Why Newton was Replaced by Einstein, and Back

Newton's Inverse Square Law NL was until the 1960s the prime example of the power of mathematical thinking visible to everybody: All of celestial mechanics can be described and computed from NL  necessarily valid from principles of conservation in any existing Universe. 

What happened in the 1960s was that Einstein's General Theory of Relativity GR, presented already in 1915, finally was adopted to serve as one of the two pillars of modern physics (the other one Quantum Mechanics QM) and so replace Newton the icon of classical physic by Einstein as icon of modern physics. 

But this transition took place only after Einstein's death in 1955, because of the very complex mathematics of GR understood by few if any making it useless in any from of practical physics. 

However in the propaganda of the cold war it served well to strengthen the world dominance of US science formed by physicists imported from Germany during WWII inventing the atom bomb. Replacing Newton by Einstein served as a demonstration of power, and all the earlier skepticism to GR could be put under the rug. And of course the Sovjet Union followed. Einstein was put in first place, but only after his death since during his life time he appeared as an "absent-minded eccentric maybe too fond of fame". 

Today the cold war is back, Einstein is still on top of the list of fame, while the rapidly developing technology of warfare is using Newton to come to expression. 

There is only an homage to Einstein GR left as an initial offset of satellite clocks in the GPS system, which in operation is annihilated by continuous synchronisation to a master clock on Earth. 

Maybe there is reason to return to a new critical analysis of Newton vs Einstein without the fame dominating the discussion.  

The discussion could start comparing Newton's absolute space against which Einstein's relative space took stand. 

Is it true that Newton's theory of gravitation needs a notion of absolute space against which absolute velocity can be measured? Does Newton say that velocity is absolute? Certainly not! Nobody would come up with such an idea. Of course velocity of an object is always measured relative to something else.

So Newton says that velocity is relative. On the other hand Newton says that rotation as accelerated motion is detectable by forces of tension arising from acceleration. Newton's rotating bucket can thus be viewed as a form of absolute rotation which does not need any outside reference. 

Note that there is a special form of accelerated motion which is not so easily detected by presence of forces and that is free fall under gravitation where all parts of your body feel the same force and no tension arises. But that is not true for a bigger object where tidal forces occur because the gravitational force is not uniform.

So the argument that Newton says that velocity is absolute and so has to be replaced by Einstein's relativity, is not correct. The argument that Newton's theory of gravitation is a necessity in any existing Universe, is very strong. The question is if there are modern physicists willing to face this reality.

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.

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 

   

 

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.

Einstein's Equations vs Precession of Mercury

When Einstein in 1916 presented a new model of gravitation in the form of  Einstein's equations, he desperately needed evidence that his model was better than Newton's. He found this in a back-of-the-envelope computation adding precisely the missing 43 arcseconds in the extra precession of the perihelion of Mercury (slight perturbation of the rotation of the elliptical orbit of Mercury of 5600 arcseconds per century from other planets), to make the prediction by Newton's model of 531 arcseconds/century made by Le Verrier in 1859 to fit exactly with the observed 574 arcseconds/century. 

Einstein thus started from the known results of 531 by Newton and observed 574 and miraculously obtained exactly the missing 43 by a very simple computation which he claimed captured the difference between his and Newton's model.  

If we ask chatGPT about this apparent miracle we get the following information:

1. Le Verrier's 531 has been confirmed to within 1 arcsecond by modern high tech computation and precise data. This is in itself a miracle. No improvement since 1859!
2. It is impossible to directly compute the observed 574 by solving Einstein's equations including in particular the other planets, because the equations are impossible to solve both analytically and computationally. 
3. Computation always start from 531 with Newton's equations and 571 is obtained as a correction of 43 claimed to be based on Einstein's equations, even if they are impossible to solve. This is also a miracle.

To get perspective on these miracles as prime evidence that Einstein's equations are more precise than Newton's, let us note 

• 1 arcsecond/century corresponds to a relative accuracy of about $2\times 10^{-9}$ per revolution of Mercury (415 revolutions/century) if errors add up linearly. 
• Data errors cannot be expected to cancel and so may well add up linearly. 
• A precision of $2\times 10^{-9}$ is thus needed in data such as planet masses, gravitational constant G, initial data, composition of the Sun, tidal motions, other celestial objects than planets, to get the precession right to say 1 arcsecond over 100 year. 
• The gravitational constant is known to at best 6 decimal places, other data with less. 

