Weak Experimental Test of General Relativity

Space.com reports in 2022 that the Theory of General Relativity GR just passed its most rigorous test yet. What was tested was the postulate of GR of the Weak Equivalence Principle WEP stating that all bodies show the same gravitational free fall, which was tested by Galileo dropping objects from the Tower of Pisa 1589-92 as a test of a prediction of Newtonian Mechanics NM. 

WEP is thus a postulate of GR, while WEP is a consequence of NM. While it is meaningful to test the validity of a postulate, it is not meaningful to use a successful such test to confirm a theory based on the postulate. If we take 1+1=2 as postulate of our favourite pet theory, we cannot say that we have confirmed our theory by verifying that 1+1=2 (as postulate). 

Since WEP is a consequence/prediction of NM, it is meaningful to test it like Galilo did to give evidence that NM is correct. 

But a successful test of WEP does not confirm GR, since WEP is a postulate of GR and not prediction. 

Modern physics is strange. 

Perihelion Precession of Mercury vs Modern Physics vs Pataphysics

Science of Imaginary Solutions: Pataphysics

Einstein's General Theory of Relativity GR (1915) is viewed to be a crown jewel of modern physics replacing classical concepts of space, time and motion under gravitational force expressed in Newtonian mechanics, by an entirely new geometric world of "curved space-time" without gravitational force. 

Newton's mechanics fostered the scientific revolution in the 18th century, while GR opened to the revolution of modern physics of the 20th century. 

At least, this is what (most) modern physicists tell us: Newton's world of mechanics has to be replaced by Einstein's GR world of geometry. More precisely, Newton's mechanics has to be replaced by GR only for extreme speeds or gravitational force/curvature, while GR and Newton agree in most cases. 

The acceptance of GR has grown only slowly over the 20th century, since evidence of superiority of GR over Newton has shown to be evasive, as expressed by fact that the first Nobel Prize directly connected to GR was given only in 2020 to Roger Penrose:

•  for the discovery that black hole formation is a robust prediction of the general theory of relativity. 

The Prize is thus given to the "discovery that GR predicts" the existence black holes, which however cannot be verified. Is that evidence that GR is correct? That GR gives a prediction, the correctness of which cannot be tested? So the Prize in Physics has been awarded to the discovery of an aspect of GR as mathematical fiction regardless of any actual real truth value of GR.  It is like discovering that a certain mythological tradition admits the existence of Unicorns, regardless of the existence of any real ones. This looks like a Nobel Prize in Pataphysics as a branch of philosophy or science that examines imaginary phenomena that exist in a world beyond metaphysics. 

The first evidence of GR was presented by Einstein in a computation using GR to correct a Newton prediction of the precession of the perihelion of Mercury (very slow rotation of the elliptic orbit around the Sun) to exactly fit with observation. But the Newton prediction was made without a computer and so could not account for the full complexity of the problem involving all other planets and unknown inner motion of the Sun and more. 

So it is not clear that Newton fails as concerns Mercury. An example of the correction brought by viewing Sun-Mercury as a true two-body problem still within Newtonian mechanics, with Mercury influencing the motion of the Sun, instead of a one-body problem with fixed Sun, is given in

• The secret of planets’ perihelion between Newton and Einstein by Christian Corda. 

This shows that the correction captured by GR can also be captured by Newton. This is not surprising since the orbit of Mercury is not extreme at all, and so Newton and GR should agree. 

If then Mercury can be taken off the list of evidence of superiority of GR, what remains are extreme cases, so extreme that not even GR can be expected to work, such as black holes, so extreme that they cannot be observed, or even predicted by GR to be honest?  

Why is it important to normalise modern physics back to Newton's mechanics? Because, Newton's mechanics works very well together with quantum mechanics, where speeds are low and gravitation weak. Hopefully this can take modern physics out of its permanent crisis since 100 years caused by an unresolvable conflict between Einstein's mechanics and quantum mechanics: From pataphysics to real physics! In particular, quantum mechanics can be relieved of relativistic mechanics since speeds are low. 

