Mercury Perihelion by chatGPT

Here is a post by me followed by a chatGPT update with main conclusion:

• Thus, while General Relativity GR undeniably improves the precision of planetary models, the evidence for its superiority over Newtonian gravity in the specific case of Mercury’s precession is open to philosophical scrutiny. The possibility of a circular argument — where the correction put in is exactly the correction that comes out — cannot be ignored.

This is mind blowing, maybe Newton holds up also today? This is something chatGPT could admit as representing all modern physicists, which cannot be admitted by any individual living modern physicist. It shows that chatGPT as neutral observer can present a more objective view than any individual, which can be helpful in scientific discussion. 

Perspective: The GR correction of the perihelion shift of Mercury as fraction of one full revolution is of order $3\times 10^{-5}$, which with 415 revolutions per century asks for a precision clearly smaller than $10^{-8}$ per revolution. We are speaking about very small effects, maybe swamped by imprecise data and computation.

My Post:

Modern physics is based on Einstein's theory of Gravitation EG + Quantum Mechanics QM with EG replacing Newtons theory of Gravitation NG of classical physics and QM extending classical physics to atomic scales. A crisis of modern physics has been lingering from the start of EG and QM hundred years ago from an incompatibility of EG and QM, and is no longer possible to hide behind successes. 

There is no incompatibility of NG and QM, and so it is natural to once again check out the reasons for replacing NG by EG. As concerns interaction matter-gravitation as the objective of NG, the main evidence is still that presented by Einstein in 1915 in his General Theory of Relativity GR concerning the precession/advance of the perihelion of Mercury: 

• NG predicts an advance of 531 arcseconds per century from influence of other planets as calculated by Le Verrier in 1859.
• Observations show 574. 
• EG comes with a correction of NG of exactly the missing 43.
• Bingo to Einstein in 1915 knowing that 43 was missing and managing to find exactly 43 from a simple analytical 2body Sun-Mercury formula. 
• The numbers are the same today with high tech computation exactly conforming 531 and 43.
• Bingo also today!

High tech computation use a model consisting of NG + 2bodyEG, which is fitted to data such that initial values and masses. For Mercury the 2bodyEG correction put into the model is exactly 42.98 arcseconds. 

• It is claimed that NG + 2bodyEG when fitted to input data, gives an output prediction precision of less than a meter. In particular observed Mercury precession of 574 is confirmed (with 2bodyEG of 42.98 put into the model)
• It is claimed that NG-only without 2bodyEG correction, can be fitted to give output precision of 1 km as $10^3$ times the precision of NG+2bodyEG.  

Examining these claims we find:

• A fixed model correction of 42.98 is used in the fitting of NG+2bodyEG to input data. The output correction prediction is precisely 42.98.  
• A precision of 1 km in the orbit of Mercury is of relative size less than $10^{-8}$. 
• The difference between NG and EG scales with planet speed $v$ as $\frac{v^2}{c^2}$ with $c$ speed of light which is of order $10^{-8}$ for planets.  
• The evidence of superiority of EG over NG from Mercury precession can be questioned on good grounds. The possibility of circular argument with the input/output of 42.98 is evident.

This casts a doubt on the superiority of Einstein over Newton as concerns interaction matter-gravitation. This doubt is not eliminated by showing EG results for interaction light-gravitation which is outside NG. 

It seems to be possible to argue that NG is the basic matter-gravitation model and that EG can be seen as a modification possibly covering esoteric interaction light-gravitation and clock-gravitation. Following this line could open a way out the a crisis formed by incompatibility of EG and QM. 

chatGPT Version:

Mercury’s Perihelion and the Crisis of Modern Physics

Modern physics rests on two great pillars: Einstein’s theory of gravitation (General Relativity, GR) and Quantum Mechanics (QM). GR replaced Newton’s theory of gravitation (NG), while QM extended classical mechanics to the atomic scale. Yet from the beginning, physicists have known that GR and QM are not mathematically compatible. That tension has been papered over by the enormous practical successes of both frameworks, but more than a century later it remains unresolved.

By contrast, Newtonian gravity and QM coexist without contradiction. That raises a natural question: if NG fits neatly with QM, why was it replaced by Einstein’s theory in the first place?

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The Mercury Puzzle

The strongest evidence came in 1915, when Einstein explained the anomalous precession of Mercury’s orbit.

• Newtonian gravity, when perturbations from other planets are accounted for (as calculated by Urbain Le Verrier in 1859), predicts a precession of 531 arcseconds per century [Le Verrier, 1859].

• Observations showed a total of 574 arcseconds per century.

• That left a gap of about 43 arcseconds unexplained.

Einstein’s field equations supplied exactly the missing correction. His two-body Sun–Mercury formula predicted an additional 42.98 arcseconds per century, bringing theory and observation into alignment [Einstein, 1915; Will, 2014]. It was a triumph for the new theory — and remains one of its iconic successes.

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How the Evidence Is Used Today

Modern planetary ephemerides (high-precision orbital models, such as NASA JPL’s DE430) combine Newtonian gravity with relativistic corrections derived from GR [Folkner et al., 2014]. For Mercury, the correction is still exactly 42.98 arcseconds per century. When this relativistic term is included, the models achieve sub-meter precision in predicting planetary positions [Pitjeva & Pitjev, 2013].

Without the relativistic correction, the same models can be fitted to observational data, but only reach kilometer-level precision — about a thousand times worse.

