Was Einstein Right, and Newton Wrong?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Misconceptions about Newton vs Einstein: Crisis!

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

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

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

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

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

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

If you still believe that Einstein should replace Newton, recall

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

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

Free Fall is Not Fall in Zero-Gravity Space

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

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

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

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

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

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

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

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

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

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

Modern Physics as Poker Game

Modern physics based on relativity theory and quantum mechanics has followed the pattern set by Einstein to continue to raise the bet without showing the cards, as in a no-limit-poker game with lousy cards, eventually forcing the other players to fold: 

1. When Einstein's Special Theory of Relativity SR (1905) was questioned, Einstein raised the bet to the General Theory of Relativity GR (1916).
2. When GR was questioned, Einstein raised the bet from scales of classical physics, to scales of the Universe including black holes which nobody dared to call. 

This showed to work fine and so the same strategy was adopted by leading physicists as concerns quantum mechanics:

1. When the physical meaning of Schrödinger's Equation SE (1926) for atoms of size $10^{-10}$ m as the first version of quantum mechanics without relativity theory, was questioned and no answers could  be given, it was replaced by Dirac's Equation DE (1930) including SR describing an electron.
2. When DE for the electron was questioned, the Standard Model SM (1960s) was developed as a theory of atomic nuclei of size $10^{-15}$ m built from the fundamental particles of protons and neutrons made up of quarks interacting by force carriers named gluons. 
3. When SM was questioned as an ad hoc model of a nucleus, String Theory ST (1980s...) was developed as an ultimate fundamental theory on a scale ($10^{-32}$ m ) which could not be called.   

ST/GR ars now being questioned, but the bet cannot be raised another time since the ultimate large and small scales have been reached. It is now time for physicists to call and to help there is a new card to play in the form of RealQM. Anyone with this card can make a call on ST/GR.

Neo-Newtonian Cosmology 2

Every time you look up into the night sky with amazement, you ask yourself the basic question of Cosmology as the science of the Universe as a whole: 

• Is the Universe infinite or bounded?                       (Q1)

An expert physicist will tell you:  

• An infinite Universe with uniform non-negative mass is empty. 

So you are left with the question typically posed by a child: 

• A finite Universe must have a boundary, but what is outside the boundary?   (Q2)

A modern expert physicist may tell you that Einstein's General Theory of Relativity offers an answer in the form of an analogy of the surface of a sphere as a 2d surface in 3d space, which is finite but yet without any boundary, in the form of a 3d surface in 4d space, which unfortunately is beyond your finite ability of understanding (and probably so for everybody). 

So you are essentially left without answer to Q1+Q2 asking an expert physicist. In the previous post I as non-expert physicist/expert mathematician outlined a possible answer along the following lines:

1. Imagine an infinite empty universe Uzero with $\Phi =0$ a zero gravitational potential with corresponding zero mass $\Delta\Phi =0$, with $\Delta$ the Laplacian differential operator. 
2. Imagine a small scale small amplitude oscillating perturbation/fluctuation of $\phi$ of $\Phi$ with corresponding small scale large amplitude mass density $\rho =\Delta\phi$ of variable sign, thus with both positive and negative mass. 
3. Gravitational force $-\rho\nabla\phi$, which is attractive/repulsive for mass densities of same/opposite sign, will collect into larger finite regions of same sign with one of them with positive mass density of finite size as the universe U we happen to live in, bordering to universa of negative mass. 
4. Substantial kinetic energy is collected from gravitational concentration of mass.    

 We are thus led to an answer to Q1+Q2 in the form:

• The universe U we live in has positive mass + lots of kinetic energy + is finite and is generated by fluctuation of a zero gravitational potential with infinite extension.

Do you see this possibility? You find details to this scenario under tag New View on Gravitation.

PS A vague idea of repulsive gravitation has been floating around as a possible origin of dark energy. 

Neo-Newtonian Cosmology 1

                                            Cosmic web of strings of positive mass.

The post Creating the Universe by Plucking a String 1  presented a new interpretation of Newton's Law of Gravitation as Neo-Newtonian Cosmology, which offers answers to the following questions viewed to motivate giving up classical Newtonian cosmology for that of Einstein: 

• What is the physics of instant action at distance?                                      (Q1)              
• Why is an infinite Universe with non-zero uniform mass distribution impossible?  (Q2)

Concerning Q2 already Newton noted that in an infinite Universe with uniform mass distribution the gravitational force at each point by symmetry will be zero, which means that the gravitational potential $\Phi$ is constant, which means that mass density $\Delta\Phi$ with $\Delta$ the Laplacian differential operator, is zero (see The Dynamics of Newtonian Cosmology by Alan Guth and Was Newtonian Cosmology Really Inconsistent? by Peter Vickers): 

• The only Universe with uniform mass distribution is an empty universe!

This very disturbing realisation together with lack of answer to Q1 has served as key motivation to replace Newton by Einstein in modern physics,  see p 96 in Relativity: The Special and General Theory by Einstein.

