2nd Law for Cosmology

A mathematical model of the Universe can take the form of Euler's equations for a gas supplemented with Newton's law of gravitation as stated in Chap 32 Cosmology of Computational Thermodynamics.  

Computational solutions of these equations satisfy the following evolution equations as laws of thermodynamics depending on time $t$ 

• $\dot K(t)=W(t)-D(t)-\dot\Phi (t)$     (1)
• $\dot E(t)=-W(t)+D(t)$,                  (2)

where $K(t)$ is total kinetic energy, $E(t)$ total internal energy (heat energy), $W(t)$ is total work, $D(t)\ge 0$ is total turbulent dissipation, $\Phi (t)$ is total gravitational energy and the dot signifies differentiation with respect to time. Adding (1) and (2) gives the following total energy balance:

• $K(t)+E(t)-\Phi(t)= constant.$          (3)

Further (1) and (2) express an irreversible transfer of energy from kinetic to internal energy with $D(t)>0$, and so serve as a 2nd Law for Cosmology giving time a direction. Recall that the theoretical challenge is to tell/show why turbulent dissipation is unavoidable. 

Computations may start from a hot dense state at $t=0$ which is seen to expand/cool (run code) (Big Bang) to maximal size and then contract/warm back to a hot dense state (Big Crunch) (run code) in an irreversible sequence of expansions/contractions until some final stationary equilibrium state with $E(\infty )=P(\infty )$. Compare with post from 2011.

How to Get a Nobel Prize

There is a new post on The World as Computation presenting a scientific method of How to Get a Nobel Prize.

Keep confidential. Do not spread!

From Modern to Post-Modern Physics

Physics has the top position in the hierarchy of sciences because physics is the science where a Principle of Objectivity (PO) comes to its fullest expression.

Modern physics was born in the beginning of the 19th century when the PO of classical physics of Newton's absolute space and time was confronted with the null-result of the Michelson-Morley experiment indicating that the speed of Earth through an aether of absolute space was zero, as if the Earth was dragging the aether of absolute space along on its path around the Sun. This was in direct conflict with the PO of the Copernican principle stating that the Earth is not the center of the Universe as the anchor of absolute space.

Einstein solved the dilemma by simply declaring that there is no aether whatsoever and then developed his special theory of relativity as an ultimate expression of a PO declaring that physical laws must look the same in all reference/coordinate systems. A physical law which takes different forms in different coordinate systems, would then not be a true fundamental physical law because it would violate PO.

Einstein thus managed to keep physics at its top position by initiating a modern form of physics in accordance with PO, based on the following fundamental expressions of objectivity:

• no-aether special theory of relativity
• universal wave function of quantum mechanics
• Cosmological Principle (CP): the universe is homogeneous and isotropic.

Modern physics thus kept the top position in the hierarchy of sciences by claiming superior full objectivity, but the price of maintaining PO has shown to be very high and has led modern physics into a free fall diverging from reality into string theory on small scales beyond rationale and cosmology on large scales beyond comprehension, topped with a new completely unknown form of dark energy as a result of CP.

From this crisis new forms of physics as post-modern physics, are now emerging where special reference systems are again allowed as in classical physics and the PO is no longer worshipped in extreme. This makes physics more like other sciences, more human and more useful. In fact, Einstein re-introduced in his general theory of relativity the aether he had eliminated in his special theory of relativity. Einstein was very clever.

I describe possible forms of post-modern physics as many-minds physics in the upcoming books:

• Many-Minds Relativity
• Many-Minds Quantum Mechanics

and the collapse of modern physics is recorded in:

• Dr Faustus of Modern Physics.

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.