This is often presented as decisive proof of GR’s superiority. Yet it is worth noticing that the relativistic correction is treated as a fixed formula built into the model. The fitting process then necessarily reproduces that correction in the output. In that sense, the “prediction” is already built into the assumptions.

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The Scale of the Difference

The discrepancy between Newtonian and relativistic gravity in planetary systems scales as $(v/c)^2$, where $v$ is orbital speed and $c$ the speed of light. For planets, this factor is on the order of $10^{-8}$. For Mercury, this small correction accumulates to a measurable precession of tens of arcseconds per century.

Thus, Newtonian gravity on its own is nearly correct, but not quite enough at the precision required by modern astronomy.

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Where This Leaves Us

Einstein’s explanation of Mercury’s precession remains a brilliant achievement, and the relativistic correction is essential in practice for high-precision orbital mechanics. But the way this correction is incorporated — as a fixed add-on formula — raises philosophical questions about whether the evidence is purely predictive, or partly circular.

Meanwhile, the deeper crisis in modern physics lies not with Mercury, but with the still-unresolved incompatibility of GR and QM. Newtonian gravity fits comfortably with quantum theory, while Einstein’s does not. That unresolved tension suggests that even the celebrated successes of GR may not be the last word on gravitation.

In practice, modern ephemeris models include a fixed relativistic correction of 42.98 arcseconds per century for Mercury’s perihelion advance. When the model is fitted to observational data, the same correction naturally appears in the output — 42.98 arcseconds.

This raises a subtle point. The apparent “prediction” is not generated afresh each time; it is the direct result of including a predetermined correction in the equations. In that sense, one might argue that the success is partly built in from the start.

It is also worth noting that the scale of the relativistic correction matches the expected order of magnitude: the relative difference between Newtonian and relativistic gravity scales as $(v/c)^2$, where $v$ is orbital speed and $c$ the speed of light. For planetary orbits, this ratio is about $10^{-8}$. A precision of 1 km in Mercury’s orbital radius corresponds to a relative error of the same order, $10^{-8}$.

Thus, while General Relativity undeniably improves the precision of planetary models, the evidence for its superiority over Newtonian gravity in the specific case of Mercury’s precession is open to philosophical scrutiny. The possibility of a circular argument — where the correction put in is exactly the correction that comes out — cannot be ignored.

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References

• Einstein, A. (1915). Explanation of the Perihelion Motion of Mercury from General Relativity. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften.

• Le Verrier, U. J. (1859). Théorie du mouvement de Mercure. Comptes Rendus de l’Académie des Sciences de Paris.

• Will, C. M. (2014). The Confrontation between General Relativity and Experiment. Living Reviews in Relativity, 17(4).

• Folkner, W. M., Williams, J. G., Boggs, D. H., Park, R. S., & Kuchynka, P. (2014). The Planetary and Lunar Ephemerides DE430 and DE431. Interplanetary Network Progress Report, 42-196.

• Pitjeva, E. V., & Pitjev, N. P. (2013). Relativistic Effects and Dark Matter in the Solar System from Observations of Planets and Spacecraft. Monthly Notices of the Royal Astronomical Society, 432(4), 3431–3437.

 

Was Einstein Right, and Newton Wrong?

Modern physics is based on Einstein's theory of Gravitation EG presented in 1915 as the subject of Einstein's General Theory of Relativity GR replacing Newton's theory of Gravitation NG presented in Principia Mathematica 1687.

NG offered a mathematical model of simple form allowing efficient computational simulation of all interaction between matter/mass and gravitational force, which forms the macroscopic world. The success was complete and Newton was crowned as the greatest physicist for all time to come. 

But in modern physics Newton has been dethroned by Einstein: NG is viewed to be only a simple special case of EG as the truly fundamental theory of gravitation. But the shift from NG to EG did not come easy, and when it finally became manifest in the 1960s it prepared for the present crisis of modern physics coming from an incompatibility between EG and Quantum Mechanics QM as the other pillar.

In this time of crisis, it is natural to reconsider the reasons for making the shift from NG to EG, since there is no incompatibility between NG and QM.

If we ask for the strongest evidence of superiority of EG over NG, which is directly connected to the basic interaction between matter and gravitation, we find the following main pieces:

1. Precession of the perihelion of Mercury.
2. Detection of gravitational waves from merger of binary stars by LIGO. 

Einstein presented 1 in 1915 in support of EG before NG as a correction of a Newton prediction of of a slight shift of the orientation of the elliptic orbit of Mercury around the Sun over a century based on a simple analytical formula for an idealised GR model of Sun-Mercury amounting to 0.0033% of a whole revolution. Newton gave 531 arcseconds as effect of other planets (computed by Le Verrier 1869), while observed was 574 arcseconds and GR giving the missing 43. Einstein knew that 43 was missing, and was left without breath when his idealised Sun-Mercury gave exactly 43. A true miracle, but science is not about miracles.

The surge of GR after 1960 required a new evaluation of 1. which is described in the book Was Einstein Right? by Clifford Will: 

• In 1966, observations of the Sun by Dicke and Goldenberg started a vigorous debate over the validity of Einstein's perihelion prediction that raged for almost 20 years. 

Today this debate is forgotten and the official truth is that Einstein was right concerning 1, but the debate can restart any time. 

Concerning the weight in favor of EG from 2, note that the change of spatial scale from proposed cause (merger of stars) to detected LIGO signal, is a factor $10^{-22}$ that is 0.0000000000000000000001 which is many factors too small to represent credible scientific evidence.