Let us now recall answers to Q1 and Q2 within Neo-Newtonian Cosmology: 

The basic idea is to view gravitational potential $\phi (x,t)$ with $x$ a Euclidean coordinate and $t$ a time coordinate, to have a primordial role from which mass density $\rho (x,t)$ is "created" by the Laplacian differential operator $\Delta$:

• $\rho (x,t) = \Delta \phi (x,t)$ for all $x$,         (G1)

assumed to act without time delay for all $t$. Mass is thus created locally for each $x$ by differentiation as an instant local operation acting at each time instant $t$.  

This is to be compared with the standard view that gravitational potential $\phi$  is created from primordial mass density as solution of the differential equation:

• $\Delta\phi (x,t)=\rho (x,t) $ for all $x$,           (G2)

represented by the integral formula

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

which requires instant action at distance and so represents a main mystery of modern physics.

We recall that the Laplacian is invariant under an orthogonal change of coordinates and so the creation process (G1) is independent of the choice of Euclidean coordinate system, which can be seen as a sign of possible physicality. 

(G1) allows "creation of something big from something small" in the following way: Let us then connecting to Q2 start from a gravitational potential $\Phi =0$ satisfying $\Delta\Phi =0$ thus with corresponding zero mass density. Let $\Phi$ be subject to a small scale small amplitude oscillatory perturbation $\phi$ creating small scale large amplitude oscillatory mass density $\rho =\Delta\phi$ by the action of second order differentiation with $\rho =\rho_++\rho_-$ decomposed into positive mass density $\rho_+$ and negative mass density $\rho_-$.  

The action of gravitational force $-\nabla\phi$ will cause attraction between mass densities of the same sign and repulsion between mass densities of opposite sign, and so will segregate the small scale variation of $\rho$ into Universa of positive mass and Universa of negative mass which repel each other and so recede. 

By the action of the Laplacian on a small scale small amplitude oscillating perturbation of a zero state gravitational potential $\Phi =0$, large scale large amplitude finite Universa $U_+$ with positive mass $\rho_+$ can been created, balanced by a corresponding negative mass Universa $U_-$ at eventually large distance. 

It is thus possible to envision a scenario where a small perturbation of a zero gravitational potential in an infinite universe by the action of differentiation + gravitational attraction/repulsion in particular generates  a finite large scale Universa with positive mass as the one we happen to experience. 

Does this mean that the scenario really starts from zero? Not quite, because starting from $\Phi =0$ satisfying $\Delta\Phi =0$ requires some spatial structure to express the Laplacian. We can see this spatial structure as a string under tension and the small scale small amplitude perturbation as a small amplitude high frequency excitation of the string. This is a form of cosmological string theory.

The creation process thus starts with an infinite spatial structure under tension but without excitation, from which the Universe we are living in is created with "a little pluck of a string".

The scenario opens to the existence of dark matter identified by $\Delta\phi$ of small magnitude but large extension, and dark energy as influence on $U_+$ from $U_-$. 

Answer to Q1: Mass is created from gravitational potential by instant local action. No need of instant action at distance. 

Answer to Q2: Start from an empty infinite Universe with gravitational potential $\Phi =0$ satisfying $\Delta\Phi =0$ and introduce a small perturbation with mass density $\rho =\Delta\phi$ of variable sign from which finite Universa of positive and negative mass emerge and diverge.

Summary: It is natural to think of the infinite zero potential/mass universe as eternal without beginning and the plucking of a string initial perturbation as the beginning of universa with non-zero mass density as a very very gentle little big bang,

The Power of Leibniz' Principle of Sufficient Reason

Leibniz' Principle of Sufficient Reason PSR states:

• Everything must have a reason or a cause.

In other words, there is nothing without reason. It is a powerful principle, but it seems to be forgotten in modern physics, where things can happen without cause as in the basic assumption of quantum mechanics with its wave function demanding a statistical interpretation, because of its multi-dimensionality. The life or death of Schrödinger's cat is supposed to be determined by the throw of a dice thus without reason in direct contradiction to PSR. 

In a previous post PSR was used to show equality of inertial and gravitational mass, which to Einstein was his Equivalence Principle EP assumed as a basic hypothesis of his General Theory of Relativity GR seemingly without reason.

We can use PSR to settle some mysteries of Einstein's Special Theory of Relativity SR concerning the rate of clocks moving with respect to each other with constant velocity (inertial motion). The rate of a mechanical clock like a pendulum cannot depend on inertial motion because the mathematical equations carrying a precise description of the functioning of the clock do not depend on inertial motion (because Newton's 2nd Law does not). There is therefore no reason for clock rates to depend on inertial motion and according to PSR they do not. This means that SR claiming such dependence contradicts PSR. 

As concerns Big Bang, SPR says that since there is no reason for a hot dense initial state to ever exist, it never happened. 

So if we hold on to PSR, then we have to give up SR. We collect:

• PSR implies EP. No need to assume EP as hypothesis as in GR.
• PSR contradicts SR. 
• PSR shows that Big Bang did not happen.

Your conclusion?

Time to Welcome Newton Back

The tragedy of modern physics is replacing Newton's Theory of Gravitation NG from 1687 with Einstein's Theory of Gravitation EG as expressed in Einstein's General Theory of Relativity from 1915. This did not happen over night, but only got momentum after Einstein's death in 1955 into a full victory for Einstein as the established doctrine today embraced by all properly educated physicists.  

