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replies to non-inertial Frames


I thank A Marlow for giving responses to my thoughts and would like to hear
further expositions on the following points. I'm not quoting previous
postings in full in order to save time and space; voyeurs to this discussion
may have to refer to previous posting to understand the comments.

Marlow and these discussions have brought up at least three versions of
mechanics: pre-20th century Newtonian mechanics (I'll call it Old Mechanics
from now on, 20th Century Newtonian Mechanics (by which I assume he means
the post-Newtonian approximation to GR), and full GR (general relativity).
One complicating feature to the discussion is that we go willy-nilly back
and forth between the three versions to suit our convenience in the
discussion. So let me address some points that Marlow made in replies to my
non-inertial: part I and II posts.
_____________________
First, regarding the analysis of the cube (book) sitting on the table,
Marlow has only one force vector on the book, I have two. And I quote,

... This contradicts the 2nd law, since there is zero acceleration.

I don't see this. It doesn't seem to contradict the 2nd law at all.
Any correct statement of the second law must start with "Relative to an
inertial frame the net force acting on an object equals ... ." Without
the initial proviso, none of the laws of Newton are valid or applicable. .
.. .

In Old mechanics (the one force vector picture) most certainly will
contradict the 2nd law. Because in old Mechanics people agree that this is
an appropriate inertial frame. If I insist that the free-fall frame is the
inertial frame (a GR idea, and I assume from what Marlow says a 20th
Century, New mechanics idea) then he is correct there is no contradiction.

I'm curious, how many force vectors does Marlow draw acting on the cube
(book) when he explains Newtonian mechanics to introductory students?

Later we have the following points:

therefore we shouldn't use these force diagrams in studying statics, even
in
inertial frames!


I simply have to disagree completely with this statement for all the
reasons
already put forward in this and other postings in this thread.

It depends on if we are calling free-fall frames THE inertial frames, if we
are then Marlow is correct in disagreeing with the statement. If we are
using the old mechanics idea of what constitutes an inertial frame then he
is not correct in disagreeing. And later we have the following:

JR>> ...I'd respond, yes; but Newtonian physics should be a self-consistent
JR>theory, ...

AM>It is.

Which version, pre-20th century or 20th century mechanics; I was referring
to pre-20th century mechanics as a self-consistent system of analysis (which
is not correct according to experiment, but I think is still self-consistent
and good to excellent approximation for the examples I'm citing.)

Let me hasten to add, if asked about the current theory that most matches
the way the world really is, I'll say GR and say that freely falling frames
are what we should call inertial frames and then Marlow's statements are
correct and match mine.
___________

And now the levitating cube example. I was talking about measuring the
forces directly on the cube by devices directly attached to the cube or
measurements of the cubes position. Marlow's reply was to use spring
balances on the capacitor that was used to levitate the charged cube. I
don't think he explained what he was doing very well, and I'd like to see it
rewritten. But assuming he is correct in saying that the spring scales will
measure a non-zero external force acting on the apparatus, I have the
following objection. I wasn't referring to the external forces acting on the
entire apparatus, we were talking about the forces acting on the cube only.
I His analysis implicitly relies on use of the 3rd law, which has its
limitations. (note: that the discussion fo this example is in the purview of
GR, therefore saying the 3rd law limitations are relativistic as was stated
in an entirely different thread doesn't help).

This led to a discussion regarding force sensors in the two different posts
which I combine together here:

Now the pressure sensors
read no force present (they all have the same reading).

Pressure sensors are obviously not appropriate tools in all circumstances.
You must use all available means for testing for forces in determining
whether or not you have an inertial frame. For example, the simple spring
stretch scale mentioned previously will do the job.

Simply try other force detectors rather than pressure sensors.


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.
. . .

I never said that pressure sensor methods were the only means of detection
of forces (possibly better, interactions), and in previous posts have
specifically mentioned fiber torsion, spring stretching, Etc.

In general, any method of making precise the pushes and pulls experienced
in real life will do. Just keep these aspects of experience distinct from
the purely kinematical concepts of position, velocity and acceleration.

Marlow did mention other items beside pressure sensors, but in the criticism
of my being thrown agains the door handle as I round a curve, the point made
was that the pressure sensor test does not measure a force; however a spring
balance will measure an outward centrifugal force; just attach it to me and
the opposite door handle and as I'm being thrown towards the door that I
will hit, it measures a force.

So just exactly when and under what circumstances and I'm allowed to use
what kind of force sensors?

Lastly form the part II post:

The work-energy theorem seems to work, namely when that force is the only

force present, the work done by it seems to equal the change in the
kinetic
energy of the object.

So you are saying, in the context of the examples that you brought up
before (a sharply turning car, people in a centrifuge), that besides the
work and energy supplied by the real inward directed interaction exerted
on you by the door that causes bruises, there is an equal amount of work
and energy supplied by the outward directed "centrifugal interaction"
that acts on you to prevent you accelerating relative to the car? That
is a very strange doubling of energy that I have not heard of before.
You ought to be able to patent that and make some money on it. In the
present state of things, I wouldn't be at all surprised if someone in the
patent office might not accept the whole idea.

