The quantum zero-point energy of a conducting spherical shell was first calculated by Boyer [Phys. Rev. 174, 1764 (1968)]. Because of the importance of this calculation and also of Boyer's uncertainty about the analytical dependence of the energy on the cutoff function, we have checked the calculation independently. We determine an analytic continuation of the energy function using the Mellin transform, and thereby show how an exact value of the self-energy can be obtained from the divergent series. We also compute an approximate value of the self-energy by extrapolating a direct numerical evaluation of the cutoff integrals. These calculations confirm Bover's result.

Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. Therefore, even at absolute zero, atoms and molecules retain some vibrational motion. Apart from atoms and molecules, the empty space of a vacuum also From… for high values of v. It diverges proportional to v4 for large v. There are two separate questions to consider. First, is the divergence a real one such that the zero-point energy really is infinite? If we consider the volume V is contained by perfectly conducting walls, very high frequencies can only be contained by taking more and more perfect conduction. No actual method of containing the high frequencies is possible. Such modes will not be stationary in our box and thus not countable in the stationary energy content. So from this physical point of view the above sum should only extend to those frequencies which are countable; a cut-off energy is thus eminently reasonable. However, on the scale of a "universe" questions of general relativity must be included. Suppose even the boxes could be reproduced, fit together and closed nicely by curving spacetime. Then exact conditions for running waves may be possible. However the very high frequency quanta will still not be contained. As per John Wheeler's "geons" these will leak out of the system. So again a cut-off is permissible, almost necessary. The question here becomes one of consistency since the very high energy quanta will act as a mass source and start curving the geometry. This leads to the second question. Divergent or not, finite or infinite, is the zero-point energy of any physical significance? The ignoring of the whole zero-point energy is often encouraged for all practical calculations. The reason for this is that energies are not typically defined by an arbitrary data point, but rather changes in data points, so adding or subtracting a constant (even if infinite) should be allowed. However this is not the whole story, in reality energy is not so arbitrarily defined: in general relativity the seat of the curvature of spacetime is the energy content and there the absolute amount of energy has real physical meaning. There is no such thing as an arbitrary additive constant with density of field energy. Energy density curves space, and an increase in energy density produces an increase of curvature. Furthermore, the zero-point energy density has other physical consequences e.g. the Casimir effect,…

to quantum computing. The ZPE energy (Zero Point Energy) is thought to pass or flux through our space … when sufficient energy is added to a gas, it ionises into a plasma. If more energy is added the electric … OBSERVER COHERENT ZERO-POINT ENERGY INCOHERENT ZERO- = POLARIZED VACUUM POINT ENERGY “FLATLAND SLOT" REPRESENTS