Why Is the Universe Average Mass Density So Small?

The average density of visible matter in the Universe is estimated to $3\times10^{-28}$ kg/$m^3$ and that of invisible matter about 10 times bigger, altogether corresponding to the mass of a few protons per $m^3$. This is very very small. 

In the Neo-Newtonian Cosmology NNC studied in recent posts mass/matter of variable sign $\rho=\Delta\phi$ is created by the action of the Laplacian differential operator $\Delta$ on a rapidly oscillating small amplitude initial perturbation $\phi$ of a zero gravitational potential distributed over an infinite Euclidean space. Gravitational force with attraction/repulsion of mass of same/opposite sign segregates mass into regions of positive mass and negative mass which repel each other and so drives expansion.  

The action the Laplacian inflates oscillations and so a very very small initial distributed perturbation of a zero gravitational potential is required to create the very small average mass density observed. It is natural to name the initial perturbation as a Small Bang apparently giving mass to matter from virtually nothing. 

The Small Bang thus creates positive and negative mass/matter distributed over infinite space and it is natural to expect positive mass/matter to be visible if $\rho=\Delta\phi$ is large enough positive, and invisible else as dark matter. The expansion effect attributed to dark energy can be viewed to be the repulsive effect of negative invisible mass/matter. 

Inflationary vs Neo-Newtonian Cosmology: Big or Small Bang?

Listening to Alan Guth outlining his Inflationary Cosmology IC in a WSU Master Class, connections to the Neo-Newtonian Cosmology NNC discussed in recent posts present themselves:

• Inflation/expansion driven by repulsive anti-gravity.
• Kinetic energy created by gravitational positive mass contraction under energy conservation. 

IC starts from a Big Bang scenario of a very hot very dense very small size state (of unknown origin) and gives arguments for a very rapid expansion in size. 

NNC starts from a high-frequency small amplitude large size perturbation of a zero gravitational potential in infinite 3d Euclidean space with zero mass density, from which by the action of a Laplacian differential operator substantial non-zero mass of variable sign is created, as a form of very gentle distributed Small Bang from which large separated regions of positive and negative mass density can form. 

In short, IC starts from a Big (concentrated) Bang while NNC starts from a Small (distributed) Bang, with more details in blog posts and Chapter 32 Cosmology of Computational Thermodynamics.

Your choice: Big Bang or Small Bang? 

I have contacted Alan Guth to get his view and will report if he responds.

Neo-Newtonian Cosmology vs Big Bang

                                      Big Bang of Ylem into Inflation. 

Big Bang is a cosmological theory suggesting that the Universe originates from a very hot very dense initial state of very small size (named "Ylem"), which through a period of very strong inflation expanded into a very large void sparsely filled with a fine cosmic web of galaxies.  

Big Bang can be dismissed with reference to Leibniz' Principle of Sufficient Reason since no clue is given to the formation of the very hot very dense very small size initial state. Big Bang describes a scenario for creation of Something Big (the Universe) from Something Big (hot dense initial state), while the real problem concerns creation of Something Big from Nothing or more reasonably: 

• Something Big from Something Small.  

Neo-Newtonian Cosmology NNC offers an alternative to Big Bang of this form. Here the initial state is a zero gravitational potential $\Phi =0$ satisfying the differential equation $\Delta\Phi =0$ with $\Delta$ the Laplacian differential operator in an infinite Euclidean coordinate space. 

From this zero initial state the Universe is then created from a small scale small amplitude large size perturbation $\phi$ of $\Phi$ with $\rho\equiv\Delta\phi$ appearing as a small scale large amplitude large size mass distribution of variable sign, which through segregation of positive and negative mass driven by gravitational force $\nabla\phi$ develops large regions with either positive or negative mass, which repel each other. Here the step from Small to Big is performed by the Laplacian differential operator acting on small spatial scales $h$ with multiplicative factor $h^{-2}$. 

NNC does not start from Nothing since an infinite empty Euclidean space capable of expressing Laplace equation $\Delta\Phi =0$ with a zero gravitational potential $\Phi =0$, is taken as given, but this is far less than the Ylem + Inflation of Big Bang. In NNC the Universe emerges from a small perturbation $\phi$ of $\Phi$ as Something Small through the action of the Laplacian and gravitational force as understood physics. 

