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    Re: The development of bubble sextants
    From: Peter Hakel
    Date: 2009 Aug 16, 16:49 -0700
    Gary,

    You are presenting a very coherent and strong argument.  Indeed, it is often more convenient to use a non-inertial reference frame with additional ("fictitious") forces, instead of transforming everything into an inertial frame, solving without any additional forces, and then transforming back.  Historically, there really was no way to decide in favor of one or the other interpretation (philosophically, in practice inertial forces are quite real), until Einstein's relativity theory appeared about a century ago.  This theory contains the so-called equivalence principle:

    http://en.wikipedia.org/wiki/Equivalence_principle

    which expresses the experimental observation (made already by Galileo) that inertial mass = gravitational mass ("charge").  This is what allowed the construction of general relativity not as a field theory (of which Newtonian gravity is an example) but as a geometrically-based one.  In Newton's theory the equivalence of masses is an unexplained coincidence.  In Einstein's theory it is automatically included by its geometric nature.  This development allowed physicists to finally make a decision on this philosophical issue.  The conclusion is that inertial forces are equivalent to gravity and hence as real as gravity itself.

    A good example is local gravity g as indicated by the plumb line.  This is real in its entirety (not just practically but also theoretically) even though we know that in addition to Earth's "true" gravity it contains a small (inertial) component due to Earth's rotation.


    Peter Hakel


    From: Gary LaPook <glapook---.net>
    To: navlist@fer3.com
    Sent: Sunday, August 16, 2009 3:59:56 PM
    Subject: [NavList 9548] Re: The development of bubble sextants


    The problem with "frame-dependent" accelerations is that they are just
    artifacts of the frame you chose to use to define the accelerations and
    therefor the forces that must have caused the accelerations are also
    arbitrary artifacts too. Since anybody can choose any gyrating,
    spinning, hopping, twirling etc., accelerating frame of reference, any
    measured motion of an object could have an infinite number of different
    forces and accelerations. If I get to choose the right accelerating
    frame I can prove that it was your nose that hit my fist. But for non
    accelerating frames of reference, inertial frames, it doesn't matter
    which frame you choose the observer will always calculate the same
    forces for any observed object. I understand that there are some
    computational advantages in some circumstances to create fictitious
    forces when dealing with rotating frames such as the earth.  For
    example, if I am demonstrating a loop to a flight student it is easy for
    me to tell him that it is centrifugal force that presses his butt into
    the seat at the top of the loop while we are upside down. This is easier
    than the real explanation that pulling back on the stick while we are
    upside increases the angle of attack of the wings causing the wings to
    create a greater force. Since we are upside down this greater force from
    the wings (lift) causes the aircraft to accelerate towards the earth at
    a rate of acceleration greater than than the rate of acceleration caused
    by gravity thereby leaving the pilot's behind behind. Even though this
    is convenient, it that still doesn't make centrifugal force real since
    it is just another fictitious force invented to allow a simple
    explanation in the looping frame of the airplane.

    gl


    ..


    frankreed{at}HistoricalAtlas.com wrote:
    > Quoting Gary:
    > "Coriolis is a fictitious force use to explain the perceived curve of the
    > flight path as observed by an observer on earth of other rotating frame
    > of reference."
    >
    > Coriolis acceleration is a "frame-dependent" acceleration. That is, it depends on the choice of coordinates that you use to define motion. The expression "fictitious force" is a technical term intended to describe this frame-dependence. Just so there's no misunderstanding, it DOES NOT mean that the Coriolis acceleration is "fictional" in the ordinary sense of the English word. Of course, Coriolis acceleration is "real" in the sense that in many circumstances you find that the natural coordinates to describe the problem are rotating coordinates. The weather on Earth or any other planet, for that matter, is nearly impossible to understand in non-rotating coordinates but quite easy to understand in coordinates which rotate.
    >
    > >From a modern perspective (modern = since the early part of the 20th century, after the development of general relativity), even the common acceleration of gravity near the surface of the Earth (at a single point) at 9.8 m/s^2 or 32 ft/sec^2 is a "fictitious force" since it can be eliminated by going to a frame of reference which is accelerating toward the Earth's center, in other words a freefall frame. And sure enough, if you place an aircraft on a parabolic trajectory with that acceleration, gravity disappears and passengers are rendered completely weightless exactly as if they are in orbit (until the plane's acceleration trajectory is changed). It is not "as if" there is no gravity; in that frame of reference, there really is "no gravity" apart from local tidal accelerations.
    >
    > Many people are able to explain the origin of the Coriolis acceleration by describing how it appears in an inertial, non-rotating frame of reference. In such a frame, the object moves on a straight line "while the Earth turns beneath it". This is very important information, of course, but it is a derivation, like an "etymology". It tells us why this acceleration must exist in non-inertial frames of reference, but it doesn't mean that it is fake or "fictional". And you surely wouldn't want to revert to the derivation once you understand why it works.
    >
    > In many ways, the expression "fictitious force" in physics has caused as many problems as the expression "imaginary number" in mathematics. Neither of these concepts are invalid or fictional or "un-real". For modern mathematics, so-called imaginary numbers have no defects, no lack of reality to them. They are what they are: solutions to algebraic equations. Likewise in physics, so-called fictitious forces are not forces to be avoided or treated as "un-real". They are what they are: forces arising from the choice of coordinates.
    >
    > -FER
    >
    >
    >
    >
    >
    > >
    >




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