onsdag 28 september 2011

Many-Minds Relativity: Hubble's Law

The American astronomer Edwin Hubble discovered in 1929 that far away galaxies seem to recede from the Earth with a velocity V approximately proportional to their distance D according to Hubble's Law:
  • V = H x D ,
where H is the Hubble constant (about 70 km/s/Mpc with 1 Mpc about 3 million light-years). The velocity V is computed from observed redshift and the distance D is determined from observed luminosity. Galaxies with greatest observed distances (about 13-14 billion light-years) appear to recede with a velocity greater than the speed of light.

Hubble's law is a corner stone in the Big-Bang theory with the Universe being initiated in a very hot dense state and then expanding under high pressure.

Let us now see what many-minds relativity has to say about Hubble's law. We recall Newton's law in its many-minds relativity form:
  • 1/(1+V) dV/dt = F ,
where V(t) is the velocity of a unit mass moving under the action of a force F and we assume the velocity of light is normalized to 1. We get if F is a (positive) constant, for t > 0:
  • V(t) = exp(Ft) - 1
  • D(t) = exp(Ft)/F - t
for the velocity V(t) and position D(t) of a galaxy starting from rest at t = 0. We see that for t >> 1
  • V/D ~ F
which looks like Hubble's Law if F = H.

But how can we motivate that F = H? What is this mystical force F (directly connecting to equally mystical dark energy) causing the Universe to expand?

Note that with the usual Newton's Law dV/dt = F, we would get V/D = 1/t which does not conform with Hubble's Law. Neither does Einstein's relativistic form with 1/(1 + V) replaced by 1/ the square-root of 1 - V^2.

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