PS1 The Nobel Prize to Penrose/GR is more precisely motivated as follows:

• A black hole is a supermassive compact object with a gravitational force so large that nothing, not even light, can escape from it. 
• In 1964, Roger Penrose proposed critical mathematical tools to describe black holes. 
• He showed that Einstein’s general theory of relativity means the formation of black holes must be seen as a natural process in the development of the universe. 
• He was also able to describe black holes in detail: at their farthest depths is a singularity where all known laws of nature dissolve.

Every word here triggers questions: Supermassive? Nothing can escape? Proposed? Critical mathematical tools? Must be seen? Natural process? In detail? Farthest depths? Singularity? All known laws of nature dissolve? 

Compare with Ethan Siegel: 

• This Is Why Scientists Will Never Exactly Solve General Relativity

Returning to Newton could offer a great relief from a 100 year spell. 

It is illuminating to inspect the picture presented by the Nobel Committee in its description of the scientific work of Penrose as concerns the nature of the interior of a black hole: 

Sometimes a picture tells more than 1000 words...

PS2 GR was initially met with deepest skepticism and was counted down and out by the 1950s. Then miraculously GR was revived in the 1960s and on, until the great triumph of detection in 2015 of utterly faint gravitational waves emitted by the most violent event thinkable in the from of collision of two black holes 1.3 billion years ago. Credible?  How much of the present crisis of physics can be blamed on GR?

Einstein before Newton as Root of Crisis of Modern Physics

ChatGPT can be used to get answers to scientific questions, which cannot readily be found in the scientific literature. This is because GPT has browsed a lot of text and is not yet smart enough to cover up if something is fishy and needs cover up.  Here is one example:

• Me: Did Einstein prove that Newton's inverse square law is wrong?
• GPT: No, Albert Einstein did not prove Newton's inverse square law of gravitation to be wrong. Einstein's theory of general relativity does not invalidate Newton's law of universal gravitation but provides a more comprehensive and accurate description of gravity in certain regimes.

So we are told that Einstein did not prove Newton's theory of gravitation with its inverse square law to be wrong. Einstein's general theory of relativity does not invalidate Newton's theory. This is what GPT has learned by reading text which thus is what some text says: Einstein gave more comprehensive and accurate description of gravity in certain regimes, not covered by Newton's theory. 

Newton's theory of gravitation including its spin-off of Newtonian mechanics fostered the scientific revolution of the 18th century and serves together with Maxwell's electromagnetics and quantum mechanics as the foundation of modern society. 

Nevertheless, we are told that we have to give up Newton's theory of gravitation/mechanics and replace it with Einstein's theory, even if Newton's inverse square law is not wrong, because there are regimes outside Newton's mechanics.

The prime such regime is electromagnetics described by Maxwell's equations, which does not include gravitation. 

So we are told that we have to abandon Newton's theory for Einstein's theory, because Newton's mechanics does not include electromagnetics.

Even if the logic is missing, this is what Einstein did in his special theory of relativity starting with electromagnetics without gravitation and then finding a form of relativistic mechanics without gravitation different from Newton's. Modern physicists following Einstein thus claim that 

• Newton's mechanics with gravitation but not electromagnetics, 

must be replaced by 

• relativistic mechanics with electromagnetics but not gravitation.  

The logic was missing and so Einstein went on to include gravitation in his general theory of relativity reducing to Newton's theory in regimes without electromagnetics. 

Einstein with followers are responsible for the present crisis of modern physics resulting from this unfortunate combination: 

• Newton has to be replaced by Einstein even in regimes perfectly covered by Newton.
• Einstein is not compatible with quantum mechanics, while Newton is.   

The crisis can be solved if Newton's mechanics is allowed to reign within the vast regimes it covers. This would restrict Einstein's relativity theory to concern only certain very extreme cases such as black holes, so extreme that even Einstein's theory can be questioned on very good grounds. 

Who is ready to take this step? Where are all the followers of Newton?

Sum up: 

• In Newton's mechanics gravitational force is fundamental. 
• In Einstein's special theory there is no gravitation at all. 
• In Einstein's general theory there is no gravitational force.  

