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?   

Do Galaxies Recede at a Speed larger than the Speed of Light?

Maximally observed redshift  z=8.

The light from far away galaxies receding from us with a speed $v$ is received with a redshift frequency factor given by the Doppler effect formula with the speed of light normalised to 1: 

• $f=\frac{1}{1+v}$

or in alternative common notation

• $1+z=\frac{1}{f}$

with $z=v$. This is a consequence of Maxwell's equations in a Euclidean space coordinate system fixed to Earth in accordance with the cosmological model of Many-Minds Relativity. There is no compelling reason to reject Maxwell's equations as a correct model of the propagation of light. There is no compelling reason to invoke any coordinate system moving with respect to Earth since observations are made on Earth not in receding galaxies. Since thus only one coordinate system is used, Einstein's special theory of relativity with objective to coordinate observations in different coordinate systems according to the Lorentz transformation, does not appear to have anything to offer.  

The largest observed redshift is about $z=8$ (see above figure) indicating a recession speed 8 times larger than the speed of light. Observations thus indicate an expansion speed of the Universe which is much larger than the speed of light. This seems to be in contradiction with Einstein's basic postulate of the speed of light in vacuum as maximal speed of both light and matter.  

In short, no real physics appears to prevent the Universe from expanding faster than the speed of light, and  this is what in fact is observed. This puts a big question mark to Einstein's basic postulate. 

Since light governed by Maxwell's equations does not seem to interact with Newton's mechanics for the motion of material bodies (explored in more detail in Many-Minds Relativity), there is no reason to expect that the speed of light sets a limit to the possible recession speed of material bodies. In Leibnizian terms, there is no sufficient reason for something like that to be true. In addition, observations show recession speeds much larger than the speed of light. Your conclusion?

Is Einstein > Newton?

Einstein: Newton, forgive me!

Modern physicists are trained to say that Newton's mechanics as the cornerstone of classical physics must be replaced by Einstein's mechanics to serve as a new cornerstone of modern physics. If you ask for reasons to give up the best we have, you get the answer that of course this would be stupid and that in fact Einstein differs from Newton only in very extreme cases with black holes as a key example, albeit beyond even Einstein's theory. 

To see what can be wrong with Newton's mechanics, let us follow the line of thought of New Newtonian Cosmology and extended Newtonian gravitation with labels to previous posts. Here all mechanics ultimately is rooted in gravitation from a primordial gravitational potential $\phi (x)$ depending on a Euclidean space variable $x$ with motion under gravitational force $-\nabla\phi (x)$. The motion of a body with position $x(t)$ at time $t$ is monitored by Newton's laws of motion with the dot denoting differentiation with respect to time:

•  $\dot v +\nabla\phi =0$                               (1)

with $\dot x = v$, which express conservation of energy as the sum of kinetic energy and potential energy:  

•  $\frac{v^2}{2} + \phi (x) = constant$.

Here $-\nabla\phi$ represents gravitational force per unit mass and (1) takes the following form for a body of gravitational mass $m$ as a collection of unit masses:

•  $m\dot v +m\nabla\phi =0$                          (2) 

Here $-m\nabla\phi$ offers a reference to measure other forces than gravitational and so (3) can be extended to Newton's 2nd Law for any force $F(x)$:

• $m\dot v = F(x)$.                                          (3)

From this relation inertial mass $m=\frac{F(x)}{\dot v}$ can be defined in terms of force $F(x)$ and acceleration $\dot v$ as a form of resistance to acceleration, with then inertial mass = gravitational mass.

The main idea is that all of motion/mechanics ultimately is governed by motion in a gravitational field given by a gravitational potential $\phi (x)$, which is connected to mass distribution $\rho (x)$ through Poisson's equation 

• $\Delta\phi =\rho$.                                     (4)

What can possibly be wrong with this model? Not with (1), nor (2), nor (3) or (4). It is a model of a mechanical universe with motion governed by gravitation according to (1) and then extended to any force according to (3) including definition of mass as resistance to motion. It is a mechanical universe without electromagnetics and light. There is here no limit to the speed a body can reach as long as the force of acceleration $F(x)$ in (3) is consistent.    

The only possibility is that adding electromagnetics to the picture, somehow will change the mechanics.

