🚀 go-pugleaf

On Apr 27, 2:28 pm, Pentcho Valev <pva...@yahoo.com> wrote:
> http://www.physlink.com/Education/AskExperts/ae13.cfm
> "So, it is absolutely true that the speed of light is not constant in
> a gravitational field [which, by the equivalence principle, applies as
> well to accelerating (non-inertial) frames of reference].

> Pentcho Valev
> pva...@yahoo.com

Upon my initial reading of this comment I erroneously assumed that it
was analogous to Nigel Calder's statement in 'Einstein's
Universe' (62, BBC, 1970) "Light travels faster and more readily
toward the center of gravity than away from it." however the link you
provided indicates the opposite viz -

>> "Would not the speed of a light beam headed toward a black hole
>> increase tremendously? We do know it could be bent by the
>> gravity of a star."

>> Asked by: Joe Thomas

>> Answer

>> "Contrary to intuition, the speed of light (properly defined)
>> decreases as the black hole is approached. In fact, one way
>> to understand the bending of light by the gravitational field
>> of a star is to regard it as resulting from the refraction of
>> the wavefront due to the fact that the part of the wavefront
>> that is nearer to the star moves more slowly than the part
>> farther away from the star. The result is that the direction
>> of advance of the wavefront is deflected toward (or around)
>> the star."

The reference to the 'bending of light' refers of course to a beam
that is traveling past a gravitational field however my
interest (as was Calder's comment)is specifically in relation to a
beam that is radially moving toward (or away from) that field.

>> If the photon, the 'particle' of light, is thought of as
>> behaving like a massive object, it would indeed be
>> accelerated to higher speeds as it falls toward a black
>> hole. However, the photon has no mass and so behaves in
>> a manner that is not intuitively obvious.

It is my understanding that whilst it is pointed out that although
photons have no rest mass they possess energy-mass of motion which
generates a beam's inherent gravitational field however this concept
is irrelevant to (but is contradicted by) the reference below to the
equivalence principle.

>> The reason for the qualification 'properly defined'
>> above is that the speed of light depends upon the
>> vantage point (frame of reference) of the observer.
>> When we say that the speed of light is decreased,
>> we mean from the perspective of an observer fixed
>> relative to the black hole and at an essentially
>> infinite distance. On the contrary, to an observer
>> free falling into the black hole, the speed of light,
>> measured locally, would be unaltered from the
>> standard value of c.

You wrote - "the speed of light is not constant in a gravitational
field [which, by the equivalence principle, applies as well to
accelerating (non-inertial) frames of reference]."

If a far distant observer ('..an observer fixed relative to [a light
source] and at an essentially infinite distance.')is looking at that
source when it projects beams of light to his right hand side and to
his left those beams will, obviously, travel away from the source at c
however if the source is rapidly accelerating in the direction of one
of those beams (A) and projects beams of light in the same directions
(A and B) the source will be 'catching up' with the tip of beam A and
relatively 'hastening away' from the tip of beam B.

From the point of view of the distant observer - the distance from the
tip of beam A to the source will be shorter than the distance of the
tip of beam B from the source.

According to the equivalence principle - if the source is located at a
fixed distance from a black hole the beam (B) that is moving in the
direction of that object will, in a given instant of the distant
observer's time, travel a greater distance from the source than beam A
moving in the opposite direction.

The fact that the speed of light (beam B) to an observer free falling
into the black hole (or one that is a fixed, near, distance from the
black hole) would be unaltered from the standard value of c is only
because his measuring rod and clock are effected by their relative
locations in that gravitational field.

This person is presumably aware of the Wallops Island experiments thus
(and in accordance with GR) knows that clocks that are located in
different gravitational tidal areas tick over at different rates and
that measuring rods can be stretched or reduced in length by
gravitational fields.

********************

"Knowledge is one-dimensional; the proper application of knowledge is
multi-dimensional. Only the extremely wise, and the exceptionally
foolish, are not prepared to change," (Confucius)