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.
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 x
i being plotted. That continuation which presumes existence between “presents” yields an epistemological construct which can model absolutely any explanation which can be conceived.
The epistemological construct is no more than a vast collection of point entities moving around in a Euclidean space. That epistemological construct is clearly flaw-free because it is clearly consistent with the fundamental equation I deduced: i.e., point entities traveling in straight lines except for point interactions (scattering) caused by the Dirac delta function interactions. But it is also a solution of utterly no use as I still can not solve the many body problem so represented. (Though I have shown that absolutely any "physical" representation of the universe can be represented by such a thing. See
my geometric proof.)
But what I have done is to show that Schrödinger's Equation is an approximation to my equation given some rather simple and straight forward assumptions (assumptions totally consistent with the assumptions used in all applications of Schrödinger's Equation). What this leads me to is my definitions of mass, momentum, energy and (even more significant when it comes to constructing a mental picture consistent with my equation) “objects”. This gives me the power to transform this “flaw-free” epistemological construct into my personal world view (that solution to the problem provided to me by
“squirrel thought” the correctness of which I can not check).
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).
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.
Are any of those explanations flaw-free? Well of course not; neither of us is all knowing and our abilities to actually analyze our own world views are so far below the requirements of such a feat that it is ridiculous to even suggest attempting such a feat. But, what I do know (as I have proved it) is that any “flaw-free” explanation must be a solution to my fundamental equation. I can use this to examine certain aspects of the problem of understanding.
The fact that any solution of Schrödinger's equation is an approximate solution to my equation implies that I have some facts about my world view (and yours) which can not be countered. First, that the universe can always be seen as a collection of energy quantized massless entities interacting via point scattering (the Dirac delta function); essentially a gas of such point “noumena” (to accord Anssi a little credit). And, second, that if we constrain our examinations to entities which are momentum quantized in the tau direction (collections of noumena which are mass quantized) we are presented with the possibility that collections of these “noumena” can remain in close proximity for extended times (collections I have dubbed “objects”). Furthermore, these objects will approximately obey Newton's mechanics.
Well, where does that get us? You and I have already reached (even before we had our first conversation) the fact that one huge portion of our world-view is constructed of objects which obey Newton's equations and, through advanced concepts of quantum mechanics (essentially Schrödinger's equation plus the many extensions which have been proposed) chemical theory, and thus the field of biology. I am not saying that any of these fields are flawless; merely that they are all connected by a logical thread in agreement with our experiences with the universe we find ourselves in.
Thus it behooves us to speak of such things in terms of my fundamental equation. This thread was dedicated to the simple issue that my fundamental equation is valid “only in the rest frame of the universe”. If it is possible for two observers to define personal rest frames which are moving with respect to one another (something held, in our scientific community, as easily arranged) a very specific constraint exists on the transformations of measurements between those two frames. That constraint is exactly the constraint commonly held as “special relativity”. What you were supposed to do with this thread was to follow the logic of the deduction of that constraint; not go off in wild directions as to the interpretations which can be attached to that fact.
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Originally Posted by Bombadil
Now in the case in which the measurements that the observers make do not follow the Lorenz transformation, the only possibility is that one or both of the observers are using a flawed explanation.
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If that transformation is not part of their explanation then their explanation is certainly flawed.
Quote:
Originally Posted by Bombadil
Now the actual scaling of the fundamental equation is just a consequence of the transformation used to change the explanation in one frame to a new frame while still keeping the fundamental equation valid.
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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.
Quote:
Originally Posted by Bombadil
Basically I’m asking how do we know that the measurements in one frame can be transformed to any other frame even if both explanations are flaw-free.
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The method of performing the transformation is part of the explanation! If it does not conform to the relativistic transformation, the explanation can be simply declared flawed.
Quote:
Originally Posted by Bombadil
This still seems to leave open the question can an object in one frame be moved to any other frame. That is are there frames that an object in one frame can’t be moved into from some other frame.
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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?
Quote:
Originally Posted by Bombadil
... or it may be as you seem to be suggesting that there is in fact a unique frame that is the only frame in which the fundamental equation is valid in.
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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”).
What I am getting at here is that my proof that Schrödinger's equation is an approximation to my fundamental equation allows me to talk about phenomena actually described by Newtonian mechanics as possible solutions to my fundamental equation (at least roughly approximate solutions). It is this fact which allows me to do thought experiments with flaw-free explanations. It should be clear to you that my fundamental equation is not itself solvable.
Have fun – Dick
