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So am I correct in concluding that in your approach *any* acceleration
relative to *any* frame always has a force corresponding to it?
To be
specific, since I clearly measure myself to have big accelerations
relative to yonder stunt pilot doing maneuvers in the sky, if I wish to
calculate in that frame I gain a force acting on me that I do not feel,
but which "mathematically functions" as the cause of the accelerations?
Why does mathematics require such a cause?
I can't help but notice that you make no mention, here or in all that
follows, of inertial reference frames or inertial trajectories (the
geodesics of either Newtonian flat or Einsteinian curved spacetime). Is
that by design. Do you ever include such in your teaching. If so, I
would be intrigued to hear how.
Very interesting. Now I see where the big differences in approach arise
from. To me forces are very real and powerful physical phenomena, whose
properties and effects can be *described* mathematically. I don't conceive
their existence as purely mathematical, and so I take there ontology very
seriously, as I am sure you have noticed from previous posts.
I thank you
for your candor and clarity. It at last clears up where the differences
lie.