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In non-relativistic and non-gravitational physics (both conditions have to be satisfied simultaneously for the following proposition to hold), energy is only defined up to an arbitrary additive shift. In this restricted context, the choice of the additive shift is an unphysical, unobservable convention. Special relativity However, in special relativity, ...

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Although, I do not know if a general proof exists, I think that the Casimir effect of a renormalizable quantum field theory should be completely understood by means of a theory of renormalization on manifolds with boundary. The key feature is that one cannot, in general, neglect the renormalization of the coupling constants in the boundary terms. Using this ...

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The energy density between the Casimir conductors can indeed be positive or negative. The calculation of Casimir energies is often done by noting that the plates impose boundary conditions on the field modes that can exist between them. Therefore in the presence of the plates, a more restricted set of modes is allowed than would be the case if the plates ...

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The objects whose number is lower in between the plates are not really particles per se but the different modes - different possible values of the wavelength or frequency, in particular - in which the particles may be created. If the distance of the parallel plates is $L$, then the electric field has to vanish at the boundary between the vacuum and the ...

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Ref [19] in the arXiv paper, C. M. Caves and B. L. Schumaker, Phys Rev A 31, 3068 (1985), gives a clean description of a parametric amplifier as the prototype of a two-photon device, at the bottom of its second page: In a [parametric amplifier], an intense laser beam at frequency $2\Omega$ —the pump beam— illuminates a suitable nonlinear medium. The ...

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The reason why the Alcubierre drive is not feasible as an FTL drive has nothing to do with absence of exotic matter; in fact, we likely had plenty of the required matter during cosmic inflation era, or something with identical geometrical effects. Physicists that dismiss it as impossible because "there is no exotic matter" play ignorance to the fact that ...

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I don't think the formation of lipid bilayers is analogous to the Casimir effect because it's a surface energy effect. However there is an effect called depletion flocculation that is very closely analogous. This happens in a polymer solution when surfaces approach more closely than the size of the polymer molecule. The polymer is excluded from the region ...

