Boomeranging through the Earth: when free fall doesn't maximize proper time
Abstract
In teaching special relativity, John Bell emphasised the value of pre-relativistic intuitions. His famous spaceship puzzle showed that, in certain cases, the older heuristics of Lorentz and FitzGerald get the right answer to a genuinely relativistic problem more reliably than the principles of special relativity themselves. In teaching general relativity, John Wheeler emphasised the value of simplicity, illustrating curved-spacetime geometry with capsules boomeranging through a tunnel along the Earth's diameter. Here I put the two ideas together. I share a simple thought experiment, involving genuinely general-relativistic effects, in which the standard GR heuristic -- ``freely falling observers maximise proper time'' -- gives the wrong answer, while the older heuristic of velocity and gravitational time dilation, applied in a single frame, gets it right immediately. The resolution involves conjugate points and the distinction between local and global extremality of geodesics, but the moral is the same as Bell's: do not let a newer slogan overwrite a perfectly sound older intuition.
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BibTeX
@misc{gomes2026boomeranging,
title = {{Boomeranging through the Earth: when free fall doesn't maximize proper time}},
author = {Henrique Gomes},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04231},
eprint = {2609.04231},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04231},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Boomeranging through the Earth: when free fall doesn't maximize proper time
AU - Henrique Gomes
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.04231
UR - https://arxiv.org/abs/2609.04231
AB - In teaching special relativity, John Bell emphasised the value of pre-relativistic intuitions. His famous spaceship puzzle showed that, in certain cases, the older heuristics of Lorentz and FitzGerald get the right answer to a genuinely relativistic problem more reliably than the principles of special relativity themselves. In teaching general relativity, John Wheeler emphasised the value of simplicity, illustrating curved-spacetime geometry with capsules boomeranging through a tunnel along the Earth's diameter. Here I put the two ideas together. I share a simple thought experiment, involving genuinely general-relativistic effects, in which the standard GR heuristic -- ``freely falling observers maximise proper time'' -- gives the wrong answer, while the older heuristic of velocity and gravitational time dilation, applied in a single frame, gets it right immediately. The resolution involves conjugate points and the distinction between local and global extremality of geodesics, but the moral is the same as Bell's: do not let a newer slogan overwrite a perfectly sound older intuition.
ER -