Holography, relativity and the spooky ellipsoids

N. Abramson
Royal Institute of Technology, Sweden
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The further away from a house we move, the smaller it appears. We could say that we are in the centre of a “sphere of observation”, which must reach the house before we can see it. The larger that sphere is, the smaller the house appears. This is natural to us and not difficult to understand. In Einstein’s Special Relativity it is stated that the faster we move past a house, the shorter it appears. We state in this paper that this is because the faster we travel, the more our “sphere of observation” is elongated into an “ellipsoid of observation”. The longer that ellipsoid is, the shorter the house appears. This contraction is not so natural to us, because to be observable the velocity has to be extremely high, almost close to the velocity of light. A similar phenomenon can, however, be studied when holography with ultrashort pulses is used for measurement. In this case the sphere of observation is also transformed into an ellipsoid of observation. Thus, according to our approach objects appear shorter because the definition of length (the metre) becomes longer, just as time moves slower because the definition of time (the second) becomes longer. The transformation of the sphere into an ellipsoid is however hidden to the observer both in the case of holography and in relativity. This spooky behaviour of the ellipsoid has resulted in a new mathematical theorem.