Before Einstein NG was viewed to be the jewel of mathematical science all times capturing virtually all of celestial mechanics through one single concise expression in the form of the inverse square law. After Einstein this jewel has lost its shine because EG is viewed to be more precise with NG only a rough first approximation. EG is viewed as a triumph of modern physics widely surpassing NG as outdated classical physics.  

But there are caveats in this success story:

• EG differs from NG to any measurable degree only in very extreme cases, if any.
• NG is computable and serves as a very powerful work horse.
• EG is not computable and so is useless in practice. 

The takeover of EG was prepared by a perceived mystery of NG articulated already from its start by in particular Leibniz as Newton's adversary, namely the apparent presence of instant action at distance in the inverse square law, which could not be explained and so was unthinkable: The gravitational attraction from the Sun is felt without time delay on Earth in its path around the Sun. With even a small delay, the Earth would spin out of orbit together with all the other planets, and this is not what is observed. 

In recent posts I have argued that it is possible to view the inverse square law from a different perspective where instant action-at-distance/fast-global-action is replaced by fast-local-action and slow-global-action, both of which are thinkable. 

Here are details in mathematical form expressing the interplay between gravitational potential $\phi$ as primordial, mass density $\rho$ and $u$ material velocity all depending on a Euclidean space coordinate $x$ and time coordinate $t$ with the dot on top representing differentiation with respect to time:

• $\rho = \Delta\phi$                    (inverse square law in differential form)
• $\Delta\dot\phi =-\nabla\cdot (\rho u)$    (conservation of mass)
• $\rho\dot u=-\vert \rho\vert\nabla\phi$            (Newton's 2nd Law)  

Here $\rho$ is created from $\Delta\phi$ by fast-local-action, changes of $\phi$ in time are created  from changes of $\rho u$ in space by slow-global-action (see previous post) and changes of $u$ from gravitational force $-\nabla\phi$ by fast-local-action. We see 3 concise simple equations in 3 variables $\phi$, $\rho$ and $u$ describing all of celestial mechanics. Amazing! How can you ever imagine to throw away this mathematical model? Compare this post: Unthinkable that the inverse square law is incorrect.

We see the Equivalence Principle EP expressed in Newton's 2nd Law with inertial mass $\rho$ on the left being the same as gravitational mass $\rho$ on the right, which makes Newton's 2nd Law take the form $\dot u=-\nabla\phi$ expressing that all objects independent of mass move the same way subject to gravitation, as experimentally observed and theoretically motivated already by Galileo. We can invoke Leibniz' Principle of Sufficient Reason to understand that inertial mass must be equal to gravitational since a reason for inequality is missing, more precisely a Universe without EP would be only chaos.

Altogether, fast-global-action (unthinkable) is replaced by fast-local-action+ slow-global-action (both thinkable). The main reason to abandon NG for EG can thus be seen to be without solid physical ground, and so Newton can be welcomed back after having been put into the wardrobe since Einstein took over in the 1950-60s.  

If NG in fact does not require fast-global-action, then EG is not needed and modern physics is not what it used to be. What will then a new modern physics with Newton instead of Einstein look like? Definitely simpler than EG and so more understandable than EG and in particular more computable than EG. Nothing but a revolution. A 2nd Scientific Revolution 350 years after the 1st initiated by the Calculus of Newton and Leibniz!

Newtonian Gravitation Does Not Require Instant Action at Distance

                                                 Instant local action.

Recent posts describe a resurrection of Newton's Theory of Gravitation NG as the prime jewel of classical physics, which in modern physics formally has been replaced by Einstein's Theory of Gravitation EG, although in practice NG still reigns. 

The main reason to throw away NG is a common understanding that NG requires instant action at distance for which physics appears to be missing. The argument is that gravitational potential $\phi (x,t)$ of NG is connected to primordial mass density $\rho (x,t)$ as the solution to the differential equation in the Laplacian $\Delta$:

• $\Delta\phi (x,t)=\rho (x,t) $ for all space coordinates $x$,           (NG1)

with the same time coordinate $t$ on both sides of the equation, with the solution being represented by the integral formula:

• $\phi (x,t) =-\frac{1}{4\pi}\int\frac{\rho (y,t)}{\vert x-y\vert}dy$           (NG2)

which appears to require instant action at distance or fast global action, because the integration variable $y$ covers all of space at a given time $t$.

But it is possible to switch the roles in NG and view the gravitational potential $\phi (x,t)$ as primordial role from which mass density $\rho (x,t)$ is "created" by the local action of the Laplacian differential operator:

• $\rho (x,t) = \Delta \phi (x,t)$ for all $x$,         (NGnew1)

which can be assumed to act without time delay for all $t$ as local action. Mass is thus created locally for each $x$ by differentiation as an instant local operation acting at each time instant $t$, as considered under the tag New View on Gravitation. 

