[PmbPhy]

It seems like a slam dunk. I'll have to research the arguments that led us away from this interpretation. Here's what Wikipedia says (https://en.wikipedia.org/wiki/Variable_speed_of_light):

"Peter Bergmann did not agree with Einstein, but left the dispute out of his earlier book[8] in 1942 to get Einstein’s endorsement. After Einstein died Bergmann wrote a new book[9] in 1968 claiming that vector light velocity could change direction but not speed. This has become a prevailing opinion in science, but not in agreement with Einstein’s unambiguous math. Bergman [sic] did acknowledge that the apparent speed of light would change in a gravity field and go to zero at an event horizon as viewed by a distant observer."

[8] Bergmann, Peter (1976). Introduction to the Theory of Relativity (1st reprint from 1942 ed.). New York: Dover. p. 221. ISBN 0-486-63282-2.
[9] Bergmann, Peter (1992). The Riddle of Gravitation (1st reprint from 1968 ed.). New York: Dover. p. 66. ISBN 0-486-27378-4.

I haven't read these books, but the latter must contain a convincing argument against VSL. Does anyone know the gist of it?

Irwin Shapiro published a few papers on the subject which were reports of experimental observations which he concluded were consistent with the slowing of light moving through a gravitational field (I think I mentioned this earlier in this thread). This is now known as the Shapiro delay. In the papers he refers to this slowing of light as the fourth prediction of general relativity. See
https://en.wikipedia.org/wiki/Shapiro_delay#Calculating_time_delay

The Shapiro time delay effect, or gravitational time delay effect, is one of the four classic solar system tests of general relativity. Radar signals passing near a massive object take slightly longer to travel to a target and longer to return than they would if the mass of the object were not present. The time delay is caused by the slowing passage of light as it moves over a finite distance through a change in gravitational potential. In an article entitled Fourth Test of General Relativity, Shapiro wrote:[1]

Because, according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path, these time delays should thereby be increased by almost 2x10−4 sec when the radar pulses pass near the sun. Such a change, equivalent to 60 km in distance, could now be measured over the required path length to within about 5 to 10% with presently obtainable equipment.

Throughout this article discussing the time delay, Shapiro uses c as the speed of light and calculated the time delay of the passage of light waves or rays over finite coordinate distance according to a Schwarzschild solution to the Einstein field equations.

You can read the article referenced at the following link
Fourth Test of General Relativity, Irwin Shapiro, Physical Review Letters 13 (26): 789–791, (1964)
http://booksc.org/book/22544794/487122

[Mike Gale (OP)]

Wow! Shapiro measured the effect in 1964. I don't mind rediscovering things for myself but it's annoying that it never came up in any of my undergraduate studies. Or maybe I wasn't paying attention.

[PmbPhy]

Wow! Shapiro measured the effect in 1964. I don't mind rediscovering things for myself but it's annoying that it never came up in any of my undergraduate studies. Or maybe I wasn't paying attention.

I'd be surprised if it did. Its not possible to cover everything in relativity in undergraduate courses. That's what graduate school is for.

[Mike Gale (OP)]

I did graduate studies in atmospheric physics. It was fascinating, but far removed from all of this stuff.

[Mike Gale (OP)]

Even so though. Shapiro's result says nothing about the penetration paradox, which is the issue at hand. Maybe I should start a new thread for that.

[timey]

Well to say so, this Shapiro delay is the first serious challenge to the premiss of my theory that I have encountered.  Unfortunately the info is on a PDF and I can't view it on my phone (no access to computer at mo) which is drats, 'cos I'm itching to read it and think the parameters of the distances involved over with respect to position of target in relation to the sun.

[Colin2B]

Wow! Shapiro measured the effect in 1964. I don't mind rediscovering things for myself

As @PmbPhy says, he did mention it earlier. As he says, not usually covered in graduate studies, but if my memory serves me he used Schwarzschild metric to calculate the effect. Im sure it's been tested by one of the space probes as well, can't remember which.

[Mike Gale (OP)]

Shapiro certainly demonstrated the coordinate speed of light, which is:
c=c_o(1-r_s/r)
But the issue at hand is the penetration paradox. That is, what is the speed of a free-falling object (in SC coordinates) when it reaches the event horizon? I started a new thread for this so people don't get distracted by the title of this topic: https://www.thenakedscientists.com/forum/index.php?topic=70228.msg512674#msg512674