An explanation of what I am talking about.

[Doctordick]

The following comment in the “Deriving Schrödinger's Equation from my Fundamental Equation” leads me to post this alternate thread.

Originally Posted by AnssiH

Perhaps it is helpful to point out here also that those symmetry constraints "on all flaw free explanations" are springing from the fact that the explicit meaning of the "data to be explained", is fundamentally unknown.

It appears to me that a little clarification on what I am doing would be worthwhile.

Perhaps it would be useful for me to point out exactly what I am talking about in my overall presentation: i.e., what we are working with and where we are going. When I was a student (some half a century ago) I was made aware of the power of symmetry arguments. As one professor once told me, “symmetry arguments are the most powerful arguments which can be made as they are the only arguments which can produce iron clad relationships out of total ignorance.”
My original purpose was to create a useful mental model of any explanation of any information so that I could comprehend exactly what could be deduced from the simple notion of internal consistency and symmetry principals. This thought resulted in what I call, “A Universal Analytical Model of Explanation Itself”, a paper within which I the development of what I call my “fundamental equation”. It is very important that the reader realize that there is utterly no content in that equation. It is no more than a exercise displaying the tautological consequences of the definitions brought forth in that paper.

1. is defined to be a numerical label for a specific undefined ontological element used in that explanation.
2. Time (as an index) is defined via the following: the past is the information being explained; the present (indexed by ) is a change in that information. refers to a specific set of ontological elements .
3. A Euclidean geometric space is defined as a mechanism to display the belonging to of interest.
4. is defined to be a numerical label attached to in order to assure identification of multiple occurences of a specific . The addition of adds a third orthogonal axis to the Euclidean display.
5. The explanation is defined to be a method of obtaining our expectations for a given collection of indices
specified by a specific . The probability is a number and the arguments are numbers, thus the result can be expressed as a mathematical relationship: . If we have an explanation, we know P and likewise, a (a method of obtaining that probability) must exist.

6., 7. and 8. These five definitions plus symmetry principals together with the undefined nature of those ontological elements are sufficient to deduce the validity of my fundamental equation. Three more definitions are then introduced as specific components of that fundamental equation: those would be energy, momentum and mass.

Thus I end up with eight defined concepts together with a tautological relationship between those concepts; mere self consistent consequences of those definitions. By showing that Schrödinger's equation is an approximation to my equation, I show that my construct (which is constrained in no way) requires all the ontological elements standing behind any explanation to obey classical mechanics in the classical limit. It follows that classical mechanics itself must be a tautology: i.e., classical mechanics must be true by definition.

I have shown that any proposed algorithm capable of answering meaningful questions about reality within my entirely general model must obey a rather simple equation. I have further shown that my model corresponds to the common picture of reality in sufficient detail to map ordinary anthropomorphic experience directly into my model: i.e., classical mechanics.

In effect, I have shown that all conceivable universes may be seen as a three dimensional space occupied by objects which are required by definition to obey classical mechanics in the classical limit. This can be taken in two different ways: one can see the result as demonstrating that our classical view of the universe (a three dimensional space occupied by objects which obey classical mechanics) is entirely general and capable of representing any conceivable universe or one can view my results as demonstrating the fact that classical mechanics is true by definition and that no classical experiment tells us anything about the universe except perhaps that our definitions are self consistent.

With regard to the second viewpoint, if one takes the position that the job of a research scientist is to search out the rules which separate the "true" universe from all possible universes, then no classical experiment can provide any guidance on the subject whatsoever. Classical mechanics is itself a tautology.

That is the central result of my presentation at this point. If you care to follow me further down this path, I will show you that the same is true of most all of modern physics.

Have fun -- Dick

[Bombadil]

Originally Posted by Doctordick

Thus I end up with eight defined concepts together with a tautological relationship between those concepts; mere self consistent consequences of those definitions. By showing that Schrödinger's equation is an approximation to my equation, I show that my construct (which is constrained in no way) requires all the ontological elements standing behind any explanation to obey classical mechanics in the classical limit. It follows that classical mechanics itself must be a tautology: i.e., classical mechanics must be true by definition.

I still don’t know if it is a good approximation or not, but I suspect that it is a useful approximation in that it tells us something about how all explanations behave, that is they behave approximately like classical mechanics in what you are referring to as the classical limit. But I suspect that a satisfactory answer for me will only come with a better understanding of the fundamental equation and a better understanding of the Schrödinger equation. The latter of which is well outside of our interest here, especially since I am not yet sure what I would consider a good approximation.

