The problem with socalled fictitious forces

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The problem with so-called fictitious forces
Hermann Härtel Guest scientist at Institute for
Theoretical Physics and Astrophysics University
Kiel haertel_at_astrophysik.uni-kiel.de http//www.as
trophysik.uni-kiel.de/hhaertel
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Content

• Examples from textbooks
• Historical review
• Results from modern research
• Consequences for teaching

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Description of experimentwith and without
inertial forces
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Inertial forces as fictitious forces
Bergmann Schaefer, Volume 2 11. Edition
Page 99 Among the forces, to be found in nature,
are finally the so-called fictitious or inertial
forces which only act within accelerated frames
of reference. (synonyms fictitious,fabulous,
jegendary, mythical, imaginary, assumed) Examples
are centrifugal forces and coriolis forces. By
selecting appropriate frames of reference these
forces can be transformed to disappear. Therefore
the name fictitious forces.
Page 241 Fictitious or inertial forces have been
introduced to be able to use Newton's 1st and 2nd
law also in accelerated frames of reference.
However, Newton's 3rd law cannot be generalized
by the same method because a counter force for
inertial forces has not been detected until today.
Page 250 The centrifugal force plays an important
role in many natural or technical processes
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The cause for inertia
Example Newtons bucket experiment
Question What is the cause for intertia? Is
there any counterforce related to the force of
inertia? Newtons answer The cause for inertia is
grounded in the existance of absolute space
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Problematic explanations in textbooks
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Historical Review 1687 - Newton Principia.
Absolute space as basic concept 1710 -
Berkeley 1715 - Leibniz Early criticism of the
concept of absolute space 1883 - Mach Die
Mechanik in ihrer Entwicklung The Science of
Mechanics a Critical and Historical Account of
its Development
Statement There is no absolute space. Request
Only relative terms are allowed to enter the laws
of physics. Prediction Mass there influences
inertia here".
1905 - Einstein Special Relativity
Einstein in his early years - was strongly
influenced by Mach. He tried to implement Machs
ideas but concluded that it is not possible to
use only relative terms but that the role of the
observer was crucial
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1848 - Wilhelm Weber Elektrodynamical force law
1999 - Andre Assis Relational Mechanics, Apeiron
Montrealas pdf-Datei available under
http//www.ifi.unicamp.br/assis
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Spherical shell interacting with a particle
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Result
We now summarize the main direct consequences of
relational mechanics when we identify it with
Newtonian mechanics

• A) We derive equations similar to Newtons first
  and second laws of motion.
• B) We derive the proportionality between inertial
  and gravitational masses.
• C) We derive the fact that the best inertial
  frame we have is the frame of distant galaxies.
• D) We derive the kinetic energy as an interaction
  energy of gravitational origin between the test
  body and the distant galaxies.
• E) We derive the fact that all fictitious forces
  of Newtonian mechanics are in fact real forces of
  gravitational origin acting between the test body
  and the distant galaxies.
• F) We derive that the inertial forces have the
  same numerical value in all frames of reference,
  though not necessarily the same form.

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Stated consequences
In our view, the theoretical concepts of

• length contraction,
• time dilation,
• Lorentz invariance,
• Lorentzs transformations,
• covariant and invariant laws,
• Minkowski metric,
• four-dimensional space-time,
• energy-momentum tensor,
• Riemannian geometry applied to physics,
• Schwarzschild line element,

• tensorial algebras in four-dimensional spaces,
• quadrivectors,
• proper time,
• Contravariant four-vectors and tensors,
• geodetic lines,
• Christoffel symbols,
• Super strings,
• curvature of space,
• etc.

have the same role as the epicycles in the
Ptolemaic theory.
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Consequences for teaching