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What I would do is to calculate the effective action from integrating at one loop the propagator in a space with boundaries. The result is quite simple, schematically of the form $\mathrm{Tr}\log \Delta$ where $\Delta(x_1,x_2)$ is the propagator in position space. Indeed, the free action is quadratic in the field, $S\sim ... 3 A friend recently brought to my attention that this experiment was actually performed 6 months after i posted the question in this site: http://blogs.nature.com/news/2011/11/light_coaxed_from_nothingness.html http://www.chalmers.se/en/news/pages/chalmers-scientists-create-light-from-vacuum.aspx Christopher Wilson from Chalmers (and his team) used the ... 3 Thank you for your interesting question. The following is what I assumed in the paper. If you accelerate to the right, the Rindler horizon to your left is a boundary beyond which things are in principle unobservable for you. So, as soon as the nearer Rindler horizon forms, the far cosmic horizon behind it becomes unobservable and therefore (following the ... 3 The Casimir effect and the Van der Waals force between two conducting plates are one and the same thing. To see this, consider the boundary conditions postulated for the Casimir effect. The electric field has to be exactly zero at the plates. Because of this, it is said, the zero point energy of the vacuum is lower in between the plates than outside, which ... 3 The Casimir effect is analogous to gravity in only one way--- it has a negative energy which varies as a power of the distance. In all other ways, it is different. The power-law is different, the cause is different, it is a quantum effect, not a classical effect, and the mediator is the electromagnetic field, not the gravitational field. Negative energy is ... 3 No. It really only creates the illusion of negative energy. It's negative relative to the space around it; which only proves that there is a small amount of positive energy in what looks like flat empty space ("zero point energy"). But it is not possible to extract negative energy from this kind of system and use it to construct an Alcubierre warp drive, ... 3 It's quite correct that you can additively shift energy, even in quantum mechanics, and one can always make the ground state carry zero energy. Nevertheless, you can still measure some other energy even in the ground state: the kinetic energy. Because$T = {p^2 \over 2m}$the expectation of kinetic energy in a given energy state is essentially its ... 2 Dear Carl, the correct paper to derive the 0.1-second lifetime of the anti-Hydrogen atom in the gravitational field is described after the very sentence you quoted. There is a "[20]" symbol which means that the sentence is justified in the reference number 20 in the list of literature at the end of the paper you quoted. So the correct paper that answers ... 2 The zero-point energy for the quantum mechanical harmonic oscillator can be related to the Heisenberg uncertainty principle (HUP). A bit oversimplified, the point is intuitively that if the mechanical energy $$H~=~\frac{p^2}{2m}+\frac{1}{2}m\omega^2 q^2, \qquad \omega ~:=~ 2\pi f,$$ is zero, then the position$q$and the momentum$p$must also both be ... 2 Virtual particles influence physics at every point of space, whether or not there is a nearby atomic nucleus or orbital. All electrons in an atom receive energy shifts analogous to the Lamb shift (from virtual photons), aside from other quantum corrections. In fact, the influence of the virtual particles only becomes truly measurable if there are some nearby ... 2 The interaction between the geometry of spacetime (how precisely it is "warped"), and energy, is a fundamental notion in general relativity. Specifically, the Einstein field equations tell us that if there is energy or momentum near some spacetime point, then the geometry nearby will bend (warp, curve, whatever you'd like to call it) in a particular way. ... 2 I think you are confusing the CMB with radiation from the apparent horizon. CMB is just relic light from the surface of last-scattering - it behaves like any light which is emitted from a source. It is totally unrelated to the Hawking radiation emitted from the horizon. A neat coincidence (as afar as we know) is that the surface of last scattering is "close" ... 2 This is an interesting question. In 3 spatial dimensions, one may compare different topologies like paralles plates, infinite cylinder, and sphere. The first 2 toplogies have the same sign for the Casimir energy, while, for the sphere, the sign is different. A short and violent answer would be "Shut up and calculate", but this is not quite satisfactory. ... 2 With casimir effect, you could modify the though experiment so as to avoid infinities (while using renormalization). For instance, instead of considering$2$(conducting) plates$D_1,D_2$with distance$d$apart, you can consider 4 plates$D_0,D_1,D_2,D_3$, with distance$(D_0,D_1) = (D_2,D_3) = L $. After having renormalised modes, for instance, in one ... 2 Following Brown, Maclay, "Vacuum Stress between Conducting Plates: An Image Solution" (DOI:10.1103/PhysRev.184.1272) consider two ideally conducting parallel conducting plates separated by distance$a$along the$z$-axis. Simple symmetry argument allows us to obtain the possible structure of vacuum stress-energy tensor$\langle T_{\mu\nu}\rangle_0$. The ... 2 No, Higgs particles do not contribute to Casimir forces. Casimir effect happens because virtual particles are excluded from the gap between two solids when the separation distance is smaller than the particle wavelength (multiplied by smallish integers). Its force is barely measurable when objects are within about a micron ($10^{-6}$m) of each other, and ... 1 Your analogy is quite right in the sense that the original derivation from Casimir between two infinite and ideal conducting plates in vacuum leads to an attraction owing to a greater number of modes "outside" than "inside" the slab they form as it is shown at the beginning of this review. Note that this pseudo counting method only holds because an ideal ... 1 As the posts above say, I believe it would just be a phantom due to a local drop in the energy density compared to the vacuum. What I'm curious about is if this might be a gauge issue. I know that some literature (http://iopscience.iop.org/0305-4470/20/10/026/pdf/0305-4470_20_10_026.pdf) has previously claimed that Casimir energies are gauge variant, and so ... 1 According to the article linked bellow the effect works using nonconductive materials as well, but electrostatic force resulting from charge accumulation on nonconductive plates can make measurement impossible. Independent measurement of systematic error due to residual electrostatic forces is neccessary even with grounded metal plates. You can read more on ... 1 The zeta function is defined to be the (unique) analytic continuation of$\zeta(s):=\sum_{n=1}^\infty n^{-s}$. This implies$\zeta(-3)=1/120$. Thus your (*) is true by definition and some theory that provides the formula$\zeta(-n)=-B_{n+1}/(n+1)$for natural numbers$n$. http://en.wikipedia.org/wiki/Riemann_zeta_function If the final result agrees with ... 1 You're asking a mathematical question. Given a function$f$, let$a_n = f(n)$, then does the limit$\epsilon \downarrow 0$exist for $$\sum a_n e^{-n \epsilon} - \int f(t) e^{-t\epsilon}?$$ The answer is no: the integral will generically only get ride of the 'hardest' divergence. The sum$\sum a_n e^{-n \epsilon}$typically (if$\{a_n\}\$ behaves reasonably ...

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I walk through a physical argument similar to what Trimok has shown in my blog article Ramanujan and the Casimir Effect. You basically assume that each available classical e-m mode is filled to exactly the level of one-half of a "quantum", and put a small box inside one twice as big. The gist of the argument goes like this (quoting from my article): We ...

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