From: mock@space.mit.edu (Patrick C. Mock)
Subject: Re: grav lensing
Originator: mock@ergos
Reply-To: mock@space.mit.edu (Patrick C. Mock)
Organization: MIT Center for Space Research
Distribution: na,sci
Date: Mon, 27 Jul 1992 19:32:25 GMT


First and foremost, standard physics predicts that a gravitational lens
will reimage point sources as point sources except for a few special
cases associated with critical alignments.  The article by Blandford et al,
Science (Vol 245, pg 824) gives the best explanation I've found.
TVF's claim that gravitational lenses should produce ring arcs or rings from
point sources conflicts with standard physics.  Further, his explanation has 
some obvious flaws which I pointed out in my last post.  Now to the specifics.

In article <Bs0KxG.Lo2@well.sf.ca.us>, metares@well.sf.ca.us (Tom Van Flandern) writes:
>  ...
>      You say you don't believe all those authors got it wrong.  That may be
> at the root of this difference of viewpoint, because it has been my
> experience that any number of experts who are working toward or expecting a
> particular result can fool themselves into that result.  You may notice that
> many of the ideas I challenge are held by a pool of "leading experts".  They
> must nonetheless be able to withstand critical scrutiny.  It is still my
> opinion that the present idea cannot withstand such scrutiny.
> 
I understand that you disagree with the leading experts.  In this case
you are also disagreeing with some very basic physics.   What I want
to emphasize is that standard physics, used by Blandford et al. and many
other authors, does not support your claim.

>      My argument is simple and easy for anyone to grasp.  The counter-
> arguments you have quoted require considerable work to grasp even the
> essentials, and then they seem so skirt the basic point I have made here: the
> *shape* of the image of a point source being gravitationally lensed will be a
> ring-arc in general, or a full ring if axial alignment is quite close.
> Moreover, that is what is observed in the only cases which everyone here
> agrees are true gravitational lenses, namely galactic clusters lensing
> background blue objects.
> 
A simple argument is not guaranteed to be right.  In this case I would
characterize your explanation as incomplete.  What you've described is 
a set of null paths.  Fermat's principle tells you which of these null 
paths are actually followed by light.

> > According to Fermat's principle only null paths for which the travel time
> > is stationary with respect to infinitesimal changes in the path contribute
> > to the observed image.  For more information on Fermat's principle and how
> > it applies to lenses in general, consult Born and Wolf, "Principles of
> > Optics", QC355.B736, or your favorite classic optics text.
> 
>      I have not yet had the opportunity to refresh myself on Fermat's
> principle.  But my recollection is that this refers to the obvious problem
> that if a ray path is delayed by one-half wavelength, one gets destructive
> interference and hence no image.  Obviously this has no applicability
> whatever to the present problem, where ray paths can differ by 10^25
> wavelengths.  And it was not invoked in the papers you cited.  If I am mis-
> recalling the importance of the principle, please outline the correct general
> argument, and I'll complete my refresh on it ASAP.  -|Tom|-

Fermat's principle was discussed in the Blandford paper.  The first
paragraph on the third page (p 826) starts "Fermat's principle."  Your
reading must have been very cursory.  The other references I gave do not
invoke Fermat's principle but they still get the same results.  Fermat's
principle is a tool that applies to any optical system.  It is not the
only method for getting the right answer but I find it conceptually
helpful.  Your recollection might be related to some specific example.

One of the best explanations I've read about photon behavior is
chapter 2 of Feynman's book, "QED, The Strange Theory of Light and Matter".
Although he does not mention Fermat's principle by name he does use
the concept of "least time" which is the essence of Fermat's principle.

Here is an explanation of the physics behind Fermat's principle as I
understand it.  This explanation relies on the quantum nature of photons
in that even a single photon will interfere with itself (ie. like the
classic double slit experiment where one photon at a time passes through
the slits and the interference pattern still appears).  

   For any optical system (ie. a gravitational lens) pick a null path
   through the system (ie. one of the paths you describe).  Associated
   with this path are an infinite number of paths that are
   infinitesimally different from the first path.  I can define this set
   of paths to be those paths which are close enough to the original path
   such that photons traveling along the paths can interact with each
   other.  Such a set of paths has a small but finite size which depends on 
   the wavelength of the interacting photons.

   If the time delay along the first path is stationary with respect to
   infinitesimal changes in the path, each path in the set has exactly
   the same time delay.  The interaction of photons along the
   set of paths results in constructive interference and light propagates
   along that path.

   If the time delay along the first path is not stationary with respect
   to infinitesimal changes in the path, each path in the set has
   a different time delay.  The interaction of photons along
   the set of paths results in destructive interference and light does
   not propagate along that path.

I want to emphasize that this is only one way to understand the physics
behind Fermat's principle.  Even if my understanding is flawed, Fermat's
principle can be proven in classical optics and and in quantum
electrodynamics and it applies to all optical systems including
gravitational lenses.  Born and Wolf (Section 3.3.2) give a proof of
Fermat's principle in term of classical optics with no reliance of quantum
effects.

Pat

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