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Re: [Phys-L] Each ray travels "as if it knew" all values of t=t1+t2



But lightning "figures out" what will be the path of least resistance
before it strikes, right?
On Apr 13, 2014 3:56 PM, "Ken Caviness" <caviness@southern.edu> wrote:

Treating it in a quantum, "sum over all histories" way:

The light acts as if it follows all paths from point A to point B, but
most of those paths cancel out: the wave arriving by almost every path
interferes destructively with the wave arriving via some other route. The
minimum time path, however, can't cancel out: the wave arriving that way
arrives first, before any other candidate for interference. So the light
wave traveling along the minimal time path is the one that actually occurs,
the one that is actually observed.

Perhaps someone with a stronger background in quantum electrodynamics
could vet that paragraph, but I believe it to be basically correct, and it
obviates any need to assume light rays that somehow "know" before they
select a path which one will end up being the least-time path.

KC

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Ludwik
Kowalski
Sent: Sunday, 13 April, 2014 12:59 PM
To: phys-L new
Subject: [Phys-L] Each ray travels "as if it knew" all values of t=t1+t2

1) On 4/12/2014 John Denker wrote: " ... Snell's law was invented and
re-invented several times, long before there was any connection to waves.
In particular, one can postulate Fermat's principle of least time as a
first principle. One can apply it on a ray-by-ray basis, as a way of
deriving and/or explaining Snell's law ... without mentioning waves."

2) Suppose the air-water boundary is a horizontal plane. Suppose a ray
(representing a collimated beam of light), travels from a point A (in air
above water) toward a point B, at the water surface. This defines the plane
of incidence. The refracted ray, passing through an underwater point C,
defines the plane of refraction. It turns out that the plane of refraction
coincides with the plane of incidence, and that the angle of incidence and
the angle of refraction satisfy Snell's law. These are experimental facts.

According to Fermat's principle, "light travels between two points along
the path which requires the least time, as compared to other conceivable
nearby paths." In this particular situation(see the figure below) the
near-by paths are all imaginable "AB plus BC."

3) What does the phrase to "postulate Fermat's principle" stands for? Does
it mean to assume that each individual "ray," emerging from the point A, is
intuitively choosing a path (choosing the point B) for which the time of
travel from A to C will be the shortest?





4) Browsing the Internet I found an interesting answer to this question.
The author wrotes: "I think it's a little misleading to say that light
'knows' the end point in advance since 'knowing' also implies some kind of
consciousness." In other word's, the Fermat's principle is not an
explanation; it is only a description. Each ray travels "as if it knew" all
conceivable values of t=t1+t2.

Ludwik Kowalski

http://csam.montclair.edu/~kowalski/life/intro.html
==========================================

P.S. Here is a link to an interesting article about Fermat's principle:
http://www.21stcenturysciencetech.com/articles/fall01/fermat/Fermat.html

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