perihelion shift was explained entirely by GR. Nevertheless, it is surprising that although Einstein claimed that general relativity could explain the anomalous perihelion shift fully, he had to get the calculation to fit , adding both SR and a mathematical correction to reduce the Newtonian contribution to gravity by a small amount . A major Einsteinian relativist, Clifford M. Will , 61 admits these factors frankly, that the explanation for the δ  actually comprises three separate components: A) The s pacetime curvature effect (GR per se ). B) The v elocity effect (SR predicts an increased mass of Mercury with motion, modifying the gravitational force). C) Nonlinearity effects (the force is determined by a Ne wtonian gravitational potential minus “a small term proportional to the square of this potential, the net force being slightly weaker than you would expect.” ) Accepting Will’s authoritative statements , this would seem to imply that Einstein’s δ  equation would have the form:

= + + where A , B & C are defined as above, the different contributions additive or subtractive and readily discernable. However this is not the case, since Einstein’s actual formula for the anomalous perihelion shift ( δ  ) of any orbit – not just that of Mercury – i s:

24 = ( 1 − )

The meaning of the other symbols is:  - ratio of the diameter to the circumference of a circle. c – the velocity of light [ sic ] in a vacuum. a – the length of the major hemiaxis of the orbital ellipse ( i.e. half the length of the long axis of the orbit). It is a measure of the size of the or bit. e – the eccentricity of the orbit. It is a measure of the shape of the orbit, comparing the length to the width of the orbital ellipse. T – the time for one orbital revolution of the object, measured in seconds . When the size and shape of the orbit are already given by a and e respectively, the orbital time T is instead a proxy measure of the gravitational power of the central body. A shorter orbital time , a smaller T , implies a stronger central gravitational field , implying a greater p erihelion - shifting effect from a heavier central body. Note too that T is measured as sidereal revolution i.e. as relative to the fixed stars, to the cosmic reference frame, rather than to Earthbound or other co - ordinates. Nevertheless, t he crucial measur e , i.e. the anti - Newtonian symbol in the formula , is c , since while c is the conventional symbol for the , here in this gravity equation it does not actually represent the speed of light but rather the alleged “speed of propagation” of gravity, presumed to be the same as that of the speed of light. Hence the use of the identical symbol.

7. Isaac Newton and the ‘Transmission’ of Gravitational Impulse s Newton’s inverse square law, his law of gravitation whereby the force of gravity is inversely proportional to the square of the distance between the bodies, 62 requires that every particle with mass “responds instantaneously to every other particle with mass irrespective of the distance between them.” 63 This concept is termed ‘instantaneous action at a distance’ (IAAD) , and is flatly denied by Einsteinian relativity, since SR denies that any impulse or information can travel faster than the speed of light. Nor did Newton like IAAD! It is inconceivable that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation in the sense of Epicurus be essential and inherent in it. And th is is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent and essential to matter, so that one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent act ing constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers. 64 These words – bracketing an oft - quoted section – are usually taken to mean that he firmly rejected IAAD . N everthe less , the last sentence shows otherwise. The immaterial cause , the agent invoked , i s God himself, a god - of - the - gaps filling in to perform the instant - aneous action at a distance ! Thus Newton could easily set aside his above - expressed frustration at IAAD s ince he treated space as the ‘Sensorium of God’. For Newton, space, like God, extended infinitely. Rejecting the notion of a medium to transmit either gravity or light, as well as setting aside Epicurus’ conception of gravity in the form of atomic weight , Newton, in writing of the human senses, concludes: And these things being rightly dispatched, does it not appear from phenomena that there is a being incorporeal, living, intelligent, omnipresent, who in infinite space, as it were in his sensory, sees th e things themselves intimately, and thoroughly perceives them, and comprehends them wholly by their immediate presence to himself. 65 In other words Newton’s Arian 66 god suffices to explain away any otherwise inexplicable phenomena of nature. So while Newton toyed with notions of an aether or a fullness permeating space, he quickly saw that such notions could not explain gravity nor remove the need for IAAD. Rather IAAD is absolutely essential in Newtonian theory to ensure that his law of gravit y work s – and his discovery is not unique here ! Discoveries in quantum theory have also uncovered a process requiring IAAD : i.e. quantum entanglement . U nlike electromagnetism, quantum influences lack a distance factor – repudiating ‘contact physics’ – so can occur instantaneously at great distances, or at least faster - than - light e.g. the positive Aspect Experiment. Conversely, the notion of a transmission medium for gravity impl ies a finite speed for the gravit ational impulse , a notion utterly inimical to the Newtonian conc e ption . This i s the case with the perihelion formula first laid down by Paul Gerber then resurrected by – despite Einstein’s denial of a transmission medium (the aether) for light! While there have been accus ations of plagiarism against Einstein, any connection between Gerber’s equation and Einstein’s seems to have been indirect through mutual contacts among physicists and astronomers. That an indirect explanation for Gerber’s possible influence on Einstein ha s to be accepted is that from the late 19 th century onward there was a powerful belief in the stagnant aether, a “transmission” or “propagation” medium for light, one that could do ‘double - duty’ for gravity too. Gerber’s own inspiration was the work of Fr ench engineer Maurice Lévy who combined Riemann’s mathematics with Weber’s electromagnetic laws whereby gravity is transmitted as an impulse traveling at the speed of light. 