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?

The Deep Truth about Newtonian Gravitation

Newton's model of gravitation is Poisson's Equation: 

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

where $\rho$ is mass density, $\phi$ is gravitational potential depending on a 3d Euclidean space coordinate $x$ and a time coordinate $t$. It is the most remarkable mathematical model of all of classical physics allowing precise computational simulation/prediction of effects of gravitational forces in complex systems, as demonstrated in the Millennium Run tracing the evolution of the matter distribution of the Universe over 2 billion light-years using 10 billion particles interacting by (PE). There is massive evidence that (PE) captures gravitation to experimental precision in all cases of any practical interest. 

In the modern phyics of today PE has been displaced from 1st to 2nd place by Einstein's Equation EE, despite the fact that PE covers all cases of practical importance. 

This degradation of PE took a long time become the official truth of modern physics. Einstein presented EE in 1915 which was met with criticism as non-physics in a form of complicated mathematics, and it was only after Einstein's death in 1955 that EE gradually came to replace PE as the true model of gravitation of modern physics. 

The key argument used to put PE into 2nd place was that PE could be viewed to require instant-action-at-distance in the sense that a change of $\rho (x,t)$ at a certain point $x$ at time $t$ would instantly affect the value of $\phi (y,t)$ for all points $y$, since (PE) as a differential equation in space represents $\phi$ in terms of $\rho$ in terms of a global summation process according to the formula with the same $t$ on both sides, thus without time delay:

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

Since instant-action-at-distance appeared to be in conflict with Einstein's Special Theory of Relativity SR, which was accepted before his General Theory of Relativity with EE, leading physicists decided to displace PE to 2nd place in modern physics.  

Let us now take a fresh look at (PE). We see a linear partial differential operator with constant coefficients as the Laplacian $\Delta$ connecting $\phi$ and $\rho$ which can be viewed in 3 ways:

1. Differential equation $\Delta\phi =\rho$ with $\rho$ as cause and $phi$ as effect derived by global integration.
2. Specification $\rho =\Delta\phi$ with $\phi$ as cause and $\rho$ as effect derived by local differentiation. 
3. Simply a coupling of equal parts without cause-effect.   

Here 2 corresponds to local-instant-action which is compatible with SR, if that is the concern.

Here 3 connects to the Pre-Established Harmony of Leibniz as a Deep Truth. It means that $\phi$ and $\rho$ are locked to each other with the Laplacian as a linear relation of simple mathematical form the same everywhere. Such a relation can be read without causation as in 3 and then in particular without demand of instant-action-at-distance. It also makes sense from computational point of view since the computational complexity of (PE) scales linearly with number of spatial mesh points. 

In discrete form (PE) takes the following form in 1d with $dx$ a space step:

• $\phi (x+dx,t)-2\phi (x,t)+\phi (x-dx,t)=dx^{2}\rho (x,t)$ 

locking $\phi$ to $\rho$ at common time $t$ by a simple linear relation which can be read both ways. 

The basic idea of 3 is explored in many posts on New View of gravitation and New Newtonian Cosmology

Let me list virtues of (PE) and Newton motivating back to 1st with (EE) and Einstein 2nd:

• Generality.
• Simplicity.
• Minimal computational complexity.
• Compatibility with Quantum Mechanics.
• Understandable to a wide audience.

As a young patent clerk in Bern in 1905, Einstein took on a role to overthrow principles of classical Newtonian physics at the same time cubism and atonal music emerged as challenges to classical painting and music. This was the emergence of modernity at the turn of the century triggered by an explosion of new technology. Today we see a return to tonal music and figurative painting as post-modernity, and so a return of Newton may also take place after an aberration into Einstein.

Mass as Gravitational Mass

Recent posts discuss the concept of mass concluding that gravitational mass appears to be primordial from which inertial mass is derived. The idea is to start with a Universe defined in terms of a gravitational potential $\phi (x,t)$ depending on a Euclidean space coordinate $x$ and a time coordinate $t$ as created in 3 steps:

1. The gravitational potential creates a mass density $\rho (x,t)=\Delta\phi (x,t)$, where $\Delta$ is the Laplacian differential operator acting instantly as a local operation in space. 

2. Mass is subject to free fall according to Newton's equations of motion subject to gravitational force $\nabla\phi (x,t)$. 

3. Redistribution of mass under free fall gives feed-back to gravitational potential.

We thus find a Newtonian Universe determined by gravitational free fall connecting motion of mass in space to gravitational force and so equating inertial mass to gravitational mass. This is a large scale in a sense complete Universe with a precise simple mathematical description, which can be complemented by electromagnetics without interference with gravitation on both macro-scale and atomic micro-scale into the Universe we can see and experience.  

