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..  

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. 

 

Accelerating Expanding Universe: Reality or Illusion?

Hubble's Law collects observations of redshifts of the light from galaxies suggesting that the Universe is expanding away from the Earth at speeds proportional to the distance from the Earth. The Nobel Prize in Physics was awarded work showing larger expansion suggesting an Accelerating Universe with redshifts seemingly corresponding to superluminal speeds at the edge of the observable Universe. 

Speculations about an enormous amount of dark energy as driver of the acceleration expansion were made but, nothing is known about this type of energy supposed to make up 68% of the total energy of the Universe. 

Other speculations seek to solve the mystery generated by the observations of large redshifts by suggesting they are just illusions resulting from measurement techniques. Like the apparent decrease of size with view distance.

Let us make a connection to Many-Minds Relativity where velocities are computed from observed Doppler effects and includes a law of adding two velocities $v$ and $w$ from composite Doppler effects of the form 

• $v+w+vw$ 

as a variant of Einstein's velocity addition law of Special Relativity. Here $v+w+vw$ is the velocity perceived by an observer X moving with velocity $v$ with respect to another observer Y observing the velocity $w$. 

The computed velocity is seen to be larger than the standard $v+w$, and will increase with increasing number of composite Doppler shifts, which could be connected to increasing distance. In the limit that gives from a nominal real velocity $v$ a computed velocity $\exp(v)$ suggesting an expansion of the Universe which is exponentially increasing with distance. We understand that this is an illusion depending on the way we compute velocities from composite Doppler shifts.

So, we have two possibilities of explaining observations of an expanding Universe: 

1. dark matter
2. illusion. 

Which is more reasonable? To believe in 1. requires a massive addition to the total energy of the Universe, a big deal. To believe in 2.  requires simply some understanding of how velocities are computed from redshift observations, no big deal. Your choice.    

Nobel Prize to Cosmology with Dark Energy

Dark energy filling the announcement of the 2019 Nobel Prize in Physics.

The previous post on dark energy and exponential cosmic expansion anticipated the 2019 Nobel Prize in Physics announced today with motivation:

• for contributions to our understanding of the evolution of the universe and Earth’s place in the cosmos

including in particular the discovery that the dark energy apparently filling 68% of the Universe,
is not understood at all.

As a compensation, the previous post contributes the understanding that the exponential expansion being observed and then believed to require massive dark energy, in fact can largely be viewed to be an optical illusion from misinterpretation of red-shifts and if true reduces the need of massive dark energy.

Take a look and see if light enters your mind. There is a new Prize to collect 2020.

And God Said Gravitational Potential!

The question if we live in a simulation is discussed by Ethan Siegel with reference to the 2016 Isaac Asimov Memorial Debate: Is the Universe a Simulation?

The debate connects to my app on Dark Energy at App Store allowing you to play with a cosmological model where gravitational potential $\phi$ is primordial from which mass $\rho$ is connected through the equation $\rho =\Delta\phi$ of local differentiation with the Laplacian differential operator $\Delta$.

In this model a fluctuation of $\phi$ around a zero initial state can create massiv positive and negative mass $\rho$ through the action of differentiation with the power of amplifying fluctuations, thus generating (seemingly out of nothing) universa of positive and negative mass which repel each other and drift apart.

What we can see may thus be one universe of positive mass with its negative counterpart since long gone beyond sight, but with the repellation still felt as dark energy.

Further, visible matter can be connected to $\Delta\phi$ being singular (like a delta-function), while dark matter may correspond to $\Delta\phi$ being smooth.

In the debate the idea of gravitation as primordial "operating system" is touched upon, but is not penetrated since the common view is that it is mass which is primordial from which gravitation magically is created by magic instant action at distance. Turning this common view around making gravitation/gravitational potential primordial, may open to understanding both dark matter and energy. What do you think?

