Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: replies to non-inertial Frames

On Sun, 28 Apr 1996, Rauber, Joel Phys wrote:

...
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).
...

I refer to Newtonian mechanics as the three laws of motion, stated with
the explicit proviso "relative to an inertial frame of reference" explicitly
included. I do not refer to the specific force law of gravitation as a
part of the framework of mechanics, any more than Hooke's law is part of
the framework called Newtonian mechanics. With this understanding we don't
need to prefix Newtonian mechanics with various adjectives, and we don't
tie it's validity to specific forms of force laws. The laws of motion
of Newton so stated are as valid and useful today as they were in the 17th
century. Then we can say that the progress made in the 20th century,
aside from quantum theory, lies in two main areas -- 1) a better
understanding of time than the one Newton used, showing that time is a
relative quantity rather than the absolute assumed by Newton, and
2) a better understanding of the nature of gravitation, replacing Newton's
instantaneous-action-at-a-distance notion.

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

I am currently teaching mechanics only to junior-senior college physics
majors, and they quickly grasp what would happen if the Earth vanished
or for some other reason stopped pushing on us, so they have no
difficulty seeing what the -mg is doing in any equation where it appears
-- it is correcting for the fact that we are using an accelerating
reference frame. Once this is pointed out, it causes no further difficulty,
and it prepares the students for the fact that, when we start treating
orbital dynamics, we must correct for the fact that the Sun also is
accelerating relative to an inertial frame, or we will get wrong mass
calculations. And we do not do this by introducing a fictitious force.
(By the way, you still have not answered how you would compute the M+m
in Newton's corrected version of Kepler's law III using centrifugal
"force" to keep things from accelerating.)

I do have lengthy discussions with a 12 year old who is interested in
science, and this exact point has come up and he seems to accept it
quite eagerly, so I think that if were teaching beginners I would do it
no differently, lest they have to unlearn later what has been falsly taught.
It is not really a particularly difficult idea, once it is pointed out,
especially if you use clear examples of how measuring kinematical quantities
relative to a jet plane doing acrobatics introduces similar accelerations.
Young people seem to relate to this right away, especially since it gives
them a chance to do what they do best: use their imaginations and put things
in a cosmic perspective where they can see Earth as our observing platform.

I think it was Einstein who noted that things should be made as simple as
possible, but no simpler.


...
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.)
...

I agree completely with the last statement, but I do not distinguish a
pre-twentieth century version of Newton's laws of motion from the ones we
use today. I believe you made that distinction because you erroneously
assumed that I was referring in a previous post to a post-Newtonian
approximation to general relativity. I was not. I have been referring
only to Newton's three laws of motion as Newtonian mechanics, whether
applied pre- or post- 20th century. Sorry for any misunderstanding there.

...
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.
...

Then attach the spring scale directly to the cube. It would still show
exactly the same thing -- attached to one side (what I called "up") the
scale would stretch, and you can see both the amount and the direction
of the force you have to apply to the cube to keep it from accelerating
relative to your lab. On the opposite side of the cube you would have to
push in the same direction by the same amount to do the same thing. On
the four remaining sides you would find you don't have to do anything to
keep the cube from accelerating. Further testing with all means of force
detection known can find no other forces acting, and so you must logically
conclude (unless you want to give up Newton's laws) that your lab must not
be an inertial frame. Why? Because in an inertial frame you do not have
to exert unbalanced forces on objects to keep them from accelerating.

(I mistakenly thought you had introduced the capacitor plates so you could
distinguish what happened when the cube was between the plates from when
it was not. In any case, apply the appropriate force detectors wherever
needed -- they will show the same thing.)

... In 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).
...

I'm not sure what you're referring to here, but I know of no limitations to
a correct statement of Newton's third law : for every force Fab (i.e.,
exerted on a by b) there exists -Fba (exerted on b by a).

I am not referring to any so called "strong" version of the 3rd law, that
adds a requirement that the forces must be along the line connecting a with
b. This is not a part of Newton's 3rd law, and it certainly doesn't apply
except very approximately in restricted circumstances. (For example, the
added requirement doesn't apply to electromagnetism, or to any modern
understanding of gravitation that excludes instantaneous action-at-a-
distance.) Could you be more specific about what restrictions you see,
and how they apply to the example being discussed of the spring scale
attached to the cube?