67 The point here is that the belief in light - speed being the maximum possible spe ed for matter and for information transfer was already the majority viewpoint at the turn of the 20 th century. In turn this situation arose primarily from complicated philosophical reasoning and culture rather than the better - known secondary theorizing su ch as the Fitzgerald - Lorentz contraction to explain the negative Michelson - Morley experiment, since that theorizing was created to justify the predominant pre - existing beliefs! Thus the perihelion shift formula of both Gerber and Einstein is not only non - Newtonian but anti - Newtonian because it assigns a finite speed, the speed of light, for the transmission or effect of the gravitational impulse. For Newtonian physics the value of the symbol c in the perihelion equation is infinite, hence the equation gives a zero result, leaving the anomalous perihelion shift unexplained due to the impulse of gravity working through IAAD, just as quantum entanglement does ! So not only did Gerber and Einstein mix with a common German - speaking physicist - astronomer milie u, but they also share d the same regnant presumption that gravity propagates only at the speed of light , rather than instantaneously . Furthermore , Gerber and Einstein share the same crucial presumption concerning the mathematical represent ation of the Su n in their calculations. GERBER: “For the calculation of the [anomalous] perihelion shift of Mercury the dimensions of the Sun and of the planet do not come into consider ation. More - over it is convenient to refer the orbit of the planet onto the Sun as the point of origin of the coordinates. ” EINSTEIN : “ Situated at the initial point of the coordinate system there is a mass - point (the Sun). The gravitational field, which this mass - point generates, can be calculated from these equations throug h successive approximation.” 68 Now l et us take Einstein’s word for it that he did not know , directly, of Gerber’s theory ! C oming from the same milieu, the aforementioned physicist Ernst Gehrcke saw that the anomalous perihelion shift of Mercury could be explained without invoking GR – Gerber himself having died in 1909 so unable to reply . Einstein nevertheless replied to Gehrcke , seeing that he… … wants to hav e us believe that the perihelion shift of Mercury can be explained without the theory of relativity. So there are two possibilities. Either you invent special interplanetary masses , which are so great and so assigned, that they yield a perihelion motion from the observed amount; here the most extremely unsatis - factory way out has naturally been given in comparison to that of relativity theory, which supplies the perihelion motion of Mercury without some special assump - tion. Or you rely on a work by Gerbe r, who already gave the right formula for the perihelion shift of Mercury before me. The experts … By “experts” in 1920 Einstein only means his acolytes since he himself is the expert. …are not only in agreement that Gerber’s derivation is wrong through and through, but the formula cannot be obtained as a consequence of the main assumption made by Gerber. Mr. Gerber’s work is therefore completely useless, an unsuccessful and erroneous t heoretical attempt. I maintain that the theory of general relativity has provided the first real explanation of the perihelion motion of Mercury. 69 Thus , despite their obvious similarities, we find no constructive agreement whatsoever between the two theo ries , unlike the other examples listed , reflecting the situation between Soldner’s Newtonian half - deflection value for light and that in Einstein’s 1911 paper, though in that case we saw that quantum spin belatedly supplie s the missing ‘factor of 2’ to the Newtonian prediction .

8. Professor Einstein and Senile Science Rather , as Einstein makes abundantly clear, the disagreement between Einstein’s and Gerber’s theories is fundamental and destructive , along the lines of Sir Karl Popper’s Conjectures and Refutations , where any scientific discovery – not merely Quantum Theory or Relativity but also the spherical Earth and the Periodic Table – can be subject to corrosive criticism, and thus dismissed as mere conjecture, refuted by concoct ing another theoretical construct and popularizing it among the scientific community. Popper outlines t he basic procedure there : The w ay in which knowledge progresses, and especially our scientific knowledge, is by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our problems, by conjectures . These conjectures are controlled by criticism; that is, by attempted refutations , which include severely critical tests. They may survive these tests; but they can never be positively justified: they can neither be established as certainly true nor even as ‘probable’. 70 This ‘critical - sceptical’ way of thinking – the criterion of falsifiability (or fallibility) where by any objective or absolute standards are rejected whenever it is desired – follows Einstein’s lead . Via this procedure, science is not only reduced to mere guesswork but can only ever end in uncerta inty. We cannot observe the spherical Earth or the Periodic Table directly in nature as both we re the result of combining a vast number of observations with complicated theory and inference (Quantum Theory and Einsteinian Relativity also of course) . The resulting uncertainty and paralysis in thinking engendered by such critical - scepticism leads to the outlook which John Horgan described as the “End of Science” and is highlighted in his more recent assessment of the implications of that book 71 by Thomas Kuhn. Kuhn held that a revolution is a destructive as well as a creative act. The proposer of a new paradigm stands on the shoulders of giants (to borrow Newton's phrase) and then bashes them over the head. He or she is often young or new to the field, that is, not fully indoctrinated. Most scientists yield to a new paradigm relu c - tantly. They often do not understand it, and they have no objective rules by which to judge it. Different paradigms have no common standard for comparison; they are ‘ incommensurable ’ , to use Kuhn's term. Proponents of different paradigms can argue for ever without resolving their basic differences because they invest basic terms – motion, particle, space, time – with different meanings. The conversion of scientists is thus both a subjective and political process. It may involve sudden, intuitive under standing – like that finally achieved by Kuhn as he pondered Aristotle. Yet scientists often adopt a paradigm simply because it is backed by others with strong reputations or by a majority of the community. 72 Einstein’s theory is incommensurable with Gerb er’s because each theory works from different paradigms , different presumptions and dogmas (despite getting the same answer due to certain crucial key presumptions !) . Hence these paradigms are very often not clear to the researchers themselves – as Kuhn baldly states above. For those who would claim that the above misrepresents Einstein’s position, they need to understand that different researchers , including Einstein especially, invest even the most basic terms , e.g. “motion, particle, space, time” with utterly different meanin gs to those commonly used , leading to the overweening predominance of abstract theoretical mathematical constructions rather than physical observations . In 1934 Einstein wrote: The theoretical scientist is compelled in an incr easing degree to be guided by purely mathematical formal considerations in his search for a theory, because the physical experience of the experimenter cannot lead him up to the regions of highest abstraction. The predominantly inductive methods appropria te to the youth of science are giving place to tentative deduction . 