But (NGnew1) is not the full story because conservation of mass is described by the equation 

•  $\dot\rho +\nabla\cdot m =0$ 

where $m=\rho u$ is momentum with $u$ velocity, and the dot on top signifies differentiation with respect to time, which takes the following form with $\phi$ primordial:

• $\Delta\dot\phi +\nabla\cdot m =0$, 

 allowing $\dot\phi$ to be expressed by the integral formula 

$\dot\phi (x,t) =\frac{1}{4\pi}\int\frac{\nabla\cdot m (y,t)}{\vert x-y\vert}dy$.   (NGnew2)

Formally (NGnew2) appears to again require instant action at distance, like (NG2), but in a different setting with $\dot\phi$ as an integral over $\nabla\cdot m$, instead of $\phi$ as an integral over $\rho$, thus in terms of small changes instead of gross quantities.

With NGnew as (NGnew1) + (NGnew2) we can thus express NG with gravitational potential as primordial with instant local action for gross quantities in (NGnew1) and formally instant action at distance only for small changes of $\phi$ in (NGnew2), for which limitation to finite speed has little influence. 

The basic critique of NG takes the form: Suppose the Sun suddenly disappears. How long time will it take before the absence of the gravitational pull by Sun on the Earth will be noticed? Instantly? And if so how?

With (NGnew2) instead of (NG2) the formal appearance of instant action is reduced to small changes instead of gross quantities. In this setting the changes of the gravitational potential are slow because velocities are small and a sudden disappearance of the Sun is not possible. 

Summary: NGnew gives a new view of NG where instant action at distance for gross quantities is not required.  Is this enough to resurrect NG? In short, here is the story of a complete harmony in the spirit of Leibniz between gravitational potential and mass without any need of fast global action: 

• Gravitational potential gives mass to matter.  (fast local)
• Spatial change of momentum (mass x velocity), changes the gravitational potential. (slow global)
• The gravitational potential of the Earth/Sun/Galaxy…changes very slowly in a coordinate system fixed to the Earth/Sun/Galaxy…

Compare with a common popular description of EG as a "theory in curved space-time":

• Matter tells spacetime how to curve.        (fast global, speed of light?)
• Curved spacetime tells matter how to move.    (fast local?)

Your choice: NG for all normal physics or EG for non-physics? 

Everybody can understand NG. Nobody can really understand EG, only pretend to do so. 

PS But what about the precession of Mercury, as proof of supremacy of EG over NG? Is it clear that NG gives incorrect prediction when full input data to a NG computation is missing? How is it possible to claim that EG gives correct prediction when EG computation for the Solar system is impossible?

Gravitation: Newton or Einstein?

Modern physics is based on an assumption that Einstein's Theory of Gravitation EG in the form of his General Theory of Relativity gives a more precise description of the true physics of gravitation than Newton's Theory of Gravitation NG. 

Is this assumption justified? What is the evidence that EG is more precise than NG? 

NG based on Newton's 2nd Law and Newton's Law of Gravitation (inverse square law) combines maximal generality with maximal formal theoretical simplicity allowing computational simulation of gravitational interaction of billions of stars/planets over billions of years. 

EG on the other hand comes with maximal theoretical complexity making computational simulation impossible for gravitational interaction already for 3 stars/planets. 

Is it then possible to verify that EG is more precise than NG? If EG is uncomputable? 

The prime evidence that EG is more precise than NG, is a back-of-an-envelope computation by Einstein in 1915 concerning the precession of Mercury showing a correction to a computation by hand using NG made in 1888 by the astronomer Simon Newcomb supposedly taking into account all the effects from the other planets, with the result of 5557 seconds of arc per century (one second of arc=1/3600 degrees). The observed precession was 5600 and Einstein's back-of-an-envelop computation came up with exactly the missing 43 arc seconds per century, which still serves as main evidence that EG is more precise than NG.

How convincing is this? Questions line up:

1. How precise is the computation by hand by Newcomb, supposed to account for all effects in the Solar system with its planets, moons and asteroids swirling around the Sun? Has the number 5557 been confirmed by best possible computation today? If so to what result? Exactly the same as Newcomb?

2. Einstein knew that 43 arc seconds were missing and so could target his correction to fit exactly. Convincing?

3. It is impossible to directly compute the precession by EG. So Einstein starts with the 5557 given by Newcomb using NG for the whole Solar system as a complex many-body system. Einstein then isolates to the two-body problem of Mercury + Sun with EG offering a correction to NG which precisely matches  the missing 43. Magic?

The weakness of Einstein's argument that EG is more precise than NG, is that direct computation with EG to this effect is impossible. It is only possible to start from a NG computation of a complex many-body problem and then isolate to a two-body problem for which EG appears as NG with an extra contribution to potential energy and use this as a correction to the many-body problem. 

It is obvious that this procedure has some weak points. Questions pose themselves:

• Is its worthwhile to spend years of study to come to at least some understanding of EG, when EG is severely uncomputable?
• Is the evidence that EG is more precise than NG convincing?
• Is it reasonable to view EG as a more precise version of NG, when only NG is computable?
• Is it reasonable to use EG as foundation of modern physics when EG is uncomputable?
• Is it reasonable to use EG only as a form of decoration, which serves no practical use?
• Is it reasonable to give up the basic concepts of space and time of Newtonian mechanics, which have served and continue to serve science and society so well?
• Is it a good idea to insist on EG when EG is incompatible with quantum mechanics? 
• Why was EG initially met with very strong skepticism?
• Why was EG accepted only after Einstein's death (and of all his original skeptics)? 