Many Big Bangs: Universe Bigger Than You Think

Astronomer Royal Lord Rees has made a statement:

• There may have been more than one Big Bang, the Astronomer Royal has said and claims the world could be on the brink of a revolution as profound as Copernicus discovering the Earth revolved around the Sun.
• Many people suspect that our Big Bang was not the only one, but there’s a whole ensemble of Big Bangs, a whole archipelago of Big Bangs.
• The theory is still highly controversial, but Lord Rees said he would ‘bet his dog’ on the theory being true.

This fits with the view I have presented in posts on a new view on gravitation, dark matter and dark energy, with gravitational potential $\phi$ viewed as primordial from which matter density $\rho$, which may be both positive and negative, is generated by 

• $\rho = \Delta\phi$, 

through local action in space of the Laplacian $\Delta$. In this model a Big Bang corresponds to a small local fluctuation of $\phi$ around zero, which generates an much bigger fluctuation of matter density by the action of the Laplacian. 

In this model substantial matter may be generated locally from small fluctuations of gravitational potential opening the possibility of an endless number of Big Bangs seemingly created out of nothing. 

You can test the model in the app Dark Energy on App Store.

Dark Energy Appearing at App Store

The app version of Body&Soul is now starting to appear on App Store with a first app on a new theory of Dark Energy now available for free download.

It gives an eye-opening experience into one of the basic mysteries of modern physics. Try it out and see if you get the idea!

Mystery of Dark Energy, Dark Matter and Inflation Uncovered?

In a series of posts (listed under Newtonian mechanics) I have explored the idea of viewing the gravitational potential $\phi (x,t)$ as primordial physical entity, with $x$ a Euclidean space coordinate and $t$ a time coordinate $t$, from which the distribution of matter with density $\rho (x,t)$ is given by (with scaling to unity):

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

by the local operation of differentiation of the Laplacian in space $\Delta$. This view possibly opens  to an understanding of the mystery of both dark energy, dark matter and cosmic inflation. Recall that (1) as the essence of Newton's theory of gravitation, also is Einstein's equation in flat Minkowski space-time.

To lift the curtain, imagine an initial state with $\phi =0$ and thus $\rho =0$ and suppose $\phi$ at time $t=0$ is  subject to a local perturbation resulting in a corresponding fluctuating $\Delta\phi$ with as much positive matter where $\Delta\phi (x,t)$ is positive, as negative matter where  $\Delta\phi (x,t)$ is negative. Suppose the initial configuration consists of negative matter surrounded by positive matter in spherical symmetry, thus a shell/ball of negative matter (red) surrounded by positive matter (blue), as in the above picture of a youtube-clip.  Note that positive matter attracts positive matter, but repels negative matter, and vice versa.

Watching the clip you see starting from rest negative (red) matter contracting under attraction and positive matter (blue) expanding under repulsion from negative matter overpowering attraction from positive matter.

If we now think of our Universe as consisting of positive matter, we thus find an expanding Universe as if driven by a mysterious force named dark energy and we thus are led to connect the origin of dark energy to negative matter.  Note that the core of negative matter oscillates between contraction and expansion, while the region of positive matter continues to expand on a much longer time scale.

We may further connect regions of positive matter where $\Delta\phi (x,t)$ is smooth as regions filled with dark matter, and then singular concentrations of $\Delta\phi (x,t)$ as visible matter.  

In this model we start from zero, and Big Bang is represented by a small perturbation of the gravitational potential $\phi$ with large output $\Delta\phi$ as balancing positive and negative matter. It is then the nature of the Laplacian as local differentiation, as an illposed or unstable mathematical operation, which can turn a small perturbation into something big like a Universe. Big Bang thus does not come out as a big local explosion, for which a reason is lacking, but rather as the effect of a small perturbation of a zero-state which is inflated by the Laplacian.

In particular, the inflation of the Universe connects to the relation $\Delta\phi =\rho$ and not as in cosmic inflation theory to yet another mystery.

Finally, with matter derived from a gravitational potential by local differentiation, the unsolved problem of the nature of action at distance does show up at all: All action is local and there is no action at distance and nothing of that sort to explain.