Modern text-books tell another story with mass appearing as (i) gravitational mass, (ii) inertial mass, (iii) rest mass and (iv) Higg's mass, all of different nature, which is is very confusing and lacks reason.  

It seems to be more reasonable to define mass as gravitational mass, which is the operational definition according to SI 2019 standard of units, and then connect other expressions of mass to this standard. 

On the other hand, the formal presence of mass $m$ in the coefficient $\frac{h^2}{2m}$ of the Laplacian in Schrödinger's Equation SE , with the mass of a proton 1836 times that of an electron, is not connected to gravitation and free fall motion.  Instead $m$ here serves as a parameter to determine spatial size, with thus a proton having smaller size than an electron in an atom.  

Different concepts of mass in modern physics.

 

How to Measure/Define Mass

This is a clarification of the previous post showing gravitational force without need of force carrier.

An instrumentalist definition of a certain quantity like mass depends on how the quantity is measured by a certain specified instrument. 

According to the SI 2019 system of units, mass $m$ is determined by a Kibble balance from gravitational force $mg$ measured as electromagnetic force, where $g$ is the local gravitational constant. 

We conclude that according to SI 2019 mass is gravitational mass as reaction to gravitational force. In other words, gravitational force as gradient of a gravitational potential is primary from which mass is derived as secondary as measured by a Kibble balance. 

This suggests that the relation between mass density $\rho (x)$ and gravitational potential $\phi (x)$ should be viewed to have the form, with $x$ a Euclidean 3d space coordinate and $t$ a time coordinate: 

• $\rho (x,t) = \Delta\phi (x,t)$           (1)

with $\phi (x)$ given and $\rho (x)$ derived by application of the differential operator $\Delta$ acting locally, rather than the standard form: 

• $\Delta\phi (x,t)=\rho (x,t)$,             (2)

with $\rho (x)$ given and $\phi (x)$ derived as solution to Poisson's equation as a differential equation.

We can view (1) as local instant action by differentiation, while (2) requires instant action at distance as integration/summation. 

By adopting (1) as the true connection between gravitational mass and gravitational potential, which fits with SI 2019 and is explored in many posts, we can thus circumvent to need of instant action at distance, which has been viewed as a stumbling stone for Newtonian mechanics, motivating Einstein's relativistic mechanics coming with many new difficulties.

Adopting (1) we thus (i) adhere to SI 2019, (ii) circumvent instant action at distance and (iii) do not need Einstein,  as a hat trick. 

In Newtonian mechanics inertial mass is defined as gravitational mass and their equivalence is not an assumption or Principle as in Einstein's mechanics. 

In the Standard Model, mass is not defined as gravitational mass as in SI 2019, but as an intrinsic quality/property carried by matter, which is formed in a very strange way by the Higg's mechanism. 

Altogether, mass as gravitational mass, appears as a very useful concept. It makes sense to define mass as gravitational mass, because gravitation is present virtually everywhere. A special feature is that free fall as motion under gravitational force, without presence of forces of other nature, is independent of the size of the mass, which defines mass as a form of sensitivity to gravitation which is additive: The mass of two particles of the same kind is twice that of one particle. 

But this is not how a modern physicist approaches the problem of defining what mass is and how to measure it. A modern physicist is trained to believe that mass according to the Standard Model is defined by QFT through the Higg's mechanism, and then connected to gravitation by General Relativity GR. The trouble is the QFT and GR are incompatible and so the mass problem is a mess problem. 

What is Wrong with Newton's Law of Gravitation?

The corner stone of classical mechanics/physics is Newton's Law of Gravitation taking the form of the Newton/Poisson Equation NPE

• $\rho =\Delta\phi$         (*)

connecting mass density $\rho (x)$ to gravitational potential $\phi (x)$, where $x$ is the space coordinate of 3d Euclidean space. 

In modern physics this mathematical model is replaced by Einstein's Equation EE in "curved space-time" of his General Theory of Relativity GR preceded by the Special Theory of Relativity SR. EE reduces to PE in flat Euclidean space without time and so EE is viewed to be a generalisation of PE into curved space-time.   

To mark a shift between classical (obsolete) physics and modern physics a lot of effort has gone into showing that NPE contradicts observations and so must be replaced by EE. In particular NPE is viewed to contradict the following consequences of SR/GR:  

1. Finite speed of light.
2. Gravitational lensing. Bending of light 
3. Time dilation. Clock rates affected by motion and gravitation.
4. LIGO detection of gravitational waves with finite speed of propagation.
5. Precession of Mercury Perihelion.  

