After looking at this some I suspect that I may be considering a couple of things incorrectly. Firstly what exactly the transformation of the fundamental equation that moves it to a new reference frame is. I have been considering this to be any terms that can be added to the fundamental equation so that it is no longer valid. This clearly is not what the transformations that we are interested in are, but rather it seems that what transformations it is that we are interested in is the addition of mass or momentum operators to the fundamental equation.
There is one other issue that I have been having that is, how do we know that the Schrödinger equation tells us anything about the fundamental equation. That is, how do we know that the V(x) term wouldn’t be so complex or in a particular form so that we can no longer use Newtonian mechanics as an approximation to the fundamental equation.
Actually I think that this issue has already been brought up although I didn’t fully realize it or how you where solving it. Simply put it is that since the equation is scale invariant we can look at it on any scale and due to all interactions taking place due to a Dirac delta function, which has only a single point that it is not zero on, this allows us to look at the Schrödinger equation on a scale in which the V(x) function vanishes. Clearly on this scale the approximations, except perhaps the last approximation used to derive the Schrödinger equation, can be justified. From what I can tell the last approximation can be justified if we consider the rest frame of the object of interest.
In this way we can derive the Schrödinger equation and in so doing show that Newtonian mechanics is an approximation to the fundamental equation when looked at on some scale.
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Originally Posted by Doctordick
I am sorry Bombadil, but I very much get the impression that some very important aspects of my presentation are just missing their mark. It seems to me that you are just attacking the problem from the wrong direction. I suspect there are two issues in play here. First, I suspect that your understanding of mathematics does not include much experience solving difficult differential equations. The single most important issue there is that no general solution to a many body problem has ever been found. The validity of my fundamental equation can not be judged through its solutions because those solutions simply are not available to us. Its validity rests entirely on my deduction and nothing else.
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This would be correct it is also a topic that I am trying to start going into.
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Originally Posted by Doctordick
If you followed my deduction of the fundamental equation, you would understand that it is no more than a proof that any explanation of anything can be interpreted in a way which obeys that equation. That is, any ontological basis may be translated into a set of points in that Euclidean space I have set up. As Anssi has realized, what we are really talking about is a general epistemological construct consistent with that hypothetical ontological basis. Persistence is the central issue of any epistemological construct. Those points which make up a given present (defined to be new knowledge added to the past, “what we knew or thought we knew” ) are simply presumed to be a new distribution of the previous present. Each time slice is presumed to consist of exactly the same elements which made up the previous slice (indicated by the use of the same index i ); however, the presumed persistence says that they existed between those time slices. This is the central issue behind the dual identification: identification via the index “i” with the further numerical label xi being plotted. That continuation which presumes existence between “presents” yields an epistemological construct which can model absolutely any explanation which can be conceived.
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Then the question is vary much given an arbitrary set of elements (the ontological basis), arbitrary in that any particular element is identical so that any differences between elements is part of the explanation and not a property of the elements themselves. How is it that someone can explain such a set of points, that is, how can someone obtain expectations about how the elements will change given only the points.
What we are in fact doing is mapping such a set of points onto a Euclidean space and using a evolutionary parameter t to ask how might we explain how the system changes with t. But this change is itself part of the explanation and a consequence of new information becoming available and in order for us to conclude what the change is we must correspond elements at one value of the parameter t with elements at another value of t (that is they are considered the same element) and in so doing we conclude that the same elements existed at every point corresponding to a value of t.
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Originally Posted by Doctordick
That any conceivable explanation can be so interpreted is the central issue; not what that explanation is to the person who dreamt it up. When you attempt to give me your explanation of anything, I make an attempt to understand what you are telling me. If that explanation is flaw-free (and I would certainly presume it is or I wouldn't bother trying to understand it as trying to understand a flawed explanation is clearly a waste of time) then your communication of your explanation can be interpreted in such a way that it obeys my equation. That is the first step! What you must remember is that your world view includes the meanings of the words you use and the mechanism you use to convey those words (sounds or electronic signals or even your own senses).
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So whether or not a flaw free explanation satisfies the fundamental equation is not the issue but rather the issue is that there exists a isomorphism between the explanation and a solution to the fundamental equation. That is, there is a mapping that preserves the result satisfying the fundamental equation.
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Originally Posted by Doctordick
Your world view is the whole magillah. I likewise possess a world view and my interpretations of the communications you put forth are just another piece of my world view. There exists no evidence at all that there is any “real” correlation between your explanation (your method of keeping track of your expectations) and my explanation of what I think I know. What I know of “other people” is no more than the explanation I have managed to construct in my own mind (my mind itself being such a construction). We are each perceiving the others view through our own solution to the problem; our own personal explanation of our experiences.
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The real question is how such a world view is constructed as there is nothing but arbitrary information to base it on even the way that we map the information before forming a world view must be part of the world view.
So what we must do is first realize that it is arbitrary information that we are dealing with then find a arbitrary method of mapping the information in such a way that we can analyze are world view and realize that it can be interpreted in such a way that it satisfies the fundamental equation?
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Originally Posted by Doctordick
Again, you seem to have the horse on the wrong side of the cart. Any flaw-free explanation of anything can be interpreted as a solution to that fundamental equation (which is only valid in the rest frame of the universe). It isn't a question of “keeping the fundamental equation valid”, it is a question of so interpreting their explanations.
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That is in order to use their explanations we must be able to interpret the explanation in such a way that it obeys the constraints put down by the fundamental equation. What we must consider is that that explanation is in its rest frame because it is simply not a valid explanation anywhere else and we are not in its rest frame.
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Originally Posted by Doctordick
Tell me, does your world view include the possibility of two inertial frames moving with respect to one another? And does your world view include the possibility that an object originally in one frame can be moved to the other: i.e., can acceleration exist?
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Certainly acceleration can exist I suspect that more of the problem here is why acceleration moves from one frame to a another how I am understanding this is that after an object has accelerated to a new reference frame in order for use to still use an explanation of the object in its rest frame we must consider that the momentum operators are no longer the same for the object in both explanations, that is our rest frame and its rest frame are no longer the same.
Now my question is what kind of number is the momentum operator that is added as it appears to be just a imaginary number that is needed for the object that is no longer in our rest frame. But wouldn’t an arbitrary complex number also be considered a new reference frame? Would acceleration still move it from one reference frame to the other or will such a reference frame even exist?
It may be that I am just trying to consider modifications that don’t or cannot exist in the fundamental equation.
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Originally Posted by Doctordick
The fundamental equation is valid only in the rest frame of the universe. That does not require a unique frame for two reasons; first I defined “time” to be what we know and “the present” to be “a change in what we know”; it follows that “what we know” is continually changing and thus it is entirely possible that the “rest frame of the universe” may change. And secondly, whenever an attempt to explain any specific phenomena is undertaken, great quantities of information concerning the universe are commonly ignored (we work out the problem in a mental environment which clearly presumes a “universe” consisting of considerably less than what is defined to be “The Universe”).
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In a sense the question here is, are we explanting the universe or is the universe the explanation. In the former we have no defense for saying if we have a valid explanation. Furthermore, we have no way to know if there is any kind of mapping between our explanation and the universe that we are explaining as we will have elements in our explanation to make it a valid explanation that need not be part of the universe and there is no way to know what the rest frame is as we don‘t know everything about the universe. In the latter case clearly the explanation has a rest frame even if it will move as new information becomes available to us either from realizing that the explanation is not valid or from new information that the explanation is based on becoming available to us. Furthermore any element that is part of a flaw free explanation that we are using is clearly part of the universe in that the universe would be inconsistent without it, which is not possible.
