Light speed as a function of space coordinate

  1. Let us consider the ideal vacuum, i.e. place with nothing in it whatsoever. With no matter, no electromagnetic field, moreover, no gravitational field. Let us try to introduce a co-ordinate system. In order to do this, we need some kind of ruler, for example, a light beam. However, providing there is a light beam in the ideal vacuum, the latter is no longer ideal, which means that no co-ordinate system can be introduced in the ideal vacuum.
  2. This leads us to the idea that three space co-ordinates and time co-ordinate are the qualities of the material world, functions of matter. Normally, the opposite is assumed, i.e. material objects existing in a time-space continuum, the latter being primary. This statement, inrespectfully of its clear scholastic nature, allows to reconsider the way which the time is being defined.
    Let us consider the simplest example - a stationary gravitational field. If a distribution of matter in space is given, one can calculate time in each point, or, to be more precise, compare a speed of time flow in two different points of space. We can speculate that time in a point is an integral function of matter distribution in the whole space, which is some kind of potential.
  3. Quite naturally, the opposite should also be true, i.e. in case we know matter distribution dependence on two co-ordinates and time, we can find the dependence on the third co-ordinate by some kind of analytic extension.
  4. Above-mentioned makes us suggest that there is a mathematical object M, which has at least a four parametric group of symmetry. Besides, it is symmetrical in respect of permutation of the first three parameters and antisymmetrical in respect the fourth one. I can hardly imagine what I am talking about, but it appears to me a very complicated object M, which differentiation with respect to three variables gives us the fourth variable after some tricks. Although knowing M alone does not allow calculating these four parameters (one has to already know three of them), existence of these four parameters is defined by M's nature. This makes things easier, because differentiation of one co-ordinate with respect to another gives the tensor of curvature, the latter immediately gives the impulse-energy tensor, and world finally failed into custom shape of the general relativity theory.
  5. One of the most amusing qualities of our world is that gravitational interaction always caused attraction of two bodies. The other, not less interesting is the time co-ordinate being significantly segregated from space ones - time can not flow backward. We still do not understand why it is so, but could suggest that they are somehow related one another.
  6. Let us assume that in our very usual three-dimensional space suddenly an object appears around which time flows backward. Intuition says that this object will either repulse gravitationally from the objects of our world or will not interfere with them at all. Let us suppose that the area of negative time flow occupied quiet a finite region in space. Is there any way to get there? Obviously, not. The closer we get to the border of the region, the slower our time flows.
    Having a lot in common with getting into black hole, this process is still very different. A body is falling into a black hole reaches the center after a finite own time, while in our case reaching the boundary of the positive and negative time flows requires infinite own time. Object can be consider as an infinitely remote one as far as the light beam is concerned, and as that located a finite distance away with regards to the co-ordinate, i.e. gravitational interaction.
    The same idea could be illustrated by other means. Let us build two spheres of the same radii around negative time region. The radius of first will be fixed and radius of another would decrease slowly in laboratory system. For the observer on the second sphere its radius would decrease as long as it will not come to the region where the slowing of time is significant. Our experience allows us explain the slowing of time only by expanding of space. Therefore, the observer will note the expanding of his sphere. According to his observation the sphere is expanding and could becomes larger then initial one. (That is similar to well-known mathematical paradox - the sphere of larger area could be place inside sphere of smaller area). When second sphere will be on the boundary between positive and negative time cluster, the time should stop, or, in other words, the radius of sphere becomes infinite. We could say that conceptions of "inside" and "outside" of stationary sphere are just reversed, or that the end of universe could be some point inside our Universe.
  7. Our full Meta-Universe looks like a four-dimensional space-time, split into clusters with different time flows. All clusters interfere by gravitation, but travelling between two clusters with positive and negative time flows are prohibited. The only travels allowed are those between clusters with the same time flow that is why a neighbor cluster should be considering as a jointed one. Clusters with the positive time flow tend with time to stick together due to gravitational interaction, because nobody requires boundaries between clusters to stay motionless. Clusters with the negative time do the same with the flow of their time, i.e. they keep dividing from our point of view. No rush...
  8. In frames of such "bubble" universe the question of birth and death of the Meta-Universe (at which point? when?) cannot be consider a such. One can speak about formation of the Meta-Universe only for a more comprehensive co-ordinate system. Nevertheless, evolution of our cluster (our Universe) can be consider. For example, as long as other clusters join our cluster, new star and galaxies can appear on the sky.
  9. Unification of two clusters increases their total entropy. It would be nice if clusters with the positive time flow were somehow compensated by those with the negative one. In such case the entropy of the Meta-Univere could stay constant, as it should be for a closed system.
  10. Well, gravitational interaction is property of space co-ordinates only; i.e. spreads at no time. However, the nature does not allow us to transfer any kind of information quicker than the speed of light. For example, the center of exploded star stays where it was. A similar problem arises when two objects impact. A mass of an object can not be changes spread enough to let the changes spread out very quickly. From this side the gravitation is very alike to a searchlight. If the beam is being rotated quickly enough, the light spot may run along a wall with any desired speed. Moreover it is possible to create a material wave of light-emitting diodes, lightened by a fast light spot. It still will not help to transfer information, because a wave by lighted diodes does not make any sense.
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Last modified
July 25, 2006

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