Re: [Phys-l] The "why" questions

[John Denker <jsd@av8n.com>]

On 11/29/2010 03:38 PM, Stefan Jeglinski wrote:

> I am not sure that I could argue persuasively because I never 
> believed I quite got it back in the day, but what about this:
>
> http://en.wikipedia.org/wiki/Kramers-Kronig_relation

That's quite an open-ended question, but let me guess that 
the intent was to ask whether the K-K relation is asymmetric
with respect to time.

If that's the intent, please ask a more specific question.

The answer is that the K-K relation purports to describe
electromagnetism, which is well known to be symmetric with
respect to time reversal.  You cannot use electromagnetism
to define the arrow of time.

However, in certain radiation problems we may choose -- quite
arbitrarily -- to consider only the retarded potentials to 
the exclusion of the advanced potentials.  That leads to a
/model/ that is less symmetric than the underlying real physics.
The advanced and retarded potentials together are symmetric.

Similarly, there is a version of the K-K relation that involves
integrating -- quite arbitrarily -- around the upper half plane
to the exclusion of the lower half plane.  That leads to an
/equation/ that is less symmetric than the underlying real
You can equally well form a mirror-image ﻼ-ﻼ relation, and
the two relations together are symmetric.

To summarize:  You can break the symmetry of electromagnetism, 
break it by hand, break it by choice ... but the underlying 
physics remains symmetric.