(hopefully not too controversial, but as John M points out, we seem to be
able to argue about anything and everything).
I think it will be helpful to restart the discussion and hopefully narrow it
down in a slow methodical fashion to the pertinent points. The discussion
at this point has bifurcated several times so that it has gotten confusing.
IMO the discussion started from perennial discussions regarding how to
interpret Newton's 2nd Law; (F = m*a for short.)
This immediately means we are using a Newtonian paradigm, so we won't worry
about SR, GR or quantum affects. This means, of course, that we aren't
talking about the actual universe either, but so what. It also, means that
Newton's 1st law may be of vital relevance.
It strikes me that this is also a discussion about the foundations of
mechanics and is therefore epistemological in origin and therefore of little
consequence. Meaning that I suspect that John D and I, when we go down into
the lab, do about the same thing in the lab, get about the same results for
measurements, and analyse and calculate about the same things with about the
same methods.
It has been asserted by many that F=ma may be interpreted as an operational
definition of force. So,
I have some unknown force acting on an object that I want to measure.
The operational procedure I have in mind presumably is somewhat as follows:
1) Find yourself an inertial reference frame and construct a coordinate
system. (Let's not get bogged down at this point about whether this is
possible, and if so how? These questions may come up in part II or III . .
., let's just agree that this can be done. The coordinate may be visualized
as something like the picture in Taylor and Wheeler's space-time (the grid
of rods and clocks).
2) from your coordinate system determine position as a function of time.
3) following established methods, determine velocities and then
accelerations.
4) from the measured accelerations use Newton's 2nd law to infer the force.
This is what I mean by using Newton's 2nd law (in a fundamental operational
way)** to determine force from acceleration. I.e. force defined
operationally in terms of acceleration.
I think everyone has agree that one can do this?
The interesting part of the discussion, was an assertion on my part that we
may be *required* to think in these terms.
There have been several instances of naysaying regarding this assertion.
They have claimed that there are other operational ways to determine force,
other than utilizing acceleration determinations.
One person pointed out that one very respected authority "Sommerfeld", has
argued that one isn't required to use acceleration as the way to determine
the value of an unknown force, but rather can use equilibrium methods.
(Hence, why I have harped on the usage of spring scales in an equilibrium
manner.)
The spring scale is a useful model for what one means to use an equilibrium
method for determing force. We do it all the time when we use a scale to
measure the weight of an object. (see Robert Cohen's recent posts).
For part II, I wish to restrict the discussion to equilibrium measurements
of force and whether or not they avoid acceleration measurements (in the
context of Newtonian Physics).
John D. has certainly brought up the valid issue of whether or not spring
scales can be used for force determinations in a non-equilibrium manner.
While this is very important, and probably necessary question to address for
resolving the interesting question, its a more difficult question and I
think the equilibrium determinations are easier to deal with at first.
___________________
Side comments.
* I have totally swept under the rug how we operationally determine mass and
whether or not that involves acceleration measurements. For purposes of the
discussion, I'm willing to stipulate that we have some independent means of
determining mass. But this question may come up again later.
**In this discussion, both off list and on list, I have seen fit to
distinguish
1) "Practical operational definitions": the usual use of the words
operational definition. This is the set of instructions that we give the
students for the procedures at hand, e.g. how to go down to the lab and use
a spark timer to measure acceleration. I don't think of this as being of
fundamental importance to the questions at hand, though they are of related
importance.
2) (fundamental operational way)= "Fundamental Operational Definitions":
Here I mean the Gedanken operations that we perform to determine, explain or
define the meaning of the physical theories. This is what I think we mean
when we say, use F=ma as an operational definition of force from
accleration.