  

Normal Physics from Extreme Physics?

Modern physics is largely based on an idea to find the truth about some physics by subjecting it to extreme tests as if that will bring out the essence. This idea was introduced by Einstein in his famous "thought experiments" of his Special Theory of Relativity SR, with trains being accelerated to speeds comparable to the speed of light, and from such speculations finding revolutionary new truths about space and time today viewed as fundamentals of modern physics. 

To accelerate a 100 ton train to a speed comparable to the speed of light requires more than $10^{20}$ Joule to be compared with the energy of the total yearly production of coal of less than $10^{18}$ Joule. 

This is the idea of of finding the true physics of light by sending single photons (whatever that is) to go through a double split and finding that a photon gets confused about what slit to pass, as the basic experiment of quantum mechanics.

This is the idea in experiments at the LHC at Cern colliding protons at close the speed of light to find out the nature of protons as fundamental building stones of an atoms/molecules together with electrons and neutrons.  

The new ESS in Lund Sweden will smash high speed neutrons into different molecules to find out their essential functioning in a normal environment.. 

This idea is also present in Einstein's General Relativity as a Theory of Gravitation supposed to replace Newton's Theory of Gravitation in extreme conditions like the collision of black holes or the Universe as a whole. 

The idea of finding normal physics from extreme physics may appear strange from classic physics point of view with generality and simplicity as leading principle and not extreme particularity of extreme complication. But it has taken a prominent role in modern physics, maybe because it is now possible to perform extremely complicated experiments concerning extreme physics and finding extremely small effects. 

An example is the proclaimed detecting of exceedingly weak gravitational waves from a collision of two black holes as an event of maximal strength, awarded the Nobel Prize in Physics in 2017. 

Experts of modern physics with (i) relativity theory + (ii) quantum mechanics the essential advancements of classical physics, are eager to reveal the fact that both (i) and (ii) are very difficult to understand. An effect is that there are many conflicting efforts to simplify with little agreement since the formation of the theories 100 years ago, now manifesting itself as a crisis of modern physics.

This is to be compared with classical theories of physics formed to be maximally clear and understandable and so also being supported by a common agreement.

You find on this blog efforts to make atom physics understandable as Real Quantum Mechanics, and macroscopic mechanics as Many-Minds Relativity.

The Role of Einstein's Theory of Gravitation in Modern Physics

The general view presented to the world by the physics community is that modern physics as physics after 1900, as opposed to classical physics before 1900,  is based on 

• Einstein's Special Theory of Relativity SR and General Theory of Relativity SR replacing Newton's Theory of Mechanics NM, together with
• Quantum Mechanics QM for atomic physics as an extension of Maxwell's Theory of Electromagnetism ME and Newton's Mechanics NM to atomic scales.

The completely new aspect of modernity are Einstein contributions to physics offering a completely new insight into basic aspects of space and time with SR presented in 1905 followed by GR in 1916 after an 11 year long hard struggle. 

But the reception by the physics community of Einstein's revelations were met with skeptics or refutation or ignorance, in particular by the Nobel committee for the Physics Prize 1921, which awarded Einstein for explaining the law of photoelectricity but with the explicit mention that his relativity theory was not included in the motivation. This situation changed only after Einstein's death in 1955, but then slowly accelerated to its position today as the fundamental theory of gravitation replacing Newton's Theory of Gravitation NG included in NM, which had served humanity so incredibly well for 300 years. The history is captured in the book Building the General Relativity and Gravitation Community during the Cold War by Roberto Lalli.

Here is a typical reaction to GR (Charles Lane Poor):

• The Relativity Theory, as announced by Einstein, shatters our fundamental ideas in regard to space and time, destroys the basis upon which has been built the entire edifice of modern science, and substitutes a nebulous conception of varying standards and shifting unrealities. 
• And this radical, this destroying theory has been accepted as lightly and as easily as one accepts a correction to the estimated height of a mountain in Asia, or to the source of a river in equatorial Africa.

This is where we stand today: Physics is based on GR for gravitation and QM for atom physics, but the big trouble is that GR and QM are viewed to be incompatible, which is a catastrophe from scientific point of view.

But NG is compatible with QM, and so it is natural to ask if it is really necessary to give up Newton for Einstein? 

A modern physicist will tell you that in fact GR reduces to NG in the case of (i) weak  and (ii) static gravitation, and then admit that this covers almost everything. In fact, what is not included in (i)+(ii) is something extremely speculative, such as collision of black holes, for which the physics is unknown and so the functionality of GR. 

In other words, NG works as well today as ever before, as the most successful mathematical theory all times, and the claim that NG has to be replaced by GR appears to have little factual basis. In fact, GR is so computationally demanding that simulation of even a simple system like the Solar system is unthinkable, while with NG this is captured in a couple of lines of code and executed on a laptop in seconds. 