Is then our expanding Universe of positive matter powered by an oscillating Universe of negative matter, with plus and minus adding to zero, resulting from an initial perturbation of a gravitational potential through the action of a Laplacian? Yes, why not? Compare with Genesis 1:1-4 with the initial perturbation just a little twist of God's finger:

The Universe as Weakly Compressible Gas subject to Pressure and Gravitational Forces

Our Milky Way Galaxy as a weakly compressible gas modeled by the Euler equations expressing conservation of mass, momentum and energy, combined with constitutive laws connecting pressure and gravitational forces to mass density.

After the excursion on Newton vs Einstein in recent posts, we are back to a cosmological model in the form of Euler's equations for a compressible gas subject to Newtonian gravitation: Find $(\rho ,m, e ,\phi ,p)$ depending on a Euclidean space coordinate $x$ and time $t$ , such that for all $(x,t)$:

• $\dot\rho + \nabla\cdot (\rho u ) =0$       (or $\frac{D\rho}{Dt} = -\rho\nabla\cdot u$)
• $\dot m +\nabla\cdot (mu) +\nabla p + \rho\nabla\phi =0$
• $\dot e +\nabla\cdot (eu) +p\nabla\cdot u +\rho\nabla\cdot m=0$,

where $\rho$ is mass density, $u=\frac{m}{\rho}$ is matter velocity, $p$ is pressure, $\phi$ is gravitational potential, and $e$ is internal energy as the sum of heat energy $\rho T$ with $T$ temperature and gravitational energy $\rho\phi$, and the dot indicates time differentiation and

• $\frac{D\rho}{Dt}=\dot\rho +u\cdot\nabla\rho$

is the convective time derivative of $\rho$, see Many-Minds Relativity 20.3 and Computational Thermodynamics Chap 32.

These equations express conservation of mass $\rho$, conservation of momentum $m$ with $\nabla p$ pressure force and $-\nabla\phi$ gravitational force, and conservation of internal energy $e$. These laws of conservation are complemented with constitutive laws connection $p$ and $\phi$ to density of the following form:

A1: Weakly compressible gas ($\delta$ small positive constant):

• $\Delta p =\frac{\nabla\cdot u}{\delta}= - \frac{1}{\delta\rho}\frac{D\rho}{Dt}$

or

A2: Compressible perfect gas ($0 < \gamma < 1 $): 

• $p=\gamma \rho T$.

B: Newton's law of gravitation:

• $\Delta\phi =\rho$ with $\phi =0$ at infinity.            

We observe

1. Similarity of $\nabla p$ and $\nabla\phi$ in momentum equation. 
2. Similarity between A1 and B connecting $\Delta p$ to $-\frac{D\rho}{Dt}$ (or $-\rho$) and $\Delta\phi$ to $\rho$.
3. $p \ge 0$ and $\phi \le 0$.

Here 1 can be seen as the Equivalence Principle (equality of heavy and inertial mass) expressing that there is no difference between gravitational and other forces (pressure) in Newton's 2nd law expressing conservation of momentum.

Further, 2 expresses that the constitutive laws A1 and B both can be viewed as action at distance if $\rho$ is viewed as the cause, but represent local action of differentiation if $\rho$ is viewed as the effect. 

For a weakly compressible gas described by A1, there is no need per se to identify a cause-effect relation between $p$ and $\rho$; it is enough to say that $p$ and $\rho$ are connected in a certain way expressing a form of "perfect harmony". 

In the same way, there is no need per se to identify a cause-effect relation between $\phi$ and $\rho$; it is enough to say that $\phi$ and $\rho$ are connected in certain way expressing a form of  "perfect harmony" in the spirit of Leibniz.

The relation $\Delta\phi =\rho$ is explored in Newtonian Matter and Antimatter with $\Delta\phi > 0$ identifying matter and $\Delta\phi < 0$ antimatter. Mind-boggling!

It may be that the above Newtonian model is just as good (or even better) than Einstein's equations as cosmological model, because it is understandable and may contain relevant large scale physics without the mysteries of "curved space-time fabric" of general relativity.

