Indeed it does. However, not all cranks are so easily detected. Tom van Flandern appears to be quite sane and rational, and a regular scientist to boot. Yet the general relativity theorists dismiss him as utterly wrong-headed. I'll take their word over his because they are an overwhelming majority and they can't all be part of a vast conspiracy to suppress this man's findings. But I'm way past out of my depth in trying to form my own judgment.
Note that the gradient of a scalar field is a vector, not another scalar. But if the field source begins to move, does the field gradient point toward the instantaneous or retarded position of the source? That depends on whether the field updates or regenerates instantly or with delay. There is no such thing as a gloval gradient: it is a vector field, which means that at every point of the trajectory, there is a (different) vector. These vectors do not even live in the same space: at each point of the trajectory, a tangent vector space is attached. To say what he did is simply incorrect.
Now, given that at different points we have different vectors, the question does indeed arize as to which of these enter physical laws. That is a regular question in physics, but once a particular law is consistent with empirical observations, it is accepted as a working hypothesis.
The author speaks here in terms of college calculus. Had he taken a course in geometry, he would not make such a statement, I am sure.
Physics has an issue that math does not. It is his understanding of mathematics that creates a dissonance in his view.
Incidentally, I would not want to give an impression that I not welcome someone disagreeing with Einstein' theory. TO the contrary, I would welcome such questioning and find it exciting. What seems to be happening here is a misstatement of the theory, or mathematics, is argued against. That is at best, and at worst we have some really basket cases. Nevertheless, thank you again for pointing me to that site.
Best regards, TQ.