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125. Also we lack the opportunity to produce shapefull images in the weak field limit. Whichever embedding constant we choose for the space-eigentime, of for instance a radial line through the Earth, the relative variations in the embedding radius will be of the order 10−9 . 4 Comments One might think that there would be no use in having the Epstein trumpet layered, since we cannot distinguish events anyway. For every single particle it makes sense however, since eigentime is certainly not periodic.
5: The absolute space using generators uµ (x) such that outmoving photons move on geodesics. 55, 4]. The thick lines with arrows correspond to photons moving out. The left one, being inside the horizon is however forced to follow the geometry into the singularity. Notice 11 That way there is no problem in dealing with trajectories that are first increasing in t and then decreasing in t for instance 28 3. The absolute metric how the photons stay at exactly 45◦ to the generating grid. Notice also that the horizon is exactly where there is a minimum in the embedding radius.
If ever we find that the Schwarzschild time along the two curves are the same, as the trajectories pass a certain spatial position - then they crossed each other in the real spacetime. 1 The Berg dynamical view The procedure above is a little awkward. There is however another, more dynamical view on the scenario. Actually the idea was introduced to me by my friend, Daniel Berg. Take for instance two moving particles, corresponding to two trajectories in the original spacetime. Suppose that at a given slice t = const in the original space, we have mapped the particles to two specific points on the Epstein trumpet, for instance to the same azimuthal angle.