If NG still works fine, what was the motivation to promote GR after Einstein's death but reject it before?

Was it the result of a stalemate of modern physics in 1960s after the immense success of the atomic bomb at the end WW2? When constructive new ideas are missing, a return to some old ideas may come to rescue.

In any case GR was lifted up from obscurity to top position, but then GR as theory had to be inspected with new eyes and this was far from easy, since GR is so mathematically demanding that it can be grasped by only a few, if any. 

Today this is handled as follows: GR is fundamental and very difficult to understand and apply, but since NG works so fine it is not necessary to dig into the theory of GR in any detail. It is sufficient to know that GR has replaced NG, while NG is used in practice. GR can then be presented as a fundamental step forward as concerns fundamental aspects of space and time as an expression of the power of modern physics. 

The only trouble is that GR is incompatible with QM, and so either GR or QM must be wrong. 

  

Conundrum of Modern Physics

A modern physicist will proudly tell you that modern physics is based on two theories: 

• Einstein's Special Theory of Relltivity SR and General Theory of Relativity GR replacing Newton's Mechanics NM.
• Quantum Mechanics QM replacing Maxwell's Electromagnetics ME and NM on atomic scales.  

Modern physics is based on SR/GR + QM, while classical physics is based on NM + ME. 

A modern physicist will then inform you that SR/GR and QM are the greatest scientific achievements of all time, each with complete agreement with all observations. The only caveat well understood from the start 100 years ago, is that SR/GR and QM are incompatible, which has plunged modern physics into a credibility crisis. Real physics cannot be incompatible/contradictory and so something must be fundamentally wrong with the mathematical models. But what?

QM can be seen as a generalisation of ME and NM to atomic scales and there is no incompatibility here. So it must be SR/GR posing the problem. 

SR without gravitation introduces new relativistic mechanics based on Lorentz transformation mixing space and time into new strange effects of space contraction and time dilation, and so dismisses NM without gravitation, because it is not Lorentz invariant, as an ad hoc requirement.

GR introduces gravitation as a geometric effect of curved space-time and so dismisses NM with gravitation as a classical field theory in Euclidean space. 

NM has thus been replaced by SR (1905) and GR (1916) as a prime achievement of modern physics with very little change into our days, as if the last word was said 100 years ago. 

But NM is the most successful theory of all times encompassing a very large range of phenomena in computable form opening to a very rich world of simulations. In contrast GR is admittedly very difficult to put to work in simulations, because it is so incredibly complicated that even the largest computer and best programmer cannot make it go. The only way to put GR to use is to let it collapse to NM, while GR beyond NM is reserved for speculations on cosmological scales, or bigger.

Newton's theory of gravitation connects gravitational potential $\phi (x)$ to mass density $\rho (x)$ by the Laplacian differential operator $\Delta$ acting in a Euclidean space with coordinate $x$ by 

• $\rho (x)=\Delta\phi$  for all $x$      (NG)

which can be viewed as an assignment creating mass by differentiation of gravitational potential and which can be motivated from conservation principles as shown in this post.  (NG) is the only possible connection between gravitational potential and matter well understood by the Creator.  You find more information on (NG) under tag New View on Gravitation.

Einstein decided to throw out (NG) as the pinnacle of mathematical thinking all times all areas. Einstein replaced (NG) by GR taking the position of Newton under the excuse "Newton, forgive me!" and so was exploited by the physics community to represent all the marvel of modern physics to the world, while his fellow physicists viewed him with pity for missing the train to modernity.

It is now time to reconsider the reasons put forward to replace NG by GR. The cost is very high, while the gains may just be fantasy. 

Newton Back! Einstein Out?

Modern physics has developed from classical physics in three steps each viewed as revolutionary:

1. Maxwell's equations 1867 describing all of electro-magnetics including light-as-wave.
2. Einstein's Special Theory of Relativity SR 1905 replacing Newton's mechanics without gravitation by relativistic mechanics.
3. Einstein's General Theory of Relativity GR 1916 replacing Newton's mechanics with gravitation by curved space-time geometry. 
4. Schrödinger's equation for atom physics.  

The present view is that a unified theory including all of mechanics + electro-magnetics + atom physics, is impossible because of severe incompatibilities between 1- 4, primarily because of SR and GR.  There is really no incompatibility between Newton, Maxwell and Schrödinger, if you do not seek incompatibility to boost your own favourite substitute.

Let us search the main reason why Newton was dismissed by Einstein and then all his followers. Newton's theory of gravitation as the main jewel of the infinitesimal Calculus created by Newton and Leibniz, describes the motion of all celestial bodies from the inverse-square law. But Newton's theory seemed to require instant-action-at-distance, which was exhibited by Newton's critics as a mystery/physical impossibility, even acknowledged by Newton himself, from a prevailing understanding that forces only can act by instant direct contact, with the history described in Newtonian Studies by Koyre. 

In GR the inverse-square-law is replaced by curved space-time geometry without instant-action-at-distance (from an ad hoc assumption that the speed of gravity is equal to the speed of light9,  thus circumventing the mystery, but at the price of an even more mysterious concept of curved space-time.