The main support to Big Bang comes from an observed apparent expansion of the visible Universe from increasing redshift of far way galaxies, which when reversed in time gives a contracting Universe possibly leading back to an Ylem. But reversing time to recreate history may be impossible in the same sense as recreating a sharp image from a very blurred one. 

The Big Bang theory was first proposed by the catholic priest and mathematician Lemaître almost 100 years ago. It is strange that nothing more credible has been produced by modern physicists.

It was further developed by Alan Guth in 1980s as inflation theory suggesting an increase of the size of Ylem by a factor of $10^{26}$ in only a small fraction of a second. Only a modern physicist could come up with something like that... 

Summary:

• NNC describes creation by known physics of the Universe from a small perturbation in an Euclidean space with Laplacian. 
• Big Bang requires Ylem + Inflation both without known physics. 

Neo-Newtonian Cosmology 3

Recent posts 1+2 in this series with further details in Time to Welcome Newton Back outlines a possible Neo-Newtonian Cosmology based on an expanded form of Newton's Theory of Gravitation with mass of both positive and negative sign with a corresponding gravitational force which is attractive/repulsive for mass of equal/opposite sign, where we happen to live in a visible region of positive mass with only gravitational attraction. 

Invisible regions of negative mass would then supply the mysterious dark energy estimated to contribute 70% of the total energy of the visible Universe filling the very large observed voids apparently without positive mass possibly driving the observed expansion of the visible Universe. 

The idea of an Anti-Universe to our Universe with all signs switched, with negative mass and anti-protons/electrons et cet, was suggested by Hannes Alfvén, Swedish Nobel Laureate in Physics 1970, in his book Worlds-Anti Worlds: Antimatter in Cosmology 1966. 

The possibility of dark energy in the form of negative mass has been proposed by Massimo Melli:

• Most of the substance of the Universe appears to consist of dark energy and dark matter, but until now scientists don't have the faintest idea about their origin and ignore what they are. 
• I believe that dark energy and dark matter could consist of tachyons formed during the inflationary phase of the early Big Bang, when time was slow or zero due to the extremely high density of the Universe. 

Melli refers to Big Bang, but one can equally well speculate about creation of mass of variable sign from a perturbation of gravitational potential as suggested in NNC 1+2 as a physically more possible little big-bang, with electro-magnetics similarly resulting from a perturbation of an electric potential creating charges of variable sign.  

It remains to explain why we can see presence of positive mass through interaction with electro-magnetics but not the negative mass supposedly filling the voids, then apparently without interacting with the electro-magnetics of our universe.  

Key Question: Why does negative mass not interact with visible light? 

We recall that atomic electrons (of positive mass) oscillating between two energy levels in an atom radiate electro-magnetic waves in the form of light, which can be absorbed into oscillating electrons in our eyes and so make a star visible to us. This gives a connection between positive mass and visible light.

In any case large voids are present, which does not fit with a universe of only positive mass. 

It is conceivable that large voids of negative mass can explain the observed expansion of the visible Universe. 

We recall the basic model of Neo-Newtonian Cosmology of immense simplicity and generality 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)
• $\vert\rho\vert\dot u=-\rho\nabla\phi$            (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 three concise simple equations in three 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.

Answer to Key Question: Dark matter as mass $\rho =\Delta\phi$ with $\vert\rho\vert$ too small to carry electro-magnetics, can by presence as negative mass in large voids drive observed expansion and as positive mass in spiral galaxies drive observed rotation. 

 

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?

Webb Telescope vs Big Bang?

The new James Webb Telescope has produced images with can be interpreted to be in conflict with the ruling cosmological theory named BigBang, or not:

• Webb Telescope: BigBang Wasn't The Beginning of Everything,
• Webb Telescope: BigBang may hold up after all. 

What to believe? BigBang or Not BigBang? The question is again on the table after a long period of dominance of BigBang. 

In recent posts (e g this followed by this) I put forward an alternative to BigBang starting from a null gravitational potential $\Phi =0$ as solution to the differential equation $\Delta\Phi =0$ with $\Delta$ the Laplace differential operator acting in an Euclidean space without boundary, from which substantial mass of variable sign $\rho =\rho_++\rho_-$ is created as the sum of positive mass $\rho_+$ and negative mass $\rho_-$ from a quickly oscillating perturbation $\phi$ of $\Phi$ of small amplitude as $\rho =\Delta\phi$, with repulsion between positive and negative mass,  eventually forming a Universe with positive mass well separated from an anti-Universe with negative mass both subject to gravitational attraction.

