Does a Physical Clock Measure in Curved Spacetime? An Operational Clarification Within Standard General Relativity IRCBHC – Independent Research Collaboration on Black Hole and Cosmology Concepts Abstract In general rela

Abstract

In general relativity (GR), common teaching phrases such as “time runs slower in a gravitational field” can blur a crucial operational distinction: a physical clock records a measurable quantity along its worldline, whereas coordinate time is a labeling convention. This paper provides a compact, GR-literate clarification suitable for advanced undergraduates and instructors. The reading of an ideal clock is modeled by the invariant proper time along its worldline, and “time dilation” is interpreted strictly as a comparison of accumulated clock readings between worldlines under a specified protocol. We connect this operational content to the 3+1 decomposition via the lapse function N, present a Schwarzschild example yielding dτ = N(r) dt for stationary clocks, and add a weak-field numerical estimate and a flat-spacetime Rindler analogy. Brief connections to precision practice (GPS, Pound– Rebka) and to physics-education research on time concepts in relativity are included. No claims beyond standard GR are made.

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