Second Law of Thermodynamics

Viscosity solutions of the Euler equations satisfy the following 2nd law:

• $\dot K = W_p + W_\phi - D$
• $\dot E = - (W_p + W_\phi ) + D$,  

where at a given time instant $t$

• $K=\int\frac{\vert m\vert^2}{2\rho}\, dx$ is total kinetic energy
• $E=\int e\, dx$ is total internal energy 
• $W_p=\int p\nabla\cdot u\, dx$ is total work performed by pressure 
• $W_\phi =\int \phi\nabla\cdot m\, dx$ is total work performed by gravitation
• $D>0$ is turbulent dissipation.

The sign of the turbulent dissipation $D$ gives an irreversible transfer of kinetic energy $K$ into internal energy $E$, which defines the direction of time. Transfer from internal energy requires $W_g+W_\phi >0$, that is expansion with $\nabla\cdot u > 0$ if $W_\phi=0$ and contraction with $\nabla\cdot u < 0$ if $W_p=0$. Note also that

• $W_\phi =- \int \phi\dot\rho\, dx =-\int\phi\Delta\dot \phi\, dx =\frac{d}{2dt}\int\vert\nabla\phi\vert^2\, dx$.

Notice that the above 2nd law does not involve the notion of entropy, and thus avoids the trap of common formulations of the 2nd in terms of an ill-defined concept without physical realization. The above 2nd law only uses the physical concepts of kinetic and heat energy, work and dissipation.

Choice of coordinate system

The Euclidean coordinate system could be fixed to distant fixed stars with the origin at the projected center of the universe. A rotation of this system would show up as extra centrifugal forces, which could explain the apparent accelerated expansion of the universe.

Uni-directional transfer of energy - Alternative pressure laws

Note that A1 implies that $W_p= - \int\delta\int\vert\nabla p\vert^2\, dx < 0$ showing uni-directional transfer of energy from kinetic energy to internal energy. Transfer in the other direction can appear with the stronger effect of compressibility in A2. Of course, combinations of A1 and A2 are thinkable, as well as a pressure analog of B in the form A3: $-\Delta p \sim e$ with $e=\rho T$ and $T$ temperature.

Recall that $W_\phi = \frac{d}{2dt}\int\vert\nabla\phi\vert^2\, dx$, thus with a positive contribution to kinetic energy $K(t)$ over time.

Basic dynamics

The basic dynamics of the above Euler model can be described as local gravitational collapse with gravitational energy being transformed first into kinetic energy and then into heat energy, followed by pressure build up setting a limit to concentration of matter, leading to cosmic web of matter separated by voids:

Visible matter would correspond to $\Delta\phi$ being singular (points, lines, surfaces), while dark matter would correspond to  $\Delta\phi$ being smoothly distributed (and positive).

PS Note that the momentum equation can be formulated:

• $\rho\dot u +\rho u\cdot \nabla u + \nabla p + \rho\nabla\phi =0$, that is
• $\dot u +\rho u\cdot \nabla u + \nabla\phi = F$ or    $\frac{Du}{Dt} + \nabla\phi = F$,

where $F$ (with here $F = - \frac{1}{\rho}\nabla p$) can be viewed as a definition of mass density normalized force $F$ in terms of acceleration $\frac{Du}{Dt}$ and gravitational potential gradient $\nabla\phi$. This connects to the common notion of gravitation(al force) as acceleration, with acceleration acting locally in space and time. Again, the basic question is the (lack of) cause-effect in the relation $\Delta\phi =\rho$, where we are not compelled to view $\rho$ as the cause and $\phi$ the effect from instant action at distance, and thus may instead view $\rho$ as the effect of the Laplace operator acting locally in space and time on $\phi$, or simply bypass the question by viewing $\rho$ and $\phi$ to be connected in "perfect harmony by the relation $\Delta\phi =\rho$ without cause-effect dynamics.  

  

No Solutions to New Years Puzzle

The New Year Puzzle has not received any convincing solutions and therefore additional clues are offered in new posts on The World As Computation:

• Repulsion between Matter and Antimatter
• Laplace's Equation as God's Equation
• Newtonian Gravitation of Matter and Antimatter
• Newtonian Unified Field Theory?