73 Indeed they are – and in this last revealing statement by Einstein we see the fate of modern science in our era . M odern physics today has reached its senile stage : its exciting but corrupted and misspent youth has crumbled away into mere “tentative deduction” where nothing is ever certain but remains merely subject to conjecture and refutation with no possibility of practical application or understanding whatsoever . All that remains is intersubjectivity – that a majority of scientists [ sic ] agree that Einstein is right and therefore Gerber’s or any other theory suggesting an alternative cause for the anomalous perihelion shift of Mercury is pre - judged to be false by the popularized (i.e. pro - Einstein) criteria of critical - scepticism. With this situation regnant, scientific progress has come to a halt in favor of rampant mathematical speculation ! Nevertheless, that both theories , Gerber’s and Einstein’s , lead to the same result for the anomalous perihelion shift of Mercury given by the very same equation, indicates not only that their key presumptions are identical but that their mathematicised theoretical edifices and particular presumptions are otherwis e physically irrelevant. Specifically Einstein’s conception of spacetime, curved spacetime and the resulting “curvature of space” (and time) is revealed, as in the case of the gravitational bending of light, to be superfluous to the experimental findings. Gerber’s and Einstein’s theories are essentially mathematical constructions, meaning that, rather than inventing yet another mathematical edifice or try ing to justify the theoretical postur es of Einstein or Gerber with tendentious reasoning, we have to lo ok further into the nature of the Sun and Solar System to find the correct answer.

9. The Primary Cause for Mercury’s Anomalous Perihelion Shift Even half a century later , there were still serious issues to be solv ed before Einstein’s GR explanation could be fully accepted. The major issue came to a head i n the 1960s – th e solar oblateness . Because the Sun rotates, it was thought that , like Jupiter and the Earth itself, the rotation would produce a quadrupole, an increased equatorial dia meter and therefore a relative concentration of mass around the solar equator, causing a clear additive effect up on Mercury’s perihelion shift. As we saw above, neither Gerber nor Einstein considered this question as they treated the Sun as a point - mass. Accurate measurements through the 1970s however essential ly excluded the existence of a significant solar oblateness, so the Einsteinian explanation appeared safe. However, the situation actually served to affirm the long - held general understanding that the material comprising the Sun’s contents would itself have an effect on Mercury’s perihelion shift , as Philipp Lenard also saw: For the still unexplained remainder of the perihelion shift it appears from the given facts – acco rding to everything normal ly lying within easy reach of colleagues hitherto – to be ascrib ed to those masses, the availability of which in the vicinity of the Sun has probably been shown from the beginning and even through the Zodiacal light. Such an expl anation for the perihelion shift cannot be avoided for long, as there exists no more exact know ledge of the mass relationships in the solar environment , nor are new insights com ing to hand otherwise . 74 Given the subsequent ly demonstrated insignificance of the solar oblateness, Lenard’s observations from 1921 remain the situation today. Therefore something vital “in the solar environ ment” ( Sonnenumgebung ) has long been overlooked in elaborating the Newtonian explanation – as opposed to Ei nstein’s “special interplanetary masses ! ” Roseveare (p. 24 table 2.2 ) unwittingly provides the answer when quoting Le Verrier’s table for the predicted mass properties of the planet Vulcan – or the equivalent intra - Mercurial Seeliger dust ring s – hypothesized to account for the anomalous perihelion shift. Mercury averages about 0.39 a stronomical units (a u ) 75 from the Sun . The table below reproduces thes e values.

Table 2: PROPERTIES OF VULCAN (or SEELIGER DUST RING S ) Distance from Sun (au) Ratio of mass to Mercury’s mass 0.310 0.07 0.271 0.17 0.232 0.35 0.194 0.68 0.155 1.29 0.116 2.66

It is clear from the table that the nearer the Sun the mass - bearing object would be, the greater the mass it would possess – and the faster it would revolve around the Sun. At 0.01 au , the hypothetical planet, as massive as Jupiter or more so, would be to uching the chromo sphere and photosphere, the very surface layers of the Sun itself, its material interacting and interchanging with the dense plasma of the Sun. As this hypothetical planet revolv ed prograde and rapidly around the Sun it would mix and merg e w ith the Sun itself ! At this point we realize that the Sun is itself not stationary relative to the cosmos, to the fixed stars. The Sun rotates on its axis, and it rotates prograde, like the planets revolving around it , its rotation averaging about 27 - 28 days ! In stark contrast, t he Sun as described in Einstein’s perihelion shift paper of 1916 – or Gerber’s of 1902 – i s a caricature , one resembl ing the complementarity treatment of a subatomic particle . They all treat the Sun as an abstract point without physical extension, while treating its rotational motion as hardly less than a mystical ecstasy, a Born - again “ wave of probability” unrelated to th e extra prograde motion of Mercury’s orbit, rather than realizing that the Sun’s major internal motion – like that of a subatomic particle – is spin! Spin, of course, is something that a point - particle cannot do – and even if a dimensionless point were spi nning it could have no effect on anything outside itself ! More significant ly , it is the prograde direction of the Sun’s own spin, its rotation, that causes most if not all of the approximately 43 ʺ of arc extra perihelion shift. Were the Sun’s rotation retrograde the bulk of the 43 ʺ of arc would be subtracted from , rather than added to, the total planetary contribution of 531 ʺ of arc to yield an overall perihelion shift of about 488 ʺ of arc ! No doubt math ematic al astrophysicists making varied approximation s as to the average rotation rate of the Sun will work out fairly exactly its contribution to the anomalous perihelion shift of Mercury. Thus if any difference remain s unaccounted for , they can work out what other factors, if any, might influence the perihelion shift – e.g. a mass concentration of heavier elements in plasma at the solar equator due to the effect of magnetic flux tubes at lower latitudes expelling such elements from the regions of most vig orous sunspot activity.