Originally Posted by Doctordick

I have shown that any proposed algorithm capable of answering meaningful questions about reality within my entirely general model must obey a rather simple equation. I have further shown that my model corresponds to the common picture of reality in sufficient detail to map ordinary anthropomorphic experience directly into my model: i.e., classical mechanics.

I am wondering at this point if you have also shown that anything that can be mapped into your model is equivalent to a classical mechanics model or are there other models that would be based on your model, that is based on the fundamental equation? I am not asking what such models would be used for or even what might be different about them or how they would be derived, but rather just do they exist?

I suspect that this question has a rather straight forward answer and I would be able to answer it if I knew more about the Schrödinger equation, and that the answer may be outside of the topic under discussion.

Originally Posted by Doctordick

With regard to the second viewpoint, if one takes the position that the job of a research scientist is to search out the rules which separate the "true" universe from all possible universes, then no classical experiment can provide any guidance on the subject whatsoever. Classical mechanics is itself a tautology.

I’m not quite sure where you draw the line. At what point do we go from looking at every possible explanation to looking at some particular explanation or explanations? I suspect that it is when we start defining elements or give values to anything in the fundamental equation, or is it when we put forward the idea that we can tell two elements apart? I suspect that these are all equivalent.

With regard to the latter I suspect that this is one thing that I keep forgetting, in particular that we can’t tell the difference between one element and any other element until we already have defined an explanation so any question of how an element behaves is of no interest because quite simply it is all part of the assumptions that we make to form a world view.

[jefft0]

Originally Posted by Doctordick

My original purpose was to create a useful mental model of any explanation of any information so that I could comprehend exactly what could be deduced from the simple notion of internal consistency and symmetry principals. This thought resulted in what I call, “A Universal Analytical Model of Explanation Itself”, a paper within which I the development of what I call my “fundamental equation”.

In your email to me, you suggested I post questions about this paper on this forum. (If I should use a different thread, let me know.)

When you introduce A, B and C, you say "B(t_k) is a finite unordered collection of elements of A." But there is a point in the paper where you start using B_k instead of B(t_k), which I like because it emphasizes that there is no implied ordering of the sets in B. (This is defined by the t introduced by C.)

Would it be correct to only use B_k in the earlier references also, instead of B(t_k)?

[Doctordick]

Originally Posted by Bombadil

I still don’t know if it is a good approximation or not, but I suspect that it is a useful approximation in that it tells us something about how all explanations behave, that is they behave approximately like classical mechanics in what you are referring to as the classical limit.

No, you are way ahead of the curve here. I am not talking about how all explanations behave. I am talking about how all ontological elements upon which those explanations depend behave; a seriously different issue. You are trying to function way out in that “all encompassing flaw-free explanation” without understanding what you are talking about. What I will end up proving is that the underlying ontological elements lying behind any explanation of anything are the physical elements commonly thought of as the underlying ontological elements of physics. It is an absolute proof that the correct answer to the question ”Can Everything be Reduced to Pure Physics? is Yes? But you will have to follow the argument to its conclusion in order to comprehend that answer. There are deeper consequences to that result than even the physicists can comprehend and that issue goes very much to your second question. (Reading the first and final page of that thread might be a very worthwhile endeavor!)

Originally Posted by Bombadil

I am wondering at this point if you have also shown that anything that can be mapped into your model is equivalent to a classical mechanics model or are there other models that would be based on your model, that is based on the fundamental equation? I am not asking what such models would be used for or even what might be different about them or how they would be derived, but rather just do they exist?

They exist, but only in your head.

Originally Posted by Bombadil

I’m not quite sure where you draw the line. At what point do we go from looking at every possible explanation to looking at some particular explanation or explanations?

Essentially we do not and that is also an issue to be discussed later.

Originally Posted by Bombadil

I suspect that it is when we start defining elements or give values to anything in the fundamental equation, or is it when we put forward the idea that we can tell two elements apart? I suspect that these are all equivalent.

The moment you begin talking about “an explanation” you are, in a very real way, fundamentally outside the issue under discussion here.

Originally Posted by Bombadil

With regard to the latter I suspect that this is one thing that I keep forgetting, in particular that we can’t tell the difference between one element and any other element until we already have defined an explanation so any question of how an element behaves is of no interest because quite simply it is all part of the assumptions that we make to form a world view.