The conclusion that the desired precision cannot be reached, cannot be avoided. There is factor of 1000 between required and available precision. Yet, the computation of the precession of the perihelion of Mercury by Einstein is still presented as prime evidence that Einstein's equations describe gravitation better than Newton and thus as an undeniable major victory of modern physics over classical physics. 

Check if this is confirmed by chatGPT after careful reading of the literature!

But at his deathbed Einstein begged: "Newton, forgive me!"

The Black Hole Of Modern Physics

Newtonian and Einsteinian Mechanics

The Universe is formed from micro-scale electromagnetics and macro-scale gravitation. The essence of modern physics, as compared to classical (Newtonian) physics, is (i) the theory of quantum mechanics for micro-scale electromagnetics/light without gravitation, and (ii) Einstein's theory (special+general) of relativity for gravitation without electromagnetics/light.  

These two theories are hailed as the greatest triumphs of human intellect all times, way beyond Newton's mechanics, but there is a caveat: Quantum mechanics is viewed to be incompatible/inconsistent with general relativity. There is no convincing theory of modern physics including both electromagnetics/light and gravitation as the building blocks of the Universe, despite the more than 100 years which have passed since (i) and (ii) were introduced. 

There is thus bitter poison in the cup of glory when modern physicists are celebrating their achievements. If (i) and (ii) are incompatible/inconsistent/contradictory, then either (i) or (ii) must be wrong. Both cannot be true. The acknowledgement by leading physicists that this is so, is then viewed to be an act of scientific heroism rather than incompetence.   

It is also admitted that there is no incompatibility/inconsistency between quantum mechanics and  (iii) Newton's gravitation, only with Einstein's gravitation (ii). It is also admitted that Newton's mechanics captures almost everything on a macroscopic scale. 

What is then the difference between (ii) and (iii), that is between Einstein's equation and Newton's equations for a mechanical system subject to gravitation? 

The quick answer is: not much! It is like putting a moustache on da Vinci's Mona Lisa, which Dali did with a simple pen stroke (+added his own eyes). Mona Lisa is a true masterpiece made by a true master, while Dali's version is a simple distortion albeit done by a genius of some sort. But an art curator may tell you that Dali's version offers a whole new view on the World, da Vinci has been surpassed.

It is the same with (ii) and (iii): Einstein's equation reduces to Newton's equation in a system without space-time curvature like the flat Universe we apparently happen to have around us. Einstein's equation is is supposed to describe some ultimate extreme case like a black hole, which however is so extreme that observation is impossible, like a true real lady with moustache never to be seen. 

To be more precise, what are the observations showing that Newton's equations have to be replaced by Einstein's? A prime example is still Einstein's correction of size 45 to the 531 arcseconds/century prediction of the very slow precession of the perihelion of Mercury's elliptic orbit around the Sun, made by solving Newton's equation including all the planets in the Solar system. Einstein thus made a small correction of about 10% to an already very small effect computed by carefully solving Newton's equations, like putting a moustache on Mona Lisa and then claiming a complete revolution of world view. Or more accurately, after modifying Mona Lisa in a way which is not observable.

Einstein computed his "correction" by hand on the back of an envelope in several attempts during the 1910s until finally getting the desired result known beforehand, while solving Newton's equations for the Solar system from scratch by hand calculation is a formidable task, of course today feasible by computer. 

Einstein thus did not solve his equation to predict the precession, because he could not and this is still the case today even with biggest possible computer. 

What is truly remarkable, is that solving Newton's equations for the Solar system within the precision offered by the uncertain values of the gravitational constant, masses/positions of planets and the Sun, gives a prediction over a century in accordance with observation. In other words, da Vinci's Mona Lisa is as perfect it can be. There is no real need to modify neither Newton's equations nor Mona Lisa!

In any case, modern physicists claim that Newton's equations have to be replaced by Einstein's equations  even if solutions differ so little that it is beyond measurement. Einstein expressed his hesitance to take this step in "Newton, forgive me". In fact, modern physicist only took this step in 1950's after 50 years of brooding. 