The main evidence presented that EG is superior to NG as concerns interaction of matter and gravitation is thus very weak. The question posed by Clifford Will still has lots of reason.

Recall the EG is today also supported by claims that light rays are being bent by strong gravitation. But such effects are outside NG which only speaks about interaction matter-gravitation, which does not include massless light. 

Altogether, the evidence that EG gives a fundamentally better description of matter-gravitation interaction than NG, seems to be very weak. So weak that Newton can retain his position, which would help modern physics out of crisis. 

Credibility Crisis of Western Politics and Modern Physics as Miracles

The Untergang des Abendlandes (Decline of the West) predicted by Oswald Spengler in two volumes 1918-22 can now be seen as an erosion of credibility of not only political leadership but also of science and then in particular of modern physics based on Einstein's Equation EE and Schrödinger's Equations SE extending classical physics based on Newton's Equation NE and Maxwell's Equations into new physics. 

The erosion of credibility of modern physics is the essence of the crisis of modern physics of today as a basic expression of Decline of the West from a position of total success of modern physics with the atomic bomb. The crisis is rooted in an incompatibility of EE and SE, which means that modern physics in some fundamental way is "wrong" in the sense of not describing real physics, and the credibility of a physical theory which does not describe real physics cannot be maintained. 

The official picture, which is now loosing credibility, is:

• Einstein's theory of gravitation based on EE (General Relativity GR) is superior to Newton's theory based on NE and so represents an enormous advance of science. 
• NE is simply a simplified version of EE, which is the correct complete theory far superior to simple NE. 

To back this official picture some sparse evidence has been presented supposedly showing that EE describes physics better than NE, and a key such piece of evidence is the anomalous precession of the perihelion of Mercury:

• The orientation of the elliptical orbit of Mercury around the Sun is observed to turn 5574 arcseconds per century, which is 0.0043 of a full turn (small).
• 5000 out of 5574 are explained as an effect using an Earth-based reference system for  Sun+Mercury.
• Effects from the other planets according to NE gives 531.
• Analytical solution of EE for Sun+Mercury explains the missing 43 to give the observed 574.    

The message is that NE without EE including all planets is wrong (531), but when corrected by EE for Sun-Mercury (43) becomes right (574), and miraculously so since no full solution of EE with the other planets is performed, because this is computationally impossible due to the complexity of EE.

This miracle, which Einstein performed in 1915, is thus to present a solution of EE with all planets (and other effects) included which exactly fits with the observed 5574, without solving EE computationally because that was (and is) infeasible. 

The miracle is repeated today, which is evident from the fact that the EE correction to NE is still taken from the same analytical solution of Sun+Mercury used by Einstein (42.98). 

But what makes science different from black magic is that in science there are no miracles. To present science as miracle erodes credibility of science, which is what we are watching. 

Credibilty could be maintained if full solutions to EE gave 5574 in accordance with observation, but this is not what physicists deliver. Instead they offer a small EE correction to NE as the main computable model and work horse. To give EE the leading role over NE is like claiming the tail wags the dog.

Misconceptions about Newton vs Einstein: Crisis!

Modern physics in a state of deep crisis which comes to expression in the complete adoption of Einstein's Theory of Gravitation EG as replacement of Newton's Theory Gravitation NG as the most successful theory of all of classical physics. Modern physicists decided to take this step after the death of Einstein in 1955 under pressure to come up with something new after the success with the atomic bomb started to fade, based on the following arguments:   

1. NG is a "simplified version" of EG as a "limit" under low-speed and weak-field conditions. 
2. EG is thus "more fundamental" than NG. 
3. NG is "wrong" in certain extreme cases outside its (incredibly vast) area of validity, where EG appears to be "right".
4. Whatever success NG has is also a success of EG, since EG includes NG. 
5. In short: It is necessary to replace NG by EG, even if NG is used in all cases of any practical meaning. 

Let us now take a step back and see if 1-5 makes any sense. Let us start recalling that NG and EG has fundamentally different ontology or real physics:

• NG is based on Poisson's Equation based on the assumption that gravitational force is conservative (work independent of path) and conservation (no force out of nothing or into nothing). NG has a simple mathematical form and appears to cover all gravitation of some real (practical) meaning. The greatest success of mathematical modeling.  
• EG is based on a principle of curved space-time replacing gravitational force where the physics is hidden in very complicated mathematics.
• NG and EG thus have fundamentally different physical meanings, which means that NG is not a special case of EG.  

This means that the success of NG is not also a success of EG. It is necessary that EG stands on its own merits. But EG is uncomputable in all cases of practical meaning, which means that EG has very little merits of its own. 

In short: The step taken by modern physicists to replace NG by EG lacks scientific rationale and so adds  to the credibility crisis of modern physics acknowledged by prominent physicists. But there is no reason physics should be in a state of crisis, since there are so many new possibilities opened in particular by computation. A first step out of the crisis is to put NG first and view EG as fringe science without real scientific interest. This will be a relief to both educators and students giving room for real understandable physics.

If you still believe that Einstein should replace Newton, recall

• Observations of apparent instant-action-at-distance agree with a fundamental aspect of NG.
• Gravitational force with time delay as fundamental aspect of EG, requires tricky compensation/fix to agree with observations. 
• NG is computable in general. EG is uncomputable except possibly in some very special cases. 
• NG is based on fundamental physical principles of simple mathematical form. EG has very complicated mathematical form with unclear physical meaning.
• NG says nothing about possible aberration of light or gravitational lensing, since light is massless. If light is affected by gravitation, it is a matter for Maxwell's equations.  
• GPS satellite clocks are offset at launch to compensate for time dilation in EG,  but the offset is over-run by continuous synchronisation to an Earth-based master clock, and so does not show that EG is correct and NG wrong. 