This signals a possible creation of something big from something small by a process of differentiation, connecting to that described in Genesis 1:4: 

• And God separated the light from the darkness.

It is further possible to connect dark matter to $\rho_+$ of small amplitude, and dark energy to influence from the anti-Universe.

The features of this scenario are:

• Pre-existence of a Euclidean space with solution $\Phi =0$ of $\Delta\Phi$, like an un-plucked guitar string tuned to 440 Hz.
• Creation of substantial mass $\rho =\Delta\phi$ of variable sign from quickly oscillating small amplitude perturbation of $\Phi$.
• Repulsion between positive and negative mass segregating $\rho$ into a Universe with positive mass and an anti-Universe with negative mass.  

We can compare this scenario with BigBang for which a key mystery is the required initial state as very hot and very dense. It may be that the Webb Telescope will show no support to anything like that and so make BigBang fade away. 

In any case, the question of why there is something rather than nothing will continue to trigger speculations. 

 

Chaitin on Fundamental Physics/Science

Famous mathematician and computer scientist Gregory Chaitin gives a harsh evaluation of fundamental physics/science:

• We live in an era of stagnation of scientific innovation.
• I am disappointed. Too much bureaucracy. The dean can count but not read.
• The system is deeply flawed.
• I hope there will be a renaissance with new fundamental ideas some day.
• Tremendous pressure to conform. We need more creative chaos.
• Universities are basically conservative institutions with tremendous inertia.
• It is better to be wrong with the majority, than to be right on your own.
• Maybe AI will give people more time to be curious...?
• and more...listen yourself... 

I can add my own experience to Chaitin's story...

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!

Modern Physics = Obsession with Measurement. Why?

The previous post Newton's Mechanics Does Not Require Absolute Space and Time recalled Newton's warning to physicists in the introduction to Principia Mathematica:

• Do not confound confound real quantities themselves with their relations and vulgar measures.

Modern physics has done the opposite in both theory of relativity and quantum mechanics as its two pillars. 

Einstein focussed in his Special Theory of Relativity SR from 1905 on coordination of measurements of space and time in different inertial coordinate systems moving with constant velocity with respect to each other, using rigid rods and standard clocks as devices, and discovered entirely new phenomena of space contraction and time dilation never heard of before. 

Bohr reduced quantum mechanics to what can be measured and then faced a seemingly unsurmountable  measurement problem. 

So both Einstein and Bohr focussed on (vulgar) measures of quantities and not quantities themselves in direct negation of Newton's warning. 

Newton viewed physics to be independent of human measurements in an understanding that the Moon follows its path around the Earth even when we cannot see it. That the world/mother continues to exist even when eyes are closed, is something a child gradually discovers. 

But Bohr can only speak about things he can measure and says that anything beyond that is hidden to our perception and understanding. An electron is not in any specific state before measurement, which in fact decides the state after measurement (like spin up or down). 

How is it possible that Bohr's view is passionately embraced by modern physicists, when it is so utterly childish? Of course the world in general goes around without any human observation/measurement.

Of course a "quantities themselves" must have a meaning in the sense that this is needed to make the world evolve from an interplay of quantities, without assistance of human observers. 

The idea of quantum mechanics that atomic reality is decided by measurement originates from the fact that the very act of measurement has an impact on the state of an atom, as a form of destructive test. In macroscopic physics this effect can usually be discarded making measurement non-destructive. 

Quantum mechanics comes with another confusing element in the shape of a multi-dimensional wave function, which has no direct physical meaning, only some statistical meaning. Measuring the wave function is thus impossible and so according to Bohr we would not be able to speak of it, but this is the favourite theme of a modern physicist. 

We recall that a mathematical model describes some physics in concise terms, like Newton's Law of Gravitation studied in recent posts:

•  $\Delta\phi =\rho$,                           (NG)

where $\phi$ is gravitational potential and $\rho$ mass density. (NG) connects two quantities which are quantities themselves (potential and mass) and we can speak about these quantities without having to measure them (which can be difficult). Physical laws thus involve quantities themselves with measured quantities being secondary. 

But we can compute quantities themselves by solving equations like (NG), and so discover their nature without measurement. Computing can be seen as a form of non-destructive testing. An obsession with computing could then be productive. But the many-dimensional wave function is uncomputable.

Paraphrasing Bohr we can say that we can only speak about quantities which can be computed. 

