Abstract
The non-Euclidean nature of space (relative to a rotating observer) is derived non-relativistically. Only the law of conservation of energy, Planck's formula, and the equivalence principle are used in the derivation.
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References
Ehrenfast, P. (1909). Physikalische Zeitscrift 10, 918. English translation: Rizzi, G. and Ruggiero, M. L. (eds.) (2004). Relativity in Rotating Frames, Kluwer Academic Publishers, Dordrecht, p. 3.
Einstein, A. (1961). Relativity, Crown Publishers, New York, pp. 79–81.
Feynman, R., et al. (1977). Lectures on Physics, Vol. II, Addison-Wesley, Reading, MA, pp. 42–49.
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Malin, S., Caler, M. Non-Relativistic Derivation of the Non-Euclidean Nature of Space. Int J Theor Phys 44, 1559–1563 (2005). https://doi.org/10.1007/s10773-005-4828-1
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DOI: https://doi.org/10.1007/s10773-005-4828-1