...
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.
...

Am I misreading something here?? The spring scale attached as you
describe will clearly measure a force on you directed TOWARD the door
handle from which you are receding. In the context of a turning car or
a centrifuge that is normally called a CENTRIPETAL force, and it is a
very real force -- if exerted, it will keep you from hitting the door
handle toward which you were headed, and by its magnitude you can tell
by how much the car differs from an inertial frame. (Inertial frames
don't require the application of such real forces to keep things from
accelerating). If it is NOT exerted, you will quickly learn the same
lesson when you get your very real bruise from the door handle toward
which you are accelerating. To stop you, that door handle must exert
a very real CENTRIPETAL force on you, just as the spring scale would
have done. Where is there any possible room for a centrifugal force in
any of this? I apologize if I'm missing something, but I don't see
any room for such without completely destroying Newtonian mechanics.

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

Already explained as best I can.


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

Agreed, the work-energy theorem works quite well, just not the way you
envisage. During the time you are thrown towards the door handle, but
before you hit, there is no force acting on you, hence there can be no
change in any form of energy. You can check this by using, say, sensitive
infrared detectors. Since real forces doing real work inevitably involve
dissipative processes (second law of thermodynamics), I predict the
infrared detectors will be triggered as soon as the door handle starts
working on your skin. The detectors will register no such evidence while
yo are merely accelerating toward the door.

The problem seems twofold: 1) you are trying to apply Newton's laws and
the theorems that follow from them (work-energy, Etc.) in frames of
reference to which they cannot be applied, and 2) you are not distinguishing
the quantities of dynamics (force, momentum, energy -- including "kinetic"
energy) from the quantities defined in pure kinetics (displacement,
velocity, acceleration).


.... The integral to the centrifugal force dot dx will equal my
change in kinetic energy...

Not in any physics that I know, unless you put in "zero" as the
value of the centrifugal force, which of course will give you the
correct zero value of change in kinetic energy (as a dynamic quantity,
kinetic energy has a simple relation to acceleration or velocity ONLY
in inertial frames).

Remember I'm measuring all kinematic quatities
relative to the car (the non-inertial frame)...

I am also measuring all kinematic quantities relative to the car. I am
rapidly coming to the conclusion, however, that there is vast disagreement
on which quantities are kinematic and which are dynamic.

... 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; ...

True, your velocity relative to the noninertial frame of the car is no
longer changing, but real work is being done, real bruises are being left,
and your kinetic energy is changing, and infrared detectors will detect
the dissipation that must accompany real physical processes.


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).

Again, please specify what limitations you are referring to, and what
relevance they have here -- I know of none.

... I don't
understand what the extra undetectable work and energy you are referring to
is; could you elaborate?

Work and energy changes from processes that cannot be detected by the most
sensitive detectors.

... (Note: a spring
balance works by measuring acceleration, we first measure the acceleration
of the object relative to the spring, then take the reading;
...

Now I am truly and totally confused. If spring balances work by measuring
acceleration, than I and every grocer in the world have been sadly misusing
them and cheating the public. I thought we were supposed to wait until
any disturbing oscillations (accelerations) had died out before we took
a reading from the DISPLACEMENT of the scale.

Are we now to confuse even purely kinematic notions such as displacement
and acceleration with each other?

... this is the
origin of the comment I made earlier that force balances work by measuring
accelerations;...

Please explain how this works, or I'm going to have a very difficult time
getting to sleep tonight.


...
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) ...

As far as I can see, we don't at all get the same answers for any
dynamical quantities such as energy, work, momentum, mass.


...
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
...

They sure do give bad results when it comes to computing dynamical
quantities, so I repeat again:

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.



A. R. Marlow E-MAIL: marlow@beta.loyno.edu
Department of Physics PHONE: (504) 865 3647 (Office)
Loyola University 865 2245 (Home)
New Orleans, LA 70118 FAX: (504) 865 2453