Conclusion Einstein’s Relativity was meant to be completed as a t hree - tier construction, with SR at its base, GR in the middle and the never - achieved Grand Unified Theory (or United Field Theory) at the summit. In t hi s last, electromagnetism was somehow to be ‘united’ with gravitation via a few all - explanatory mathematical concepts , Einstein’s vision for i t being “neither to incorporate the unexplained nor to resolve any paradox. It was purely a quest for harmony . ” 76 Th is situation has now changed radically, since with the redundancy – i f not outright disproof – of GR the high regard it has traditionally been given is shown to be sorely misplaced. Hence too, critical attention must now be directed to SR since it led ‘logically’ to the misconceptions of GR , especially as Einstein admitted Gehrcke’s severe charge that “relativity leads to solipsism , a claim that every expert will welcome as merely a joke .” 77 A vast literature by these experts , including mathematics - dominated journals like General Relativity and Gravitation , ha s been devoted to reconciling quantum theory with GR. The evidence above demonstrate s that these efforts are entirely misplaced and futile – quantum theory stands firm while GR is at best a misconceived relic of faulty early 20 th century th eorizing . Likewise the popularized misconceptions derived from GR, such as gravity wave s, gravitons and spacetime metrics, are merely mathematical fantasies, not physical entities. Yet f rom the Newtonian material discussed above, as well as Einstein’s elevation to a secular saint, we see that the issues covered by GR are not mere arcane que stion s of science but heavily emotionally charged issue s that, since they concern cosmology , also concern major questions of religion and cultural outlook and th erefore philosophy as well. For example , modern physicists like Steven Weinberg, imbued by Einstein’s theorizing, disparage philosophy altogether, contrasting the ‘unreasonable effectiveness’ of mathematics with “the unreasonable ineffectiveness of philosophy.” For Kantian philosophy “the most shocking thing about Einstein’s theories is that they demote space and time to the status of ordinary aspects of the physical universe, aspects that could be affected by motion (in SR) or gravitation (in GR).” 78 N ot just the professional philosophers of science but modern philosophy itself ha s agreed with this assessment, humbling themselves entirely, abandoning any critical stance towards such modern theorizing – this being the post modern condition , where so - called science like Einstein’s dictates answe rs to philosophy instead ! Hence, t hat recourse has had to be made here to 19 th century philosophers (Nietzsche & Sorel – see endnotes ) to understand the implications of Einstein’s teaching , is because of the latter’s over whelming negative influence upon more recent philosophy , which in consequence has fawned upon Einstein and relativity uncritically ; as we find today among the horde s of self - identified atheists, sceptics and humanists! We find this too in Karl Popper’s philo sophical works , full of unabashed hagiography like this quote from Cornelius Lanczos: If somebody asked ‘Who is the greatest modern physicist after Einstein?’ the answer would be: Einstein again… [ because ] had somebody else discovered relativity, his other discoveries would still make him the second greatest physicist of his time. 79 Likewise “ s o much has [relativity] been assimilated into human knowledge that it is sometimes overlooked altogether,” 80 reminding us how the Sun’s rotation has also been overlook ed in uncovering the cause of the anomalous perihelion shift of Mercury ! 81 “The most unfortunate effect of the Einstein myth is the enshrinement of the belief, rejected for 400 years, that science is incomprehensible, that only an initiated priesthood can fathom its mysteries. … Science was [now] something to believe in, not something which should be understood.” 82 The 400 years of science’s freedom from an academic - religious priesthood refers to the liberator himself , Galileo, Einstein’s true st opponent, a fact not fully understood even by Eric Lerner who wrote these words . 83 Thus the larger question emerging from this work is that a n ew cosmology is long overdue , one that recognizes the infinity of the universe as against the false inference of a finite universe arising from a Big Bang. This does not mean a return to the Steady State Theory however, especially as startling new evidence is emerging for a cosmic dipole in the fine structure constant, 84 nullifying the presumption as to the cosmos being homo - geneous and isotropic. The Plasma Cosmology championed by Eric Lerner is partway there , but at present remains stunt ed, and not only by its residual belief in GR. The Nobel - Prizewinning physicist Philipp Lenard became the only consistent opponent of Einstein’s relativity in the interwar era – and Einstein recognized him as such; hence Lenard nowadays has been treated little better than a pantomime villain , fit only for a dunking! 85 Whereas Einstein took recourse into mysticism, into incom - prehensibil ity, into an ‘inner harmony’ of the universe along the lines of Spinoza, Lenard sharply distinguished between human - created (especially mathematical) mysticism and the true physically - based mysteries of nature in “The Boundaries of Our Understanding . ” The complete comprehension of any given natural process is impossible. Because of the interconnectedness of nature, such comprehension would involve under - standing the totality of the infinite world – from which we, in the true sense of the word, must remain forever infinitely removed if for no other reason than because of the finiteness of our body to which our cognitive spirit is bound . It is not possible from our range of experience to grasp too much at one time; even the successive comprehension of infinite ly many things of limited extent would take an infinitely long time. This accounts for the fact that beyond every uncovered mystery of nature we find an even greater mystery. 86 The infinite universe can thus be increasingly understood – as an unc overed mystery, but not as mysticism conjured from mathematical and/ or other source s . However, this non - mystical understanding can never and will never come to completion. What still remains in our epoch , and what Lenard too failed to achieve, is to uncover the philosophical criteria by which such judgments about nature’s mysteries can be soundly affirmed against mathematical and other mysticism .

