Re: [Phys-L] Two questions on General Relativity

[John Denker <jsd@av8n.com>]

On 3/26/22 12:42 AM, Antti Savinainen via Phys-l asked about:

> 2) "The speed of light is slowed down in a gravitational field."

I cannot imagine how that could be true.

I would define the speed of light, indeed the speed of anything,
in terms of *local* measurements ... and locally, general
relativity reduces to special relativity. For any small-enough
region, Minkowski geometry works fine.

By way of analogy, you can draw a map of your garden without
worrying about the curvature of the earth. For any small-enough
region, Euclidean geometry works fine.

> Does the modern interpretation of GR still maintain that the speed of
> light depends on the gravitational potential

I don't think the modern interpretation ever said that.

Suggestion: Get a copy of Misner Thorne Wheeler _Gravitation_.
It is a very good book. It exhibits a love of physics, with
style and panache, rather like the Feynman lectures. It has
a very high ratio of words to equations, which makes it
relatively easy to read, especially considering the intrinsic
complexity and subtlety of the subject matter.

It was written 50 years ago, but it was ahead of its time
then, and it has held up quite well. In particular, the
2017 reprinting has a new 14 page preface that identifies
a few sections that have gone out of date, most of which
are near the end of the book and have to do with experiments
and observations. 50 years ago there were no serious
observations of black holes, gravitational lensing of
distant galaxies, gravitational waves, et cetera.

==> Suffice it to say that no change in our understanding
of the speed of light is on the list.

The preface is here:
  http://staff.ustc.edu.cn/~jmy/PREFACE%20TO%20THE%202017%20EDITION%20MTW.pdf

The book begins with a no-nonsense review of special relativity.
So despite the title, it is the best reference on SR I know.

MTW does not contemplate any notion of non-constant speed of
light. It disclaims this explicitly on page 297 and page 304,
and implicitly more-or-less everywhere.

Meanwhile, gravitational redshift is a thing. It can be
understood without fiddling with the speed of light. MTW
discusses this at several points:
-- On page 63 we find section 2.8 "The Centrifuge and the Photon"
 which discusses redshift using acceleration in a centrifuge,
 so it addresses both of the pending questions: equivalence and
 redshift.
-- On page 187 redshift is linked to conservation of energy,
 and to curvature of spacetime.
-- et cetera..............

If there is a "modern" interpretation that Kip didn't know
about in 2017, it must be very modern indeed.

===

There are situations where EM waves propagate at a speed less
than c, for instance in waveguides or in refractive media.
Even so, this does not change our understanding of "the"
speed of light, including the constancy thereof.

=============

> The author cites Einstein's paper in 1911.

I don't pay much attention to things like that, for multiple
reasons:

A) In 1911, the whole idea of spacetime was only 3 years old,
and Einstein had spent one of those years poo-pooing the idea.
His results on general relativity were still 4+ years in the
future. So if he said something not quite right in 1911, that
has no bearing on anything.

B) More generally, I don't may much attention to who said what
whenever. Physics is supposed to be about getting the right
answers. It's not supposed to be a cult of personality. It's
not supposed to be hero worship.

Einstein was smart, but even so, he made some mistakes. I
can't get excited about this.

Sometimes I make reference to Galileo's principle of relativity.
I get tremendous amounts of pushback over it. More pushback on
that than anything else, which is astonishing given the number
of provocative things I've said. I was informed that it was
"Einstein's" principle of relativity, as "everybody" knows.
To that I say, ahem, I read Galileo's book and I am quite
certain he has almost 3 centuries of priority on that idea.

Similarly I am astonished when people who really ought to know
better claim Einstein invented the idea of spacetime. There
are hundreds of popular articles and TV shows that claim that.
In fact Minkowski invented it. Even after Einstein read
Minkowski's paper he initially thought the idea was worthless
... although before long changed his mind and used the idea in
his later work, including (!) general relativity.

This problem is getting worse not better. Nowadays every bit
of clichéed new-age relationship advice circulates on Faceborg,
attributed to Einstein.