On Fri, Jun 12, 2020 at 1:53 AM smitra <smi...@zonnet.nl> wrote: > On 11-06-2020 02:01, Bruce Kellett wrote: > > > Energy and momentum are conserved locally, even in GR where global > > energy conservation fails in a non-static universe. > > Not in the sense you are suggesting. Energy and momentum are constant in > a closed volume and one can then write down the conservation law in a > local form. But this so-called "local conservation of energy and > momentum" does not mean that it's conserved in the sense of having a > constant value everywhere. >
Bullshit. Energy-momentum conservation comes from translational invariance of the Lagrangian in space and time. Local conservation is ensured in GR by the vanishing of the covariant derivative of the Stress-Energy tensor. Local in this sense means on the scale of the galaxy or more. In the absence of a time-like Killing vector in an expanding universe, this conservation breaks down on larger scales, such as the scale of the Hubble expansion. If you have a theory that violates local energy-momentum conservation in the above sense, then your theory is wrong. Local conservation does not mean that energy necessarily has the same constant value everywhere. ......... > >> The expectation value of these energies do fluctuate. > > > > You can introduce coupled harmonic oscillators, but that is not how > > you form a quantized field theory. Such fluctuations arise from > > non-local couplings -- they are not fluctuations of the original > > quantum field. Energy-momentum is locally conserved, even in GR and an > > expanding universe. > > > > The Casimir effect, the effective negative pressure of the vacuum is > another way to see that your arguments based on local energy > conservation are wrong. Vacuum fluctuations in the local energy density > do exist and they have measurable effects. > I wondered when this would come up. It is always the last resort of those who contend that vacuum fluctuations in local energy densities are real. I remember reading a comprehensive review of the Casimir effect in a scholarly article in Rev. Mod. Phys. a few years ago. Unfortunately, I did not keep a reference, and I have been unable to find this paper again. But I do remember the main points of the analysis: They discuss the Mickey-Mouse Comic-Book explanation of the Casimir effect in terms of supposed vacuum fluctuations, but they dismiss this approach as insufficiently general. They give a detailed account of the Casimir effect in terms of generalized van der Waals forces. The reason for preferring this explanation (over vacuum fluctuations, sidestepping the question of whether these fluctuations exist or not) is that the van der Waals explanation extends seamlessly to the Casimir effect between irregular surfaces -- indeed, to the attractive force between a point and a plane surface -- where the fluctuation model is silent. Bruce -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQ1die94Efw4kOL63Mdn_L4ZuFk5Wzmt1iRvpsfht3ABA%40mail.gmail.com.
