This is the posting that I referred to in my last replies in this thread. I
want to discuss several issues and only partial resolutions here. The
discussion of this posting is done using the frame work of pre-20th century
Newtonian mechanics, that is without reference to GR. The reason is for
definiteness of discussion and because this works just fine for almost all
macoscopic phenomena that we observe (this is why this is the physics needed
by most civil engineers); and more importantly because that was the
understanding I had when I originally made my first comments.
Let me summarize the conclusions I've made so far (note: this would
not agree entirely with the conclusions Marlow makes from the discussion).
Everyone agrees that there are effects when you make measurements
in a non-inertial frame of reference. Marlow wishes to only call them
accelerations, I see no point in being so dogmatic about that and feel quite
comfortable with multiplying by mass and call the resulting entity a
"kinematical" force. I feel uncomfortable with using the term "fictitious"
to describe the resulting entity; the reason being the effects are real as
measured in the non-inertial frame of reference and the word "fictitious"
has connotations of unreality. I don't think one can make measurements in
the non-inertial frame that can distinguish these terms as their
introduction is
precisely so you can use the 2nd law and 3rd law (and hence all
of mechanics) in non-inertial frames and analyze things consistantly and get
correct answers. (Marlow disagrees with this measurement statement, but it
seems to me that he has to use different ways of measuring forces to suit
his needs, i.e. pressure sensors when that gives the answer he wants, namely
no force when I'm flying towards the door handle, but we must use spring
balances on the capacitor plates, not the object that I want to measure the
forces on, in my levitating example; however I'm not allowed to use spring
balances when I measure the force on me as I'm flying
towards the door handle)(note: this was written before I saw Marlow's last
reply.)
The heart of this discussion really gets down to how to define
forces. And this is not an easy thing to do precisely; and perhaps
impossible. I have gone back and reread what several noted
authors have said on the matter and I wish to paraphrase and
quote for the edification of the list.
___________
First I went back and read my Principia (The Motte translation
revised by Cajori, printed by the
U. Cal. press)
Interestingly enough there is no mention of inertial frames in
the statements of the first three laws, nor in the paragraph explanations
below them. This doesn't hurt Marlow's postion however
as there is an entire proceeding chapter where Newton defines his
terms (in archaic english which I find hard to understand, so I may have
misinterpreted some points). I think Newton rather clearly distinguishes
between "true motions" and "apparent motions"; presumably those
motions caused by "real" forces and those caused by "kinematical"
forces. He emphasizes that the true motions are those relative to an
absolute frame of reference.
This means to decide if a force is a real force or not we must be
able to refer the motion to an absolute frame. Ernst Mach critisized the
standard interpretation of Newtonian mechanics on this very point. In a
very real operational sense, the absolute frame is a "fiction" since we can
never know if we are doing our measurements relative to it, as
opposed to some non-inertial frame.
Now let me quote Marion's well known mechanics text (parenthized
comments are mine), equations are expressed verbally, the ellipsis will
denote the usual skipped verbage:
"These laws are so familiar that we sometimes tend to lose
sight of their true significance (or lack of it) as physical laws. The first
law , for example, is meaningless without the concept of "force" . . . The
question of the frame of reference with respect to which the "uniform
motion" is
to be measured is discussed in the following section. In pointing out
the lack of content in Newton's first law, Sir Arthur Eddington observed,
somewhat facetiously, that all the law actually says is that every
particle continues in its state of rest or uniform motion in a straight line
escept insofar as it doesn't. . . .
The second law provides an explicit satement: force is
related to the time rate of change of 'momentum'. . . . therefore Newton's
second law can be expressed as (an equation here, force
equals the time derivative of P equals the time derivative of
mass times velocity). (my comment: I might add, or if the mass of the
object is immutable then we may say force equals mass times the time
derivative of the velocity) The definition of force becomes complete and
precise ony when 'mass' is defined. Thus the first and second
laws are not really 'laws' in the usual sense; rather, they may be
considered definitions. Because length, time, and mass are concepts
normally already understood, we use Newton's first and second laws as the
operational
definition of force."