But there is a way to get around instant-action-at-distance even in Newton's theory, which is explored in posts on New View on Gravitation. The basic idea is that gravitational potential is primordial with mass secondary as the result of local instant differentiation. 

We may thus see a return of Newton, and let us then recall that Newton's world can be constructed starting with free fall of a small test particle of unit mass with velocity $v$ in a given gravitational field $\phi (x)$ depending on a Euclidean spatial coordinate $x$ described by:

•   $\dot v=-\nabla\phi$,                     (N0)

where $\dot v$ as the time derivative of $v$ is the acceleration of the test particle under the gravitational force $-\nabla \phi$. Accordingly the time of Newtonian success was named "the dot-age". 

(N0) is then generalised to small material bodies of mass $m$ as collections of $m$ particles of unit mass expressing that all small bodies fall freely the same way in a given gravitational field according to

• $m\dot v =-m\nabla\phi$.               (N1) 

We here assume the material body to be small so that $\nabla\phi$ is the same for all parts of the body. 

The next step is to transfer gravitational force $\nabla\phi$ to mechanical force $f=-\nabla\phi$ e g  hanging a unit mass in a unit linear spring and measuring its elongation under gravitation. This makes it possible to generalise (N1) to Newton's 2nd Law for a body of mass $m$ 

• $m\dot v= mf=F$                           (N2)                        

where $F$ can be gravitational or mechanical force. 

The final step is to express Newton's law of gravitation in the form given by the mathematician Laplace as the differential equation

• $\Delta\phi (x) =\rho (x)$ for all $x$,          (NG1)

where $\rho (x)$ is mass density and $\Delta$ is the Laplace differential operator, which thus connects to gravitational potential to mass density. 

The common view is that presence of a unit point mass at $\bar x$ generates a contribution $-\frac{4\Pi}{\vert x-\bar x\vert}$ to $\phi (x)$ as an apparent instant-action-at-distance. But it is possible to turn the connection around and view instead $\rho (x)$ as being generated as

• $\rho (x)=\Delta\phi (x)$       (NG2)

where the process of differentiation is local and as such can an be instant in the same way as a contact force.

It is thus not necessary to dismiss Newton's theory of gravitation as requiring mysterious instant-action-at-distance, and thus combine with Maxwell's and Schrödinger's equations into a unified model of the world as outlined in Many-Minds Relativity, Real Quantum Mechanics, Computational Thermodynamics, Computational Turbulent Incompressible Flow and Computational Black-Body Radiation.

This means that Newton, as the greatest physicist all times, is welcome come back again to constructively contribute to a unified model of the world without fundamental incompatibilities and so leave SR and GR without mission and open a way out of the current crisis of modern physics. This has been a main theme of this blog with more details to come.

In particular, with the gravitational potential as primordial with everywhere presence there is no vacuum or complete emptiness of mysterious nature.  Moreover, it opens to connect regions in space where the gravitational potential is smooth with derivatives of only moderate size, to dark matter. Further, (NG2) opens to negative mass being created subject to repulsion from positive mass as a possible source of dark energy,

After all, the world must be rational to exist at all and so must be possible to describe in rational mathematical terms like (N2) + (NG) without incompatibilities. It is impossible that the world is incompatible with itself. Only models of the world can be incompatible if incorrect is some way.

Einstein's Happiest Thought made him Unhappy

Why was the later Einstein so unhappy?

It started with a young Einstein expressing that "his happiest thought" was the following:

• The gravitational field has only a relative existence... Because for an observer freely falling from the roof of a house – at least in his immediate surroundings – there exists no gravitational field.

It was the pivotal thought to allow Einstein to take the step from his 1905 Special Theory of Relativity SR without gravitation, to his 1916 General Theory of Relativity GR including gravitation. 

Einstein's happy thought was to view free fall of a (small) object as a state without internal forces (stress free) with all parts of the body accelerating the same way subject to a gravitational force being constant over the body, and then draw the conclusion in the absence of internal forces that the body was not subject to any force at all. This brought GR with gravitation back to SR without gravitation. 

Recall that a body in free fall is subject to gravitational force, which is constant for an infinitesimally small body, but for a body with extension gives rise to internal tidal forces, like the gravitational force from the Moon creating tidal waves in the oceans of the Earth. To view free fall as inertial motion without gravitational force lacks reason. 

In any case, Einstein considered a (small) observer O1 with closed eyes under 

• inertial motion (SR)
• free fall (GR)

Einstein noted that in both cases O1 would feel to be stress free without internal forces, and so it would be impossible for O1 to distinguish between inertial motion and free fall from the presence of internal forces, since they would be zero in both cases. But to a stationary observer O2 in a Euclidean coordinate system following the motion of O1, there would be a clear difference between inertial motion as motion with zero acceleration and free fall as accelerated motion. This would also be clear to O1 when opening the eyes.

But Einstein did not take the position of O2 or O1 with open eyes, but instead made a distinction between inertial motion as motion in flat space-time and free fall as motion in curved space-time, which led him to GR. 

