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14

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, ...


6

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 ...


5

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 ...


4

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 ...


4

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 ...


4

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 ...


4

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 ...


4

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

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

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

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, ...


2

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 ...


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

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

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

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

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

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 ...


1

Partial answer: Because the distance between the plates is finite, you have a natural correspondence between the quantum Casimir problem, and a thermodynamic problem. In fact, in a $d$-dimensional space, if you calculate the Helmholtz free energy, in a grand-canonical formalism, for a perfect photon gaz (so with zero chemical potential), with the ...


1

When you have two parallel mirrors you get standing waves between them, and the standing waves can only form if the spacing between the mirrors is a half integral number of wavelengths. Exactly this principle is used in the Fabry-Perot interferometer. The restriction of the wavelength happens because if the mirror spacing is not a half integral number of ...


1

The zeta function always has poles, depending on the number of dimensions you're working in. For $d=4$ you will generically have poles at $s=2$ and $s=1$ (but only there). The sum $\sum_n \omega_n^{-s}$ only converges if $\text{Re } s > 2$ (staying in $4d$ for simplicity). So in every case you'll encounter, you will need to use 'analytic continuation'. ...


1

I'm happy to see that Mike himself has replied to the question (being him the author of the paper in question, and the inertia-as-a-cosmological-casimir-cutoff effect idea), but i wanted to underline a few items. A derivation of a MOND-like acceleration cutoff for inertia as proposed by quantised inertia using heuristic by physically sound arguments, which ...


1

Casimir force is an effect of interaction of two neutral but quantum mechanical plates. Neutral means they are not globally charged. Quantum mechanical means they consist of many real particles and fields bound together with laws of quantum mechanics. When people use the conditions of ideal conductivity of plates and write the filed boundary conditions like ...


1

Since the electronic wave function around the cylinder as well as the piston decays exponentially, a few atom's diameters should be enough to totally eliminate interaction. The forces between unpolarized materials are called van der Waals or London forces, but the usually act at a distance smaller than 1 nm. I'm not sure about one atom (2-2.5 Angström for ...


1

All interactions at the quantum dynamical level are subject to an analysis with Feynman diagrams, and the Casimir effect is not different in this case. Virtual pairs are internal lines in Feynman diagrams. R.L.Jaffe has a arXiv paper that goes into the detail on the Casimir force and corresponding diagrams. the abstract: In discussions of the ...



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