Science Forums 2

[Doctordick]

Originally Posted by Bombadil

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 I have been considering this to be any terms that can be added to the fundamental equation so that it is no longer valid.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.

I am not sure of exactly what you mean by “we are interested in”. We are interested in any transformation which can be defined and exactly how the defined transformation should be performed and what the meaning of the transformed solution is (that depends very much on exactly what kind of transformation one is talking about).

Originally Posted by Bombadil

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.

If you examine the deduction of my fundamental equation, you will discover that a very important step in that deduction is the proof that, no matter what patterns the valid elements may have, there always exists a set of hypothesized elements such that the rule will constrain the valid elements to exactly those required patterns. When one makes the approximations required to deduce Schrödinger's equation (doing all the required integration), that self same rule ends up being a function of “x”. Thus the meaning of the original proof is simply that, under the approximations made, there always exists some function of x which will require the behavior of any specific element to obey Schrödinger's equation where V(x) is that function. Is it possible that V(x) could be so complex that we can no longer use Newtonian mechanics? That depends on what you mean by “use Newtonian mechanics”. If you mean, “so complex that we can not solve the problem”; sure, there are a lot of Newtonian problems so complex that solution has eluded the scientific community for centuries. But can that be taken as evidence that Newtonian mechanics is false (false in the sense that even if the approximations used are valid, Newtonian mechanics is still false)? I think not.

Originally Posted by Bombadil

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.

It seems to me that you are confusing two very different issues here. Deriving the Schrödinger equation and showing that Newtonian mechanics is an approximation to the fundamental equation has nothing to do with any scale issues. Objects are defined to be collections of elements which remain in a coherent structure over a sufficiently long time to be thought of as individual entities. You should understand that one of the major approximations necessary to be made is that the energy of the entities must be approximately given by . That means that the kinetic energy (the energy of motion) must be small compared to : i.e., the elements going to make up that object cannot have net relativistic velocities with respect to the rest frame of the object. This is a fundamental constraint on Schrödinger's equation. That further means that V(x) cannot be so large to generate relativistic Newtonian velocities. The net result is that the collection of elements going to make up objects (such as my mirror assembly) cannot have relativistic velocities relative to one another. It follows that the directions of the individual elements making up the objects are all on essentially parallel paths, moving at v_?. Any deviation from those parallel paths must be small.

Originally Posted by Bombadil

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.

I think I will go over to Anssi's position on that. We are talking about an epistemological construct to explain a collection of elements which we know nothing about. We have a collection of elements associated with the index t_i. It is the moment we presume persistence (that "element i" in a collection at t_k is the same element as "element i" in a second collection at t_q) that we need to attach a new numerical label x_i in order to assure that these are still individual labels (in order to keep the fact that persistence is a presumption) which can be associated in any manner. This step starts us down that deduction of my fundamental equation.

Originally Posted by Bombadil

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.

I get the impression that you are trying to confuse yourself. There are three steps involved here and you need to understand each of those steps before proceeding to the next. First there is the deduction of my equation (which has to do with explaining an arbitrary past; that is why my first step is to define time). Second, is the proof that Schrödinger's equation is an approximation to that equation. And, third, is the demonstration that the picture requires the same relativistic transformations as does Maxwell's equation. Mixing and mushing with these three different issues is a procedure just crying to confuse you.

I really think that what you are trying to do is to achieve epiphany; trying to get your brain (that source of squirrel thought) to give you solution you don't have to think about.

Most of what you say seems to be so “off the wall” that I don't have the interest to go down those paths. I have discovered a very good reason why our view of the world obeys the laws of physics; I have not discovered a way of creating a world view. As I have said many times, actually solving my equation is beyond possibility (it is that proverbial many body problem). Logical thought is insufficient to the job; only “squirrel thought” (which is beyond logical examination and thus can not be proved to be without flaw) is actually capable of providing even a rough solution. But we can talk about rules that the explanation must obey! And that is the very essence of science.

Actually finding solutions is another problem entirely and I will eventually talk about such things (as I believe there is a simple solution to AI); however, I will not approach that issue until I have communicated my deductions in their entirety.

Have fun -- Dick