Universality of Free Fall: Newton vs Einstein

Hawking in Free Fall

Newton's theory of gravitation is described by

• $\rho =\Delta\phi$  (mass density $\rho$ given by gravitational potential $\phi$),      (1)
• $a =-\nabla\phi$  (Universality of acceleration $a$ in Free Fall = UFF),                     (2)

and is extended to Newton's mechanics by a multiplication of (2) by $\rho$ to get

• $\rho a = f$   (Newton's 2nd Law mass x acceleration = force)                        (3)

with force $f$ defined through gravitational force $-\rho\nabla\phi$. Here gravitational mass from (1)-(2) = inertial mass from (3) also named Equivalence Principle EP. 

We see that in Newton's mechanics, UFF serves as a basic postulate, while EP appears as a consequence and does not need to be added as an independent postulate.   

In Einstein's General Theory of Relativity GR, EP serves as a basic postulate, while free fall universality is the same as "geodesic free fall in curved space-time" as the new feature of GR expressed in Einstein's (field) equations.  

We see that both Newton's mechanics and Einstein's mechanics satisfy UFF and EP and one may ask if that is enough to make them effectively express the same thing? 

Now UFF alone would seem to specify motion under gravitation and so Newton's and Einstein's Universa would move the same way under free fall. 

We can also ask what the difference can be between free fall under gravitational force according to Newton (2) and "geodesic free fall" according to Einstein's GR? 

Newton (2) extends by multiplication by mass density $\rho$ and so only applies to bodies having positive mass, and so Newton does not say that massless light is subject to gravitational free fall. 

 

On the other hand, in Einstein's GR light is subject to a form of "geodesic free fall" even if it is massless. 

We understand that Einstein differs from Newton by including light without mass to be subjected to gravitational force acting on bodies with mass. Is this a fair description?       

Modern Physics vs Classical Physics

After at chat with ChatGPT I have learned that the essential difference between modern and classical physics is that the postulates of modern physics, the postulates of relativity theory and quantum mechanics, are not directly testable experimentally, while this is a key requirement of classical mechanics. 

It seems to be more constructive to discuss physics with GPT than with a living modern physicist typically taking a very defensive position admitting nothing. 

Now, a physical theory based on postulates about facts of physics, which cannot be directly tested experimentally, and thus cannot be directly falsified, runs the risk of being a self-fulfilling prophecy without real value. This may well be the case concerning relativity theory based on postulates of (i) general principle of equivalence of gravitational and inertial mass and (ii) general covariance of physical laws, which cannot be tested experimentally. 

Laws or Postulates of classical mechanics, such as Hooke's Law, Coulomb's Law, Fourier''s Law  and Newton's Law of Gravitation, can all be tested and verified experimentally. A theory based on postulates of basic laws of physics express logical consequences of these laws. If the postulates can be verified, then the theory is valid. If not, the theory lacks factual basis and has no value.

In modern physics the fundamental principle of testability of basic postulates, has been given up and so may reduce to free speculation. A return to classical physics with testable postulates is necessary. There is no reason to start with postulates which cannot be directly tested. Unless you want to invent a new theory based on speculations possibly without factual basis, and so become a modern physicist of reputation.  Your choice! 

Newton is Back!

Cam Newton is Back!

The main advancements of physics the last 100 years consist of (i) quantum mechanics as physics on small scales, and (ii) Einstein's relativity theory as physics on large scales. This proclaimed success story of modern physics is shadowed by a realisation that (i) and (ii) are inconsistent/incompatible, and so cannot both be true.  

While quantum mechanics opens classical physics to new atomistic scales, Einstein's relativity theory represents a definite break with Newton's theory of gravitation as the crown jewel of classical physics. The key question concerns the connection between mass density $\rho$ and gravitational potential $\phi$, which is represented by Newton's equation 

• $\Delta\phi (x,t)=\rho (x,t)$.                  (N1)

where $\Delta$ is the Laplacian differential operator with respect to a Euclidean space coordinate $x$ and time coordinate $t$, or by Einstein's equation in coordinate free form.  (N) is the form of Newton's inverse square law given by the mathematician Laplace. 