But NPE says nothing about propagation of light or the rates of clocks and so 1-3 cannot be viewed to contradict NPE. 

As concerns 4, it is well known that a delay in the action of the gravitational pull on Earth from the Sun will make the Earth orbit away from the Sun. Finite speed of propagation of gravitational force thus appears to contradict the stable orbit of the Earth. In EE this is explained as a form of compensation of the delay in some form of prediction effectively cancelling the delay to no delay. Strange.

So the evidence against NLG shrinks down to 5 with the claim that NPE gives an incorrect prediction of the observed orbit of Mercury, while that of SR/GR is correct. But making a prediction requires input of positions and velocities of all celestial objects in the Solar system at some specific time and in addition their masses and G. To claim that NPE gives the wrong prediction in the form of a very small deviation from observation requires a very accurate NPE computation taking all celestial objects including their internal motion correctly into account. Such a computation has not been made. 

Another argument against NPE is that it requires a notion of absolute time, something which is supposed to contradicts the relative time of SR. Is this a valid argument? 

In the sequence of posts on Neo-Newtonian Gravitation I have tested the idea that the gravitational potential $\phi (x)$ is primordial from which mass density is $\rho (x)$ is delivered by the local action of the Laplacian according to (*) as if time does not enter. 

Combining NPE with Newton's 2nd Law $F=am$ law brings in a notion of time since acceleration as change of velocity per unit of time refers to time, as well as velocity as change of position per unit of time. This gives a notion of local time for each body interacting with all other bodies through the time-less gravitational potential, which does not ask for coordination of local times into a global time. Maybe Newtonian mechanics in fact does not require a notion of global time? Only a notion of a global time-less gravitational potential. 

NASASpaceNews vs Neo-Newtonian Cosmology

NASASpaceNews reports on Dr. Richard Lieu's groundbreaking theory that gravity could exist without mass which connects to posts on Neo-Newtonian Cosmology with a new view on the connection between mass density $\rho (x,t)$ and gravitational potential $\phi (x,t)$, which can take two different forms with $\Delta$ the Laplacian differential operator in 3d Euclidean x-coordinates and $t$ is time :

• Given $\rho(x,t)$, find $\phi (x,t)$ by integration: $\phi =\Delta^{-1}\rho$.  (1)
• Given $\phi (x,t)$, find $\rho (x,t)$ by differentiation: $\rho =\Delta\phi$.  (2)

Here (1) represents the standard view with mass creating gravitational potential, while (2) offers a new view with gravitational potential creating mass as the essence of Neo-Newtonian Cosmology. 

(1) requires a mechanism for instant action at distance (global integration), which has not been found.

(2) involves instant local action (local differentiation), which is thinkable.

(1) starts out with positive mass, while (2) starts out with a gravitational potential for which $\rho (x) =\Delta\phi (x)$ can have variable sign as the main idea of Lieu. Negative mass repels positive mass and so acts like dark energy, while dark matter appears as small $\Delta\phi >0$ in regions where $\phi (x)$ is smooth. 

In short, Neo-Newtonian Cosmology is in line with Lieu's theory by NASA presented as groundbreaking. But there is a basic difference, since Lieu adheres to (1) rather than (2). 

The idea of particles carrying mass is fundamental in (1), but no dark matter particles have been identified, nor any particles with negative mass. But with (2) the focus is instead on the nature of the gravitational potential $\phi$, which does not have to be particle-like and so opens to forms of $\Delta\phi$ without particles including dark matter and dark energy.  

Euclide vs Big Bang vs Standard Model

• ESA's Euclid mission is designed to explore the composition and evolution of the dark Universe. 
• The space telescope will create a great map of the large-scale structure of the Universe across space and time by observing billions of galaxies out to 10 billion light-years.
• Euclid will explore how the Universe has expanded and how structure has formed over cosmic history, revealing more about the role of gravity and the nature of dark energy and dark matter.

Big Bang is a cosmological theory stating that the Universe was created from a very hot very dense state of temperature $10^{32}$ Kelvin and size of a pinhead after $10^{-44}$ seconds, and then inflated/expanded into it's presently observable size of 10 billion light-years and average temperature of 3 K. Big Bang was invented by modern physicists in the 1960s searching for a mission after having completed the Standard Model of elementary particle physics, and is today accepted by almost all physicists. 

The previous post recalls that Leonard Susskind as leading theoretical physicists today, has come to the conclusion that the work on the Standard Model has to start over again, and so also the cosmological theory including Big Bang based on the Standard Model. OK?  