The question remains: Why has modern physicists driven themselves into an impossible situation with two main theories which are inconsistent/incompatible, if there is not really any good strong scientific reason to do so?  If Newton is ok also today? Why has Einstein been chosen to be the icon of modern physics, thus reducing Newton? Which were the leading physicists in the creation of this myth?  

The crisis of modern physics witnessed by leading modern physicists may be seen as the inevitable result of a contradiction originally created by a young patent clerk desperately searching for scientific recognition, and succeeding! 

The aspect of small correction beyond observation is also present in Einstein's $E=mc^2$ with the mass defect in chemical/nuclear reactions too small to measure, a formula known by everybody as a fetish of modern physics without real meaning. Einstein's physics thus concerns corrections to known physics, so very small that experimental verification invariably rises more questions than answers.

Recall that according to $E=mc^2$ fully turning 1 grain of sand (as 0.000001 of 1 kg) into energy would suffice to heat an ordinary home in Sweden one year. One grain of sand! This would be 1 billion times more efficient then burning carbon, and 100-1000 times more efficient than what can be reached in a nuclear reaction. In other words, only a very small fraction of mass is really "equivalent" to energy, and so $E=mc^2$ has little if any meaning, yet is the beacon of modern physics visible to everybody.  

Recall that the mass $m$ viewed to effectively be transformed into energy $E$ in a nuclear reaction, is computed from $m=\frac{E}{c^2}$ and then shows to be 100-1000 smaller than the total mass involved. The "equivalence" of mass and energy thus appears as a formality from assuming $E=mc^2$, which has driven modern physics into a dead-end of contradiction. If anything: mass is not "equivalent" to energy. $E=mc^2$ cannot be used to predict the energy release in a chemical/nuclear reaction, because the small fraction effectively released is hidden. 

Recall the previous post on the new 2019 SI specification of unit of mass (kg), which is explicitly based on $E=mc^2$ thus making this relation into a definition including also a specification of the speed of light $c$ to be exactly 299792458 m/s in a specification the unit of length m.

The cornerstones of Einstein's contribution to science, $E=mc^2$ and the constancy of $c$, thus appear as definitions or SI agreements, which are to be viewed to be true independent of any physical reality and as such are empty of physics in the same way that the specification that there are 100 centimeters on a meter does not say anything about reality.  

Mathematicians make a clear distinction between between definition or agreement, which cannot be false, and theorem, which can be false or true. This is expressed in mathematical text by clearly announcing Definition: and Theorem:.  

Modern physicist make no distinction between between definition or agreement, which cannot be false, and physical law, which can be false or true. $E=mc^2$ and constancy of $c$ are thus introduced as definitions/agreements and then turned into physical laws, which cannot be false. This opens a black hole to modern physics.

Or is it ok to use $E=mc^2$ in the form $m=\frac{E}{c^2}$ to define mass in terms of energy $E$ and $c^2$ as an agreement among physicists (to be accepted by also the people). Does it hurt to make a possibly arbitrary agreement about something and then adjust other things accordingly. Of course we can agree that there are 50 centimetres on a meter and adjust measure accordingly. It could be a bit awkward but would cause a collapse of physics. In this spirit we could view $E=mc^2$ as a formality, which does not have any real consequence, just an empty gesture to salute Einstein. But by Occam's Razor such an empty gesture could as well be dispensed with.  Insisting would just add to the mystery of modern physics.

We may compare with Newton's 2nd Law $F=am$ with $F$ force, $a$ acceleration and $m$ inertial mass, which is the analog of the corresponding relation for gravitational force, gravitational acceleration and gravitational mass as primordial with thus force defined as gravitational force. Here $F=am$ gets real physical meaning by the fact that inertial mass = gravitational mass. In other words, the gravitation potential is primordial making bodies move according to gravitational forces thus prescribing motion to other (ultimately electromagnetic) forces. In this sense $F=am$ is a physical law and not only an agreement.    

How Smart is Ed Witten?

From Quanta article: A Physicist’s Physicist Ponders the Nature of Reality

Ed Witten is supposed to be the smartest physicist of our time, maybe of all times. What does that mean? How smart is then Ed? Well, let us listen to what Ed has to say about the Unreasonable Effectiveness of Mathematics in Physics coined by Eugene Wigner:

• It is uncanny how powerful mathematics is in understanding physics.
• Newton's inverse square law with its power two was only understood through Einstein's field equations of general relativity and then as the geometrical fact that the surface of a sphere scales with its radius squared. 