What is truly interesting here is that “fundamental modern physics” is exactly isomorphic to my fundamental equation. A rather unexpected result with deep and profound consequences.


Hi jeft0, it is nice to see a post from you.

Originally Posted by jefft0

In your email to me, you suggested I post questions about this paper on this forum. (If I should use a different thread, let me know.)

There seems to be no strong response to this thread so it seems to be as reasonable as any other.

Originally Posted by jefft0

When you introduce A, B and C, you say "B(t_k) is a finite unordered collection of elements of A." But there is a point in the paper where you start using B_k instead of B(t_k), which I like because it emphasizes that there is no implied ordering of the sets in B. (This is defined by the t introduced by C.)

Would it be correct to only use B_k in the earlier references also, instead of B(t_k)?

Sure, if you feel that makes more sense then I will go along with it.

Somehow, if I were doing it again, it seems to me that identifying A with “undefined ontological elements” would be a plus if it were done in a way which didn't confuse the masses.

Have fun -- Dick

[jefft0]

Originally Posted by Doctordick

Sure, if you feel that makes more sense then I will go along with it.

Somehow, if I were doing it again, it seems to me that identifying A with “undefined ontological elements” would be a plus if it were done in a way which didn't confuse the masses.

I'm not at the point yet where I could be confused by what the terms are identified with. I'm just trying to make sure I follow the equations. (I think I have enough math background to do this and I'll try to not get sidetracked by interpretations.)

Another basic question: I may be tempted to say that the type of element in the set B_k is a pair of real numbers, but I suspect I would be wrong (even though the paper uses phrases like "all elements in B_k"). Rather, I must resist the temptation to identify what the elements of the set B_k actually are by giving them a mathematical type - we don't assume we can know this. Instead, we are simply giving each a label which is mapped to a point . The set of is not B_k but is simply a set of points from the x, plane. (And, in the equations, we are not working directly with elements of B.)

Am I on the right track?

[Bombadil]

Originally Posted by Doctordick

No, you are way ahead of the curve here. I am not talking about how all explanations behave. I am talking about how all ontological elements upon which those explanations depend behave; a seriously different issue. You are trying to function way out in that “all encompassing flaw-free explanation” without understanding what you are talking about. What I will end up proving is that the underlying ontological elements lying behind any explanation of anything are the physical elements commonly thought of as the underlying ontological elements of physics. It is an absolute proof that the correct answer to the question ”Can Everything be Reduced to Pure Physics? is Yes? But you will have to follow the argument to its conclusion in order to comprehend that answer. There are deeper consequences to that result than even the physicists can comprehend and that issue goes very much to your second question. (Reading the first and final page of that thread might be a very worthwhile endeavor!)

Ok so all that you have done is show that any particular element will behave according to the Schrödinger equation and while you have defined the form of V(x) the actual value of V(x) is defined by the remainder of the universe.

I read the first and final page of that thread it seems to me that the main reason that any one thought that everything can’t be reduced to pure physics is that they are only interested in what can be predicted. It may be the case that such predictions aren’t possible due to never knowing what elements aren’t known or possible to an extent but quite impractical due to the complexity of the problem. But if all that is of interest is explaining what we already know then obviously a function exists that will explain the data. The question of if the data will continue to match such a function is only of interest if it is predicting things that we want to know about.

Originally Posted by Doctordick

What is truly interesting here is that “fundamental modern physics” is exactly isomorphic to my fundamental equation. A rather unexpected result with deep and profound consequences.

How I am understanding this right now, is that the Schrödinger equation tells us something about the elements in any explanation but it tells us nothing about the actual explanations in that even though the Schrödinger equation approximates Newtonian mechanics it doesn’t tell us anything more, because Newtonian mechanics is just a more particular explanation that is derived from quantum mechanics as a result of the Schrödinger equation.

[Doctordick]

Hi Jeff,

Sorry I have been slow to answer. We have been out of town and out of touch with the internet for this last week.

Originally Posted by jefft0

I'm not at the point yet where I could be confused by what the terms are identified with. I'm just trying to make sure I follow the equations. (I think I have enough math background to do this and I'll try to not get sidetracked by interpretations.)

That is probably good.

Originally Posted by jefft0

Another basic question: I may be tempted to say that the type of element in the set B_k is a pair of real numbers, but I suspect I would be wrong (even though the paper uses phrases like "all elements in B_k").