Real Quantum Mechanics gives a new formulation of quantum mechanics in terms of quantities themselves in the form of charge densities and potentials, which are computable.  

Many-Minds Relativity gives an alternative to SR which conforms to the SI standard of meter and second.

PS The ultimate expression of obsession of measurement is the proclaimed detection of gravity waves by LIGO (Nobel Prize in Physics 2017) resulting from the most violent physical event possible (collision of two black holes) supposed to send an echo reaching Earth 1.3 billions of years later, a signal so faint that detection required an accuracy smaller than the width of a human hair over the distance from Earth to the nearest star!  

Mixing Space and Time is Not Physics

According to Leibniz space is coexistence as something sharing the same time, while time is a measure of change of coexistence. The atoms making up the arm of a clock coexist and the change of the position of the arm expresses passage of time. The shadow of a sundial expresses coexistence, while the slow change of the shadow represents a measure of rate of time geared by the Sun.

The 2019 SI Standard defines rate of time in seconds by a standard caesium clock, while spatial distance in meters is defined in terms of travel time of light setting the speed of light to be exactly c=299792458 meter per second. Here time and space are clearly separated and cannot be mixed together into some form of space-time, which has come to serve as a mantra modern physics introduced by Einstein and followed up by the mathematician Minkowski.

To make it possible to speak of space-time Einstein introduced the new concept of event as physics which can be described by a single space coordinate $x$ at some specific time $t$ as a space-time coordinate $(x,t)$. This eliminates all physics of spatially extended bodies consisting of coexisting atoms, which cannot be described by a single spatial coordinate, that is essentially all of physics. What remains is an idealised flash taking place at $\bar x$ at time $t=0$ and then following the trajectory $x=\bar x+ct$. Einstein was then led to the Lorentz transformation supposedly connecting space-time coordinates of one and the same event in different coordinate systems, which led him to the Special Theory of Relativity SR.

An analysis of SR shows that it is based on the false premise that a flash of light sent out in one coordinate system can be identified with a flash sent out in a different coordinate system. 

The result is that SR does not describe the physics of extended bodies consisting of coexisting spatial parts but only space-time events and then in an incorrect way. The net result is that it is not mandatory to replace Newton with Einstein, as the main feature of modern physics, as discussed in recent posts.   

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?

Newton's Mechanics Does Not Require Absolute Space and Time

                                                          Local time. 

Newton expressed in the beginning of his monumental Principia Mathematica (Book I p 81-82) a direct warning to not view measured quantities of space and time as the quantities themselves:

• Wherefore relative quantities are not the quantities themselves, whose names they bear, but those sensible measures of them (either accurate or inaccurate), which are commonly used instead of the measured quantities themselves.
• And if the meaning of words is to vie determined by their use, then by names time, space, place, motion, their measures are properly to be understood; 
• and the expression will be unusual, and purely mathematical, if the measured quantities themselves are meant.
• Upon which account, they do strain the sacred writings, who there interpret  those words for the measured quantities.
• Nor do those less defile the purity of mathematical and philosophical truths, who confound real quantities themselves with their relations and vulgar measures.  

But this is exactly what Einstein did in his Special Theory of Relativity with its measuring apparatus of rigid rods and clocks, which in modern physics has replaced Newton's mechanics as being based on concepts of absolute space and time which cannot be identified and so have no meaning.

But interpreting Newton's concept of space and time as "quantities themselves" as "absolute time and space" is not what Newton had in mind understanding of course very well that position and time are both relative and not absolute.  

What Newton said was that if a clock stops, it does not mean that time itself stops. Nothing strange. 

The period of a pendulum clock scales with the square root of length divided by gravitational strength, and so in particular will run slow at higher altitude. But this does not mean that time stops in a space station with effectively zero gravitation. Normal processes of ageing of a human body continue even in weightless state. 

The caesium atomic clock is the most precise clock use to measure time. The rate of such a clock does not change much with changing environment but a dependence on e.g. temperature can be expected. 

In any case the World outside human influence somehow goes around without the help of Swiss clocks and then with local rates of change geared by local physical conditions somehow expressing the rate of local time itself, which is the time entering into Newton's 2nd Law as a law of local acceleration subject to local force. 

The ruling idea of modern physics is that Newton's inverse square law of gravitation requires instant action at distance, which requires global simultaneity and thus universal absolute time, which is viewed to be absurd, and so Newton's time itself must be replaced by Einstein's relative time. 