Newton's equation is well understood and for given mass density $\rho (x)$ as given data, the gravitational potential $\phi$ as solution to (N1) can quickly be computed on a computer. On the other hand, Einstein's equation is poorly understood and virtually impossible to solve. The common view is that solutions to Einstein's equation reduce to solutions of Newton's equations except for very extreme situations of black holes beyond the range of both equations. 

The question is then why Newton's theory of gravitation has to be replaced by Einstein's? What is wrong with (N1) if it covers everything of interest? The standard answer is that (N1) requires instant action at distance since the solution of the differential equation (N1) in analytic form is given by the integral equation  

• $\phi (x,t) = -\frac{1}{4\pi }\int\frac{\rho (y,t)}{\vert x-y\vert }dy$,      (N2)

connecting $\phi (x,t)$ to $\rho (y,t)$ for all $y$ without time delay since the time $t$ on the left is the same as on the right side. The solution formula (N2) expresses that the process of solving is global seemingly instantly connecting $x$ with all $y$. 

So do we then have to accept that Newton's theory of gravitation requires instant action at distance, which is impossible? Do we have to give up all the wonderful physics Newton offers to humanity, and instead rely on Einstein, who is very difficult to understand and use? 

Not necessarily, since it is possible to view (N1) with a different perspective, which does not ask for instant action at distance. The first option is to turn (N1) around to instead

• $\rho (x,t)=\Delta\phi (x,t)$                 (N3)

which thus specifies $\rho (x,t)$ in terms of data $\phi (x,t)$ by the local operation of differentiation, which does not ask for global instant action, only local instant action. 

A second option is to relax (N1) into the equation

• $\epsilon\dot\phi (x,t) = \Delta\phi (x,t)-\rho (x,t)$,       (N4)

with $\epsilon$ a small positive number, and the dot signifies differentiation with respect to time. This is referred to as parabolic relaxation turning (N4) in a heat equation, where $\phi (x,t)$ can be updated by time stepping without instant action at distance. Since $\epsilon$ is small, solutions of (N4) closely agree with solutions of (N3). 

Both (N3) and (N4) connect to Leibniz' principle of pre-established harmony connecting $\rho$ and $\phi$ according to both (N1) and (N3) like two entities playing both roles of data and solution in full harmony.

This may give new light to the basic idea of modern physics of force carrier particles supposed to transmit forces over distance, named gravitons in the case of gravitational force. But no gravitons have been detected, which questions the utility of that idea, and so Leibniz may tell us something even today.

The above argument extends to electromagnetism captured in Maxwell's equations with charge connected to electric potential/field by Coulombs Law.  

Summary:  It is possible to argue that Newton's law of gravitation does not necessarily require instant action at distance in a real physical sense, and so there is no real reason to replace Newton's theory of gravitation by Einstein's. If we allow Newton to come back, then modern physics may be relieved from  the inconsistency/incompatibility trauma brought by Einstein:  

• Newton/Maxwell + quantum mechanics = harmony. 
• Einstein + quantum mechanics = disharmony!  

We are then back to the old idea that all interaction ultimately boils down to "instant touching" like touching the chin of your beloved, in full harmony. 

Birth of Modern Physics: Relativity of Simultaneity

In 1905 Einstein pulled the carpet under classical physics by showing that common agreement cannot be reached whether two events at different locations in space are simultaneous in the sense of taking place at at the same time, coined as relativity of simultaneity. Einstein did this in a "thought experiment" showing that synchronisation of clocks to show the same time, is impossible if the clocks are widely separated in space because of the time delay in communication even at the speed of light. Einstein argued:

• So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.

Einstein claimed this showed Newton's mechanics to be wrong, because it required absolute simultaneity, which could not be established. This was a revolution forming the new modern physics based on Einstein's theories of relativity: 

• Newton is wrong because of relativity of simultaneity!

But stop! If we give up Newton, then we have very little left to cope with for all matters of life, since Einstein's mechanics is so difficult to both understand and use. 

In particular, the GPS system builds on precise synchronisation of satellite clocks orbiting the Earth, which thus is proved to be possible. What more of "absolute simultaneity" can we ask for?  