Dark Age of Physics?

To celebrate the 2011 Nobel Prize in Physics I have written the post Accelerating Expansion Without Dark Energy? on the new home at The World as Computation of My Book of Knols.

More about the dark age of physics as presented by the Nobel Laureates here.

Cosmology as Thermodynamics with Gravitation

It may be that the large scale dynamics of the universe (cosmology) can be described as the thermodynamics of a compressible gas subject to gravitation in the form of the Euler equations, see Computational Thermodynamics (Chapter 32).

The basic laws of thermodynamics resulting (by integration in space) from the Euler equations, take the form:

1. dK/dt = W - D + GP (conservation of (total) kinetic energy K)
2. dE/dt = - W + Q + D (conservation of (total) internal/heat energy E)

where

• W = Integral P div V dx is work by pressure P on velocity V
• GP = Integral Phi div V dx is work by (negative) gravitational potential Phi on V,

Q is a heat source and D is turbulent dissipation. Notice that

• W + GP = Integral (P + Phi) div V dx,

showing the similar action of the pressure P and gravitational potential Phi with P + Phi > 0

under accelleration with dK/dt > 0.

The standard cosmological model is that of Friedmann-Lemaitre-Robertson-Walker (FLRW) which expresses 1. + 2. assuming the validity of the Cosmological Principle (CP) of an isotropic and homogeneous universe.

CP is extremely restrictive by reducing space dependence to a simple scale factor depending only on time with the FLRW model being simply a system of two time-dependent scalar equations. CP predicts a decelerating expanding universe, while observations show instead acceleration, and thus CP must be abandoned, and cosmology thus today struggles to get out of the paralyzing grip of CP.

Let us then see what 1. + 2. may tell in a case without CP. Let us then assume that the gas/universe starts out at rest as a hot compressed sphere (centered at the origin of a Euclidean coordinate system) subject to a heat source Q > 0 and develops in a Big Bang scenario according to 1. + 2. as follows (assuming here for simplicity that D = 0):

• expansion (dK/dt > 0) with W + GP > 0 sustained by Q > W.

In words: the heat source Q creates a pressure P sufficiently large to expand the gas under

gravitation with W + GP > 0. For a perfect gas P = Rho T where Rho is density and T temperature. It is natural to connect T to the intensity q of the heat source by the Poisson equation

• - Laplace T = q

which in the case of constant q gives T(r) quadratic and dT/dr linear in the distance r to the origin. With Rho roughly constant that leaves a pressure gradient dP/dr which is also linear resulting in a velocity V_1(r) increasing linearly in r from V(0) = 0 during Big Bang. Wiith q variable, velocities V_1(r) with sublinear (or superlinear) variation may also arise.

After the initial Big Bang expansion phase just described, assume that the heat source Q is turned off, and the gas expands mainly by inertia with dK/dt = 0 from the initial velocity V_1(r), with W = 0 and Q = 0 assuming that inertia dominates gravitation. The initial velocity V_1(r) will then be carried to later time.

A sublinear V_1(r) could then, when observed at some later time and taking the finite speed of light into account, be interpreted as an indication of an accelerating expansion corresponding to a Hubble constant seemingly increasing with time, with more distant galaxies appearing to have a smaller Hubble constant.

This was the observation giving the 2011 Nobel Prize in physics. But the observed acceleration could be an illusion reflecting a sublinear velocity V_1(r) resulting from specifics of the pressure gradient forcing during the initial Big Bang expansion. This would reflect that inertia dominates gravitation on intergalactical scales, while gravitation would balance inertia on galactical scales (compare with The Hen and the Egg of Dark Matter).

In this case there would then be no need to introduce any dark energy behind the observed acceleration, because an illusion is an illusion, and physics could focus on something more constructive than searching for something that may not exist, as in the Scarlet Pimpernel:

We seek him here, we seek him there,

Those Frenchies seek him everywhere.
Is he in heaven? — Is he in hell?
That damned, elusive Pimpernel.