So what does Ed mean with uncanny? Instead of unreasonable? Well, uncanny means strange or mysterious. It does not seem to be very enlightening, rather the opposite but certainly in line with the accepted view that both quantum mechanics and general relativity as the two incompatible pillars of modern physics, are both strange. But what does it mean when the smartest physicist of all times is stating that physics is strange? Isn't that strange?

Next, concerning Newton's inverse square law, Ed does not seem to be well informed when stating that Einstein gives the first field equation for gravitation explaining the power lay, since this was done by Laplace in his monumental Celestial Mechanics in 5 volumes 1798-1827 in the form of the equation 

• $\Delta\phi (x) = 4\pi\rho (x)$           

with $\Delta$ the Laplacian differential operator with respect to a space coordinate $x$, and $\phi (x)$ is  the gravitational potential corresponding to the mass distribution $\rho (x)$. 

With $\rho (x)$ as a unit point source at $x=0$ the potential $\phi (x)=\frac{1}{\vert x\vert}$ with corresponding gravitational force scaling with $\vert x\vert^{-2}$ as the power two law. So Laplace explained the power two, long before Einstein.

How can it be that Ed has forgotten Laplace? Isn't that strange? 

Compare with recent posts on New Newtonian Cosmology. 

Here is an alternative view on math:

• The Reasonable Effectiveness of Computational Mathematics

Here is more of Ed's wisdom:

• Mathematics is the language in which the laws of physics are formulated.
• It is uncanny because it is as if the Universe has been created by a mathematician. Hahhah...
• Reality, as far as we can understand, is described by laws which are interesting and subtle mathematically.
• Calculus is universal.

Listen to Unzicker asking about Witten's responsibility as world-leading physicist:

• Are you not afraid of misleading 7 billion people?

Witten: Not at all! I think we should now go on to other questions.

Test question to Ed: What to say about global warming from human emission of CO2 from burning of fossil fuel?

Physics Needs Help

Eric Weinstein delivers as a Big Think the message that

• Physics needs a new lone genius.
• Do we need a radical rethinking?
• Is there something wrong with the fundamentals?
• Is Einstein in fact wrong to slip in space-time?
• But the question is, why are they (the physics community) stumped?
• Is it (the help) going to come from some completely strange source, maybe somebody who is a self-teacher off the grid (like Einstein or Weinstein)?

Is there any reason to listen to (W)einstein, as an outsider? Yes, why not? The scene is open. In particular, Einstein's space-time mix appears to be a stumbling block and may well be ready for revision...compare with Many-Minds Relativity...

Connection between Neo-Newtonian and Einsteinian Gravitational Theory

                                                 Hen laying eggs by local action. 

If you are a strong supporter of Einstein's general theory of relativity, like almost all modern physicists, then maybe you would be open to see the following connection with the Neo-Newtonian
theory I have been exploring in recent posts, with the gravitational potential $\phi$ viewed as primordial and matter density $\rho =\Delta\phi$ as derived by local action in space of the Laplacian $\Delta$ and with the gravitational potential playing the same role as the "space-time curvature" of Einstein:

• space-time curvature tells matter to move along geodesics
• gravitational potential tells matter to move according to Newton's 2nd Law

with 

• space-time curvature connected to matter by Einstein's equation
• gravitational potential connected to matter by Poisson's/Newton's equation.

This connects to the iconic summary of general relativity by John Archibald Wheeler:

• Spacetime tells matter how to move; matter tells spacetime how to curve,

where the "telling" goes both ways. 

But maybe it is enough that the "telling" only goes one way, maybe it suffices that the gravitational potential tells where matter will be and how it is to move. After all, it is only the equality $\rho =\Delta\phi$ that counts and thus has to be established is some way, and then possibly through one-way communication from $\phi$ to $\rho$ in some form of local action. 

Maybe it is enough to understand/explain how a hen can lay an egg by local action in a poultry yard, and leave out the much more difficult problem of how a hen can come out of an egg by global action outside the poultry yard.