I want to break my responses into three parts as several seperate issues
have cropped up and I don't want any individual posting to be too long. If
I misinterpret anybody's statements, I apologize and assume that you will
correct me response postings:
The way I interpret a lot of what A Marlow has said is the following:
(the two quotations I refer to as I and II are at the bottom of this
posting)
Marlow seems to use as an operational definition of a force,"those readings
that pressure sensors give you". (For purposes of this discussion I assume
we may consider the object in question to be a small cube with mass which
has pressure sensors located on each of its 6 faces.) If this is one's
operational definition of forces then I agree with what Marlow says in
quotes I and II below. Particularly quote II regarding the analysis of
forces acting on the cube which is sitting on the table (cube instead
person) as analyzed in general relativity in a free-fall frame (free-fall
frames being the analogous frame of an inertial frame in Newtonian
mechanics). I.e. there indeed is an unbalanced force on the cube as its
world line deviates from the geodesic with an acceleration of +32 ft/s^s.
However, I don't think this is a good way to operationally define forces
acting on our cube, because it leads to certain conundrums; (if I'm wrong
here correct me, its not completely thought out).
a) If we decide to analyze the cube on the table using Newtonian Mechanics,
in a Newtonian inertial frame, we are forced to say gravity is a fictional
force and my force diagram for the cube will have only one force vector on
it and therefore there is an unbalanced force. This contradicts the 2nd law,
since there is zero acceleration. This ought to confuse a student who is
using force diagrams and the pressure sensor definition of a force. And
therefore we shouldn't use these force diagrams in studying statics, even in
inertial frames!
I should point out that free-fall frames are not inertial frames in
Newtonian physics.
One reply to this conundrum, is that I have it exactly correct and that is
why Newtonian physics doesn't match reality and why we need the General
Theory of Relativity.
I'd respond, yes; but Newtonian physics should be a self-consistent theory,
even if it doesn't match experiment and I think the paradox above can also
be viewed as a self consistancy problem with how one defines forces, within
Newtonian Physics. (More with this thought after I hear the responses.)
b) A more serious conundrum in my opinion.
Put a charge on the cube and levitate it between large parallel plate
capacitors (again in a uniform gravitational field as in the above example).
Now the pressure sensors
read no force present (they all have the same reading). And this now
contradicts the General relativity analysis of quote II. In a free fall
frame there is the +32ft/s^2 acceleration (the acceleration which deviates
the world line of the cube from being a geodesic, i.e. the free-fall path of
an identical uncharged cube) , but the pressure sensors indicate no force
present; GR says there is a force present, because the worldline is
deviating from the geodesic.
Conclusion: The pressure sensor method only can detect contact forces and is
not useful for non-contact forces, and therefore is inadequate as an
operational definition of force.
Joel Rauber
rauberj@mg.sdstate.edu
_________________
Quote I (regarding object in equilibrium on tabletop)
Again, all accelerations of your monitor, relative to the frame of the
table, cancel to zero -- only in that sense is it in "equilibrium."
There is a real unbalanced force on the bottom side of the monitor, and
only on that side, as pressure sensors placed all over the skin of the
monitor would show. Thus it is clearly not in a force equilibrium, and
this exact same force nonequilibrium result would continue to be shown
in whatever reference frame you decide to use for measuring accelerations.
If you use an inertial reference frame (free falling frame) then you
would find that the acceleration also corresponds to the unbalanced upward
force on your monitor.
____________
Quote II
Why do we not feel
any force of gravity, but only the push of the Earth upwards on the soles
of our feet? Why do pressure sensors not reveal any force but the push
upward by the surface of the Earth? Why do pressure sensors register
zero force on all sides when we are falling with an acceleration of
g = 32.2 ft/s*s relative to the surface of the Earth? (I.e., when
we are in freefall?) Einstein finally answered these questions in
1916 -- The only force acting on us when we are standing on the
surface of the Earth is the electromagnetic push of the Earth on the
bottom of our feet. This causes an acceleration of 32.2 ft/s*s
relative to an unaccelerated (i.e., inertial) frame of reference. We
incorporate therefore an extra acceleration of -32.2 ft/s*s in all
our acceleration terms when working relative to the Earth's surface
simply to compensate (as Coriolis taught us to do) for the fact that
Earth is not a true inertial frame. Once this was cleared up, Einstein
was able to go on to show that gravitation was the very real grip that
curved spacetime holds on matter, dictating how matter should move
in freefall, and defining what an inertial frame is. Forces, such as the
electromagnetic, then cause matter to accelerate away from inertial
trajectories. A good start toward understanding all this is to recognize
clearly the nature force in other situations, and not get in the habit of
confusing it with accelerations.