Science Forums 2

[Bombadil]

Originally Posted by Doctordick

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).

So then in all of the analysis’s of the problems that you put forward there is no need for the actual transformations. All that is necessary is that the problem is analyzed in such a way that both observers, that is the rest and the moving observer, obtain the same result when observing a clock that they are at rest with.

Originally Posted by Doctordick

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).

I suspect that part of the problem here is that while I can understand how the Schrödinger equation is arrived at I have very little idea as to what it suggests other then that it can be used to derive Newtonian mechanics. Before I take an in-depth look at the topic, which I plan to do when I have a sufficient understanding of the necessary math, do you know of any sites that might give me an idea of the kind of things that the Schrödinger equation implies? I am thinking of taking a closer look at Wikipedia as it looks like it explains it somewhat but I’m not sure if this is the best place to begin trying to get a better understanding of what the Schrödinger equation implies.

Originally Posted by Doctordick

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.

Even with the sum of the mass being greater then zero will the sum of the mass operators still sum to zero? (I am understanding these terms to be the differentials to on the left side of the fundamental equation) in order for the fundamental equation to remain valid while only the term



which represents the probability of what the actual mass is that all elements under consideration have where the integral is over all elements being considered?

In a similar way the energy operator must be zero however this does not imply that the energy defined by



must also be zero. Again the integral is taken over all elements under consideration.

Originally Posted by Doctordick

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.

So then the speed of an element that has zero movement along the axis will have a constant speed (this is entirely due to arbitrary constants that are part of the fundamental equation) What is important is that the speed is only defined if both time and distance are defined and that no mater what reference frame we are in we must observe the same events in other frames. That results in simultaneity as you have demonstrated it to be preserved.

For instance supposing that we use a unit rod as a way to measure distance, then in order to actually measure an object we must make measurements on both ends of the rod at what we consider to be simultaneous measurements, which requires that we define what we consider to be simultaneity something which must differ from one frame to anther due to the fact that your clock must behave the same way in any reference frames but that the observation of a clock in a different reference frame will differ. That is, events that appear simultaneous in one frame need not appear simultaneous in any other frames.

Also couldn’t we define velocity by defining the oscillator to have a unit velocity then by defining either distance or time define the remaining one by properly considering the requirements for events to happen simultaneously? While it seems that we could do this in order for us to define the remaining measurement we would have to use what we consider to be a unit length or a unit of time so that we would have to come to the same conclusions. Although it seems that it would perhaps be impractical to use an oscillator to define velocity for most proposes.