: re -Riemann tensor not curvature tensor. - The curvature tensor is just another name for the Reimann tensor. Sometimes it's even called the Riemann curvature tensor

I am saying that I disagree with that naming. :

: re - There is no such tensor so it implies no such thing. - Sure there is. The components of the tidal force tensor are a subset of the components of the curvature tensor. Your can look it up in either MTW or Ohanian.

You misread. As I said you may define one if you wish as gmn ; ls but this does not really give you the experienced tidal forces. Thus, even though this is a tensor it is not truly a tidal "acceleration" tensor. It's definitely not a tidal "force" tensor. There is no such thing. And I think you mistake this for gmn , ls which is not the same thing. This is not even a tensor.

: :

re - : Not under a short enough proper time ... - What's your point? The question was whether velocity affects tidal force - not whether or how tidal effect can be ignored. That's a separate issue. It is the difference between "does distort" and "will distort."

I made my point as to how velocity affect tidal force. Reread it.

:

: re - : again you misunderstand local. - Nope. Don't put words into my mouth. There is a well-established criterion in MTW for determining when a region of space-time can be called locally flat. Loosely speaking - If, within a given amount of time and given a specified precision, no relative acceleration of test objects is detected then that region of space-time is referred to as "locally flat." The questioner asked about tidal forces. You addressed local aspects, not I. :

re - SO what? - What kind of question is this?

The so what, is that I never said that I was mearly applying this to point particles. It is that it is easy to see tidal force as with other local accelerations you just mention vanish in a local frame of free fall. I answered the question and then added that whether or not the object was in a local frame of free fall Vs one with external forces played a more important role as to the measurements of tidal forces. You disagreed, before really considering what I just said. This is evident in that your last paragraph here actually agrees with what I actually said. Instead of looking for disagreement where there really isn't one, try to understand what are obviously well informed points of view. Your MTW quote is practically a repetition of what I already said.