The main weakness of Big Bang is that no explanation is even attempted for the existence of a very dense very hot initial state: Creation of a 10 billion light-years Universe from a pinhead lacks physics. Of all Creation Myths in world history, Big Bang must be the most nonsensical.

So we have to start over again. I have been led to a model described in these posts as Neo-Newtonian Cosmology based on viewing gravitational potential $\phi (x,t)$ with $x$ a Euclidean coordinate and $t$ a time coordinate, as primordial role from which mass density $\rho (x,t)$ is "created" by the local action of 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 of variable sign is thus created locally for each $x$ by differentiation of a fluctuation as an instant local operation acting at each time instant $t$.  

The model is complemented by viewing electric potential $\psi (x,t)$ with $x$ a Euclidean coordinate and $t$ a time coordinate, as primordial from which charge density $\epsilon (x,t)$ is "created" by the local action of the Laplacian differential operator $\Delta$:

• $\epsilon (x,t) = \Delta\psi (x,t)$ for all $x$,         (G1)

assumed to act without time delay for all $t$. Charge of variable sign is thus created locally for each $x$ by differentiation of a fluctuation as an instant local operation acting at each time instant $t$.  

Let us collect basic elements of Neo-Newtonian Cosmology:

1. Mass/matter (ordinary and dark) and charge densities of variable sign are created by the Laplacian acting on fluctuations of zero gravitational and electric potentials. 
2. Attraction/repulsion of mass of same/different sign and charge of different/same sign creates microscale charges of different sign (Hydrogen atoms = proton + electron) and macroscale mass Universa of different sign moving away from each other (dark energy).
3. Kinetic energy in each Universe created by gravitational collapse. 
4. Start from 0 mass. Split into 0 = (+mass) + (-mass). Separate macroscale (+mass) from (-mass).
5. Start from 0 charge. Split 0 =(+charge)+(-charge). Combine microscale (+charge) with (-charge).

 

Testimony by Leading Physicist Leonard Susskind

Leading theoretical physicist Leonard Susskind sums up his experience at the end of his career as follows:

• I can tell you with absolute certainty that String Theory is not about the world we live in.
• We have to describe our world. That is our purpose.
• So we need to start over. We have a lot of work to do. I do not know of any young people doing that. 
• String Theory combines quantum mechanics and relativity in a very beautiful way. There is no other theory that reconciles quantum mechanics and relativity. 
• String Theory does not describe the real world. 
• Is there anything else? Not to my knowledge.Wolfram's hypergraph is a failure. I do not know who Eric Weinstein is. Penrose believes in all sorts of stuff that I do not believe in.
• So we need to start over again.
• To students: Think for yourself and do not listen to old people. What should you work on? I don't know and if I knew I would be working on it myself. Don't be afraid, follow your curiosity. 
• If you do not think that you can do that, you are probably in the wrong field.
• So we need to start over...

What can we get out of this? Well, yet another confession that modern theoretical physics is in deep crisis.

Anything new? Yes, Real Quantum Mechanics is in perfect harmony with Neo-Newtonian gravitation/cosmology. Don't be afraid to check out. Do not listen to old physicists. 

See also Sabine Hossenfelder: The Crisis in Physics is Real: Science is Failing.  

Consciousness: From Unity to Diversity to Unity

We read in the book A Universe of Consciousness by Edelman and Tononi as intro to Chapter 3: Everyman's Private Theatre: Ongoing Unity, Endless Variety:

• Our strategy for explaining the neural basis of consciousness is to focus on the properties of conscious experience that are the most general, that is, that are shared by every conscious state. 
• One of the most important of these properties is integration or unity. Integration refers to the fact that a conscious state cannot be subdivided at any one time into independent components by its experiencer. This property is related to our inability consciously to do more than two things at once, such as adding up a check while carrying on a heated argument. 
• Another key, and apparently contrastive, property of conscious experience is its extraordinary differentiation or informativeness: At any moment, one out of billions of possible conscious states can be selected in a fraction of a second. We thus have the apparent paradox that unity embeds complexity—the brain must deal with plethora without losing its unity or coherence. Our task is to show how it does so.

We learn that unity and differentiation are (apparently contrastive) important aspects of consciousness. 