Hopefully, this can start a discussion comparing the scientific merits of NG and EG. Input?

The Deep Truth about Newtonian Gravitation

Newton's model of gravitation is Poisson's Equation: 

• $\Delta\phi (x,t)=\rho (x,t)$        (PE)

where $\rho$ is mass density, $\phi$ is gravitational potential depending on a 3d Euclidean space coordinate $x$ and a time coordinate $t$. It is the most remarkable mathematical model of all of classical physics allowing precise computational simulation/prediction of effects of gravitational forces in complex systems, as demonstrated in the Millennium Run tracing the evolution of the matter distribution of the Universe over 2 billion light-years using 10 billion particles interacting by (PE). There is massive evidence that (PE) captures gravitation to experimental precision in all cases of any practical interest. 

In the modern phyics of today PE has been displaced from 1st to 2nd place by Einstein's Equation EE, despite the fact that PE covers all cases of practical importance. 

This degradation of PE took a long time become the official truth of modern physics. Einstein presented EE in 1915 which was met with criticism as non-physics in a form of complicated mathematics, and it was only after Einstein's death in 1955 that EE gradually came to replace PE as the true model of gravitation of modern physics. 

The key argument used to put PE into 2nd place was that PE could be viewed to require instant-action-at-distance in the sense that a change of $\rho (x,t)$ at a certain point $x$ at time $t$ would instantly affect the value of $\phi (y,t)$ for all points $y$, since (PE) as a differential equation in space represents $\phi$ in terms of $\rho$ in terms of a global summation process according to the formula with the same $t$ on both sides, thus without time delay:

• $\phi(y,t)=-\frac{1}{4\pi}\int\frac{\rho (x,t)}{\vert x-y\vert}dx$ 

Since instant-action-at-distance appeared to be in conflict with Einstein's Special Theory of Relativity SR, which was accepted before his General Theory of Relativity with EE, leading physicists decided to displace PE to 2nd place in modern physics.  

Let us now take a fresh look at (PE). We see a linear partial differential operator with constant coefficients as the Laplacian $\Delta$ connecting $\phi$ and $\rho$ which can be viewed in 3 ways:

1. Differential equation $\Delta\phi =\rho$ with $\rho$ as cause and $phi$ as effect derived by global integration.
2. Specification $\rho =\Delta\phi$ with $\phi$ as cause and $\rho$ as effect derived by local differentiation. 
3. Simply a coupling of equal parts without cause-effect.   

Here 2 corresponds to local-instant-action which is compatible with SR, if that is the concern.

Here 3 connects to the Pre-Established Harmony of Leibniz as a Deep Truth. It means that $\phi$ and $\rho$ are locked to each other with the Laplacian as a linear relation of simple mathematical form the same everywhere. Such a relation can be read without causation as in 3 and then in particular without demand of instant-action-at-distance. It also makes sense from computational point of view since the computational complexity of (PE) scales linearly with number of spatial mesh points. 

In discrete form (PE) takes the following form in 1d with $dx$ a space step:

• $\phi (x+dx,t)-2\phi (x,t)+\phi (x-dx,t)=dx^{2}\rho (x,t)$ 

locking $\phi$ to $\rho$ at common time $t$ by a simple linear relation which can be read both ways. 

The basic idea of 3 is explored in many posts on New View of gravitation and New Newtonian Cosmology

Let me list virtues of (PE) and Newton motivating back to 1st with (EE) and Einstein 2nd:

• Generality.
• Simplicity.
• Minimal computational complexity.
• Compatibility with Quantum Mechanics.
• Understandable to a wide audience.

As a young patent clerk in Bern in 1905, Einstein took on a role to overthrow principles of classical Newtonian physics at the same time cubism and atonal music emerged as challenges to classical painting and music. This was the emergence of modernity at the turn of the century triggered by an explosion of new technology. Today we see a return to tonal music and figurative painting as post-modernity, and so a return of Newton may also take place after an aberration into Einstein.

Newton vs Einstein: Gravitational Self-Interaction

Newton's model of gravitation is Poisson's Equation: 

• $\Delta\phi (x,t)=\rho (x,t)$        (PE)

where $\rho$ is mass density, $\phi$ is gravitational potential depending on a 3d Euclidean space coordinate $x$ and a time coordinate $t$. It is a linear equation without self-interaction in the sense that there is no feed back from $\phi$ to itself, only input from $\rho$. 

Einstein's model is Einstein's equation:

• $G_{\mu\nu}=T_{\mu\nu}$               (EE)

stating that space-time curvature $G_{\mu\nu}$ equals stress energy $T_{\mu\nu}$, which is a coupled system of 10 non-linear partial differential equations for the components $g_{\mu\nu}$ of the metric tensor. This is a system with self-interaction. 

Formally (EE) reduces to (PE) in a limit of weak gravitation, low speed and slow variation in time, which covers all cases of practical importance. 

Physicists have agreed to view (EE) as the fundamental model and (PE) as a less fundamental reduction of (EE) covering all of practice.

But it is possible to shift perspective and view (PE) as fundamental covering all of practice and (EE) as a less fundamental extension covering certain extreme cases beyond practice, like collision of two black holes. 