References Bohm, David , Quantum Theory , Dover, New York (1989){1951}. Born, Max, Nobel Lecture 1954, Nobel Prize Lectures , Elsevier, Netherlands (1972) . ------, Max, The Born - Einstein Letters , trans. Irene Born, Macmillan, London (1971) . Cassidy, David C., Uncertainty: The Life & Science of Werner Heisenberg , W. H. Freeman & Co., New York (1992) . Clark, Ronald W., Einstein, the Life and Times , Avon, New York (1984) . Corngold, Stanley, Walter Kaufmann: Philosopher, Humanist, Heretic, Princeton University Press, NJ (2019). Einstein, Albert, Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes, Annalen der Physik 35 (1911) 898 - 908. ------, Albert , Erklärung der Perihelbewegung des Merkur aus allgemeinen Relativitäts theorie, Sitzungsberichte Preussischen Akademie Wissenschaften Part 2 (1915) 831 - 839 . ------, Albert, Die Grundlage der allgemeinen Relativitätstheorie, Annalen der Physik 49 (1916) 769 - 822. ------, Albert , Mein Antwort ü ber die anti - relativitätstheoretische G.m.b.H., Berliner Tageblatt, Freitag, ( 27th August 1920 page 1 ; editorial comment p. 3) . ------, Albert, Ideas & Opinions , Wings, Crown, New York (1954). Einstein, Albert, H. A. Lorentz , H. Minkowski & H. Weyl, The Principle of Relativity , with notes by A. Sommerfeld, trans. W. Perrett & G. B. Jeffery, Dover, New York (1952) . Gamow, George, The Great Physicists from Galileo to Einstein , Dover, New York (1961). Gerber, Paul, Die Fortpflanzungsgeschwindigkeit der Gravitation, Annalen der Physik (Leipzig) 52 (1917) 415 - 441; reproduced from “Die For tpflanzungs geschwindig - keit der Gravitation”, Programmabhandlung des städtische Realgymnasiums zu Stargard im Pommerania (1902) . Goudsmit, Sam, Guess Work: The Discovery of the Electron Spin, Delta ( Netherlands ) 15 (1972) 77 - 91 . Israel, Hans, Erich Ruckhaber & Rudolf Weinmann, ed s ., Hundert Au toren Gegen Einstein , R. Voigtlanders Verlag, Leipzig, Germany (1931). Jaki, Stanley L ., Johann Georg von Soldner and the Gravitational Bending of Light, with an English Translation of His Es say on It Published in 1801, Foundations of Physics 8 (1978) 927 - 950. Kragh, Helge, The fine structure of hydrogen and the gross structure of the physics community 1916 - 1926, Historical Studies in the Physical Sciences 15 (1984 - 1985) 67 - 125 . Kuhn, Thomas S., The Structure of Scientific Revolutions , (2 nd edition with postscri pt), University of Chicago Press, Chicago (1970). Lenard, Philipp, Über die Ablenkung eines Lichtstrahls von seiner geradlinigen Bewegung durch die Attraktion eines Weltkörpers, an welchem er nahe vorbeigeht, von J. Soldner, 1801, mit einer Vorbemerkung vo n P. Lenard, Annalen der Physik 65 (1921) 593 - 604. ------, Philipp, Deutsche Physik (in 4 vols.) Vol. I, Lehmann, (1943). Lerner, Eric J., The Big Bang Never Happened , Simon & Schuster, London (1991). Lofts, Mark J., The Geometric Ax e s Theory of Nuclear Structure: Explaining Odd - N Stability ( 50 V , 180 Ta, 23 5 U) and Octupole Nuclei, General Science Journal No: 8324 (27 th July 2020). Newton, Isaac, Philosophical Writings , ed. Andrew Janiak, Cambridge Texts in the History of Philosophy, Cambridge University Press, UK (2004). Pais, Abraham, Subtle is the Lord , Oxford University Press, UK (1982). Popper, Karl R., Conjectures and Refutations: The Growth of Scientific Knowledge , Routledge and Kegan Paul, London (1963). ------, Karl R., Quantum Theory and the Schism in Physics , ed. W. W. Bartley III, Unwin Hyman, London (1982). ------, Karl R., Unended Quest , preface by Chancellor Helmut Kohl, Routledge, London (1992) . Roseveare, N. T., Mercury’s Perihelion from Le Ve rrier to Einstein , Clarendon Press, Oxford, UK (1982). Sorel, Georges, From Georges Sorel. Volume 2: Hermeneutics and the Sciences , ed. John L. Stanley; trans. John & Charlotte Stanley, Transaction Publishers, New Brunswick, New Jersey, USA (1990) . Thomas, Llewellyn Hilleth, The Motion of the Spinning Electron, Nature 117 (April 10 th 1926) 514. ------, Llewellyn Hilleth, The Kine matics of an Electron with an Axis, Philosophical Magazine (January 1927) 1 - 22. Uhlenbeck , George E., Fifty Years of Spin: Personal Reminiscences, Physics Today (June 1976) 43 - 48. Weinberg, Steven , Dreams of a Final Theory , Hutchinson Radius, London (1993) Will, Clifford M., Was Einstein Right? Oxford University Press, Oxford (1994) .