We find precisely these aspects in the connection between gravitational potential $\phi (x,t)$ and mass density $\rho (x,t)$ as the basic relation of Neo-Newtonian Cosmology in mathematical terms expressed as follows, with $x$ a Euclidean space variable and $t$ a time variable:

• $\Delta\phi (x,t)=\rho (x,t)$     for all $x$ and $t$         (1)
• $\rho (x,t) := \Delta\phi (x,t)$  for all $x$ and $t$        (2)

where $\Delta$ is the Laplacian differential operator acting on the space variable $x$ and $:=$ is computer code for assignment. We thus express the connection between $\phi$ and $\rho$ in two different forms: 

In (1) $\phi (x,t)$ appears as a global solution for all $x$ and given $t$ of the Poisson-Laplace equation $\Delta\phi =\rho$ with $\rho$ given, which can be expressed as an integral over all of space:

• $\phi (x,t) =-\frac{1}{4\pi}\int\frac{\rho (y,t)}{\vert x-y\vert}dy$       (3)

In (2) $\rho (x)$ for a given $x$ is assigned the value $\Delta\phi (x)$ involving given local values of $\phi (y)$ for $y$ close to $x$. 

We understand that (1) represents a global summation process as integration, while (2) is a local process of extraordinary differentiation or informativeness. 

We thus find a mind-body relation in terms of $\phi$-$\rho$ expressed in (1) + (2) with $\phi$ representing global unity/mind/logos and $\rho$ local diversity/body/spirit. 

With the same $t$ on both sides in (3) formally requires instant action at distance, but since the kernel $\frac{1}{\vert x-y\vert}$ in (3) is quickly decaying with increasing $\vert y\vert$, instant action at distance is not required. In other words, (1) can be slow, while (2) as local process can be fast and must be to fit observation. 

Altogether, we see that the general features of consciousness presented by Edelman and Tononi, can be expressed in precise mathematical form in a cosmology context. 

Unity of consciousness restricts attention to only one thing at the same time, which can be seen as a limitation of performing (1) + (2) for only one mass density distribution/thing at a time, because of limited processing brain power.   

Incompressible Turbulent Fluid Mechanics vs Mind-Body

     Da Vinci contemplating incompressible fluid flow to solve the hard problem of consciousness.

Recall the previous post and the basic model of Neo-Newtonian Cosmology in terms of gravitational potential $\phi$ as primordial, mass density $\rho$, momentum $m$ and $u=\frac{m}{\rho}$ 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, as a model describing all of celestial mechanics:

• $\rho = \Delta\phi$                                    (inverse square law in differential form)
• $\dot\rho +\nabla\cdot m=0$                       (conservation of mass)
• $\dot m +\nabla\cdot (um)+\rho\nabla\phi=0$    (conservation of momentum: Newton's 2nd Law)  

We compare with the basic model of all of (inviscid) incompressible turbulent fluid flow as Euler's equations:

• $\nabla\cdot u=0$                                        (incompressibility)
• $\dot\rho +\nabla\cdot m=0$                       (conservation of mass)
• $\dot m +\nabla\cdot (um)+\nabla p=0$    (conservation of momentum: Newton's 2nd Law)  

where $p$ is pressure. Here incompressibility is imposed as a stipulation rather than law of physics, which can be realised through the physical law:

• $\Delta p = -C\nabla\cdot u$                        (pressure law)

where $C$ is a large positive constant forcing $\nabla\cdot u$ to be small. We see that pressure $p$ and gravitational potential $\phi$ serve similar roles in Newton's 2nd Law steering the dynamics, and that both appear as solutions to a Poisson equation with infinite speed of propagation of effects from source to solution. We see that the pressure has the double role to drive the flow while securing incompressibility.  

We thus see that both $p$ and $\phi$ act as omnipresent immaterial controls of dynamics with instant connection to a whole material universe, as solutions to Poisson's equation with source of material form, thus as connection immaterial-material or mind-body in the setting of consciousness in recent posts.

Gravitational Potential: Primordial Omnipresent Immaterial

This is a further reflection on Neo-Newtonian Cosmology expanding on the PS in the previous post on the work by Rupert Sheldrake on morphogenesis geared by immaterial presence.

The basic idea is that primordial omnipresent immaterial gravitational potential $\phi$ has been created from an infinitesimal fluctuation of a zero potential from which mass density $\rho$ emerges by the action of the Laplace differential operator $\Delta$:

• $\rho =\Delta\phi$    (*)   

inflating fluctuations into substantial mass density of variable sign. The gravitational potential assigns mass to material matter consisting of positive and negative electric charge densities emerging from an electric potential as in (*). 

The action of gravitational force separates matter into larger regions of substantial positive and negative mass, which repel each other as if subject to dark energy, with some part of $\Delta\phi$ appearing as immaterial dark mass. Further, gravitational collapse of regions of positive mass generates massive kinetic energy as vacuum energy. 