But as discussed in recent posts and under the tag New View on Gravitation, it is possible to view Newton's law of gravitation as an expression of local instant action, which only involves local time. 

It is thus possible to return to Newton taking advantage of all the marvellous simplicity and accuracy of Newtonian mechanics, and so not continue clinging to Einstein's relativity theory with all mysteries and difficulties it brings along. 

Newton's warning was directly addressed to coming generations, but it did not reach Einstein who apparently did not read even the introduction to Principia and so was free to question Newton's mechanics on loose grounds, and so be elevated to be the portal figure of modern physics whose wisdom cannot be questioned.  

So what do you say? Was Newton's warning well founded?

More from Principia Book I showing that Newton did not ask for any absolute space and time:

• But because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures of them. 
• For from the positions and distances of things from any body considered as immovable, we define all places ; and then with respect to such places, we estimate all motions, considering bodies as transferred from some of those places into others. 
• And so, instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; 
• but in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. 
• For it may be that there is no body really at rest, to which the places and motions of others may be referred.

It is a common tactic in a debate to assign an idea to your opponent, which is not really carried by the opponent, so as to forcefully distance yourself from this idea (straw man argument). This is what modern physicists do when the claim Newton's mechanics requires absolute space and time, and then distance themselves from such a stupid idea.  

  

The World = Differentiation + Integration

The mathematics of the Calculus of Leibniz and Newton allows a description of the World as the result of competing actions between differentiation and integration expressed as the Fundamental Theorem of Calculus as follows in non-technical terms: 

• differentiation followed by integration = no change
• integration followed by differentiation = no change 

thus with differentiation the inverse of integration and vice versa. In other words, the World can be seen as a competition/combination between 

• increasing difference: separation: differentiation as local process: destabilising
• decreasing difference: mixing: integration/summation as global process: stabilising.

In the previous posts we saw that small scale mass density and charge density can be "created" by differentiation seemingly "out of nothing" followed by integration to create large scale order over time. The kinetic energy driving this process comes from concentration of matter with decreasing gravitational potential energy. Details of this process is given in the books listed on the blog including in particular Computational Thermodynamics and The Clock and the Arrow decoding the direction of time, together with Real Quantum Mechanics decoding atom physics.

Calculus describes a World with positive mass and charge of variable sign, generated by the Laplacian differential operator, geared by gravitational force on large scale and arising from integration electrostatic force on small scale.

Creating the Universe by Plucking a String 2

The previous post outlined a possible mechanism to create a large scale Universe $U$ of non-negative mass density $\rho$ from a small scale small amplitude perturbation of a zero gravitational potential with mass density "created" from a gravitational potential $\phi$ by the instant action of the Laplacian differential operator $\Delta$ acting in a Euclidean space with coordinate $x$ according to the assignment   

•  $\rho (x,t)= \Delta\phi (x,t)$ for all $x$ and $t>0$,               (G)

where $t$ is a time coordinate starting at time $0$. The only force in $U$ so far is gravitational force $-\rho\nabla\phi$ which together with Newton's 2nd Law describes the dynamics in $U$, which is large scale.

The physics of $U$ is in a second step expanded with an electric potential $V$ with electric field $E=\nabla V$ as a small scale small amplitude perturbation of a zero electric potential with small scale large scale amplitude electric charge $q$ of variable sign created by an assignment analogous to (G):

• $q(x,t)=\Delta V(x,t)$ for all $x$ and $t>0$,                          (E)                 

with $q=q_++q_-$ split into $q_+\ge 0$ and $q_-\le 0$. A further contribution is given by connecting $E$ to a magnetic field $B$ through Maxwell's equations into electro-magnetics.

The result is a Universe including large scale large amplitude physics of gravitation and small scale large amplitude electro-magnetics created from small amplitude perturbations according to (G) and (E) through the action of $\Delta$, as a Universe created by plucking two strings. 

Note the fundamental difference: 

• Gravitational force is attractive/repulsive between masses of same/opposite sign. 
• Universe of positive mass density separated from Universe of negative mass density. 
• Electric force is repulsive/attractive between charges of same/opposite sign. 
• Gravitational potential strong on large scale because mass density is non-negative and so add without cancellation, but weak on small scale.
• Electric potential is strong on small scale short range but weak on medium/large scale because charge density has variable sign with cancellation.
• Electro-magnetics of light on small/large scale. 
• Laplacian differential operator fundamental as instant local action. 
• No need of instant action at distance.  
• The relative strength of electrostatic and gravitational force between a proton and an electron is nearly $10^{40}$.  

