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    Re: The development of bubble sextants
    From: Gary LaPook
    Date: 2009 Aug 17, 00:59 +0200

    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.
    frankreed@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 
    > -FER
    > >
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