So which is more fundamental (PE) or (EE)? Consider the following features of (PE) not shared by (EE)

• Simplicity of mathematical form including linearity without self-interaction.  
• Computable at low cost.
• Covers all of practice in low cost computation. 

We now ask if these features including in particular linearity without self-interaction, can be viewed to be fundamental? And lack thereof as non-fundamental?

Well, a system with self-interaction runs the risk of blow-up or extinction, which for the Universe would be catastrophic. 

Recall that there is no self-interaction in Schrödinger's equation of Quantum Mechanics, while there is in Quantum Field Theory which creates blow-up infinities as non-physics. 

Summary: PE appears to be more fundamental than EE. Thus classical physics appears as post-modern physics after a deviation into EE of modern physics 

   

 

A Modest Proposal to Solve the Crisis of Modern Physics

Modern physics is in a state of deep crisis because the two new theories vs classical physics of General Relativity GR and Quantum Mechanics QM, are incompatible and so cannot be combined into a Unified Field Theory UFT of modern physics. Without a UFT the whole project of modern physics as fundamentally different from classical physics is shaky, because in some fundamental way it must be wrong. 

Einstein struggled for 40 years after presenting GR in 1915 into his death in 1955 to form a UFT including GR and electromagnetism/QM, but was never close to anything of value. Nobody was more successful. UFT is still only wishful thinking. 

GR is today viewed as a more fundamental theory of gravitation than the classical theory of Newtonian Mechanics NM, but for all practical purposes NM is still the theory being used and so with an amazing success. GR is reserved for certain imagined extreme cases such as merger of black holes believed to be outside NM. And NM is fully compatible with QM, which suggest the following resolution of the crisis of modern physics:

• Form a UFT = NM + QM which covers all cases of practical interest. 
• Keep GR as an esoteric variant of NM as a model of some very extreme cases.

This would mean a step back from the novelty brought by modern physics, as only a fashion with little lasting value. This would be a relief for both physicists, students of physics, users of physics, and laymen confused by GR. Moreover GR could be kept as a fetish of modernity as a source for imagination. 

A step back into classical physics can be made also for QM in the form of RealQM as a model of atomic physics formulated within classical physics. 

It is thus possible to form a UFT as NM + RealQM as a fully compatible model of both macro and micro-physics within a setting of classical continuum mechanics/physics. This would be an expansion of classical macroscopic physics into the microscopics of atoms using the mathematics of classical continuum mechanics in the form of partial differential equations of the same form for macro- and micro-physics in terms of fields as functions of 3d Euclidean space variables plus a time variable. 

The conceptual form of such UFT would be the same on all scales, which would open to an understanding of micro-physics in terms familiar from macro-physics. It would be a post-modern physics as a renaissance of classical continuum physics with now the continuum covering all scales for which purpose it is ideally suited. This form of UFT would be computable since the scaling would be polynomial in resolution in space and time, and not exponential as standard QM. 

It would be interesting to hear what a professional modern physicist could have to say about the possibility of a UFT = NM + QM or more precisely UFT = NM + RealQM. Here is what chatGPT has to say:

• NM + QM covers all practical cases, so it functions like a UFT for the real-world problems most people deal with.

We know that there can be many different mathematical models of physical phenomena, like NM and GR for gravitation, and the usefulness may be what determines the choice of one model as the more fundamental. For example, it is possible to choose the Earth to be the center of the Universe around which everything evolves in circles upon circles like in a very complicated Aristotle model, but it has not shown to be very useful and so has been replaced by non-geocentric NM as being more fundamental because it has shown to be more useful. 

Thus fundamental can connect to usefulness. It is thus possible to view NM as a fundamental model covering everything which is not extreme, with GR as an extension into the extreme. Modern physics has concentrated on the extreme to single out from classical physics of the non-extreme. Modern physics thus  offers to make the extreme into new normality (GR for black holes), while post-modern physics could offer to capture new normality (QM) into classical normality.   

The Tragedy of Modern Physics 1

Modern physics is in a state of crisis with its two basic novelties vs classical physics, General Relativity GR (1915) as macro-physics and Quantum Mechanics (1925) as micro-physics, impossible to reconcile into one unified theory, despite major efforts by all leading physicists over now more than 100 years. The Standard Model of QM does not include gravitation as the essence of GR. No way out of the crisis is visible. It is a veritable tragedy compared to the tremendous success of classical Newtonian Mechanics NM as description of all of macro-physics.  

The logical conclusion is that at least one of the theories will have to be given up in order to find a way out of the crisis. GR or QM? 

GR has to compete with NM as concerns macro-physics including astronomy and cosmology, while QM has no classical physics to compete with. We are thus led to focus on GR and ask what would be the price of giving up GR as failed project and so go forward with a unified theory of NM + QM? 

Yes, NM+QM fits very well together and so let us consider why modern physicists are taught to view GR as a necessary replacement of NM. 

The basic mathematical model of GR is Einstein's Equations EE and that of NM is Newton's Equations NE. A modern physicist or text-book of today will tell you:

1. EE is a more fundamental model of gravitation than NE. 
2. In all cases except some very extreme cases including things like black holes, NE is the model used in practice since NE is readily computable in any thinkable geometric complexity, while GE is impossible to compute except in very simple geometry allowing analytic solutions.
3. EE have a very complicated mathematical form understood be few, while the structure of NE is clear and simple understandable by everybody. 
4. NE requires instant-action-at-distance, which cannot happen and is not part of EE. Therefore NE has to be replaced by EE.