Altogether, structures as planetary systems and galaxies emerge from an omnipresent gravitational potential acting as immaterial organiser by assigning mass to matter in a form of cosmological morphogenesis. Here informations is directed from potential to mass density, which is the opposite of the current paradigm: 

• Each atom attracts all other atoms in the Universe with short time delay.   (**)     

With (*) as primary process, (**) appears as a secondary slow process. 

The main trouble with (**) is that the physics of the connection/attraction between atoms has no answer. The current idea of some form of particles carrying attractive force between all atoms in the Universe has not been fruitful. It remains to see if (*) is more fruitful. In particular (*) is local and as such can be instant without assistance of force carrying particles.

Connecting to the 2024 Nobel Prize in Chemistry on protein folding, it may be that the total electric potential of a protein, like the total gravitational potential, acts as an organiser of the morphogenesis of the folding. See this post with connection to Real Quantum Mechanics.

 

Vacuum Energy from Fabric of 3d Euclidean Space

The Head of Theoretical Physics at Cern Gian Guidice presents an idea of Big Bang powered by energy stored in the "fabric of space and time" as "vacuum energy", in an interview about the question "What happened before the Big Bang"?

This connects to the Neo-Newtonian Cosmology presented in previous posts starting from a small oscillating perturbation $\phi$ of a zero gravitational potential $\Phi = 0$, which creates mass density $\rho$ of variable sign through the action of the Laplace differential operator $\Delta$ on $\phi$ as

• $\rho =\Delta\phi$    (*)   

The action of differentiation inflates small oscillations of $\phi$ around zero into large oscillations of mass density of variable sign. By the action of gravitation mass separates into larger regions of positive and negative mass, which repel each other as if subject to dark energy, with small positive $\Delta\phi$ appearing as dark matter. Further, gravitational collapse of regions of positive mass generates massive kinetic energy seemingly out of nothing as vacuum energy.

The action of the Laplacian $\Delta$ in the equation $\rho =\Delta\phi$ thus offers explanations of (i) vacuum energy, (ii) dark energy and (iii) dark matter,  as an expression of the "fabric of 3d Euclidean space". If true, simplicity shows to be more powerful than the complexity of the current state of the art.

PS Matter made up electrons and protons appears as an analog to (*) with $\phi$ electric potential and $\rho$ charge density of variable sign, which form atoms and molecules into structures of matter as the material world endowed with mass from the gravitational potential. This leaves open the possibility that part of the gravitational potential remains to create dark mass according to (*) without material form. This connects to speculations by in particular Rupert Sheldrake. 

Cosmological Principle? Cosmological Constant?

This is a continuation of previous posts on Neo-Newtonian Cosmology NC, with focus on how it was overrun by Einsteinan Cosmology EC as prime ingredient of modern physics. 

It is common in physics, when you know nothing, to assume some form of uniformity like homogeneity or isotropy or equal probability, which gives a background for mathematical modelling. As concerns cosmology as the science of the Universe as a whole, this takes the form of The Cosmological Principle CP stating that on sufficiently large scales: 

• The Universe is homogenous and isotropic.
• In other words: There is no special place and no special direction.  

You can learn this from e g the book Cosmology: The Origin and Evolution of Cosmic Structure by Coles and Lucchin presenting modern cosmological models based on Einstein's General Theory of Relativity  GR with the following key message:

• CP was introduced by Einstein with inspiration from Mach's Principle MP stating that Newton's 2nd Law somehow carries input from the large scale structure of the Universe. 
• CP is supported by Cosmic Microwave Background Radiation CMB.

Einstein somehow had to eliminate Newton from the picture and could do so using CP arguing: 

• An infinite Newtonian Universe with constant mass density is an empty universe. (*)

This is because the only solution to Poisson's equation $\Delta\phi =\rho$ in the whole of 3d space with $\rho$ a nonnegative constant, is $\phi = C$ with $C$ constant and so $\Delta\phi =0=\rho$. 

Referring to MP Einstein could further argue that the local geometry somehow was "curved" by influence from the large structure of the Universe, or the fixed stars in the terminology of Mach's time. MP came out as an attempt to explain the Newton Bucket experiment addressed in the post Absolute Rotation: Newton or Mach? showing that Newton was right and so that MP is invalid. 

Even if his arguments were weak, Einstein managed to set the physics community on a train to Cosmology based on GR one of the two pillars of  modern physics. To make this work and get around (*) Einstein had to introduce a Cosmological Constant $\Lambda >0$ (and then retract as his biggest blunder).  