CP reflects the following extension of Galileo's departure from geocentrism into heliocentrism:

• If the Earth is not the center of the Universe, then there is no center of the Universe at all.

Incidently, this connects to Einstein's elimination of any form of aether (see Many-Minds Relativity)

• If my aether is not everybody's aether, then there is no aether at all.

CP connects to the first rule of the Jante Law identified by the Danish-Norwegian author Aksel Sandemose in his novel A fugitive crosses his tracks, as a characteristic of Scandinavian mentality:

• Don't think you're anything special,

which expresses the Galilean principle:

• If I am not special, then nobody else is special.

But the Jante Law is today questioned (also in Sweden) and so maybe CP also should be questioned?

Cosmology as Thermodynamics without CP and Dark Energy

The basic cosmology model is the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric expressing Einstein's field equations in the special case of an isotropic and homogeneous universe according to the Cosmological Principle (CP) stating that no place or direction is better than another, in the form of (i) Friedmann's equation, combined with a (ii) fluid equation.

Friedmann's equation expresses (i) conservation of kinetic energy + gravitational energy, and the fluid equation expresses (ii) conservation of internal energy (heat energy), and thus the FLRW model is nothing but an expression of the basic laws of thermodynamics under the CP of an isotropic and homogeneous universe.

FLWR/CP predicts that the expansion of the universe should slow down by gravitation, and this is the background to the 2011 Nobel Prize of physics for observations of instead acceleration. The Prize is given for the surprising observation that FLWR/CP is wrong!

But is it surprising that FLWR/CP is wrong? Is it surprising if CP is not valid? Of course not!

CP is a incredibly strong assumption and FLWR is an incredibly simplistic model. There is no real reason to believe that such a simple model could say anything correct about the expansion of the universe.

The Noble Prize is thus awarded for the observation that an incredibly simple model of the universe is not correct at all. This is surprising.

Even more surprising is that based on this incredibly simple model and observations that the incredibly simple model is not at all correct, the conclusion is drawn that there is a completely unknown new form of energy named dark energy which is needed to make the simplistic incorrect model less simplistic and incorrect.

But there is another more reasonable conclusion to draw and this is to see what thermodynamics without CP can tell about the universe, maybe without any need to invent any completely new form of energy named dark energy.

This connects to previous posts on dark energy and will be the subject of upcoming posts.

Nobel Prize of Dark Energy

By a funny coincidence my previous post Hubble Law Without Dark Energy appears to have triggered the 2011 Nobel Prize in Physics for

• the discovery that the Universe is expanding at an ever-accelerating rate

with the following motivation:

• The discovery came as a complete surprise even to the Laureates themselves.
• If the expansion will continue to speed up the Universe will end in ice.
• The acceleration is thought to be driven by dark energy, but what that dark energy is remains an enigma - perhaps the greatest in physics today.
• What is known is that dark energy constitutes about three quarters of the Universe.
• Therefore the findings of the 2011 Nobel Laureates in Physics have helped to unveil a Universe that to a large extent is unknown to science.
• And everything is possible again.

But to introduce a completely new phenomenon of dark energy as explanation of the seemingly accelerating expansion of the Universe, does not seem to help understanding much, if understanding is what science is about.

In the previous post I reflected over a simple idea to explain the observations, based on expansion by inertia from an initial inflated state resulting from a Big Bang expansion driven by a pressure increasing with distance caused by a heat source creating a velocity also increasing with distance. Observations made today would then represent space-time cuts with again velocities increasing with distance. The velocity distribution would then be set by the pressure distribution in the Big Bang expansion determined by the specifics of the heat source, without any need to introduce new forces (beyond inertia) of unknown nature.

Note that the observations of more distant (dimmer) far away galaxies than expected behind the Nobel Prize, would correspond to a sublinear increase of velocity with distance at the start of the inertial expansion after Big Bang expansion, which would not as such appear to be surprising. The surprising observations may thus in fact not be so surprising, which is surprising.

Remember what Einstein adviced:

• Everything should be made as simple as possible, but not simpler.