As an aside, it is quite clear that the proper adjustment to our geometry which will yield the standard concept of gravity as a pseudo force is a change in the presumed measure of that geometry: i.e., instead of seeing the speed of light as slower in a gravitational field we could just as well see the speed as unchanged and the distances as increased. After all, once time is defined, distances are reckoned via the speed of light. Though that satisfies the original goal expressed above, the idea of refraction (the speed of light being slowed in a gravitational field) is a much simpler expression of the solution. It is certainly most convenient method of finding the proper geodesics. In fact, there is a very simple view of the situation which will yield exactly that result.
Won’t seeing light as slowed in a gravitational field be equivalent to seeing the distance measured along the
axis as being scaled to make up for all objects still having a constant velocity in your x,y,z,
geometry, and since light still cant travel along the
axis, since it is still massless, in effect we are scaling the
axis and saying that objects are moving a shorter distance in the x,y,z,
space instead of scaling the x,y,z axis’s and saying that objects are traveling a longer distance as viewed from outside of the gravitational field. Of course since the
axis can’t be directly measured and actual location on it makes no difference such an effect could not be noticed.
Any physical object (any structure stable enough to be thought of as an object) must have internal forces maintaining that structure. Any interaction with another distant object must be via the virtual particle exchange I just commented about. Thus it is that one would expect the fundamental element of that physical object interacting via that delta function would have its momentum altered, not the whole object; however, that alteration would create a discrepancy in the structure of the object under discussion. Since that object must have internal forces maintaining its structure, it is to be expected that those internal interactions (which are also mediated by delta function exchange forces) will bring the trajectory that interacting fundamental element essentially back to its original path (at least on average).
This is the effect that you are referring to as refraction, that is this sort of moving back and forth of a object is causing it to move slower in the
direction even though the object really is not going any where as a result the object will travel slower in the
direction even though the object is not traveling a long distance in the x,y,z space and can effectively remain in the same spot?
If the distant object and the object under observation are not moving with respect to one another (they are moving parallel to one another in the tau direction), the net effect of that refraction is to curve the paths of the two objects towards one another: i.e., there will be an apparent attraction between them. It is also evident that, since the mass of the source object (the source of these bosons external to the object of interest) is proportional to the total momentum of that object, one should expect the apparent density (as seen from the object of interest) should be proportional to its mass: i.e., one should expect the exchange forces to be proportional to mass.
I don’t understand why this is unless it’s that since one of the objects is moving slower in the
direction the object must move in the x,y,z direction to make up for it. But, didn’t you just say that the object would counter this movement with internal forces, at least on average, and so would not move in the x,y,z directions at least on average. Or is the idea that since this is only on average an object is still capable of moving along the shortest path in the x,y,z,
space which would bring the objects closer together due to the maximum velocity as seen from outside of the gravity well being slower closer to the massive object. In which case is this what you are suggesting results in gravity? If this is the case I’m not entirely sure as to why an object would try to follow the shortest path except perhaps that it would move the furthest along it on average.
Also, how do we know that the source of these bosons is proportional to the total momentum of the object?
Clearly the interaction just discussed arises from differential effects in the basic interactions thus it will amount to a force considerably less than the underlying force standing behind that differential effect. Thus it is that the two forces I have already discussed (the forces due to massless boson exchange: shown to yield electromagnetic effects and the forces due to massive boson exchange: shown to yield fundamental nuclear forces) will end up being split into four forces. Differential effects will yield a correction to both basic forces which correspond quite well with the forces observed in nature. The differential effect on massless boson exchange yields what appears to be a very weak gravitational force (weak when compared to the underlying electromagnetic effects) and the differential effect on massive boson exchange yields what appears to be a very weak nuclear force (weak compared to the underlying nuclear force). What is interesting is that the “weak nuclear force” can be shown to violate parity symmetry whereas the “weak electrical force” (gravity) does not. This is a direct consequence of the fact that the nuclear exchange bosons are massive.
Just why is it that this is resulting from the differential effects? Does it have something to do with this effect resulting from how far an object moves rather then an interaction due to the delta function, and in effect, this is a result of conserving the total distance that the object moves rather then an interaction due to the delta function?
Also, are you saying that gravity was left out in the derivation of the Dirac and Maxwell equations and that gravity is a correction factor and so in effect there is no so called graviton rather there is a correction to the magnetic field which results in gravity? If so I don’t understand how we know that these forces where left out of the Dirac and Maxwell equations other then that people have looked for such a thing and not found it, or is this some kind of average effect that can only be noticed if a large number of particles that form an object is considered.