Science Forums 2

[Bombadil]

Originally Posted by Doctordick

The actual problem here is that the fundamental equation is no longer valid (we are simply no longer in the rest frame of the original object and our altered is thus no longer a solution to the correct equation). What we have is the fact that our mental model of reality must include the fundamental symmetry that all solutions, in the absence of outside influence, must transform to valid solutions to the correct equation in the center of mass system of any collection of data. This symmetry appears to imposes a major constraint on the character of the possible solutions . In reality,it does not as the scale invariant nature of our mental model provides a straight forward resolution of the difficulty.

So would the new after being changed to a new frame still describe the behavior of the element if we had the correct solution for or would the new function no longer describing the correct behavior of the elements. It also seems to me that the new function would no longer expand in a spherical manner but would expand in an elliptical manner.

Originally Posted by Doctordick

It turns out that we are quite lucky in that the consequences of the above symmetry have already been completely worked out long ago by others. Notice that, if one ignores the Dirac delta function (as it has no spacial extension) my fundamental equation is a simple linear wave equation in four dimensions with wave solutions of fixed velocity. The constraint spoken of above is exactly the same constraint placed on the conventional Euclidean mental model of the universe by the fixed speed of light in Maxwell's equations. As we all know, if we constrain ourselves to linear scale changes, it turns out that there exists one very simple (and unique) relativistic transformation which maintains a given fixed velocity for all reference frames moving with constant velocity with respect to one another.

So the fundamental equation without the Dirac delta function is just the equation of an expanding sphere, (is it actually an expanding wave and only the distance that it has expanded is of interest?) and the speed at which the wave is expanding is defined by k. So what happens if we don’t ignore the effect of the Dirac delta function? Will it still be an expanding wave function where the only change is that it behaves in such a way that the value of it at any other element is always zero?

Originally Posted by Doctordick

Thus the wave function is non zero only on the surface of a sphere expanding at a specific velocity (which I am calling v_? for the time being). What is important here is that this must be true in both frames (if it is not true in the primed frame, the non-zero portion of will not be on the surface of an expanding sphere). That is, both frames must yield exactly the same probability distribution; it is the two frames of reference which are different, not the probability of finding that elemental entity.

So we are considering an expanding sphere for each set of elements that make up an object, and the probability for any object in the rest frame of some other object and the probability when all elements are considered or any other set of elements must be equivalent if the objects can truly be considered separately. But, what if they can‘t be considered separately? Will the Lorenz transformation still need to be applied, or will we no longer be able to apply the Lorenz transformation to the objects?

Originally Posted by Doctordick

To begin with, during the design stage, I want my standard clock to be “at rest” in my coordinate system. In the deduction of Schrödinger's equation, I ended up integrating over all tau dependence and defined momentum in the tau direction to be mass. Clearly the fact that my clock is to remain a coherent object requires that, if it is to be “at rest” the major components must have mass: i.e., the important component of the momentum of the majority of the underlying elemental entities must be in the tau direction.

So is this due to the only possible function that describes the objects that make up your clock must have a constant derivative to as a result the object will have a positive mass?

I suspect that you may have overwhelmed some people with the length of this post (although I really don’t see any problem with it), you have answered quite a few questions and I have managed to read the whole thing. But I think that it is perhaps best if I don’t try and ask all of my questions at once, so when you answer this I will continue. Also I should have a P.M for you in a couple of days.