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The Euclidian Curved Space and the Galilean Relativity
© 1999

Alberto Mesquita Filho

 

 

2 Actual and virtual location

......Let us consider the observation of a coin from a viewpoint in the prolonging of its main axis (picture 10). In this case, t is the time the light cast or reflected by the coin takes to reach the observer's eye. If c is the speed of light, the center of the coin O is b = ct from the observer. Being b an astronomic value, for example 1 year-light; and finally being the diameter of the coin also equal to b = 1 year-light. Follow our reasoning as you observe picture 1.

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Picture 1: explanation in the text

......The edge of the coin is at distance b'> b from the observer. Consequently, the image of the coin which reaches the observer suffers a "spatial and temporal distortion", that is, at the same moment the observer receives some pieces of information about the coin which are generated as different times proportionally late to the distance of the point from the center. In our example the delay is equal to 43 days  (Pythagoras). If the coin keeps its structure through time, and if the observer and the object are still in relationship to each other, this effect shall not provoke consequences that could be observed. Reversibly, if some structural changes happen, that coin may never show itself to us as it actually is. Then we may talk about the existence of an actual location which translates the coin as it is at the moment and place where is is; and about the existence of a virtual location, related to the way the coin shows itself from the places its parts occupy or occupied in space, but in a disposition which never existed and portrays the superposing of images generated at different times.

......In order to make this virtual location clear, let us imagine an extreme case: the instant and local disappearing ¾as if it were magic¾ of the whole coin. For a year the observer will not notice its disappearing and, to all intents and purposes, its universe will not present any local changes during such period, not event at the place where the coin apparently is. After a year and 43 days, he will clearly feel that the coin is being consumed from its center to its edge. Every day his perception of location will be different and so different from the real one that it will manifest itself through images which never existed at any time (the coin changing into a ring).

......I would say that virtual location is related to the set of proprieties an object manifests to its observer, all of them subdued to changes exclusively generated by the observer's location in time and space. The presented coin occupies a real location but it manifests itself at every point of space through an apparent or virtual location.

 

© 1999