This was what Einstein did in his special theory of relativity SR stating that the mass $m$ of a body will increase with speed and so slow down acceleration under constant force to limit the speed to stay below the speed of light. But SR does not include gravitation and thus says nothing about Newton's mechanics, and then maybe nothing at all. So Einstein gave up SR and turned to General Relativity GR as a modification of Newton's theory of gravitation, but an observable modification only in some extreme case where even GR falls short.

Sum up: There does not seem to be any reason to question that Newton's mechanics does not describe a mechanical Universe. Both SR and GR are viewed as modifications of Newton's mechanics however so small that they do not seem to matter. Newton >> Einstein!

Physicists will tell you that GPS works because of SR and GR, but is not factually correct. GPS works because satellite clocks are synchronised with a master clock on Earth and their positions are surveyed. Simple Euclidean geometry as part of Newtonian mechanics. If you understand this, you will get a kick to a healthy scepticism as concerns SR and GR and maybe you get incentive to take a look at Many-Minds Relativity presenting both critical analysis and new perspectives. 

In addition, observations of redshift of far away galaxies show that they are receding from us with a speed larger than the speed of light, so Einstein's basic assumption of SR appears to be invalid. 

On large scale the Universe consists of a gravitational potential $\phi$ creating mass $m=\Delta\phi$ moving under gravitational force according to Newton's 2nd Law $\dot v+\nabla\phi =0$. Isn't that neat?

If thus Newton is ok, what is left to Einstein?  

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.    

E=mc2 as Fetish vs Atomic Bombs

In addition to the experimental tests of $E=mc^2$ of the previous post, let us consider a bit more the difficulties of such tests. On microscopic scale the required accuracy is hard to reach in a convincing way. This includes both nuclear and chemical reactions measuring mass before and after reaction. It is possible to restrict the science to just consider the binding energy as it is, as a form of energy, without connecting it to any mass defect which is difficult to assess.  

In any case, on macroscopic scale the accuracy requirement may be less of a problem and so we may envision the following tests:

1. Stretch an elastic spring to give it energy to do work. According to $E=mc^2$ its mass should increase. Compare with an unstretched otherwise identical string using a balance scale and record the difference. 
2. Similarly, use a balance scale with two weights in balance to record if heating changes the balance.    

Would we be able to measure an increase of mass from stretching or heating both increasing energy? That would certainly be most surprising and the measurement accuracy would again not be sufficient to validate anything like that. So such experiments would probably be inconclusive and not serve to validate $E=mc^2$.

Neither does it seem possible to get a validation on cosmic scales, since if increasing the speed of a planetary object would increase its mass, it would not change its reaction to a gravitational potential since all objects independent of mass react the same way.

We conclude that it seems exceedingly difficult to verify the truth of $E=mc^2$ on any scale. What about the possibility of disproving it?  First, one would ask for theoetical support and then we enter muddy waters including Einstein's argument from 1905 and so theory is not sufficient. To disprove it experimentally is also hard since it requires even better accuracy than verification. 

The net result is that $E=mc^2$ is hard to verify/disprove since it is such a small effect. It is like verifying/disproving the existence of ghosts, which is impossible. Does this mean that we can anyway assume that $E=mc^2$ or that ghosts exist, since it does not change anything? Occam's Razor then tells us that it is better to forget all about it, since it does not seem to serve any purpose. Or maybe it does:

The magic formula $E=mc^2$ then appears as a fetish carried by physicists used to boost their importance by connecting the formula to the undeniable power of nuclear energy and weapons. Is this the true role of $E=mc^2$? Is this the reason that still after 118 years there is no real verification, only countless suggestions that there is. A fetish does not need any verification only an agreement that it brings magic power.

A final reflection: $E=mc^2$ connects mass, which is gravitational mass, with $c$ as the speed of light as a stream of "photons" without mass. This certainly seems contradictory. But the argument goes like this: The momentum of a photon is given $p=\frac{E}{c}$ where $E$ is its energy, and momentum is formally given by $p=mc$ with $m$ the mass of the photon and $c$ its velocity. So we derive $E=pc=mc^2$. Voila!

The only trouble is that the photon is massless with $m=0$, so the argument has no meaning, which is an indication that also $E=mc^2$ is without real meaning: To rely on photons without mass traveling with the speed of light to conclude something for bodies with mass traveling at much smaller speeds, seems to be completely off-the-wall. But it is modern physics at its best. 

Experimental Test of E=mc2?

