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Proper Time of a Clock Moving in a Uniform Gravitational Field
New Phys.: Sae Mulli 2020; 70: 374~382
Published online April 29, 2020;
© 2020 New Physics: Sae Mulli.

Jae Hyun HAN1, Dong Sik KIM2, Eun Seok KIM3, Won-Young HWANG4*

1Korea Port Logistics High School, Gwangyang 57707, Korea
2Gwangju Science Academy for the gifted, Gwangju 61005, Korea
3Gwangju High School, Gwangju 61412, Korea
4Department of Physics Education, Chonnam National University, Gwangju 61186, Korea
Correspondence to:
Received August 12, 2019; Revised March 6, 2020; Accepted March 9, 2020.
cc This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
What is time-flow rate of a clock moving in (a uniform) gravitational field? We can get the solution by using only the basic facts of special relativity. Just like a circle is invariant under a rotational transformation, a hyperbola is invariant under a Lorentz transformation. Based on the Lorentz invariance of the hyperbola, we can obtain the coordinates of a constantly acceleration observer, the Kottler-Moller-Rindler coordinate. The coordinate is now that of (a uniform) gravitational field, due to the equivalence principle. We show that the time-flow rate of a clock moving in (a uniform) gravitational field we can derived by using the Kottler-Moller-Rindler coordinate and a space-time diagram.
PACS numbers: 03.30.+p
Keywords: Accelerated observer, Kottler-Moller-Rindler coordinates, Time-flow rate, Relativity

May 2020, 70 (5)
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