No you would be correct. Both x and tau are no more than numerical labels: i.e., stand-ins for actual labels used in the explanation being represented by the function , which generates the probability of B_k. It is when the “model” proposes to denote the information represented by the total set of labels going into making up B_k as points on the x axis that the need to introduce tau arises and that is an issue you need to understand. Thus the model becomes a set of points in an Euclidean space.

Originally Posted by jefft0

Rather, I must resist the temptation to identify what the elements of the set B_k actually are by giving them a mathematical type - we don't assume we can know this. Instead, we are simply giving each a label which is mapped to a point . The set of is not B_k but is simply a set of points from the x, plane. (And, in the equations, we are not working directly with elements of B.)

In a sense we are. We just do not have that representation expressed in what is called “English” (or any other language for that matter); nonetheless, what we have (once we actually have a specific B_k assembled via that third coordinate t_k) is exactly the same information we would have in an explanation expressed in a language.

It is very convenient to think of the information available to us as expressed in an unknown language. Each fundamental element of that language is a single specific label and every “communicated message” is essentially a specific B_k. All we have to do is translate that language into the one we prefer (English for this forum). In this picture, do you not find the fact that everyone sees “reality” as an assemblage of physical elements in a Euclidean space changing position (moving about) as time changes a rather interesting thing?

Originally Posted by jefft0

Am I on the right track?

I presume you are but I am not in your head so I do not know for sure.

Now to Bombadil's post.

Originally Posted by Bombadil

Ok so all that you have done is show that any particular element will behave according to the Schrödinger equation and while you have defined the form of V(x) the actual value of V(x) is defined by the remainder of the universe.

That does not really capture the essence of what I have proved. I have shown that “every” specific element in any conceivable universe (when represented as a set of points in a Euclidean space) will behave in accordance with Schrödinger's equation and that there always exists (for every such element) a Schrödinger potential V(x) (defined by the rest of the universe) which will yield exactly that observed motion.

By the way, dimensionality of that picture is another issue we have not yet gotten to and perhaps now is the time to discuss that issue. I think I will open another thread concerning the most probable reason we see the universe as having three dimensions. In my head, that is an issue worth some serious thought.

Originally Posted by Bombadil

I read the first and final page of that thread it seems to me that the main reason that any one thought that everything can’t be reduced to pure physics is that they are only interested in what can be predicted. It may be the case that such predictions aren’t possible due to never knowing what elements aren’t known or possible to an extent but quite impractical due to the complexity of the problem. But if all that is of interest is explaining what we already know then obviously a function exists that will explain the data. The question of if the data will continue to match such a function is only of interest if it is predicting things that we want to know about.

I would put a slightly different twist on the question. If our interest is in explaining “what we know” and “what we know” is continually changing, what we should be interested in would be the simplest way of obtaining a new solution consistent with the “new” entirety of “what we know”: i.e., the simplest way in which those “ontological labels” could be changed such that “all the data known” is still explained. That brings up the issue that “changing labels” are themselves a interesting aspect of our explanations and right there we have some strong interest in how those points might move in that hypothetical space.

Originally Posted by Bombadil

How I am understanding this right now, is that the Schrödinger equation tells us something about the elements in any explanation but it tells us nothing about the actual explanations in that even though the Schrödinger equation approximates Newtonian mechanics it doesn’t tell us anything more, because Newtonian mechanics is just a more particular explanation that is derived from quantum mechanics as a result of the Schrödinger equation.

Well now, I don't really feel that “it tells us nothing about the actual explanations”. First of all, Newtonian mechanics is not exactly “a more particular explanation that is derived from quantum mechanics”. Long before Newton lived, most everyone saw the world as a collection of “things” distributed in a three dimensional Euclidean space. The positions of these things, for the most part, were fixed and only people and animals (plus waves and winds attributed to gods, entities quite similar to people) moved or caused movement. Newton came up with some very powerful mathematical relationships lying behind motion. His discoveries were called “Newtonian mechanics” and were not at all an explanation derived from quantum mechanics.