The effect is a toy Universe of large scale non-negative mass density + small scale charge density of variable sign + large/small electro-magnetics of light captured by Newton + Maxwell + Schrödinger as a unified theory. Einstein has no role to play.

Creating the Universe by Plucking a String 1

Under the label New View on Gravitation I have tested the idea of letting gravitational potential $\phi (x,t)$ with $x$ a Euclidean coordinate and $t$ a time coordinate, 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 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 one Universe of positive mass and another 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 $\Phi =0$, a large scale large amplitude positive Universe $U_+$ with positive mass $\rho_+$ has thus been created, which is balanced by a corresponding negative mass Universe $U_-$ at eventually large distance. 

It is thus possible to envision a scenario where a small perturbation of a zero gravitational potential by the action of differentiation + gravitational attraction/repulsion generates a large scale Universe with positive mass thus representing "creation of something very big from something very small".  

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. 

The creation process thus starts with a 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 $U_-$. 

 

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. 

Galilean-Newtonian Relativity

A common view today is that Newtonian Mechanics requires the notion of absolute space, which however cannot be identified, and so is used to motivate a departure into relativistic mechanics in the form of Einstein's Special Theory of Relativity SR without gravitation and General Theory of Relativity GR with gravitation.

But Newtonian Mechanics is already relativistic in the sense that it takes the same form in all Euclidean coordinate systems moving with constant velocity with respect to each other (so called inertial systems) and so it is impossible by experiment to identify a special system to act as absolute space. This is because both Newton's 2nd Law N2 and Newton's Law of Gravitation NG take the same form in all inertial systems. This was well understood already by Galileo. 

We have seen in posts on New View on Gravitation that NG can according to Laplace be formulated as the local assignment

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

where $\rho (x)$ is mass density and $\phi (x)$ gravitational potential depending on a Euclidean space variable $x$ and $\Delta$ is the Laplacian differential operator. Viewing (NG) as assignment means that somehow matter is endowed with mass through that action of the Laplacian on the gravitational potential.

Since the Laplacian is invariant under both translation and rotation, it follows that so is NG and thus the generation of mass from gravitational potential does not depend on choice of coordinate system, which is a natural requirement. 

On the other hand, N2 is not invariant under rotation since centripetal forces from acceleration arise. It is thus possible to detect rotation by experiment such as Newton's Bucket. 

Conclusion: Newtonian Mechanics is relativistic in the Galilean sense of taking the same form in all inertial systems, and so does not require the notion of absolute space. Thus there does not seem to be any compelling reason to replace Newtonian Mechanics by SR/GR mechanics. Adding propagation of light to the mechanics picture motivates a modification on celestial scales as shown in Many-Minds Relativity. 

Remark:In Newton's Bucket experiment it can be decided that it is the bucket which rotates vs the fixed stars (and not the other way around) by considering the evolution in time from an initial state with the bucket at rest with respect to the fixed stars. With this point of view a Euclidean coordinate system determined by the fixed stars, may serve as an absolute space, but it is also possible to connect coordinate system to the Sun, Earth, or your living room. 

Gravitational Potential as Primordial without Instant Action at Distance

                                           Gravitation cannot be stopped. Why?

New Newtonian Gravitation explores a view that gravitational potential $\phi (x)$ is primordial as generator of both space with Euclidean coordinate $x$ and matter with density $\rho (x)$ by the assignment

• $\rho (x)=\Delta\phi (x)$ for all $x$ and all time       (NGnew)

as instant-local-action performed by Laplace's differential operator $\Delta$. 

This is to be compared with the standard view with instead matter density primordial and gravitational potential generated as solution to the differential equation

• $\Delta\phi (x)=\rho (x) $ for all $x$ and all time       (NGold)

with gravitational force $-\nabla\phi$ from instant-action-at-distance. (NGold) thus harbours the main unresolved mystery of Newtonian gravitation motivating Einstein's General Theory of Relativity GR supposedly without need of instant-action-at-distance. (NGold) and also GR ask for some form of graviton particle as force carrier, which has not been found, and is not needed in (NGnew). The standard view is that all atoms in the Universe are connected/attracted to each other by exchanging a stream of gravitons as force carriers, which is an absurd idea.  