Let us seek experimental test for the cornerstone of modern physics Einstein's $E=mc^2$. We find on MIT News 2005: E=mc2 passes tough MIT test (as a celebration to Einstein's Annu Mirabilis 1905):

• MIT physicists report the most precise direct test yet of Einstein's most famous equation, E=mc2. And, yes, Einstein still rules. 
• The team found that the formula predicting that energy and mass are equivalent is correct to an incredible accuracy of better than one part in a million. That's 55 times more precise than the best previous test. Team member prof. Pritchard says:
• "In spite of widespread acceptance of this equation as gospel, we should remember that it is a theory. It can be trusted only to the extent that it is tested with experiments....If this equation were found to be even slightly incorrect, the impact would be enormous -- given the degree to which [it] is woven into the theoretical fabric of modern physics and everyday applications such as global positioning systems."
• (We meet here the common claim by physicists that GPS relies on relativity theory ($E=mc^2$), which is not the reason GPS works). 
• The mass loss was obtained at MIT by measuring the difference between the mass of the nucleus before the emission of a gamma ray and after. 
• Pritchard informs: "Determining the mass difference requires the individual masses to be measured with the incredible accuracy of one part in 100 billion -- equivalent to measuring the distance from Boston to Los Angeles to within the width of a human hair! This doesn't mean it has been proven to be completely correct. Future physicists will undoubtedly subject it to even more precise tests because more accurate checks imply that our theory of the world is in fact more and more complete."

Ok, detection of the mass loss required a measurement accuracy of one part in a billion (0.000000001) since the measurement was made on a single nucleus emitting a gamma ray. To measure mass defect it would seem to be better to involve a more easily measurable bulk of mass. To measure the mass/weight of a pile of sand, it would be senseless to measure the mass/weight of each grain of sand and then add up. It would be more sensible to seek to measure the mass defect in some nuclear reaction since it would require less precision, like the mass defect in an atomic bomb explosion...

In any case Pritchard admits that this does not suffice to be sure that $E=mc^2$ is exactly correct. And this is needed, because if $E=mc^2$ is not exactly correct, then the floor of modern physics collapses. If $E=mc^2$ is only approximately correct, then an abyss of questions opens: What is then missing? In my case, how much can I rely on $E=mc^2$? Which mass cannot be converted to energy and vice versa?  The suspicion from previous posts comes back again: Is $E=mc^2$ just and agreement, and as such always exactly correct, like the statement that there are 100 centimetres on a meter, for which experimental verification would be met with laugh.

A detailed inspection of many tests supporting the suspicion is given in Mass-energy equivalence not experimentally verified with punch line 

• It was not a verification of E = mc2, but just another experiment to deduce the mass of the neutron. To date, we have not measured the true mass of the neutron to any degree of accuracy; we only have a deduced estimate of the neutron mass based on the mass-energy equivalence of E = mc2.

We understand that the mass defect of the neutron, used as a proof of the correctness of $E=mc^2$, in fact is computed from $E=mc^2$ because the true mass of the neutron cannot be measured with enough accuracy. And so the mass defect is an agreement and not verified physical fact.  

Conservation of Mass/Energy vs Biggest Flaw of Modern Physics?

The previous post took a look at the proclaimed mass defect in chemical and nuclear reactions releasing energy: A mass defect or loss of mass exactly corresponding to the energy release is to be computed from $E=mc^2$. This showed a flavor of agreement/definition instead of actual real physics with mass defect in contradiction to conservation of mass (1) as a basic principle of physics. We also exhibited the origin of mass as reactivity to a gravitational potential. 

We may compare with conservation of energy (2) as the other basic principle of physics. Here energy is seen as potential to do work and can take the form of potential (e g chemical) energy or kinetic energy connected to motion. If now according to Einstein's $E=mc^2$  energy is "equivalent" to mass, then the two conservation laws (1) and (2) can be replaced by simply conservation of mass + energy (3), which is what Einstein had in mind, presumably: Mass can be converged to energy and vice versa, while the sum mass + energy remains constant. Fair enough. Clearly (3) follows from (1) + (2) and so cannot be disputed. 

But (1) and (2) do not follow from (3) in the presence of mass defect. If mass is really converted to energy,  then neither mass nor energy is conserved, only their sum mass+energy.

So here we stand. Two entities of different origin, mass as reactivity to gravitation, and energy as potential to do work, have been made “equivalent” as an expression of some deep modern physics expressing that mass+energy is conserved, but not both mass and energy separately. 