In fact, the origin of quantum mechanics lies in the mathematical relationships implied by Newtonian mechanics. The beginnings of quantum mechanics came about through examination of methods of solving the differential equations arising in Newtonian mechanics. That alone is a long story far beyond this forum. Newtonian mechanics was a very powerful invention for explaining a lot of phenomena central to common reality and quantum mechanics was a major advance on that power. What is important about the transformation to quantum mechanics is the fact that, given quantum mechanics as correct, all of Newtonian mechanics can be shown to be an approximation to gross quantum mechanical solutions. Likewise what I have begun to show (and I will show much more) is that quantum mechanics is an approximation to gross solutions to my fundamental equation. And, since my equation and the mental picture behind that equation is no more than a tautological explanation of any body of unknown information, it implies that the common “physics” explanation of any phenomena lies (at least as a gross approximation) is fundamental to any explanation of anything.

In other words, modern physics (or at least a rather simple variation of that picture) lies as a basis behind any explanation of anything. If any ontological elements behind your explanation of anything cannot be reduced objects explainable by my equations (which can essentially be called “valid modern physics”) then your explanations are flawed or inconsistent in some way.

Have fun -- Dick

[Bombadil]

Originally Posted by Doctordick

I would put a slightly different twist on the question. If our interest is in explaining “what we know” and “what we know” is continually changing, what we should be interested in would be the simplest way of obtaining a new solution consistent with the “new” entirety of “what we know”: i.e., the simplest way in which those “ontological labels” could be changed such that “all the data known” is still explained. That brings up the issue that “changing labels” are themselves a interesting aspect of our explanations and right there we have some strong interest in how those points might move in that hypothetical space.

Would I be correct in saying that changing labels is what would be interpreted as movement or is movement more closely related to the mass, energy, and momentum of the element of interest? Of course any such movement can only be defined in comparison to the remainder of the universe so that it is just part of V(X).

Originally Posted by Doctordick

In other words, modern physics (or at least a rather simple variation of that picture) lies as a basis behind any explanation of anything. If any ontological elements behind your explanation of anything cannot be reduced objects explainable by my equations (which can essentially be called “valid modern physics”) then your explanations are flawed or inconsistent in some way.

How I am understanding this, it is also true though that there exists an explanation that can explain any behavior of a collection of objects no matter how they behave. So that it is always possible to reduce any behavior to one described by “valid modern physics”.

[Doctordick]

Originally Posted by Bombadil

Would I be correct in saying that changing labels is what would be interpreted as movement or is movement more closely related to the mass, energy, and momentum of the element of interest?

No such thing as “motion” actually exists in the data being explained (the past is a static structure). Movement is an aspect of your explanation which allows different possible labels to refer to the same defined entity as time changes: i.e., a numerical index on the x axis in the present (a change in the known past) is taken to refer to the same entity at a different position in that “past” (what was known prior to the addition of the present). The explanation of course sees the past as a collection of “presents” made up of the same entities.

Originally Posted by Bombadil

Of course any such movement can only be defined in comparison to the remainder of the universe so that it is just part of V(X).

This is a bit twisted. V(x) is the source of the “force” (force is something which changes momentum: i.e., changes the value of the partial with respect to x) which changes the momentum of the entity described by x. It is the measure of things like position and time which are a function of the remainder of the universe. The form of V(x) is also a consequence of the rest of the universe.

Originally Posted by Bombadil

How I am understanding this, it is also true though that there exists an explanation that can explain any behavior of a collection of objects no matter how they behave. So that it is always possible to reduce any behavior to one described by “valid modern physics”.

Yes! But that requires “valid” modern physics. At the moment there are a few problems with modern physics which need to be fixed and I will show you these problems down the road.

Have fun -- Dick

[jefft0]

Originally Posted by Doctordick

No such thing as “motion” actually exists in the data being explained (the past is a static structure). Movement is an aspect of your explanation which allows different possible labels to refer to the same defined entity as time changes: i.e., a numerical index on the x axis in the present (a change in the known past) is taken to refer to the same entity at a different position in that “past” (what was known prior to the addition of the present). The explanation of course sees the past as a collection of “presents” made up of the same entities.

When describing , you say it is a function of a "set of elements", e.g. . The use of the term "set" implies that there is no order to the elements. But if we want to say is a function of a set of elements, we would write , where is standard set notation. However, you don't do this, and I think for good reason because it is not a "set of elements", it is a "vector of elements", where the order as listed in the vector matters.

Is it fair to say that there is some extra information encoded in the fact that that you use a vector and not a set , where the position in the vector from one t to the next matters (to associate it with the same entity for different t)? It seems this is the way to make sense of your quote above. (I'm trying not to get hung up on your repeated use of the word "set" by assuming it always means "an unordered collection of elements with no duplicates".)