Speed of light and the equivalence principle In 1913 Albert Einstein wrote:

"I arrived at the result that the speed of light is not to to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis."

Is the first statement - referring to time dilation in a gravitational field - still considered valid in this form among physicists today? What did Einstein mean by the second statement? Is he talking about the weak or the strong equivalence principle?
 A: In 1913 Einstein was still working on general relativity and it was not complete. Furthermore, it would be decades before the community, including Einstein, really began to understand the important concepts of spacetime geometry. This quote is very early and is not really correct by modern understanding, with a century of hindsight.
The speed of light in an inertial frame is c, and the speed in a non-inertial frame need not be c. Those facts hold equally well both in the flat spacetime of SR as well as the curved spacetime of GR. The only difference is that in curved spacetime inertial frames are only local, which is the heart of the equivalence principle.
A: The quote isn't strictly wrong, but it may convey a false impression about what constant or inconstant speed of light would mean. It suggests to me that when it was written, Einstein had identified the problem, but hadn't yet started looking in the right place for the solution.
Suppose you and I start together in a free-fall orbit far from a large mass. I give you two nanosecond-counting clocks and a 10-light-nanosecond long stick. You take the clocks and the stick and go to an orbit much closer to the mass, such that your escape velocity is much greater than mine.
You arrange the clocks so they are lined up with me, positioning the stick between them.
I shoot a laser pulse towards you.
Some time later:
You, standing a little bit to the side and equidistant between the clocks, see the laser pulse illuminate the first clock, which happens to read $0 ns$ at that moment. Exactly 10 nanoseconds later in your frame, you see the laser pulse illuminate the second clock, which reads $10 ns$. Dividing 10 light-nanoseconds by 10 nanoseconds gives you the same speed of light as you measured before you left, confirming that the speed of light is the same for all inertial observers.
Some time later:
I see the light bounce off of the first clock, which reads $0 ns$. More than 10 nanoseconds later in my frame, I see the light bounce off of the second clock, which reads $10 ns$. Since I can see that the light traveled across the 10 light-nanosecond stick between clocks, I know that the speed of light is the same for you over there as it is for me over here, but nonetheless I measured light take more than $10ns$ to travel 10 light-$ns$. The only way to explain the observed events is that the geometry of spacetime must be different where you are than it is where I am, such that your frame has time dilation relative to my frame.