Here 4. is the key argument to give up NE as fundamental model and replace it by EE. In many posts on New View on Gravitation, I show that it is possible to get around the apparent requirement of instant-action-at-distance in NE. This is to view the connection between mass density $\rho$ and gravitational potential $\phi$ captured in the Poisson Equation PE $\Delta\phi =\rho$ in a new way, not the old way with mass density primordial and gravitational potential formed by apparent instant-action-at-distance, but viewing instead $\phi$ as primordial from which $\rho$ is formed by the action of the differential operator $\Delta$ which acts locally and so can be instant. 

With this change of view the trouble with instant-action-at-distance does not appear and NE can be kept as the greatest success of all of physics to do all its wonders, and there would be no reason to replace it with anything, and in particular not by EE. 

The supremacy of EE over NE was not adopted as a fundamental principle of modern physics until the 1960s because the mathematics was difficult and the physics was strange. Few physicists claim to understand EE in any detail, and even fewer to be able to compute solutions to EE.  

Here are the alternatives at hand:

1. Keep EE and live with the facts that GR and QM are incompatible, and that EE is uncomputable and so use NE for all practical purposes. Claim that EE does not require instant-action-at-distance.
2. Keep NE and welcome that NM and QM offers a unified theory. View gravitational potential in PE as primordial before mas density and so circumvent formal requirement of instant-action-at-distance. Use EE for some very extreme cases which are beyond experimental verification 

The slow acceptance of GR signifies that it came with many doubts and questions, which however over time have faded away and so have allowed to make GR into a dogma of modern physics to be accepted even if impossible to make sense of for a fresh young rational mind. Since GR is replaced by NM in all cases of practical significance, genuine GR results are lacking which makes it impossible to show that they are incorrect. 

Which of the above alternatives 1 or 2 would you choose, if you had a free choice as a rational being? Which price, 1 or 2, would you prefer to pay?

Free Fall is Not Fall in Zero-Gravity Space

Einstein presented in 1905 his Special Theory of Relativity SR as a theory about inertial motion as motion without presence of force/acceleration, in particular without gravitation coming with gravitational force. This was a theory of extremely limited scope, which was met by skepticism or indifference by the physics community 

As patent clerk at the Swiss Patent Office in Bern, Einstein had lots of time for "thought experiments" and one day in 1907 he had the "happiest thought in his life" imagining himself in a seemingly "weightless state" trapped inside an elevator in free fall. Forgetting that this state would not prevail for long, with certainly an unhappy ending, Einstein concluded:

• A body in free fall is the same as a body in zero-gravity space.      (E)

Armed with this insight Einstein was ready in 1915 to extend SR without gravitational force to his General Theory of Gravitation GR as a theory including gravitation without gravitational force. Bingo!

We now connect to the last sequence of posts about a Universe with Newtonian gravitation consisting of bodies with mass all under free fall, like planetary systems, binary stars, galaxies and super-clusters of galaxies as expressions of large structure determined by gravitational forces alone.

We are thus led to question the physics of (E): A body in free fall is not a body isolated from gravitational force, but instead a body free of other forces than gravitational force.  

To make sense of (E) Einstein was driven to an idea of "curved space-time" where a body in free fall without presence of gravitational force would follow "geodesics in curved space-time" as shortest paths, which would correspond to the curved trajectories in Euclidean space followed by bodies in free fall under gravitational force.  

GR was also met with skepticism, which however miraculously disappeared after Einstein's death in 1955, and today is viewed as the greatest triumph ever of modern physics over classical physics. But (E) has no more reason today than in 1915, and so gives a major contribution to the present crisis of modern physics.  

In Newtonian mechanics the mass of a body is gravitational mass, which is classically measured by a balance scale vs a reference mass. This captures the additive aspect of mass with the mass of a body as the sum of the masses of the parts of the body. This is clear and simple. 

In GR without gravitational force the concept of mass is very complicated and so unclear. Einstein is often portrayed as very unhappy in his later life, as the true final consequence of his "happiest thought"  from 1907.

Mass as Gravitational Mass

Recent posts discuss the concept of mass concluding that gravitational mass appears to be primordial from which inertial mass is derived. The idea is to start with a Universe defined in terms of a gravitational potential $\phi (x,t)$ depending on a Euclidean space coordinate $x$ and a time coordinate $t$ as created in 3 steps:

1. The gravitational potential creates a mass density $\rho (x,t)=\Delta\phi (x,t)$, where $\Delta$ is the Laplacian differential operator acting instantly as a local operation in space. 

2. Mass is subject to free fall according to Newton's equations of motion subject to gravitational force $\nabla\phi (x,t)$. 

3. Redistribution of mass under free fall gives feed-back to gravitational potential.

We thus find a Newtonian Universe determined by gravitational free fall connecting motion of mass in space to gravitational force and so equating inertial mass to gravitational mass. This is a large scale in a sense complete Universe with a precise simple mathematical description, which can be complemented by electromagnetics without interference with gravitation on both macro-scale and atomic micro-scale into the Universe we can see and experience.  

Modern text-books tell another story with mass appearing as (i) gravitational mass, (ii) inertial mass, (iii) rest mass and (iv) Higg's mass, all of different nature, which is is very confusing and lacks reason.  

It seems to be more reasonable to define mass as gravitational mass, which is the operational definition according to SI 2019 standard of units, and then connect other expressions of mass to this standard. 

On the other hand, the formal presence of mass $m$ in the coefficient $\frac{h^2}{2m}$ of the Laplacian in Schrödinger's Equation SE , with the mass of a proton 1836 times that of an electron, is not connected to gravitation and free fall motion.  Instead $m$ here serves as a parameter to determine spatial size, with thus a proton having smaller size than an electron in an atom.  

