Energy Conservation, Lorentz Invariance and a Second Dimension of Time
Abstract
The law of conservation of energy can be stated: Energy can neither be created or destroyed but only converted to from one form to another. Laboratory experiments demonstrating that no energy is lost or gained during a conversion have been rare. Interestingly, there is a close connection between energy conservation, Lorentz violation and the possibility of a second dimension of time. We explore this connection within a model of Lorentz invariance that incorporates a second dimension of time. The model's Lorentz transformation matrix reduces to the well-known one-dimension of time version in the limit of a parameter that defines the relative size of the extra dimension. If the parameter is finite, one might misinterpret the energy equivalence of mass or observe a deviation from the accepted time dilation formalism. We explore different experimental limits on this new parameter including Lorentz violating parameters from the Standard-Model Extension.
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BibTeX
@misc{elliott2026energy,
title = {{Energy Conservation, Lorentz Invariance and a Second Dimension of Time}},
author = {S. R. Elliott and R. Massarczyk and S. Zahir},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01626},
eprint = {2609.01626},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01626},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Energy Conservation, Lorentz Invariance and a Second Dimension of Time
AU - S. R. Elliott
AU - R. Massarczyk
AU - S. Zahir
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01626
UR - https://arxiv.org/abs/2609.01626
AB - The law of conservation of energy can be stated: Energy can neither be created or destroyed but only converted to from one form to another. Laboratory experiments demonstrating that no energy is lost or gained during a conversion have been rare. Interestingly, there is a close connection between energy conservation, Lorentz violation and the possibility of a second dimension of time. We explore this connection within a model of Lorentz invariance that incorporates a second dimension of time. The model's Lorentz transformation matrix reduces to the well-known one-dimension of time version in the limit of a parameter that defines the relative size of the extra dimension. If the parameter is finite, one might misinterpret the energy equivalence of mass or observe a deviation from the accepted time dilation formalism. We explore different experimental limits on this new parameter including Lorentz violating parameters from the Standard-Model Extension.
ER -