This corresponds in Newtonian terms to expand $\Delta\phi =\rho$ to $\Delta\phi - \Lambda\phi =\rho$ with non-zero solution $\phi =-\frac{\rho}{\Lambda}$ for $\rho$ constant. 

CMB has been questioned as simply noise without relation to any Big Bang hot dense homogenous initial state. 

Summary: The arguments to replace Newton by Einstein as concerns the large scale structure of the Universe are weak. The scientific price to pay anyway doing so, is very large,

Mass: Inertial = Passive Gravitational = Active Gravitational

Maybe, it is now time for Newton to return? Maybe I was wrong? In any case: Newton forgive me!

The basic model of Neo-Newtonian Cosmology takes the following form in terms of gravitational potential $\phi$ as primordial, mass density $\rho$, momentum $m$ and $u=\frac{m}{\rho}$ 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)
• $\dot\rho +\nabla\cdot m=0$                       (conservation of mass)
• $\dot m +\nabla\cdot (um)+\rho\nabla\phi=0$    (conservation of momentum: Newton's 2nd Law)  

A basic property of this model is conservation of energy in the sense that total energy $KE + GE$  with $KE$ total kinetic energy and $GE$ total gravitational energy, does not change over time: 

• $\frac{d}{dt}(KE+GE) = 0$        (conservation of total energy)

with 

• $KE = \int \rho\frac{u^2}{2} dx$
• $GE = -\frac{1}{2}\int\vert\nabla\phi\vert^2dx$. 

In this model we have identified 

• inertial mass = passive gravitational mass                        (Galileo's Equivalence Principle EP)
• passive gravitational mass = active gravitational mass     (Newton's EP)

with 

• inertial mass = mass $\rho$ in $\rho\frac{u^2}{2}$
• passive gravitational mass = mass $\rho$ in $\rho\nabla\phi$
• active gravitational mass = mass $\rho$ in $\Delta\phi =\rho$. 

In other words, the model has only one form of mass appearing in three different contexts with equality expressed as Galileo's EP and Newton's EP as fundamental features of Newtonian mechanics in the form of Neo-Newtonian Cosmology.

We recall that Einstein used Galileo's EP as a Postulate for his General Relativity (probably also with less exposure Newton's EP). 

Leibniz' Principle of Sufficient Reason shows that Galileo's EP (universality of free fall) cannot be false since sufficient reason is lacking, while violation of Newton's EP would violate conservation of total energy. 

Conclusion1: The basic model of Neo-Newtonian is simple, universal and computable, and it is unthinkable that it is not fundamentally correct. There is no sufficient reason to replace it by General Relativity, which is the opposite of both simple and computable. Recall that a main dilemma of modern physics is the apparent incompatibility/contradiction between its fundamental pillars of Einstein's relativity and Schrödinger's quantum mechanics, while Newton and Schrödinger are fully compatible. More precisely, the incompatibility of the pillars means that modern physics lacks foundation and that is a root cause of the present crisis witnessed by everybody including Sabine Hossenfelder in next post. Contradictory physics cannot be real physics. You cannot turn both left and right at the same time without breaking apart.

Conclusion2: Kinetic energy KE can increase from decreasing GE from increasing $\vert\nabla\phi\vert^2$ from concentration of mass as the engine of gravitational collapse, which gives an endless source of kinetic energy. 

Question: Neo-Newtonian Cosmology and Einstein's Cosmology/General Relativity both start from Galileo's EP + Newton's EP. Does it mean that Einstein agrees with Newton? Probably not, since the basic idea of modern physics is that Einstein does not. The difference appears to be that Einstein demands Lorentz invariance as his incarnation of a Principle of Relativity, while Newton is happy with Galilean invariance. So we have Einstein-Lorentz against Newton-Galileo. What is your bet? Newton-Galileo reigned from 1600 to 1955, while Einstein-Lorentz took over in the 1970s along with the decline of modern physics into our days. Time for Renaissance of Newton-Galileo?

PS1 Recall that the Lorentz transformation lacks physical meaning and so must Lorentz invariance, while Galilean invariance expresses real Newtonian physics. 

PS2 Recall that the above model naturally suggests low intensity distributed $\rho =\Delta\phi\ge 0$ as dark matter and naturally extends to negative $\rho =\Delta\phi$ of as origin of dark energy. Here ordinary matter (protons and electrons) are assigned Inertial = Passive Gravitational Mass, while it is possible (but not necessary) to make a distinction for dark matter with only a role as Active Gravitational Mass thus without Inertial = Passive Gravitational Mass (recall this post). This would mean making a distinction between matter and mass with ordinary matter being assigned mass as Inertial = Passive Gravitational Mass, while dark matter would not be assigned any and so represent mass but not matter..  

