Publication Date
12-1-2024
Abstract
From the physics viewpoint, energy is the ability to perform work. To estimate how much work we can perform, physicists developed several formalisms. For example, for the fields, once we know the Lagrangian, we can find the energy density and, by integrating it, estimate the overall energy of the field. Usually, this adequately describe how much work this field can perform. However, there is an exception -- gravitational field in General Relativity. The known formalism to compute its energy density leads to 0 -- and by integrating this 0, we get a counterintuitive conclusion that the overall energy of the gravitational field is 0 -- while hydroelectric power stations that produce a significant portion of world's energy show that gravity {\it can} perform a lot of work and thus, has non-pzero energy. The usual solution to this puzzle is that for gravity, energy is not localized. In this paper, we show: (1) that non-locality of energy can be explained already on the Newtonian level, (2) that the discrepancy between energy as ability to perform work and energy as described by the Lagrangian-based formalism is ubiquitous even in the Newtonian case, and (3) that there may be a possible positive side to this non-locality: it may lead to faster computations.
Original file
Comments
Technical Report: UTEP-CS-24-52a
To appear in: A. I. Shevchenko and Yuriy P. Kondratenko (eds.), Philosophical Transactions of the Royal Society A: Mathematical, Physical, and Engineering Sciences, DOI 10.1098/rsta.2023.0290