fredag 7 oktober 2011

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)
  • 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?

3 kommentarer:

  1. Could there be a likeness between the expansion of the universe and the supersonic expansion of a compressible gas?
    If so, this would explain why the expanding universe accelerates near its outer edge.

  2. Also.
    I think that there could be also a similitude with the continuity equation of a rising gas within the planetary atmosphere as d(ρw)/dz = 0 implies ρw = Const and then w = Const/ρ. So w increases as long as the air climbs.
    What is more believable?

  3. Maybe, but I think one should first check if the acceleration is only an illusion. If the acceleration is real, it must require some force but no force is known, only speculations about dark energy and some cosmological constant.