Is this a step forward to a deeper understanding of the Universe? This connects to the biggest flaw of modern physics which is to not offer a consistent theory including both gravitation and quantum mechanics, despite tremendous efforts by the sharpest minds over more than 100 years. Quantum Mechanics and General Relativity of Gravitation are Incompatible!! What can be the reason? After all, the Universe is built from the (a) quantum mechanics of atoms + (b) gravitation. How could (a) and (b) be incompatible? What would a Universe look like if being formed from incompatible physics? An Incompatible Universe?

Is it so that we if we insist that (a) and (b) are the same corresponding to energy being "equivalent" to mass according to $E=mc^2$, then we seem to be led into a dead end where everything is confused or "incompatible". It is like claiming than man = woman, a principle which is causing a lot of confusion in society. For sure there are shared aspects but if two different concepts are made "equivalent" by agreement/definition, then confusion is created. 

It may well be that if gravitation/mass is kept different from atoms/energy, then process can be made, while if confusion is allowed to reign, then no progress is possible. Ready to try?  Take a look at the listed labels on the blog: new quantum mechanics and extended Newtonian gravitation which are certainly compatible! 

In the next post I will investigate what concrete evidence there is that $E=mc^2$ is true physics, and not just an agreement. To prepare recall that Einstein somehow "derived" this relation in his Special Theory of Relativity to be a consequence of a postulate stating that all observes independent of inertial motion will have to measure the speed of light so that they get the same value named constancy of the speed of light. In other words, they have to use clocks and meter sticks to meet this end. More precisely, since 1983 all observers are demanded to use the SI Standard meter stick as the distance traveled by light over a certain length of time. The SI Standard thus commands all observers to agree on the same value of the speed of light: one light second/second = 1. 

But a command, or agreement if no observer objects, is just an agreement and as such is void of true physics. That the Earth is round is not an agreement, but a true physical fact. The agreement before was that the Earth is flat, and it is only recently that this agreement has evaporated. It would today be silly to say that Earth is round because we have agreed that it is. It is not agreement that makes the World go around. It goes around even if there is disagreement. But it is very difficult to get a modern physicist see the difference between agreement and physical fact, definition and theorem in mathematics.  

Modern physicists all agree that the Standard Model is correct, and so this is the way Nature is even if very strange...but understanding that real science boils down to showing that something is not so strange...

Here is an article leading into the next post: 103 years Later. Einstein Proven Correct. So it took modern physicist 103 years to come up with some real experimental evidence of $E=mc^2$. But the experiment is very tricky and so can be questioned. If $E=mc^2$ is indeed correct physics as the incarnation of modern physics, why has it been so difficult to verify experimentally? It would seem more likely that since it is so difficult to demonstrate, it cannot be true physics. Only an agreement that the Earth is flat, which you can argue is true in some sense agreed upon, but which is not really the whole story.  

Mass Defect vs Conservation of Mass

Here is the standard view connecting mass defect to $E=mc^2$.

Material bodies consist of matter formed by the elementary particles of protons and electrons, which do not ever decay and so express conservation of matter. The amount of matter is measured by the number of protons and electrons (and neutrons composed thereof). Matter is connected to gravitational mass manifested by free fall acceleration in a gravitational field scaling with the strength of the field, while being independent of the amount of matter/mass. As a result, all material bodies exhibit the same gravitational acceleration independent of composition. Conservation of matter translates to conservation of mass in the sense that mass does not change under gravitational free fall.

Assuming that inertial mass = gravitational mass, which is a cornerstone of both Newton's and Einstein's mechanics, it follows that all material bodies independent of composition react in the same way subject to gravitation or acceleration.

In particular, material bodies do not get ripped apart under gravitation, as the basic observation by Galileo. Further, a body in free gravitational fall will gain speed while loosing potential energy, while its mass will be conserved and not change. 

In chemical reactions the composition of molecules consisting of atoms consisting of protons and electrons change, but mass is conserved within measurement precision. So far so good. 

If we now bring in Einstein’s $E=mc^2$ as the golden apple of his Special Theory of Relativity SR, that is the idea that somehow mass $m$ is ”equivalent” to energy $E$ mediated by the factor $c^2$ with $c$ the speed of light, then things become strange. Einstein thus claims that in an exothermic chemical reaction releasing heat energy, there must be a corresponding mass defect with a loss of mass although the number of protons and electrons is the same after as before. However, this defect is too small to be measured, but in principle according to Einstein it is there, even if it cannot measured. This sounds like ghost science claiming ghosts to exist even if they cannot be detected.