He then goes on to point out that the 3rd law is not a general
law as it only applies if the force exerted by one object on another object
is directed along the line connecting to the two objects. This aspect of
the 3rd law was discussed in another thread, sort of.
So, one way to define a force then is operationally, by observing
the objects acceleration. If I stop there then I believe Marlow is
absolutely correct in saying I've reduced dynamics to kinematics. But there
is nothing wrong with that and "my" physics is perfectly consistent in doing
that, I get the same answers that Marlow gets to analysizing problems; we
predict the
same trajectories for the motion of objects under the influence of forces.
I must confess, and I think Marlow would agree here, that the
above viewpoint is intellectually unsatisfying. Therefore, I must
distinguish the "kinematic" forces from the ones where I can identify a
physical agent as the cause, Marlow's "real" forces. I must do this so that
dynamics is not simply reduced to kinematics.
Here is why I like the term "kinematic" force. Precisely because
it emphasizes the point that Marlow makes, namely it is a kinematic effect!!
A real effect none-the-less, hence my dislike of the term "fictitious". I
like to call the mass multiplied by the coriolus acceleration, as Marlow
would have us say, for example, a force because it acts like a
force when measurements and analysis are confined to a non-inertial frame of
reference. Our Oceanographer, pointed out that that is exactly how they
analyze things.
Let me now mention what Feynman had to say on the issue (Marlow
should like this). This comes from section 12-1 of the first volume of his
lectures. The section is entitled "What is a force". He first discusses
using the 2nd law as a definition of force and then rather strongly rejects
the idea, but not because it gives wrong answers, it doesn't. He puts into
words quite well (as he always does) the unsatisfying intellectual feeling I
was describing above.
Let me quote briefly a few spots:
"The real content of Newton's laws is this: that the force is
supposed to have some 'independent properties', in addition to the law F =
ma; but the specific independent properties that the force has were not
completely describe by Newton or anybody else, and therefore the physical
law F=ma is an incomplete law".
Amen to that!!(Probably why it may be impossible to give a precise
definition of a force, other than the kinematical one). He goes on,
"It implies that if we study the mass times the acceleration and
call the product the force, i.e. if we study the characteristics of force as
a program of interest, then we will find that forces have
some simplicity; the law is a good program for analyzing nature,
it is a suggestion that the forces will be simple."
I might interpret this as well as other items he states in that
chapter as saying that we can't give a precise definition of force (the
reason I have not done so in this thread, despite calls to do so).
What does he have to say about "kinematic" forces. He calls them
pseudo-forces, I like that better than "fictitious" forces. He does say they
do behave as forces (I interpret to mean that they do all the things we
expect of forces) and I quote: (parentheticals are my comments)
"That is, since Moe's coordinate system is accelerating with
respect to Joe's, the extra term ma (ma is the psueodo-force) comes in, and
Moe will have to correct his force by that amount in order to get Newton's
laws to work"
In other words you can get Newton's laws to work in a non-inertial frame of
reference (i.e. apply Newton's 2nd law to the non-inertial frame);
if you introduce the kinematical forces. You do this to reproduce the real
effects that they have in that frame of reference, namely how do you predict
the motion of objects in that frame of reference.
I shall end here and hope that this will be my last long post on
this issue (but I doubt it), I reserve the right to make smaller reply
posts. Again I thank A Marlow for the time and effort he has put into these
discussions to try to correct my thinking and more importantly trying to
keep us folks on the list on the path of the straight and narrow, I
understand physics all the better for it. We are all more or less guilty of
more imprecision at times than is optimal. I also thank the others who have
interjected from time to time with comments, and I thank those who have read
this thread and not tried to squash it flat. I think it deals with the
fundamental issues behind Newtonian Mechanics and therefore is intrinsically
interesting. In a few weeks I'll be off the list for the summer as I plan to
do some experimental testing of gravitational potential energy and the
work-energy thm and conservation of energy in the Appalachian mountains and
I don't care to carry a laptop with cellular phone hook-up to the net, its
too heavy and I can't afford the phone bills either.