Arbitrary Frames

  • James J. Callahan
Part of the Undergraduate Texts in Mathematics book series (UTM)


How can the inherent subjectivity of individual observations lead to conclusions that are objectively real, that is, to conclusions that become physical laws? Our answer is the principle of relativity: Any physical law must be formulated the same way by all observers. So far, though, “all observers” has been limited to Galilean observers in inertial frames. Why, Einstein asked, should there be such a limitation? In particular, can it be justified objectively, on physical grounds? In the decade following 1905 he found that gravity could not be described using only the inertial frames of special relativity; he became convinced that “there is nothing for it but to regard all imaginable systems of coordinates, on principle, as equally suitable for the description of nature” ([10], page 117). This is the principle of general relativity. Using it as a foundation, Einstein was able to create a new and revolutionary theory of gravity.


Gravitational Field Doppler Effect Gravitational Potential Coordinate Frame Inertial Frame 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • James J. Callahan
    • 1
  1. 1.Department of MathematicsSmith CollegeNorthamptonUSA

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