But Einstein comes back in the case of nuclear reactions, claiming that the enormous release of energy in a nuclear explosion exactly corresponds to a mass defect according to $E=mc^2$, exactly. This is still under conservation of number of protons and electrons, since like in a chemical reaction only the composition (now of the nucleus) changes. And since the energy release is so big the mass defect is now measurable and then turns out to exactly match $E=mc^2$. Can anyone question this? In particular since the match is so precise! Exact!

Now the mass concept of SR is mysterious since it is supposed to change with velocity vs different observers using different reference frames moving with different velocities, and so be observer dependent, which appears to conflict with conservation of mass. If mass/matter is number of protons and electrons and this number does not change, then how can it be that different observers have different conceptions of mass? Are they not able to count?

This is a question which a child can pose, but it seems that physicists have no better answer than: Yes that is strange, but this is the way it is. Just accept it!

But it is easy for a suspicion to grow that in SR mass defect is computed from $E=mc^2$ to exactly fit with observed heat energy release. The mass defect would then not be the result of a measurement, which would be viewed to be superfluous, since anyway it is to be computed from $E=mc^2$. In other words, A = mass defect is claimed to be a consequence of B = $E=mc^2$. That is, B implies A or assuming B we obtain A. 

Now there is a lot confusion concerning the logic of implications, since often A implies B is viewed to be the same or at least a consequence of B implies A. But this is not correct logic. Nevertheless this incorrect logic is often used as argument to support that indeed $E=mc^2$ must be correct, since there is so much energy released in a nuclear explosion. But there is nothing in a nuclear reaction that has anything to do with the speed of light. 

Another thing to remember is that the mass-corrections from SR only become significant for speeds comparable to the speed of light. In the atom or the nucleus nothing is moving att such speeds and som the relevance of SR for atoms and nuclei is hard to motivate. You find as Many-Minds Relativity and analysis different from SR of measurements/perceptions of mass at velocities comparable to the speed of light. 

The net result is that conservation of mass and mass defect appear to be contradictory, and since there appears to be very good arguments for conservation of mass, we are led to conclude that mass defect is an illusion created by assuming $E=mc^2$ and computing mass defect from observing energy release. In particular, the argument that the existence of nuclear explosions proves $E=mc^2$, can be seriously questioned, even if modern physicists view it like undeniable evidence. 

Recall that $E=mc^2$ is derived from an assumption that all observers measure the same speed of light independent of inertial motion, which however is not an assumption (which can be wrong) but an agreement or definition (which cannot be wrong), since the unit of length (meter) is nowadays agreed to be measured in terms of the distance traveled by light over a certain length of time determined by the same atomic clock for all observers. This gives support to our  suspicion that $E=mc^2$ is also an agreement/definition from which mass defects are agreed to be computed in a certain way. The fact that computed mass defects exactly agree with $E=mc^2$ is a sign that we face an agreement/definition rather than physical fact. 

Nobel Physics Laureate: Quantum Mechanics is an Inconsistent Theory

Roger Penrose, who received the Nobel Prize in Physics 2020, makes the following statement in a recent  illuminating  discussion with Jordan B Peterson: 

• Quantum Mechanics is an Inconsistent Theory! 

In other words, the theory of quantum mechanics as expressed in terms of Schrödinger's equations, does not make sense as theory about physics of reality. Penrose here takes the same position as did Schrödinger himself. 

This is also the view I have arrived at after a fruitless search for the physical meaning of Schrödinger's equation. In this regard, quantum theory is similar to Einstein's special theory of relativity, which also lacks meaning in the sense of some form of real physics, a fact admitted by Einstein himself. 

The soul of modern physics is carried by the theories of quantum mechanics and relativity, and if these theories are empty of real physics, then this should pose a problem for modern physicists. But this does not seem to be the case. 

It connects to the tragedy of fluid mechanics by Nobel Chemistry Laureate Sir Cyril Hinshelwood captured as a split between 

• practical fluid mechanics (hydraulics) observing phenomena which cannot be explained, 
• theoretical fluid mechanics explaining phenomena which cannot be observed,  

thus a total collapse of science. 