I don't understand the objection. During the time I'm thrown from my seat
towards the door handle I am accelerating and the work energy theorem works
quite well. The integral to the centrifugal force dot dx will equal my
change in kinetic energy. Remember I'm measuring all kinematic quatities
relative to the car (the non-inertial frame). Once I'm in contact with the
door handle the none of the forces present are doing any mechanical work as
my kinetic energy isn't changing (nor is my velocity vector changing
direction! in this frame of reference; I'm well aware that you can have
accelerations and non-balanced forces without mechanical work being done)

... And from all of this, all of mechanics seems to
follow. (I hope this last isn't too rash of a statement, but I'm sure it
will be corrected if need be.)
...

A very strange version of mechanics, which I wouldn't depend on to give
consistently valid results.

It is not strange at all. I recall the post from the oceanographer who said
this is exactly how they do things. And that is the point, you can apply
Newton's laws in non-inertial frames of reference consistantly if you admit
the existence of "fictitious forces", er "kinematical" forces, er "apparent"
er "pseudo" forces, because they behave in non-inertial frames exactly like
forces in inertial frames behave.
...
Its for this reason that the idea of treating these terms as real forces
is
useful. It in fact allows me to avoid a lot of mental gymnastics to be
able
to simply say that these are forces measured in this particular frame of
reference, along with all other measurements made in that frame.


How do you avoid getting the extra undetectable work and energy, and what
do
you do about Newton's Third Law? Just throw it away?

I don't throw away the 3rd law (which has its limitations anyway). I don't
understand what the extra undetectable work and energy you are referring to
is; could you elaborate?
_______________
And now the spot where Marlow has the most important objection to what I'm
saying, and in the end I may agree with him.

That is the reason for my not liking the word "fictitious" because there
is
a "real" effect. In this vain I'm more comfortable with "apparent
force";
I also like the suggestionof "inertial force", although I understand the
objection that was raised against that. I still prefer so far the term
"kinematical force", since the effect is a kinematic effect.
...

What is the problem with using the proper kinematical name --
acceleration -- for what you agree is a kinematic effect? Could you be
very specific about the objections you feel toward this very real term
for the very real kinematic effect being described?

and what is wrong with me using the term force after I multiply the
acceleration by the object's mass? (as long as I make the careful
distinctions, only necessary if I'm to compare to measurements taken in an
inertial frame of reference, which I've made regarding these terms). The
effects are real, hence the dislike of the term "fictitious"

and later

... Namely, I measure an acceleration
associated with them, by plotting the position of my object in the frame
of
reference (non-inertial of course, that's where I'm doing the
measurements).

This makes your notion of force a purely kinematical notion. Why waste the
perfectly good term "force" on concepts that already have perfectly good
names?

You got me here!!!! (more or less) and here the discussion must get very
philosophical. One good consequence of this discussion is it has gotten me
to reread a lot of what has been said regarding the basics of mechanics
(I'll mention what I've read in a later post) The 2nd law comes damn close
to defining force kinematically. If we say that it in fact does (I don't
want to, to come in a later post) then that is the end of the story and
everything is self-consistent with that viewpoint.

In fact I argue that operationally the 2nd law in effect does; Because in my
windowless room watching an object, the only armament I have for analyzing
the motion of the object is to make kinematical measurements of its postion
as a function of time, and blindly apply the 2nd law. (Note: a spring
balance works by measuring acceleration, we first measure the acceleration
of the object relative to the spring, then take the reading; this is the
origin of the comment I made earlier that force balances work by measuring
accelerations; hence why I thought Marlow brought up the idea of measuring
forces with the pressure sensors).

The problem with the above viewpoint is that it reduces dynamics to
kinematics; while OK mathematically and doesn't lose the self-consistency of
the theory. (Marlow and I get the same numerical answers to problems) it
does seem to me to be intellectually unsatisfying (and here I'm guessing I
agree with Marlow). I'll post more on this later.
_________

Two last thoughts:

If you do not know whether you have an inertial or a noninertial frame,
you have no right to be applying Newton's laws! They simply give bad
results in a noninertial frame.

Newton's laws do not give bad results in non-inertial frames, if you admit
the existence of these other kinds of forces

Students, PLEASE do not try this at home (or in homework), or you will
continually be getting wrong results, along with some right ones --
but that's the problem: you will be so confused you won't be able to
tell which are which.

Here I fully agree!!!!!!!!!!!; when you take away the vitriol and careless
misstatements, this whole discussion gets down to some basic philosophical
underpinnings of Newton's theory of mechanics and some very bright minds
(far brighter than mine) have wrestled with this for lifetimes, specifically
Newton, Mach, Eddington and Einstein in particular, others in general
(Rauber and Marlow for example, and every colleague I've ever met who really
sat down and really tried to understand the 2nd law)

Joel Rauber
rauberj@mg.sdstate.edu