It is natural to ask the following

• What role does simultaneity serve for the World to go around?
• Is absolute simultaneity necessary for Newton's mechanics to make sense? 

To get perspective recall how Max Jammer concludes his comprehensive treatise Concepts of Simultaneity:

• While the concept of events occurring at different places in space but at the same moment of time (i.e., distant simultaneity) is the subject of heated discussions, the analogous concept of two events occurring at different moments of time but at the same place in space has hardly, if ever, been given serious attention. 

We thus see the following spectrum of possibilities:

1. Two events happen at the same place at the same time.
2. Two events at distant places happen at the same time.
3. Two events at the same place happen at different times.

We understand that 1. is a case of interest: Two bodies collide/meet/interact at a certain place and then necessarily at the same time. To say that the collision happens at different times would make no  sense. 

Jammer declares that 3. has little interest. We agree. Compare with Kilroy was here!

What then about 2? For bodies interacting only by local contact, we are led back to 1. 

As concerns interaction at distance the common view is that simultaneity plays a role, in particular as concerns gravitation, since it is commonly viewed to involve instantaneous action at distance seemingly requiring some form of simultaneity. This is expressed through the connection between mass density $\rho (x,t)$ and gravitational potential $\phi (x,t)$ through Poisson's equation expressing Newton's Law of Gravitation:

• $\Delta\phi (x,t) = \rho (x,t)$                   (classical law of gravitation)

with $x$ a Euclidean space coordinate and $t$ a time coordinate. The common view is that $\rho (x,t)$ is given at a certain time $t$ with $\phi (x,t)$ at the same time $t$ emerging from a global solution process of Poisson's equation (global integration process) corresponding to instantaneous action at distance. 

But it is possible to turn around the perspective and view instead $\rho (x,t)$ to be locally generated from $\phi (x,t)$ at time $t$ by a local differentiation process,

• $\rho (x,t)=\Delta\phi (x,t)$                   (new law of gravitation)

 which again leads back to 1. This is the basic idea of New Newtonian Cosmology.  

We conclude that 2. may very well have no real intrinsic interest, and so Einstein's motivation to dismiss Newton may lack substance. 

In short: Simultaneity/clock synchronisation is important for a system like GPS to work, or more generally to coordinate human acitivities, but does not play a role in physics without human intervention. Newton's theory of gravitation does not necessarily require instant action at distance/absolute simultaneity, since there is an option requiring only local action (with automatic simultaneity).

The obsession with Einstein in modern physics appears as a main factor in the present crisis of modern physics.  

Many physicists including Stephen Hawking tell people that GPS works because satellite clocks are adjusted according to both Einstein's special and general theory so as to run at the same rate and so show absolute simultaneity, which of course is in contradiction to Einstein's starting point that this is impossible. 

In fact, clocks are continuously synchronised to a base clock on Earth and so the use of relativity theory is superficial and so only show-off. The fact that GPS works is not evidence that relativity theory is correct. 

Note that if we accept that all interaction is local (and then instant) so that we do not have to invoke  instant action at distance, then we do not have to worry about simultaneity and absolute time, as long as we only consider physics without human presence. This means that physical time is local in space and proceeds at a rate given by local conditions as a measure of rate of change. Only when introducing human time required for coordination of human activities, does simultaneity and clock synchronisation serve any real purpose.  Of course, with similar local conditions, we may expect time as rate of change to be similar. 

Sum up: Newtonian physics can be viewed to work without synchronised clocks measuring absolute time. Time can be viewed to be local in space as a measure of local change of state. Understanding that there is no compelling reason to replace Newton by Einstein opens to a resolution of the crisis of modern physics.

Think of that!  

PS We may compare functionality of the following two systems: 

• The bus will leave at 12.00.           (modern society)
• The bus will leave when it is full.  (classical physics)

Einstein's Principle of Relativity vs Free Society

In the previous post we searched for the basic postulates of Einstein's General Theory of Relativity and came upon Einstein's Principle of Relativity EPR presented as follows on Wikipedia:

• In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference (space-time coordinate systems).

