Science Forums 2

[Bombadil]

Originally Posted by Doctordick

Now, the original problem was to obtain a flaw-free explanation of “any dynamic collection of data” in the universe. That means that “both” observers are using exactly the same explanation! Whatever specific phenomena those observers use to establish their units of measure, that phenomena must be an excellent example of that “flaw-free explanation”: i.e., by excellent I mean that the nature of the phenomena behind these measures is presumed to be well understood. The interesting thing here is that, due to the “rules” being enforced by a Dirac delta function, that “flaw-free” solution must be scale invariant. That means that, if the two observers are dealing with “well understood bodies of information which are totally independent of the linear motion of their personal frame of reference”, there exists no such “well understood phenomena”: i.e., a unique linear measure can not be established (the problem is scale invariant and therefore the solution must be scale invariant).

Are you referring to an explanation that is capable of explaining any set of data because it seems that if two different observers are using different sets of data to arrive at an explanation while their expectations may be the same for some subsets of the date that overlaps between them the actual explanations may differ. In fact if they did not give the same expectations one of them would seem to have to be flawed or at least incomplete.

Or perhaps you are only referring to the phenomena that is presumed to be well understood in which case since it is a well understood phenomena we can presume that any observers that considers it to be a well understood phenomena must use the same explanation of it.

I assume that by, “by excellent I mean that the nature of the phenomena behind these measures is presumed to be well understood.” that you mean that the object must behave the same over any particular measurement. That is if something is measured at one time and then at a latter time then the measurements will agree or if a particular event is measured at one time the same event will have the same measurements at a latter time. And so by using such a property to define a measure a unit measure will always have the same properties (they will be considered to be the same length) in any frame.

Now since any flaw-free explanation must be scale invariant there must exist frames in which two rods defined to be a unit of measurement by any particular event that is the same property of the explanation was used to define the units of measure. The unit measures will differ when compared with each other. In fact this goes even further in that if the two observers are using any well understood property of their explanation to define their measures, any two events that are scale to each other will appear to be the same event. So there is no way to tell one frame from a frame that is scaled up or down from the other.

The problem is that if we try to compare the two different observers measurements we will come up with different measurements and so will come up with different events when measuring any particular event. That is the observers will not agree on what they see.

Originally Posted by Doctordick

The way out of that problem is the fact of that very scale invariance itself. We have already established that the only possibility which leaves the form of the fundamental equation identical in both frames (under the assumption that a solution does exist) is exactly the transformation deduced by Lorentz and Fitzgerald. That alone is actually insufficient as it does not eliminate the possibility that “no flaw-free solution exists”: i.e., it is possible that the only flaw-free solution demands one unique frame of reference and, if you are not using that frame, your solution is flawed. If true, that possibility would pretty well destroy the field of physics as an exact science.

So the solution is that if the scale of the flaw-free explanations differ by exactly the Lorentz transformation then both observers can measure the same events and while their measurements will not agree they will agree on what happened if the measurements are transformed into any particular reference frame.

This does not however prove that the explanation obeys the Lorenz transformation only that if it does then there is no frame that is proffered over any other frame and that measurements in one frame can be changed to any other frame.

Originally Posted by Doctordick

Thus I finish the essay by presuming that there does exist phenomena capable of establishing linear measure in those coordinate systems which is in accordance with the Lorentz-Fitzgerald solution. Note that I am not presuming that “all phenomena” are in accordance with that solution; however, when I am given that specific established linear measure, the approximate validity of Schrödinger's equation as a solution to my fundamental equation allows me to design objects in an arbitrary “rest frame”. This empowers me to design a “clock” and thus define time in exactly the same way in two non-accelerating frames moving with respect to one another. I then show explicitly that those clocks yield exactly the time relationship required. At this point, I have proved that, not only is the standard relativistic transformation the only possibility but that it is indeed totally consistent with my fundamental equation.

So this is what the reason for using an element that has zero movement in the direction is for. It gives a very convenient way to define time or distance assuming that one has already been defined, because such elements will have the same speed no matter what frame they are in after speed has been defined. Its speed is in fact scale invariant, that is, no matter what the scale of the equation is after speed has been defined it’s speed will be the same in any frame. And so it can be used in any reference frame and the same result will be arrived at. However the speed being invariant is not necessary, all that is necessary is that objects in different frames behave in the same way independent of the scale.

Now since Schrödinger’s equation is a solution to the fundamental equation this allows you to define a particular object in a rest frame to be a unit of distance. The question then becomes the problem of moving such an object from one frame into any other frame. Now when you say,

Originally Posted by Doctordick

Now, I have already shown that a given solution in the rest frame is easily transformed to a solution where the frame of reference is no longer at rest. Such a transformation is simply obtained via multiplication of by the simple function

.

This change in will simply add P/n to the momentum in the x direction of every elemental entity in the universe (the universe consisting of the elemental entities which make up that independent object). In other words, the transformation simply adds P to the momentum of the object and thus the object is no longer at rest in the rest frame used to solve for . Thus it is that we can always transform a solution in the rest frame of one object to a solution in the rest frame of the other (note that the transformation also requires a change in energy which is just as easily obtained).

This shows that there exists a way on moving from one frame to any other frame that is adding momentum to the fundamental equation. Now when we compare this to the Schrödinger equation, adding momentum in this way results in adding velocity to a object to change it to a new reference frame.

Originally Posted by Doctordick

The only aspect of that fact that I am using is that the behavior of “objects” (collections of fundamental elements which can be seen as physical structures) will essentially obey common sense behavior of standard objects. In particular, the structure I call a mirror assembly can be seen as a classical object in a four dimensional Euclidean space which will obey simple conservation of momentum in that geometry.

So all that is being used is that energy and momentum will behave like they do in Newtonian physics and that it is possible to form objects?

Originally Posted by Doctordick

This would be true except for one subtle fact. The tau dimension is totally fictional and, in the final analysis, the actual distribution of our points in the tau direction can not have any effect on our final “flaw-free” solution. Thus, in a sense, it is impossible for any actual valid data to establish a unique frame of reference in that direction. In a sense, although velocity in the tau direction is defined, real motion in the tau direction is essentially undefinable. The fact that one can not define a rest frame with regard to motion in the tau direction, seems to me to imply that this data need not be so constrained.

So in effect since movement along the direction has no effect in the finale analysis of the problem and any difference from zero of the terms would just be integrated out and so would make no difference in the final analysis of the problem. So there is no reason to assume that there is any reason that the mass operators will sum to zero as it will have no effect in the final analysis of the problem.

Originally Posted by Doctordick

I think you are overlooking a much more fundamental issue here. Everyone is defining “simultaneity” via the assumption that the speed of light is the same in both directions and that is the basis of the problem here. All physicists in the universe could just do all their calculation in the rest frame of the background radiation. Then they would all agree and there would be no problems with identifying “simultaneity”.

But isn’t it also true that if we where to try and define simultaneity in any other way then the results would still have to differ from one frame to another. Unless of course, we define simultaneity to only exist in a particular frame and use it as the rest frame and do all of our calculations in that frame which is not a practical solution to the problem.