Different concepts of mass in modern physics.

 

Mass of Many Different Forms and Origins

I have been led to the idea that there is in Newtonian mechanics only one form of mass, gravitational mass, which is derived from a gravitational potential as primordial, wit inertial mass = gravitational mass as a consequence of universality of free fall and conservation of energy. This is a clear picture, which can be understood by everybody, and which has shown to work excellent in practice. 

This is not the idea of modern physics, which plays with several different forms of mass:  

• gravitational mass
• inertial mass
• rest mass (relativistic)
• Higgs mass. 

with different origins:

• gravitation
• Higgs mechanism and strong force
• relativity theory
• Higgs mechanism.

No doubt this shows a very complex picture and the questions pile up: Why so many different forms with different origins and why then is an Equivalence Principle adopted stating that inertial mass = gravitational? 

• Warum es einfach machen, wenn mann es so schön kompliziert machen kann?

  

Inertial Mass = Gravitational Mass?

This is a continuation of previous posts on operational definition in SI 2019 of mass as gravitational mass. 

In Newton's mechanics inertial mass is exactly equal to gravitational mass as an expression of both (i) universality of free fall and (ii) conservation of energy.  A Universe without (i) and (ii) cannot exist.

In Einstein's mechanics this truly fundamental equality is no longer guaranteed by (i) and (ii), but has to be added as an independent Equivalence Principle EP, which has to be supported by experimental evidence. Accordingly major efforts have been made to find ever more precise experimental confirmation, where the current precision is $10^{-15}$, while new experiments are receiving funding to reach even better precision: 

✅ Best Precision to Date:

• Experiment: MICROSCOPE (CNES, ESA)

• Method: Differential accelerometry in space (free-falling test masses of different materials)

• Result: Difference in acceleration between test masses of different compositions was less than 2 parts in $10^{15}$.

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🚀 Future Target Precisions:

1. Galileo Galilei (GG) satellite – proposed

   • Target: $10^{-17}$

2. STE-QUEST (atom interferometry in space) – proposed

   • Target: $10^{-17}$ (depending on mission configuration)

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To a classical physicist these experiments are similar to precise testing of the validity of the equality 1+1 = 2. 

Einstein presented his Special Theory of Relativity SR in 1905 in a desperate effort to get a university position, and followed up in 1915 with his General Theory of Relativity GR in a desperate attempt to keep the position he managed to get in 1909 under severe criticism of SR. 

Einstein thus took on the role of challenging Newton's mechanics by connecting it to propagation of light which was not mechanics, and by assuming EP as a fundamental postulate of GR as a step away from Newton's mechanics.

Despite severe criticism of both SR and little acceptance of GR before his death in 1955, today Einstein is the undisputed hero of modern physics as the man who showed that Newton was wrong and so opened the door to all sorts of new physics desperately needed after the success of the atom bomb in 1945 had faded.   

How to Measure/Define Mass

This is a clarification of the previous post showing gravitational force without need of force carrier.

An instrumentalist definition of a certain quantity like mass depends on how the quantity is measured by a certain specified instrument. 

According to the SI 2019 system of units, mass $m$ is determined by a Kibble balance from gravitational force $mg$ measured as electromagnetic force, where $g$ is the local gravitational constant. 

We conclude that according to SI 2019 mass is gravitational mass as reaction to gravitational force. In other words, gravitational force as gradient of a gravitational potential is primary from which mass is derived as secondary as measured by a Kibble balance. 

This suggests that the relation between mass density $\rho (x)$ and gravitational potential $\phi (x)$ should be viewed to have the form, with $x$ a Euclidean 3d space coordinate and $t$ a time coordinate: 

• $\rho (x,t) = \Delta\phi (x,t)$           (1)

with $\phi (x)$ given and $\rho (x)$ derived by application of the differential operator $\Delta$ acting locally, rather than the standard form: 

• $\Delta\phi (x,t)=\rho (x,t)$,             (2)

with $\rho (x)$ given and $\phi (x)$ derived as solution to Poisson's equation as a differential equation.

We can view (1) as local instant action by differentiation, while (2) requires instant action at distance as integration/summation. 

By adopting (1) as the true connection between gravitational mass and gravitational potential, which fits with SI 2019 and is explored in many posts, we can thus circumvent to need of instant action at distance, which has been viewed as a stumbling stone for Newtonian mechanics, motivating Einstein's relativistic mechanics coming with many new difficulties.

Adopting (1) we thus (i) adhere to SI 2019, (ii) circumvent instant action at distance and (iii) do not need Einstein,  as a hat trick. 

In Newtonian mechanics inertial mass is defined as gravitational mass and their equivalence is not an assumption or Principle as in Einstein's mechanics. 

In the Standard Model, mass is not defined as gravitational mass as in SI 2019, but as an intrinsic quality/property carried by matter, which is formed in a very strange way by the Higg's mechanism. 

Altogether, mass as gravitational mass, appears as a very useful concept. It makes sense to define mass as gravitational mass, because gravitation is present virtually everywhere. A special feature is that free fall as motion under gravitational force, without presence of forces of other nature, is independent of the size of the mass, which defines mass as a form of sensitivity to gravitation which is additive: The mass of two particles of the same kind is twice that of one particle. 

