Science Forums 2

[Doctordick]

Hi Bombadil,

After reading your post, I get the distinct feeling that you do not understand what I am doing here. I am not presuming anything about the transformations required. I am merely asserting that my fundamental equation must be the same in both reference frames. That is, that when the two observers (in the two different frames) examine the same phenomena, they obtain the same expectations. Initially, the phenomena I am examining is probability of an event at a specific point at a specific time. They are essentially solving the same problem. It follows that, no matter how they define their measure of x and t, the same actual events must be described (the actual events which take place have utterly nothing to do with the reference frame used to describe them).

That examination produces the standard relativistic transformations without actually defining how distance and time are measured and thus, without defining any value for .

Once I describe the phenomena (as displayed in the drawings I show) distance can be defined anyway one chooses: i.e., I merely let the initial observer define the distances used in his four dimensional coordinate system. I can use the transformation equations to define the so called “moving observer's” distance measures from the initial observer's units. Time is a little different; I need to define a mechanism to measure time consistent with picture I have presented (a four dimensional Euclidean space with “massless” entities obeying a wave equation) where the tau component is to be integrated out as it is a fictional element. I have to design a "clock".

Originally Posted by Bombadil

So then t is nothing more then a way of telling if two or more elements can interact and is not an axis that is moved along. That is elements can interact if they try to occupy the same location at the same value of t.

Essentially yes. Before you even begin to think about the relativistic transformations being discussed in this thread, you need to understand the fact that Schrödinger's equation is a valid approximation for the behavior of individual elements of any explanation. As I have said to Anssi, my deduction has nothing to do with reality as it is a tautological construct. It is only after the proof that Schrödinger's equation is a valid approximation for any possible explanation of anything that we can begin to relate my fundamental equation to the common concept of reality held by modern physicists (that is, the concepts of energy, momentum and mass).

Originally Posted by Bombadil

Also didn’t you at the same time require mass to sum to zero in order for the fundamental equation to be valid which would also mean that the total energy must be zero.

In my representation, mass is defined to be momentum in the tau direction. This fact is what leads to the kinetic energy representation so long as which brings up the need to define mass.

Originally Posted by Doctordick

Notice that, if the term is moved to the right side of the equal sign, we may factor that side and obtain,

At this point, I will invoke a third approximation. I will concern myself only with cases where to a high degree of accuracy. In this case, the first term on the right may be replaced by -2iq and, after devision by 2q, we have ...

What is important here (and you should take careful note of) is the fact that if q is negative, the appropriate factor to set approximately valid is . In that case, the second term on the right may be replaced by +2iq = -2i(-q) (but -q is a positive number if q is negative) and thus it is that after division by 2|q| we get exactly the same thing we got in the original case.

What I am getting at here is that the energy is not a vector quantity but is rather related to the magnitude of the momentum. The energy of an entity with momentum in the opposite direction is still positive. Thus under my definition of mass is always a positive quantity even when the momentum in the tau direction is opposite. So, no, the mass does not sum to zero even though the momentum in the tau direction of all the elements in the universe must sum to zero.

Originally Posted by Bombadil

In both of these cases is a positive value the only possible value resulting in all elements having a zero mass and momentum? The energy must of course then be zero in order for equality to hold.

Wrong!

Originally Posted by Bombadil

But wouldn’t even an element that is not interacting with other elements have to have interacted with other elements in order to be known which implies that at some point it had a defined speed and that if an element interacts at some future time that its speed can be defined during the time that it wasn’t interacting or does it only have a defined speed while it is interacting with other elements?

You are missing the entire import of the presentation. We have not yet defined a measure of either distance or time. Thus it is that speed is still undefined. However, the fundamental equation is essentially analogous to a “wave equation” when interactions are ignored. It is the fundamental equation itself which sets that fixed undefined “speed” . K is an arbitrary constant, however, once it is set, the magnitude of that undefined speed is set for all elemental entities in the universe (so long as they are not interacting). The interactions take place at a point and “a point” has a very very small existence (actually zero by definition) therefore, no matter how often interactions take place there is always a smaller scale such that we can talk about the speed when they are not interacting. Remember, our explanations are explaining a finite amount of information thus the number of required valid interactions can not be infinite.

When I say the speed is undefined, I mean that the definition of speed requires we know how to measure distance and how to measure time. No matter how distance is defined, the distance an entity moves in some fixed time “t” is equal to the speed times that time so it is quite reasonable to work with specified distances rather than the actual speed. Since I am working with a non-dispersive wave equation in four dimensions, I know that distances traveled in fixed times are exactly the same for all entities when displayed in that four dimensional space.

At any rate, since this equation specifies our expectations in a four dimensional universe where all probabilities dependence on tau must vanish, the speed of any element must be whatever that set speed happens to be but the “apparent” speed (in the three dimensional picture after the tau coordinate is integrated out) can have that value only when the element is moving orthogonal to tau (or it has no momentum in the tau direction: i.e., it is massless). An element moving in the tau direction will appear to be standing still and the “apparent” velocity of any massive entity is bounded by zero and that set speed .

Originally Posted by Bombadil

So the momentum associated with an element traveling in the positive direction is the same as that which is associated with an element traveling in the negative direction and weather the derivative is positive or negative has no effect on the value of the momentum?

Momentum is a vector quantity and direction is a significant issue. You are apparently confusing “magnitude” with the vector nature of momentum.

Originally Posted by Bombadil

Here, are you still using the definition for the value of sine in the above equation, I think that you are?

The angle theta is the angle between the tau axis and the path of the entity being discussed. The velocity along that path is undefined but nonetheless fixed (by the form of the fundamental equation; which is essentially a wave equation). After integrating the tau dependence out, the apparent distance something moves (d = vt) is related to the actual distance it moves (which is in the four dimensional space) by exactly that same factor . This is no more than a simple way of expressing relationships in the diagrams I have drawn.

Originally Posted by Bombadil

Here I’m not sure I understand your use of instead of as this seems to be how distance is scaled for a moving observer.

I presume you meant to write instead of what you actually wrote. I am analyzing everything from the representation in my drawings. You, on the other hand, seem to ignore the drawings and apparently are trying to apply your understanding of the appropriate transformations. The whole issue here is that we are examining explicit events defined in my four dimensional space and obeying my fundamental equation in order to deduce the appropriate transformations. If you do not understand the drawings, you cannot deduce the transformations. And we cannot use something we have not deduced to be valid. What I am using is the fact that, if the moving observer's distance measures are going to obey the transformations deduced in part one of this presentation then I can use the inverse of that transformation to deduce the actual locations of points the moving observer uses to establish his distance measures. Remember, both observers are examining exactly the same phenomena.

Originally Posted by Bombadil

Also, do you mean that the speed that the observer measures for the speed that the clock is receding from him is the same as what his speed moving away from the clock is measured to be in the rest frame?

Yes that is exactly what I am saying.

All I get from reading your response is that you do not understand my presentation. Try starting from the beginning and thinking about it one line at a time. You need to have every step clear in your head before going on. This is a logical deduction, not a zen thing that will eventually pop up in your mind. You need to understand the documentation.

Have fun -- Dick