As always with Einstein, there is an ambiguity both concerning "the same form" and "admissible coordinate systems". In any case the key example is Maxwell's wave equations for the propagation of light in a vacuum which read the same letter by letter under Lorentz coordinate transformations, which Einstein took as leading model when formulating Einstein's equations to include the coordinate system itself (space-time geometry) in a new bewildering form of mathematics/physics (understood by nobody including Einstein himself). 

Ok, so "same form" appears to mean letter by letter or identically the same, or invariant. This is not the case with Maxwell's equations under a Galilean transformation, as the fundamental connection between $(x,t)$ space-time observations by two observers A and B in two Euclidean systems moving with constant velocity $v$ with respect to each other, a situation making perfect physics sense with space coordinates simply shifted by $v\times t$. 

But a wave equation like Maxwell's changes form under Galilean transformation and so according to Einstein is not admissible, while Lorentz transformation is admissible. This means that A and B are not allowed to freely make observations in their respective coordinate system and then seek to coordinate the best they can as in Many-Minds Relativity, but B is dictated to observe what A has observed and vice versa with the connection given by Lorentz. 

On the other hand, Newton's equations of motion are invariant under Galilean transformations, which thus appear to be "admissible", but not so to Einstein who insists that because they are not Lorentz invariant they have to be dismissed and be replaced by Einstein's equations.   

A comparison is natural between a free society where independent citizens are free to express what they observe (under e g Galilean transformations) and compare/coordinate, and a dictatorship with BigBrother dictating what can be expressed independent of individual observation (under e g Lorentz transformation). 

In this perspective EPR expresses that we all have "the same form" as long as we all use "admissible frames of reference". Einstein's principle of relativity then paradoxically expresses absolute equality without any relativity with BB dictating what is "admissible" to observe. 

Hopefully this can help to handle the syndrome of "relativity theory anxiety" which is widely spread and like "climate anxiety" makes life miserable for many people. The cure is in both cases a little bit of rational thinking. 

In short: Einstein's basic idea that laws of physics must take the same form in different coordinate systems is so directly contradictory that only a god-like mind could come up with to a human mind such a strange idea. But it so happened and it changed the meaning of the science of physics from classical relativity to modernity of equality and so opened to "the crisis of modern physics" witnessed by so many.

 

Postulates of Newton's vs Einstein's Theory of Gravitation?

Modern physicists claim that Newton's Theory of Gravitation NTG must be replaced by Einstein's General Theory of Relativity GR as a mathematical model of motion on scales from planetary to galactic. 

The basic postulate of NTG is the Poisson equation $\Delta\phi =\rho$ connecting gravitational potential $\phi (x)$ with mass density $\rho (x)$ in terms of a Euclidean space coordinate $x$. This relation can mathematically be deduced from the following two physical principles

1. Gravitational force $F(x)$ is conservative and as such is the gradient of a potential: $F(x)=-\nabla\phi (x)$. 
2. The divergence of $F(x)$ expresses presence of mass density (as a sink): $\nabla\cdot F(x)=-\rho (x)$.

Together 1+2 give $\Delta\phi =\rho$. Voila! It is very hard to argue that 1 or 2 are not valid if there is anything like gravitational force giving rise to the motion of celestial objects. If 1 is not valid, then energy can be created out of nothing, and if 2 is not valid then gravitational force can created out of nothing. 

It thus appears impossible to argue that 1 and 2 are not correct, that is, impossible to argue that NTG is not correct. In particular, in NTG as a consequence of 1+2:

• gravitational mass = inertial mass   (E) 

If there is anything in physics for which questioning lacks reason, it is NTG as a consequence of 1+2. Yet, that is what Einstein did, even if he excused himself by: Newton, forgive me! 

What are then the basic postulates of GR?  (which have to differ from 1+2 unless Einstein=Newton).

A search does not give any clear answer like 1+2 for NTG, but here is one option commonly viewed to capture (some of) the essence of GR:

• General Principle of Relativity GPR: Physical laws take the same form for all observers independent of motion, also named covariance. 
• Equivalence Principle = E.

Gravitational force has a fundamental role in NTG, but no role in GR. Nevertheless it is agreed that GR reduces to NTG except in utterly extreme situations such as a merge of two black holes. So somehow GR must include also 1 and 2, and so there must be something more than GPR+E. But what? 

