Re: Missing Matter
- From: Charles Francis <charles@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Fri, 2 Dec 2005 09:48:26 +0000
In message <QNzW+lAFYKjDFwNr@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, Charles Francis <charles@xxxxxxxxxxxxxxxx> writes
But the square law would have the universe at 1/30 its current size at decoupling. If decoupling is at a particular density (is it?) then I get 30^3 times the amount of matter at decoupling. That seems like a lot too much.This seems to be the mistake. When calculating redshift from a distant galaxy the reference frame for the initial state is determined only from the red-shifted light arriving from the galaxy, and the square law applies. But the CBR defines a comoving reference frame by looking at light from all directions. In this case distances are rescaled such that the standard linear law applies. So I have the standard factor of 1000 for the expansion since decoupling.
I haven't cheated honest. At the beginning of section 3 I have said:
Typically in quantum theory experiments require a measurement of the initial state and a measurement for the final state, and are such that reference matter used for the initial measurement is rigidly related to that used for the final one; either the same coordinate axes and clock are used in both measurements or the coordinate axes and clocks are calibrated to each other. As seen in section 2.4 this requires a renormalisation of energy momentum, such that geodesic motion and the principle of equivalence are restored. But in measurements on light from a distant object it is not possible to define a prior relationship between the reference matter used for the final measurement and the matter from which the photon is emitted. Light received at the origin has been transmitted from an event on the light cone, so that the only information we have about the initial state comes from measurement of the final state. There is then no renormalisation of energy-momentum, and cosmological redshift is read from 2.4.2:
The CBR defines the same reference frame for both the initial and final measurements (comoving coords) hence energy momentum is renormalised back to the standard values.
--
Best regards
Charles Francis
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