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Re: [Phys-l] g...



On 11/18/2006 05:57 PM, Hugh Haskell wrote:

Calling g, and acceleration, or even dressing it up with the new
symbol a_g, isn't going to solve the problem, IMO. The point is, that
g is *not* and acceleration. It happens to have the units of
acceleration because of an "accident" but that is really irrelevant
to the physics. It also makes it easier to understand why all object
accelerate the same way under the influence of gravity alone, whereas
the same is most definitely not true with electricity.

I need the next level of detail here. Taken separately, several
steps in that argument make sense. Taken collectively, they don't
add up; they don't suffice to support the conclusion.

Given that g has /units/ of acceleration, we agree that that doesn't
prove that g "is" acceleration. By way of analogy, torques and
Lagrangians have the same unit, but we don't think that torques "are"
Lagrangians.

However, as the saying goes, absence of evidence is not evidence of
absence.

If two quantities have different dimensions, it is strong evidence
that the quantities have different meanings. In contrast, if the
dimensions are the same it proves /nothing/. They quantities might
be the same, or they might not.

It's going to take more than PbBA to convince me that g should not
be considered an acceleration.

The mention of "electricity" also lacks traction. The electric field
generates a force per unit charge, which is not even dimensionally an
acceleration. The gravitational field generates a force per unit mass,
which (in the absence of valid arguments to the contrary) is eligible
to be considered an acceleration.

Note that in this context, as in many others, technical terms appear
as part of multi-word expressions. For example, it is conventional
and sensible to write:

F = F1 + F2 + F3 + ...
where
F = "the" force
F1 = the electrostatic force
F2 = the force due to the string
F3 = the force due to the rubber band
... et cetera.

Each of these quantities (F, F1, F2, F3, ...) is considered "a" force,
while F _per se_ is considered "the" force. This requires some fine
parsing of the language, which can be a burden on the students ... but
it is the language that people use, and students will have to get used
to it.

In this spirit, surely g is not "the" acceleration, but it looks to me
like it is "an" acceleration. It may or may not be the acceleration of
any tangible object, but -g is the acceleration of the frame (or,
equivalently, g is the acceleration of a hypothetical test particle
relative to the given frame).