Notes 1. He labels this system K ʹ (K - prime) but that symbol is here replaced with L for legibility. 2. Fritz Hasenöhrl, Zur Theorie der Strahlung in bewegten Körpern, Annalen der Physik 15 (1904) 344 - 370 ; Berichtigung , Annalen der Physik 16 (1905) 589 - 592 . 3. Gamow pp. 184 - 187. 4. Einstein (1911) p. 101 §2 paragraph 2. 5. ... wir annehmen, daß die Systeme K and L pysikalisch genau gleichwertig sind, d. h., wenn wir annehmen, man könne das System K ebenfalls als in einem von einem Schwerefeld freien Raume befindlich annehmen; dafür müssen wir K dann aber als gleichförmig beschle unigt betrachten. Man kann bei dieser Auffassung ebensowenig von der absoluten Beschleunigung des Bezugssystems sprechen, wie man nach der gewöhnlichen Relativitätstheorie von der absoluten Geschwindigkeit eines Systems reden kann. (Einstein 1911 p. 899 w ith original emphases; note that s yst em L is called ‘K - prime’ in Einstein’s article; English translation without original emphases in Einstein, 1952 p. 100). 6. Einstein used the symbol h for height, but that symbol is the usual representation of Planck’s constant! Likewise with his use of γ for acceleration, where this symbol is usually used for photons, particularly gamma rays. 7. Einstein (1911) pp. 105 - 106. 8. Einstein (1911) p. 106 ; AnnPhysik p. 906: “ ...wir müssen aber an Stellen verschiedenen Gravitationspotentials uns verschiedenen beschaffener Uhren zur Zeitmessung bedienen. ” 9. In that era most non - German - speaking peoples (later nations) in Eastern Europe used German as their scientific language, Russia being the major neighboring exception. 10. Strong magnetic fields lead to the Paschen - Back Effect which reduces spectral line splitting to Zeeman triplets only. 11. E.g. the prominent double orange - colored spectral lines from a sodium lamp. 12. As illustrated in Bohm p. 349, where each line on the right side of figure 5 is actually a double line comprising the ‘fine structure’. The names attributed to the lowest frequency new spectral lines revealed by the Stark effect – sha rp , principal , diffuse and fundamental ( s , p , d , f ) – derive from the reinterpretation of the Zeeman effect that Stark enabled. When a magnetic field was first imposed upon the electric field, the s line remained sharp in that only the fine structure appeared. The p line revealed the principal feature of Zeeman effect, the triplet. The d line revealed a diffuse broadening of the spectral line, later resolved into five lines; when finally the f line was decoded as a sp lit into seven lines, the experimenters at last understood the fundamental features of spectral line splitting in electro - magnetic fields. Adding in the fine - structure and alkali doublets enabled the elaboration of the structure of the Periodic Table from spectra alone . 1 3 . Kragh p. 85. 14. Bohm §15:13 p. 349. 15. This being the ‘Copenhagen Interpretation of Quantum Theory.’ 16. Presumably most of these progressive physicists would not have backed Einstein’s extreme Left stance in 1938 when he expresse d his support for Stalin’s show - trials ( Born - Einstein Letters # 73 p. 130, material edited out in the post - Soviet - Union 2 nd edition), hence Kragh’s hesitation at the ‘left’ label! 17. Kragh p. 70. 18. Born - Einstein Letters #41 p. 70. 19. Quoted in Kragh p. 80. 20. Kragh p. 81. 21. Kra gh p. 83. 2 2. Kragh pp. 86 - 90, 102. 23. Kragh pp. 99 - 100, 108. 24. Kragh p. 125 n. 188; for Jordan s ee https://en.wikipedia.org/wiki/Pascual_Jordan 25. Kragh p. 101. 26. Kragh pp. 101 - 102. 27. Kragh p. 102. 28. Kragh p. 102. 29. Cassidy pp. 207 - 211 ; spin had also been suggested independently by Ralph Kronig and Alfred Landé but, each of them being close to the established primarily German - speaking theorists, were not encouraged to develop the idea (Kragh p. 114). 30. Goudsmit p. 83. 31. Uhlenbeck p. 47. 32. The correct p hysical interpretation of Schrodinger’s equation and quantum spin was given by Eric Lerner (pp. 362 - 364, 369 - 373) in uncovering the nature of plasma vortices. Lerner in turn attributed the vortex theory of subatomic particles to Soviet physicist Lev Landa u, without realizing that Johannes Stark had treated electrons likewise, correcting the earlier dynamid theory of Philipp Lenard, which had charged rather than magnetic poles for the vortices. The author’s own work on the vorticial basis of atomic nuclear structure is based upon these various insights (Lofts, 2020). 33. Bohm §§16:24; 17:1 - 4 pp. 383 - 392. 34. Bohm §9:28 - 29 p. 196. 35. Goudsmit p. 80, lines 3 - 4. 36. Goudsmit p. 79. 37. Goudsmit p. 87. 38. Goudsmit p. 88. 39. Goudsmit p. 88; Thomas ’s own articles are listed in the references, these showing that Einstein’s relativity somehow resolves the factor of 2. 40. Uhlenbeck p. 48. 41. Born (1954) p. 266. 42. Born (1954) p. 262. 43. Cassidy p. 209. 44. Jaki (1978) 939 - 948; Lenard (1921) repub lished in German only t he significant non - mathematical part of the text, indicating Soldner’s Newtonian reasoning. 45. Jaki p. 947. 46. Jaki p. 935. 47. Jaki p. 948; Lucretius , De Rerum Natur ae (On the Nature of the Universe) I:431. 