Moreover: If GR includes 1+2, then E appears redundant, since it is a consequence of 1+2. 

So we are left in confusion: What are the basic postulates of GR?

Note that Einstein uses GPR to discriminate laws of physics which take different mathematical form in different coordinate systems, thus discriminating almost all laws of physics as not proper laws of physics. Einstein can thus discriminate NTG on the ground that it is not Lorentz invariant. Newton would respond by saying that NTG is Galilean invariant and that is good enough and there is no reason to ask for Lorentz invariance. What would Einstein say? Any suggestion? 

Why Not GUT/TOE as Newton+Maxwell+Schrödinger?

There is a Grand Unified Theory of physics GUT (or Theory of Everything TOE) in the form of Newton's Mechanics + Maxwell's Electromagnetics + Quantum Mechanics expressed as partial differential equations over continua of 3d Euclidean space coordinate systems and time:  

1. Newton's equations of macroscopic motion of matter/mass subject to gravitation.  
2. Maxwell's equations for light without mass/charge and matter with charge.
3. Schrödinger's equations for microscopics of electromagnetics.

But this form of GUT is rejected by modern physicists following Einstein in his pursuit of replacing Newton's Mechanics by his General Theory of Relativity GR from 1915 initiated by his Special Theory of Relativity SR from 1905. 

Einstein was driven by a fixed idea (strike of genius?) that physical laws must take the same form independent of the choice of coordinate system, named covariance. He found this to be the case for Maxwell's equations taking the same mathematical form under Lorentz transformations, but not Galilean transformations. Einstein observed the opposite to be true for Newton's equations and so, seemingly out of the blue, he decided that Newton's Mechanics had to be replaced by his new theory of relativistic mechanics in the form of SR/GR. This was a monumental proclamation which was for a long time met with much skepticism, but gradually through clever marketing has come to represent the major advancement offered by modern physics as opposed to classical Newtonian physics. 

Einstein’s leading idea that mathematical expressions (formulas, equations) of physical laws must literally letter by letter look the same in different coordinate systems, is absurd. It is the same as saying that there can be only one language word by word letter by letter, describing a common physical world. Of course the choice of coordinate system in general will affect the letters of the mathematical expression of a physical law. Nevertheless Einstein used his fixed idea to discriminate Newton’s equations because they changed form under Lorentz transformations. And after 50 years of brooding modern physicists jumped the band wagon against Newton. 

Critics point to the following consequences replacing Newton by Einstein/SR/GR:

• SR/GR is claimed to differ from Newton's Mechanics only in utterly extreme situations, such as black holes or space ships approaching the speed of light, so extreme that even SR/GR falls short.
• SR/GR is incompatible with quantum mechanics, and thus makes modern physics into non-physics without a GUT.
• SR/GR is understood by very few, if any, and so its practise is sparse, while Newton's Mechanics is understood and practised by many.    
• Presented experimental evidence concern detection of extremely weak signals from extremely massive violent large scale cosmological phenomena, such as gravitational waves from the merger of two black holes in the LIGO experiment.

In this light the following questions come up: 

• Is it necessary to replace Newton by Einstein? 
• Is GUT in the form of Newton+Maxwell+Schrödinger impossible? 

A modern physicist would answer Yes! to both questions, even at the cost of giving up the idea of GUT. A modern physicist will then have to motivate why Newton must be replaced by Einstein,  even if it means a collapse of physics as science. 

Einstein is famous for his "thought experiments" as a chain of arguments within a theory such as SR, twisted to serve as external/experimental confirmation of the correctness of the theory. In particular, the constancy of the speed of light (in vacuum) is an agreement resulting from the thought experiment of agreeing to use the Lorentz transformation, which allows SR to prove itself to be true or allowing Einstein with 100% confidence to proclaim that nothing can prove SR to not be true!  Because it is an agreement! 

But agreements can be broken, and what happens if the agreement to coordinate observations in different inertial systems according to the Lorentz transformation, is given up? What compels observers to follow such a dictate?