Gravitational Mass of Visible Matter vs Invisible/Dark Matter

The previous post (on Neo-Newtonian Cosmology NNC) about dark matter asks if invisible/dark matter connected to a primordial gravitational potential  $\phi$ through the Laplacian differential operator $\Delta$, may not react to gravitational force $-\nabla\phi$ in the same way as visible matter, maybe not at all. 

The halo of invisible/darl matter supposedly surrounding a galaxy would then contribute to gravitational force as an explanation of observed rotation, but would not itself be subject to contraction by gravitational force. 

There would thus be a fundamental difference between visible and invisible/dark matter beyond visibility: Visible matter has gravitational mass (equal to inertial mass), while invisible/dark matter has zero gravitational mass thus acting as a passive contributor to gravitational potential without feedback from gravitational force.

(This is sometimes referred to as active and passive gravitational mass, with the meaning of active and passive switched from a perspective that mass is primordial.) 

There would thus be fundamental difference between the galaxy and the surrounding halo depending on the nature of $\Delta\phi$ as high-density-localised visible or as low-density-distributed invisible.   

The current paradigm of Big Bang + Inflation as Post-Newtonian Cosmology suffers from basic questions without answers such as: What was before Big Bang? What was driving initial very rapid Inflation?

Neo-Newtonian Cosmology offers answers to these questions, and more. Maybe it is time for Newton to come after having been replaced by Einstein during 100 years of confusion.

Cosmology is troubled by the apparent impossibility of detecting any particle nature of dark matter. The basic idea of modern fundamental physics is that of particles as some form of point-like little things which can be captured in particle accelerator detectors, but no dark matter particles have been found, not even by the giant particle detector at LHC (see human scale bottom): 

        Dark matter cannot be detected in a particle accelerator, because it is a large scale phenomena.  

Visible Matter vs Invisible/Dark Matter

The apparent gravitational presence of invisible/dark matter is a key open problem of modern cosmology. 

Recent posts seek an answer as Neo-Newtonian Cosmology NNC starting with a primordial gravitational potential $\phi$ as a rapidly oscillating small amplitude perturbation of a zero potential from which mass density 

• $\rho\equiv\Delta\phi\ge 0$ 

is created through the action of the Laplacian differential operator $\Delta$ acting in a Euclidean infinite space. 

We assume a decomposition $\rho =\rho_v +\rho_{iv}$ with $\rho_v$ as substantial and localised representing visible matter, and $\rho_{iv}$ as small and distributed representing invisible/dark matter with clear separation. With $u=u_v+u_{iv}$ as total matter velocity decomposed into velocity $u_v$ of visible matter and $u_{iv}$ that of invisible dark matter, NNC takes the following concise form:

1. $\rho_v+\rho_{iv} = \Delta\phi$                           (inverse square gravitational law in differential form)
2. $\dot\rho_v =-\nabla\cdot (\rho_v u_v)$                   (conservation of visible matter)
3. $\dot\rho_{iv} =-\nabla\cdot (\rho_{iv} u_{iv})$                 (conservation of invisible/dark matter)
4. $\dot u_v=-\nabla\phi$                                    (Newton's 2nd Law for visible matter) 
5. $\dot u_{iv}=-\nabla\phi$                                  (Newton's 2nd Law for invisible/dark matter) 

We see that the total gravitational force $-\nabla\phi$ acts on both visible matter and invisible/dark matter in qualitatively different ways, with precise motion of visible matter as high density + localised and imprecise motion of invisible/dark matter as low density + distributed. 

The observed velocity distribution of visible matter of spiral galaxies can now be understood as driven by gravitational force from $\nabla\phi$ resulting from presence of high density localised visible matter together with presence of  low density distributed invisible/dark matter.

The key assumption is that visible matter as high density localised in the form of protons and electrons carries electromagnetics, while invisible/dark matter as low density distributed of unknown form, does not. 

Here high density localised represents stars and galaxies separated by large apparent voids, while low density distributed may represent a large halo around a galaxy, see below. 

It is natural to extend to dark energy as $\Delta\phi <0$ as small + distributed with an effect of anti-gravity or repulsion between matter of different sign (and attraction for same sign).

NNC naturally explains an expanding Universe from repulsion between matter of different sign.

Questions: 

• Why does the dark matter halo not gravitationally contract? Is the density too small? Is the rate of contraction very small? Is it possible that the invisible/dark matter does not react to gravitational force, only contributes to gravitational potential? 
• Is the visible galaxy formed from a primordial halo by gravitational contraction of in its center into visible matter? 

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.