48. See Pais pp. 47 , 318 - 319; Popper (1992) especially pp. 128 - 132. Also Karen C. Fox & Aries Keck, Einstein A to Z (John Wiley & Sons, Hoboken, New Jersey 2004) p. 268 ‘Spinoza’; however this book is otherwise gravely flawed in attributing false and base motives to Einstei n’s opponents. 49. In contrast, Einstein’s relativity i s usually part of the advanced physics curriculum in Australian high schools at senior level. 50. Lerner pp. 122ff. 51. Pais p. 311 . 52. Pais p. 305. The public cult of Einstein is linked both to his ‘modesty’ and his belief in determinism as uttered forcefully in 1929 on the very weekend of the Wall Street Crash: “I claim credit for nothing; everything is determined, the beginning as well as the end, by forces over which we have no control . It is determined for the insect as well as for the star. Human beings, vegetables or cosmic dust, we all dance to a mysterious tune, intoned in the distance by an invisible piper.” (Clark p. 422) 53. The name ‘Walter Kaufmann’ here refers to the postw ar Nietzsche scholar, not the late 19 th century physicist of the same name. “The memorial to Walter Kaufmann composed by the Princeton Philosophy Department recounts the story of Kaufmann’s first meeting with Albert Einstein. Einstein asked Kaufmann abou t his recently completed thesis, and on hearing that it dealt with Nietzsche, ‘Einstein’s wonderful face expressed great shock, and he said “But that is simply dreadful.” This gives some idea of Nietzsche’s reputation in 1947: one associated with brutalit y, madness and the Nazis’.” (Corngold p. 614 note 25). 54. Walter Kaufmann, ed. The Portable Nietzsche , Penguin (1976) p. 270 : Th us Spoke Zarathustra III:2:2; Kaufmann’s introduction to the third part of Zarathustra (pp. 260 - 263) does not describe the con tent of this section in any detail. 55. It is customary to treat Nietzsche as irrelevant to science because he was not a scientist. Nietzsche began as a critic of Socratic thinking in The Birth of Tragedy , but an independent parallel course was followed by Georges Sorel, who in Le Procès de Socrate (1889) criticized Socratic thought – at a time when Nietzsche was not yet widely recognized nor his work translated into French! While his philosophy is less developed than Nietzsche’s it agrees on the fundam ental issues, but, far more important, Sorel was scientifically trained, being an engineer before embarking on his philosophical studies, his ideas substantiating Nietzsche’s positions toward modern science. In the essay ‘Science and Morals’ (1900) Sorel writes that “under some form or other, determinism is shown to be the adversary of [genuine] science, for it always ends in affirming the powerlessness of our creative forces; thus we have science only insofar as we have the power to govern t he world . The philosophers who claim to impose respect for immanent forces on us or to subject us to the so - called laws of history are asking us to abandon our reason and recognize mysterious powers.” (Sorel p. 131) 56. This extends from §§3 - 21, comprisi ng the bulk of the article, the ‘practical’ implications only laid out tersely in §22. 57. Tensors are changes f rom one vector to another in space . GR’s tensors are qualitatively different as they are applied to space itself. 58. Roseveare p. 10; the ‘ orbital precession of Mercury’ is an alternative name for the perihelion shift, not a different phenomenon. 59. Th is Greek - derived symbol is termed ‘bar - omega’ or ‘curly - pi’! 60. https://en.wikipedia.org/wiki/Mercury_(planet)#Advance_of_perihelion (accessed 30th/8/2020 ). 61. Will, Was Einstein Right? p. 94. 62. And directly proportional to the product of the masses of any two gravitating bodies. 63. See https://en.wikipedia.org/wiki/Speed_of_gravity . (accessed 30th/8/2020). 64. Newton pp. 102 - 103 , from 4th Letter to Richard Bentley. 65. Newton p. 130, from Query #28 to the Opticks . 66. Arianism, such as today p racticed by the Jehovah’s Witness church which holds Newton in the highest regard, rejects the usual Christian teaching of the Trinity, asserting instead that the Hol y Spirit is merely the power of God, and Jesus Christ a mere human. 67. https://en.wikipedia.org/wiki/Paul_Gerber (accessed 1st / 9 /2020) . 68. The original German reads: GERBER (1902) p. 437 : “ Für die Berechnung der Perihel bewegung des Merkur kommt die Ausdehnung der Sonne and des Planeten nicht in Betracht. Außerdem ist es bequem, den Lauf des Planeten auf die Sonne as Anfangs punkt der Koordinaten zu beziehen. ” EINSTEIN (1 915) p. 832 : “Es befinde sich im Anfangspunkt des Koordinaten systems ein Massenpunkt (die Sonne). Das Gravitationsfeld, welches dieser Massenpunkt erzeugt, kann aus diesen Gleichungen durch sukzessive Approx imation berechnet werden.” 69. Herr Gehrke w ill glauben machen, daß die Perihelbewegung des Merkur auch ohne Relativitätstheorie zu erklären sei. Es gibt da zwei Möglichkeiten. Entweder man erfindet besondere interplanetare Massen, die so groß und so v erteilt sind, daß sie eine Perihelbewegung von dem wahrgenommenen Betrage ergeben; dies ist natürlich ein höchst unbefriedigender Ausweg gegenüber dem von der Relativität stheorie gegebenen, welche die Perihelbewegung des Merkur ohne irgendwelche besondere Annahme liefert. Oder aber man beruft sich auf eine Arbeit von Gerber, der die richtige Formel für die Perihelbewegung des Merkur bereits vor mir angegeben hat. Aber di e Fachleute sind nicht nur darüber einig, daß Gerbers Ableitung durch und durch unrichtig ist, sondern die Formel ist als Konsequenz der von Gerber an die Spitze gestellten Annahmen überhaupt nicht zu gewinnen. Herrn Gerbers Arbeit ist daher völlig wertlo s, ein mißglückter und irreparabler theoretischer Versuch. Ich konstatiere, daß die allgemeine Relativität s theorie die erste wirkliche Erklärung für die Perihelbewegung des Merkur geliefert hat (Einstein 1920) . 