So far so good, but Einstein's goal was to form a unified field theory including both gravitation and electromagnetics, which required electromagnetics to also be expressed in curved space-time. Einstein worked on this problem incessantly since 1916 to his death in 1955, however without any success. 

This was the reason Einstein was so unhappy during his later life. 

Is it also the destiny of a modern physicist in quest for a unified field theory including GR, to be unhappy?

Not necessarily, since it is possible to form a unified field theory including Newtonian mechanics and electromagnetics because this possibility was opened with the 2019 SI meter Standard, as exposed in recent posts. Would you be interested in exploring this possibility, and get happy? Then send me a note and I will help to get started, to the best of my knowledge. Ok?

Einstein, the loneliest man in town as smart as a man can be but: He ain't got rythm.

The Equivalence Principle of General Relativity

Bodies of different mass fall the same way.

The pillars of modern physics are quantum mechanics and Einstein's General Theory of Relativity GR, which is based on the following Equivalence Principle EP:

• inertial mass = gravitational mass.                          

In Newtonian Mechanics NM including Newton's Law of Gravitation, EP is not an assumption but instead a necessary consequence of the fact that in NM, as experimentally verified by Galileo dropping different objects from the tower of Pisa while supplying also a theoretical justfication: 

• all bodies independent of mass accelerate the same way in proportion to gravitational force.  

More precisely, with A acceleration and F gravitational force per unit mass, in NM we have 

• A = F

which we can write 

• MA = MF

where M is mass, as an expression of Newton's 2nd Law: mass x acceleration = force. We see that $M$ appears on both sides as an expression of EP. 

Summary: EP is automatically satisfied in NM. It does not make sense in NM to introduce EP as an assumption. On the other hand, EP is an assumption of GR. EP is self-evident in NM but not so in GR, where (P) is made into assumption as if it is possible that inertial mass is different from gravitational mass. This makes GR into a strange perturbation of NM with the following question: What makes GR different from NM when they share the same EP? 

Objective of Quantum Mechanics to Predict Outcomes of Experiments?

Leading modern theoretical physicists can tell you:

• The objective of quantum mechanics is to predict outcomes of (quantum mechanical) experiments. 

You may find this a bit strange. Isn't the objective of theoretical physics to understand physical processes. In the case of quantum mechanics, that would be to understand the microscopic physics of atoms, electrons, protons, neutrons and more. But this is not possible in the case of quantum mechanics, since in the words of Richard Feynman:

• Nobody understands quantum mechanics.

So what is left is the to predict outcomes of experiments, which seems a bit like betting on a horse race. Or is the theoretical physicist simply mocking with you, to avoid further questions?

Ok, if the experiment agrees with the prediction, then you may view that as support to an idea that the theory is correct, in that specific case. But to confirm a theory by experiments requires massive experiments. It is not enough, in general, to make just one experiment and then say that the theory is correct. Maybe that experiment was very special? 

In any case this practised a lot: To confirm Einstein's General Theory of Relativity GR, it was enough with one observation of a very slight change of the apparent position of a star during the solar eclipse on May 29 in 1919 (the perihelion shift of Mercury was not a prediction). For a second confirmation, we had to wait until the LIGO gravitational wave detection at 09.51 UTC on 14 September 2015 of two ~30 solar mass black holes merging about 1.3 billion light-years from Earth. But that was also a very special case. In any case, GR is now considered to be fully confirmed by two very special/extreme (and questionable) observations. 

Similarly, the Standard Model of fundamental physics is supposed to now be fully confirmed by very special experiments at LHC completed in 2012 showing existence of the Higgs boson after a 40 year long fruitless search, as a little jump on an energy graph. 

But if the experiment does not agree with theoretical prediction, what to do? Throw the theory away because it fails on one experiment? Maybe quite reasonable if the experiment is relevant. The alternative is to modify the theory by e g some new parameter to agree with the experiment, but then the prediction aspect is missing. Of course it is also possible to modify the experiment until agreement with theory, but again without true prediction.

To fully confirm a general theory by experiments is impossible. To confirm a general theory by very special experiments, as seems to be the current standard, is not very convincing to me. 

Newton's theory of gravitation is a general theory, which is supported by a generality of  experiments/observations and contradicted by none, and can be understood from conservation principles. It can serve as the role model for all of theoretical physics.

 

If the element of understanding is missing, then theoretical science seems to reduce to fitting theory to experiment or vice versa. Is this the reason for the current crisis of fundamental physics? 

What then about GR? Again, we have a theory which is very difficult to understand. Einstein said he could not understand it, but how is it possible to formulate a theory without understanding it? Of course a modern physicists would proudly say that there are two main theories of modern physics, quantum mechanics and GR (which happen to be contradictory/incompatible), and then act as if he/she understand these theories quite well, if not in full detail, while showing no willingness to go into a discussion about specifics of the theories and referring instead to the very rich literature explaining GR written by people who really understand GR.  

It means that a modern theoretical physicist will have to struggle with general theories, which cannot be understood nor confirmed by experiments, since only very special experiments are available, if any at all.

At the same time the modern theoretical physicist must give the impression of understanding and presence of confirmation.