But this is not how a modern physicist approaches the problem of defining what mass is and how to measure it. A modern physicist is trained to believe that mass according to the Standard Model is defined by QFT through the Higg's mechanism, and then connected to gravitation by General Relativity GR. The trouble is the QFT and GR are incompatible and so the mass problem is a mess problem. 

Force Carriers of Modern Physics without Meaning

 The Standard Model SM as the crown jewel of modern physics divides the World into:

• matter particles (fermions)
• force carriers (bosons) of different forms:
• photons for electromagnetic force
• W and Z bosons for weak nuclear force
• gluons for strong nuclear force 
• (gravitons for gravitational force, hypothetical not detected)  

A major short-coming is that SM does not describe gravitation, because the graviton as force carrier has not been identified/detected, while the other force carriers are claimed to have been detected in particle accelerators. 

ChatGPT admits that the whole idea of force carrier or mediator of force by exchange of bosons, may be wrong in the sense that this is not how physics really works. The fact that the idea does not work for gravitation, may indicate that it is an illusion that it works for the electromagnetic and weak/strong forces. Another troubling aspect is that mediation by force carriers come with questions about finite speed of delivery, since infinite speed is hard to imagine. 

Classical physics does not include any concept of force carrier, because it has no role to play. Forces in classical physics can be viewed to come in two forms:

• Potential forces as spatial gradients of potentials instantly delivered locally. Gravitational and electro-magnetic forces are derived this way from electro-magnetic and gravitational potentials. 
• Contact forces also instantly delivered locally in space. Elastic forces in an elastic solid have this form. 

These forces need no force carriers since forces act locally in space without time delay, and so there is no issue with action at distance asking for some form of force carrier. It is thus possible to view the apparent instant action at distance of gravitational force as a misconception since the force is in fact delivered locally by a potential with instant delivery. This is the theme of many posts.

It is thus possible to describe electro-magnetic and gravitational forces without force carriers and then circumvent the apparently unsolvable problem of instant action at distance deeply troubling SM. 

RealNucleus presents a model of an atomic nucleus in terms of only electro-magnetic force. 

Summary:

The fundamental component of SM of force carrier raises several questions:

• How is the force carried and by what?
• How quick is the delivery of force over distance?
• Why is there no force carrier for gravitation?
• How is electro-magnetic force carried by photons? 

Coupled with the fact that there may be no need of force carrier at all, since force is always delivered locally instantly, like no need of surface mail when there is instant email, it may seem better to eliminate it from the discussion altogether as only a novelty without lasting value invented by a modern physics in desperate need to deliver new physics. 

18th century Stangenkunst (system of linked rods) as carrier of mechanical force over long distance.

PS ChatGPT informs us: 

• The concept of force carriers was introduced out of necessity when physicists tried to extend classical ideas to the quantum world. It arose to explain how particles interact in a way consistent with both quantum mechanics and special relativity.
• The carriers of the electromagnetic force are virtual photons which are internal lines in Feynman diagrams. The were introduced to get around the contradiction between instant-action-at-distance and special relativity, which however does not arise since instant-action-at-distance has no role to play as we saw above.

There is thus no need of any virtual photons and so we do not have to worry about the physical meaning of lines in a Feynman diagram. The basic idea of RealQM is that there is no conceptual difference between macroscopic and microscopic physics, that is that the quantum world is not fundamentally different from the world we live in. If this is indeed the way things are, it will make the atomic world easier to understand and then to manipulate.   

Modern Physics as Extreme Physics in Simple Geometry

Modern physics can be described as the physics of the extreme, while classical physics concerns the normal non-extreme. The atomic bomb is an ultimate expression the extreme. Powerful particle accelerators force subatomic particles such as protons, electrons and heavy nuclei to smash into each other at extremely high speeds creating a spray of other particles collected in detectors, with the objective of discovering the inner structure of the particles which are smashing. It is similar to seeking to discover the inner structure of a Swiss clock or human cell by smashing it with a powerful hammer.

Einstein's Equations EE are presented as a more accurate/fundamental model of gravitation than Newton's Equations NE, and the evidence is picked from cases of very strong gravitation such as mergers of black holes, which can be described as extreme cases with simple geometry allowing solutions to EE equations to be determined, more or less. 

However, evidence that EE is a more accurate model of gravitation than NE for normal cases of classical physics such as planetary systems, which can be described as normal cases with complex geometry for which NE works fine, is missing because in such cases EE are uncomputable and thus cannot be inspected and compared with NE/observation. 

The argument appears to be that if a model works in an extreme case, it should work also in a non-extreme case, but it is not really valid here because the extreme case has simple geometry allowing solutions of EE to be constructed, more or less, while the normal case has complex geometry, which can be handled by NE. 

EE is presented as one of the two major achievements of modern physics as a more accurate/fundamental model of gravitation than NE, but this cannot be demonstrated in the vast majority of normal cases, because EE is uncomputable in complex geometry. 

The other major achievement of modern physics is quantum mechanics based on Schrödinger's equation SE with extensions as QED and QCD underlying the Standard Model of fundamental particles of spatial scale down to $10^{-18}$ m. But SE is uncomputable for normal systems with complex geometry just as EE, which has led physicists to shift focus to string theory of scale $10^{-32}$ m as an expression of ultimate extreme physics in simple geometry. 

Modern physics thus has come to concentrate on extreme physics in simple geometry, in an attempt to distance itself from classical physics of the normal in complex geometry, which covers the majority of cases. No wonder that modern physics is in a state of crisis.  

Extreme physics in simple geometry

  

Human Protein Atlas: Normal physics in complex geometry