70. Popper (1963), p. vii. 71. The Struct ure of Scientific Revolutions ; see especially Postscript §6. 72. https://blogs.scientificamerican.com/cross - check/what - thomas - kuhn - rea lly - thought - about - scientific - truth/ 73. “The Problem of Space, Ether and the Field in Physics” (1934) in Einstein ( 1954 ) p. 283. 74. Für den damit noch unerklärten Rest der Perihelverschiebung erscheint es bei der geschilderten Sach - lage und nach allem sonst bisher Bekannten sehr naheliegend, ihn denjenigen Massen zuzuschreiben, deren Vorhandensein in der Sonnennähe von vornherein wahrscheinlich and durch das Zodiakallicht sogar angezeigt ist. Diese Erklärung der Perihelverschiebung wird man so lange nicht a bweisen können, als keine genauere Kenntnis der Massenverhältnisse in der Sonnenumgebung vorliegt oder als nicht sonst neue Erkenntnisse zu Hilfe kommen. (Lenard AnnPhysik pp. 599 - 600) 75. One astronomical unit is the Earth’s aver age distance from the Sun. 76. Pais p. 23. 77. Einstein (1920): “ Herr Gehrke behauptet, daß die Relativitätstheorie zum Solipsismus führe, eine Behauptung, die jeder Kenner als Witz begrüßen wird. ” 78. Weinberg pp. 136 - 137, the whole chapter devoted to subjugating philosophy to Einstein’s teachings. 79. Popper (1982) p. 35, quoting Lanczos’ Albert Einstein and the Co smic World Order (1965). 80. Clark p. 135 . 81. An engineer, one Hans Israel (Israel, Ruckhaber & Weinmann, 1931 p. 15 ¶10) also realized that the Sun’s rotation influenced Mercury’s anomalous perihelion shift, but he attributed it to an electrical effect rather than extrapolating from the Newtonian gra vitational effects of the planets: i.e. “Unseres Erachtens kann aber durch das rotierende Sonnenelektro potential eine Fesselung des Merkurs sich ergeben, durch die er schneller eilt.” 82. Lerner p. 127; see also p. 116. 83. Nor understood by the hundred authors who wrote against Einstein in German (Israel et al., Hundert Autoren gegen Einstein, 1931) where Galileo is mentioned merely twice (pp. 88, 94), and in both cases bracketed with Newton and the latter’s conceptions, revealing that the wider scienti fic community – and not just in Germany since there were French, Yugoslavian, American and Dutch contributors – was and still is entirely at a loss in understanding the philosophical basis of physics. Not a surprise either when ongoing Western prejudice a ttributes this very book to the Nazis, despite the fact that the Nazis did not come to power until 1933! 84. See https://en.wikipedia.org/wiki/Fine - structure_constant (accessed 2nd/9/20 20). 85. E.g. Cassidy p. 343 and works like The Man Who Stalked Einstein by Bruce J. Hillman, Birgit Ertl - Wagner & Bernd C. Wagner, (Lyons Press, Guilford, Connecticut 2015) which ends in a commonplace Einsteinian paradox viz. “The most incomprehensible t hing about the world is that it is compre - hensible.” Also see Einstein (1920) where he identifies Lenard as his most formidable opponent. 86. Lenard (1943) Vol. 1 Introduction §18 p. 13. Grenzen des Begreifens : Das vollständige Begreifen irgendeines Naturvorganges muß aber für unmöglich erachtet werden; es fiele solches Begreifen wegen des Allzusammenhangs in der Natur mit dem Begreifen der gesamten unendlichen Welt zusammen, und davon müssen wir im wahren Sinne des Wortes stets unendlich weit entfernt bleiben allein schon wegen der Endlichkeit unseres Körpers, an welchen unser begreifender Geist gebunden ist. Es ist uns erfahrungs mäßig nich möglich, allzuvieles auf einmal zu erfallen, und selbst abwechselndes Erfassen unendlich vieler Di nge von endlichem Ausmaß würde unendlich lange Zeit erfordern. So kommt es, daß wir hinter jedem enthüllten Geheimnis der Natur immer noch ein größeres Geheimnis gefunden haben.

Corrections :

Section 3 para 10: ‘conformation’ replaced by ‘confirmation’. Section 5 para 10: “expect sophistry to combine the two together…” replaced by “expect detailed investigations aimed at combining the two explanations together…” (This is the only substantial change to the text as such investigations cannot be presumed to be mere attempts to justify GR but will include genuine research to uncover hitherto obscure connections among optics, fluid mechanics and Keplerian - Newtonian cel estial mechanics, working back from quantum theory.) Section 6 para C): rewritten to correct brackets, remove the phrase ‘for Einstein’ and add ‘slightly’ to correct the quotation. Section 8 para 4: “ cause of the anomalous ” replaced by “ cause for the anoma lous ” . Conclusion para 3: “ Yet modern philosophy, not just the philosophers of science , have … ” replaced by “ Not just the professional philosophers of science but modern philosophy itself has … ” Ibid. para 5: ‘anisotropic’ replaced by ‘isotropic’. Note 80: ‘Clarke’ corrected to ‘Clark’.