In both cases scientists are helped out by the fact that the basic equations (Schrödinger's and Navier-Stokes equations) are uncomputable. Thus true comparison between theory and reality cannot be made and so it is possible to claim that true solutions to the equations always agree with reality, even if these solutions cannot be found. And so the spectacle can continue.

Finally Physics Laurate in Physics Speaks Out on Climate Alarmism

Climate alarmism can continue to bog down western societies into preindustrial state in a meaningless race to reduce CO2 emission as long as physicists do not speak out and tell that this has no physics rationale. Sadly to say, physicists have kept silent and so the destructive charade has been allowed to continue.

Now finally a Nobel Laureate, Prof John F. Clauser, Nobel Prize in Physics 2022, speaks out in unmistakably clear terms as reported by CO2 Coalition: 

• The popular narrative about climate change reflects a dangerous corruption of science that  threatens the world’s economy and the well-being of billions of people. 
• Misguided climate science has metastasized into massive shock-journalistic pseudoscience. In turn, the pseudoscience has become a scapegoat for a wide variety of other unrelated ills. 
• It has been promoted and extended by similarly misguided business marketing agents, politicians, journalists, government agencies, and environmentalists. 
• In my opinion, there is no real climate crisis. 
• There is, however, a very real problem with providing a decent standard of living to the world’s large population and an associated energy crisis. 
• The latter is being unnecessarily exacerbated by what, in my opinion, is incorrect climate science.

This should open the mouth of all physicists with some knowledge of basic physics, Nobel Laureates or not. Let us see this happen. In particular, the Royal Swedish Academy of Sciences handing out the Nobel Prize in Physics, now must retract its stated support to climate alarmism formed to serve a political agenda and return to science. I have reminded the Academy about its duty to serve science and not opportunistic politics and report the response.  

What is Equality in Physics?

In modern western society the concepts of equity or equality plays an important role. Equality can refer to equality of possibilities or equality of outcomes in a democratic system or equality of everybody in an Orwellian sense in a communistic society. Equity can refer to equality over different gender/sex and can connect to an idea of equality woman = man and man = woman.

We also find extreme forms of equality in 1984: War is Peace, Slavery is Freedom....

We understand that equality can express both a truth and serve as a disguise or cover-up of a truth. 

We also remind of the difference of the statement A=A expressing identity and B=A typically expressing that B inherits certain aspects of A (but not all). Often these aspects are not specified completely and the statement thus sometimes is open to confusion.  

The previous post discussed two different expressions of equality in physics: 

1. inertial mass = gravitational mass.
2. mass = energy, energy = mass 

Here 1. represents a truth resulting from viewing inertial mass to be an expression of (derived from) gravitational mass and thus the same. 

2. is Einstein's E=mc2, which is viewed to be the corner stone of modern physics. Since in physics energy is power to do work, it says that a body falling in a gravitational field doing work, such as the falling water in a Hydropower Plant, will loose energy (gravitational potential energy) and thus should loose mass according to 2. So there will be less water coming out than coming in to the plant, in contradiction to the physical principle of conservation of mass. A physicist would argue that the difference is too small to be noticed, but surely it is there, in principle. 

In any case a suspicious mind may wonder if that there is something fishy with the statement that energy = mass = energy (E=mc2). Ok, so more precisely Einstein does not say that mass and energy are equal, only that they are equivalent without specifying in what sense. But even so, as shown in the above example, a forced equivalence of mass and energy seems to lead into a strange contradiction.

It connects to Orwell's War = Peace which as identity is absurd, but as equivalence certainly has been used to justify a war by claiming that the aim is peace, that is Peace = War.  

We learn that equalities of the form B = A with B not identical equal to A, can (purposefully) be ambigious and need further specification to be meaningful. Seeking a specification of the meaning of energy = mass (E=mc2) may well lead to the conclusion that the equality does not make much sense. 

A contemporary physicist of course will claim that both chemical and nuclear exothermic reactions releasing energy suffers from a corresponding loss of mass according to E=mc2, which at least in the case of nuclear reactions is measurable and then shows to always exactly match E=mc2, nota bene if only properly measured. Any measurement not complying with a dogma of E=mc2 then must be corrected.

Phyisc is full of ambiguities as concerns equality. A first check is always to see if the units on both sides of the equality sign are equal. Sometimes this is also used to derive an equality by "dimensional" analysis.