The reason matter is viewed as primordial as generator of gravitational potential, is of course that matter is visible (except for dark matter) while gravitational potential/force is invisible. 

Replacing (NGold) by (NGnew) replaces unthinkable instant-action-at-distance mediated by gravitons as force carriers, by thinkable instant-local-action and so does not force giving up Newtonian gravitation as the formidable success of mathematical thinking it is. 

(NGnew) with gravitational potential as primordial without gravitons may explain why it is impossible to "stop gravitation" by some form of barrier in the same way as light can be prevented entering your bedroom by pulling the curtains.

It is impossible to prevent local action by setting up some barrier to influence from outside. We can compare with "external enemies" which can be stopped at the border, and "internal enemies" which can show up anywhere and so cannot be stopped. 

(NGnew) gives a rationale why blocking gravitation is impossible.

Summary: (NGnew) is compatible with observations that gravitation cannot be prevented from acting out. There is no space which is free from gravitation. The gravitational potential is everywhere but you cannot see it, only its action on matter like Newton's falling apple. The gravitational potential as primordial can generate both space and matter. There is no vacuum. Space is generated when being filled with gravitational potential generating matter. Is this a new revelation, or already dismissed?

Compare with fancy of Gravity with an On/Off Switch.

Poincare vs Relativity Theory

A recent post points to the fundamental difference between material objects with positive mass and immaterial objects with zero mass such as light with connection to the concept of luminiferous aether as immaterial medium for propagation of light under intense discussion as a puzzle of the modern physics emerging at the turn to the 20th century with Einstein's Special Theory of Relativity SR as one solution attempt.  

The mathematician Poincare played a key role with main idea described as follows in Einstein 1905-2005 (eds Darrigol et al):

• Poincare actually never abandoned the ether. But he refused to regard it as an ordinary kind of matter whose motion could affect observed phenomena.
• In his lectures of 1899 on Lorentz’s theory, he wrote: I consider it very probable that optical phenomena depend only on the relative motion of the material bodies present –light sources and apparatus– and this not only to first or second order but exactly.

This is precisely the idea I have pursued in Many-Minds Relativity describing propagation of light from emitter to receiver by Maxwell's equations in a coordinate system locked to the receiver, keeping full compatibility with Newtonian mechanics. 

It is natural to compare with propagation of elastic waves in an elastic (material) bar oriented along an $x$-axis of a Euclidean $xyz$-coordinate system together with a similar bar oriented along an $x^\prime$-axis moving with velocity $v$ with respect to the $x$-axis with coordinates connected by the Galilean transformation $x^\prime = x-vt$. Each bar acts as a (material) medium for wave propagation or ether with the same wave speed, and we thus have two ethers represented by the $x$-axis and the $x^\prime$-axis moving with constant velocity with respect to each other, and so being connected by a classical Galilean transformation expressing relativity.      

We can turn this into a similar situation for propagation of light by assuming that the two elastic bars now represent two (immaterial) aethers or coordinate axes connecting emitter to receiver, with the same light speed 

We understand that in both cases aethers locked to coordinate systems act like media or "universa" for wave propagation, which thus are "carried along" with the motion, which is compatible with the null result of the Michelson-Morley experiment triggering SR.

The bottom line is that there is no role for the Lorentz transformation of SR to serve to guarantee the same speed of light in different coordinate systems, since this is already the case if the medium for light propagation is carried along with the motion under Galilean transformation. Therefore SR is not needed and so can be dismissed as a curiosity, as acknowledged by Lorentz. It seems to me that this must have been the position of also Poincare, even if not clearly being spoken out under the intense pressure to come up with something spectacular at the birth of modernity. In this regard Poincare could not compete with Einstein.

More by Poincare:

• Experiment has revealed a multitude of facts which can be summed up in the following statement: It is impossible to detect the absolute motion of matter, or rather the relative motion of ponderable matter with respect to the ether; all that one can exhibit is the motion of ponderable matter with respect to ponderable matter. (1895) Compare this post.
• Laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation; so that we have not, and could not have any means of discerning whether or not we are carried along in such a motion. Compare this post.
• Indeed, experience has taken on itself to ruin this interpretation of the principle of relativity; all attempts to measure the velocity of the earth in relation to the ether have led to negative results. This time experimental physics has been more faithful to the principle than mathematical physics; ... but experiment has been stubborn in confirming it And finally Michelson has pushed precision to its limit: nothing has come of it.

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.