On the consequences of a probabilistic space-time continuum.

(I) Introduction:

Our understanding of gravity has been evolving since the time of Newton. Using a spherical system of coordinates, Newton described gravitational force, at a distance r, due to a mass M, acting on a unit mass, by his famous equation: F(M, r) = GM / r2, where G is the universal gravitational constant. This has worked quite well for a long time and, of course, continues to work in explaining most of the phenomenon we encounter in our everyday lives, such as calculating the trajectory of a probe to a planet within the solar system and calculating the trajectory for an artificial satellite around the earth.

The next big leap in our understanding of gravitation occurred with Einstein's General Theory of Relativity (which I will designate as GTR). In the GTR, the spatial coordinates and time were considered to be on equal footing. Instead of describing an event in a three dimensional space, (x, y, z) with time being considered a universal and absolute entity without any relation to the spatial coordinates, an event was described in a four-dimensional space-time coordinate system. With this, if we have two events, separated in space, at (x, y, z, t) and (x', y', z', t') where x ≠ x', y ≠ y', z ≠ z', then it was not necessary that t = t'. The GTR described the entire phenomenon equally well where Newton's theory for gravitation (hereby designated as NTG) was found to be applicable. The GTR also was consistent with Bohr's correspondence principle in that it was reducible to NTG for weak gravitational fields. However, the GTR was found to be more accurate in describing phenomenon where the gravitational fields were very strong and where the NTG gave only partially correct answers, such as the precession of the planet Mercury's orbit. NTG gave an answer that was 1/2 of the actual measurement, while GTR gave an answer that agreed with the measured value almost exactly. The GTR has also been successful in describing and predicting various other phenomenon and has so far stood the test of time and experimentation. Hence, if there is to be another theory for gravitation, it will have to, as per the correspondence principle, be reducible not only to NTG, but also to GTR.

One of the limitations that have been noted very soon after the development of GTR by Einstein was that the GTR was not applicable to the atomic and sub-atomic phenomenon. The atomic and sub-atomic phenomenon is described by the Theory of Quantum Physics (henceforth referred as TQP). In TQP probability not only plays a major role but also is considered to be a characteristic of the sub-atomic world. The TQP is also consistent with the correspondence principle, as it reduces to classical physics for large masses, as it must, since classical physics has stood the test of both time and experimentation since it's formulation. The GTR does not have probability in it's description of gravitation and therefore it is unknown what phenomenon can be explained and/or predicted if one introduces a probability coordinate into the space-time continuum (hereby designated as STC) of the GTR.

In this article, I am proposing to add probability to the STC with certain characteristics and from this make certain predictions and possibly explain some of the phenomenon that have been discovered but for which a definite explanation has so far been lacking.

(II) The probabilistic space-time continuum:

We will start with the STC of the GTR, where there is no matter and where every point is fully described by the set of coordinates (x0, x1, x2, x3), (where x0 = t, x1 = x, x2 = y, x3 = z). We will use the short hand {xi}, where i = 0,1,2,3. Now, to each point {xi} in this STC we add a probability coordinate, P0, and call it the baseline probability. Hence, each point in this empty STC is described by {xi, P0}. The probability coordinate, P0, is as much an intrinsic characteristic of the STC as any of the xi. This new coordinate space with probability as one of its coordinates we will call probabilistic space-time continuum (which we will designate by PSTC).

(III) The effect of matter on the PSTC:

According to the GTR, in the presence of matter each of the points {xi} is affected in a specific way. It is found that a mass M changes the geometry of the STC and this change in the geometry is given by a specific set of equations called the "Einstein's field equations" which connects the geometrical distortion of the STC to the matter causing the distortion. This distortion of the STC geometry by the mass M is taken to be the gravitational field of the mass M. GTR goes into details as to how objects in this distorted STC are supposed to behave and found that their behavior is similar to the behavior of a body as described by NTG due to a mass M when weak gravitational fields are considered. Just as matter affects {xi} it also has an effect on the probability coordinate, P0. In the presence of matter, the P0 "splits" into two components, PA and PR. PA is the probability that an object at the point {xi, PA, PR} will have an effect that will make it move towards the mass M, while PR is the probability that the same object at the same point, {xi, PA, PR}, will have the effect that will make it move away from the mass M. Hence, in the presence of matter a point in PSTC, {xi, P0} will change into {xi, PA, PR}. This changing of P0 into PA and PR we will call "splitting" of the baseline probability P0. The P0 has a baseline value of 1/2 (which I will derive later). Thus in empty PSTC each point is described by {xi, 1/2} and in the presence of matter the {xi, 1/2} "splits" into {xi, PA, PR}.

(IV) The characteristics ofPAandPR:

To describe the...