fredag 30 september 2011

Hubble Law Without Dark Energy

The expansion of the Universe observed by Hubble is commonly connected to a mystical form of dark energy (and/or to a mystical cosmological constant of relativity theory). It is natural to ask if Hubble's observation can be explained by Newtonian mechanics without mysticism?

Hubble observed that far away galaxies appear to recede from the Earth with a velocity V proportional to distance D according to Hubble's Law:
• V = H x D ,
where H is Hubble's constant (about ~ 70 km/s per 1 Mpc ~ 3 million light-years).

Let us assume a Big Bang scenario with the Universe starting out at time T_0 = 0 in a hot dense uniform spherical initial state centered at the origin of a Euclidean coordinate system, and then expanding under a pressure gradient force increasing linearly with the distance to the origin. This could be the force from a (quadratic) pressure satisfying a Poisson equation with constant right hand side connecting to a heat source of constant intensity.

Allowing the Universe to expand from rest under this force for a certain length of time T_1 will bring it into a state with velocity V(r,T_1) increasing linearly with distance r to the origin, that is in accordance with a Hubble Law V(r,T_1) = H_1 r.

Assume now that after time T_1 the expansion force disappears, reflecting that the heat source is no longer active. The Universe will then expand with each galaxy having a constant radial velocity increasing linearly with the distance to the origin at any given time.

Assume now that the galaxies of the Universe visible at a time T > T_1 are observed by an observer at the origin measuring velocity through red-shift and distance by brightness.

Assuming first an infinite speed of light, the observer will thus record
• D(r,T) = r + V(r,T_1) (T-T_1)
• V(r,T) = V(r,T_1) = H_1 r
for a galaxy at distance r at time T_1. Thus
• V(r,T)/D(r,T) = H_1/(1 + H_1(T-T_1)) = H(T) for a galaxy at distance r,
which is again a Hubble Law (recorded at the specific time T), with a modified Hubble constant
H(T).

The conclusion is similar in the case of a finite speed of light causing a linear shift in time of observation depending on the distance to the origin.

We have thus derived a Hubble's Law which is consistent with a Newtonian Big Bang scenario with an initial expansion phase from a uniform hot dense state with accelleration from a pressure force from a constant heat forcing, into a state with expansion velocity proportional to distance, which is then maintained under continued expansion with constant velocity and heat forcing put to zero.

The apparent increase of expansion velocity with distance is here not an effect of a permanent accelleration, but instead a reflection of the linearly increasing velocity of an initial expansion under linearly increasing pressure compatible with a constant heat source.

Notice that the fact that the observer can see only visible galaxies, makes it impossible to detect if the apparent increase of velocity with distance is the effect of (i) a constant contiunued accelleration or (ii) an accelleration during an initial expansion phase after which the expansion force is shut off.

In the case (ii) there is no need to introduce any dark energy to explain Hubble's Law and since (ii) is consistent with observation, by Ockham's razor, it seems to be preferable. We understand that (ii) is a universe with large scale structure governed by inertia and not gravitation, a universe described by Newton's 2nd law.

A similar conclusion is obtained with the Newton law of many-minds relativity of the form
• 1/(1+V) dV/dt = F,
which allows the initial expansion to be exponentially fast with a velocity V(r,t) = exp(rt) which is superlinear in the distance r in accordance with observations of accelerating expansion.

11 kommentarer:

1. Dark energy is not needed to explain Hubble's law. But Hubble's law does not apply throughout the whole universe. There is not a constant linear relation between distance and velocity. It is this departure from Hubble's law that requires explanation, and for which dark energy is currently the most widely accepted. Your post argues from completely flawed premises and thus comes to completely erroneous conclusions.

2. You may be right that dark energy is commonly used to "explain" the observed departure from Hubble's Law, but the question remains how to derive Hubble's law describing an expanding universe. I made a connection to inertial expansion initiated by a linearly varying pressure force consistent with a constant heat source using basic Newtonian mechanics (or the modified Newton law of many-minds relativity). So what are the flawed premises I use? Initial expansion by linear pressure? What is the erroneous conclusion? Hubble's Law?

3. OK, forget about dark energy then. My point is that Hubble's law can be motivated by elementary Newtonian mechanics.

4. I deleted a comment by mistake.. Please resend.

5. Comment by Anonym:
Your flawed premise is your notion that the observed approximately linear relation between distance and recession velocity is somehow related to dark energy. It is not. Dark energy never has and never will be required to explain the Hubble Law in the local universe. The basic meaning of the Hubble Law was worked out 80 years ago by Lemaitre, Friedman, and others. Try reading Lemaitre's 1925 paper, "A homogeneous Universe of constant mass and growing radius accounting for the radial velocity of extragalactic nebulae".

6. "My point is that Hubble's law can be motivated by elementary Newtonian mechanics. "

and so what? You can, if you really want to, understand the concepts of the Big Bang and the expanding universe without knowing relativity. And if you're content with this undergraduate level of understanding, then great. But you're not giving any profound insights into physics here.

7. Of course it is not profound, because it is simple. If relativity is not needed in cosmology, relativity is not needed at all, which will make life much simpler (and thus more constructive) for a humanity suffering under the burden of incomprehensible relativity theory.

8. Relativity is needed in cosmology.

9. For what purpose?

10. To understand phenomena such as black holes, quasars, binary pulsars, supernovae, gravitational lenses, cosmic rays, etc etc etc. Do you really not know this?

11. Does relativity really explain all these phenomena? And what about dark energy?