Sometimes multiple different concepts are hiding behind
one name. This is a recipe for endless confusion.
This does not necessarily mean that we should keep one
concept and get rid of the others. Oftentimes all the
concepts are valid and useful, and all we need to do is
give them new names.
The example for today is gravity, also known as gravitation.
A) One type of gravity is characterized by the equation
F1 = m g 
where g is the acceleration of "gravity" in some chosen
reference frame. This is almost certainly the first
type of gravity that students encounter.
In accordance with Einstein's principle of equivalence,
this type of gravity can be zeroed out by choosing a
different reference frame.
B) The other type of gravity is characterized by the equation
|F2| = G M m / r^2 
This type of gravity cannot be zeroed out, not by
choosing a different reference frame or by any other
In more detail: The g vector in Spain is very nearly
equal-and-opposite to the g vector in New Zealand.
By choosing a suitable reference frame you can zero
out one or the other, but not both at the same time.
At some risk, we can write
|g2| = G M / r^2 
However, it must be emphasized that the g2 that appears
in equation  is rarely if ever equal to the g
that appears in equation . In typical terrestrial
situations g2 is the largest contribution to g, but
the other contributions are definitely not negligible.
As for naming these things, equation  is widely known
as the law of /universal/ gravitation.
For quite some time I have been struggling to find a
good name for equation . The opposite of "universal"
is "local" but that doesn't capture the correct idea.
The crucial idea behind equation  is not that it is
local, but that it is frame-dependent.
You can't just say that  is relative and  is not,
because the g vector is always relative; the only
question is relative to /what/. Equation  tells us
to measure the g vector relative to some chosen reference
frame. Equation  tells to measure the g vector in
Spain relative to the g vector in New Zealand.
Unless/until somebody comes up with a better word, I'm
going to call equation  the _framative_ gravity.
That's a contraction for "frame-relative".
As for equation , I'm mostly content to call it the
universal gravity. However ... one could argue that
by combining equation  with Einstein's principle of
equivalence, we discover that universal gravity doesn't
directly tell us about the g vector at all, but rather
about place-to-place differences in g. In other words,
the only universal thing about equation  is the
Therefore on alternate Tuesdays I'm tempted to call
equation  the equation of universal tidal stress.
I'm not saying this is perfect, but it does have some
I am quite aware that talking about tidal stress runs
the risk of confusing students ... but OTOH taking about
universal gravitation in a way that is inconsistent with
the equivalence principle runs a far greater risk of
far more serious confusion.
I leave it as a question: Does anybody out there have a
better way of thinking about and talking about the two
different "gravity" concepts?