Re: Postulates of Relativity and The Cosmic Background - Question

Paul Valois:
>Thanks for the reply.
>
>It don't understand what a "dipole moment" is. I understand that the
>word "dipole" in reference to the Cosmic Background refers to the
>dichotomy between extremes in the brightness of the background, but I
>couldn't find a sufficiently dumbed-down article on the web that
>explains what a "dipole moment" is.

A dipole moment is something that points in a particular direction.
For example, consider a bar magnet:
.<-.
. .
S <---- N
. .
. <-.

The field lines point in the direction from the nort pole toward
south pole. The dipole moment characterizes the directionality of
the magnet.

>Some of the observed dipoles are due
>to our own motion, some to the galaxy's motion, some due to the motion
>of galactic clusters, and the rest is fossilized anistropy from the Big
>Bang, right?. Is the use of the word "moment" here related to motion?

The term ``moment'' is very general and it is used to characterize
a ``directionality,'' so it indicates the isotropy (or equivalently,
anisotropy) some quantity. A dipole moment measures an offset from
zero _and_ the direction of the offset. It depends upon what you define
as zero. The dipole moment is also called the average or mean value.
A quadrupople moment describes the deviation about the mean value
and is also called the standard deviation. You can go on to define
higher order moments, too. The dipole moment of the cosmic background
is defined by the asymmetry of the redshift in different directions
_with_ _respect_ _to_ _the_ _earth_. The velocity ``zero'' would represent
cosmic background radiation that is isotropic, i.e., red shifted by the
same amount in all directions. The cosmic dipole moment represents an
asymmetry in the redshift. That is, the cosmic background is redshifted
by different amounts depending upon which direction you look. The overall
asymmetry is called the dipole. If te redshift were the same in all
directions, it would indicate the sources were all receding at the
same velocity _on_ _average_. By convention, we call this zero because
we are interested in the extent to which the velocity differs from
the average velocity in which the background would be isotropic.

The cosmic background dipole is related to motion because the redshift
is related to motion. The dipole is not necessarily indicative of any
point representing an absolute frame however, because the existence
of a dipole moment doesn't imply the existence of _any_ point for which
the dipole moment is zero. Consider the magnet above. It has a dipole
moment, but there is no way to orient the magnet such that the magnetic
dipole moment is zero. In terms of the cosmic background, the existence
of a dipole moment, doesn't imply that you can move at some velocity
at which the dipole moment vanishes, i.e., that the cosmic backgound
appears isotropic, i.e., it doesn't imply that you can find some
velocity relative to the earth that define an absolute velocity of
zero.


.

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