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Freeze it in liquid helium. Any gas inside will condense out. Spin it quickly then stop it. The internal turbulence of the spinning gas will be visible with a sensitive detector. Apply a short sharp impact to one side. If there is gas inside, the sound energy peak from the sound transiting the gas will be temporally distinct from the spectrum of the sound ...


For 1. In principle, the refractive index of a true vacuum is identically 1. For air at atmospheric pressure, the index is 1.000293 for visible light. Therefore, you should be able to determine the deviations between in refractive angles for a jar filled with air and one under vacuum. Since we're talking deviations on the order of one in ten thousandth, it's ...


You can use electric discharge of appropriate frequency, as its threshold in gas depends on pressure (and frequency).


The fact that the energy-momentum tensor is called the source of curvature doesn't mean that there can't be any curvature where there is no energy-momentum. In fact, even if $T_{\mu\nu}=0$ across all spacetime, there are still nontrivial solutions of Einstein's equations, in the form of gravitational waves. You should remember that $T_{\mu\nu}$ is a ...


We first note that the vanishing of the Ricci tensor does not imply the vanishing of the Riemann tensor. Thus the vacuum equations, $R_{\mu\nu}=0$, do not imply that spacetime is flat. The vacuum equations tell us that certain linear combination of components of the Riemann tensor vanishes. When solving differential equations, one usually has to worry ...


(Moving this from my comment to an answer) Yes, the electric field simply penetrates the glass wall and charges (the electrons) placed in that field will feel a force and move. The glass does not really interact with the charges on either side, so you might as well remove it completely (theoretically).


It all depends on what kind of sensitivity you want in pressure measurement. If you just want to distinguished a vaccum state from atmospheric pressure, then there are many non-destructuve ways: index of refraction of air at atmospheric pressure (and a few orders of magnitude down) is different from 1 - optical interferometry. if you apply a temperature ...

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