Found Phys https://doi.org/10.1007/s10701-018-0137-4 Energy and Uncertainty in General Relativity F. I. Cooperstock 1 · M. J. Dupre 2 Received: 5 June 2017 / Accepted: 2 January 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The issue of energy and its potential localizability in general relativity has challenged physicists for more than a century. Many non-invariant measures were proposed over the years but an invariant measure was never found. We discovered the invariant localized energy measure by expanding the domain of investigation from space to spacetime. We note from relativity that the finiteness of the velocity of propagation of interactions necessarily induces indefiniteness in measurements. This is because the elements of actual physical systems being measured as well as their detectors are characterized by entire four-velocity fields, which necessarily leads to information from a measured system being processed by the detector in a spread of time. General relativity adds additional indefiniteness because of the variation in proper time between elements. The uncertainty is encapsulated in a generalized uncertainty principle, in parallel with that of Heisenberg, which incorporates the localized contri- bution of gravity to energy. This naturally leads to a generalized uncertainty principle for momentum as well. These generalized forms and the gravitational contribution to localized energy would be expected to be of particular importance in the regimes of ultra-strong gravitational fields. We contrast our invariant spacetime energy measure with the standard 3-space energy measure which is familiar from special relativity, appreciating why general relativity demands a measure in spacetime as opposed to 3-space. We illustrate the misconceptions by certain authors of our approach. B F. I. Cooperstock cooperst@uvic.ca M. J. Dupre mdupre@tulane.edu 1 Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, BC V8W 3P6, Canada 2 Department of Mathematics, Tulane University, New Orleans, LA 70118, USA 123