Well, my last post to this topic was almost ten years ago. Three years ago I published a book on my proof. I have discussed that book with a number of people who have looked at it and only recently came to the conclusion that they all misinterpret something I thought was obvious. I thought it might be reasonable to post a rather simple analysis of what is essentially my opening position.

My book, (see http://foundationsof...cs.blogspot.com) is actually little more than a logical proof that modern physics is essentially nothing more than the consequences of requiring internal consistency within our explanations. That proof is based upon the fact that explanations must be expressed with a language, essentially a finite collection of concepts designed to provide a representation of one's experiences.

Our knowledge of the universe is built entirely on our personal perceptions. That these perceptions arise from our interpretations of earlier experiences is an issue seldom, if ever, considered by the scientific community. Fundamentally, we must be able to identify what it is that we perceive before we can make use of those perceptions to build a mental model of them. What I am trying to point out is that we are not born knowing what our experiences signify. That is a subject we must learn as children long before we build any real knowledge of the universe. It must also be understood that humanity has through out history developed thousands of different languages. The fact that such a thing can be accomplished opens many interesting issues.

Clearly every human (including the most brilliant scientist who ever lived) can be seen as beginning life as a child born without a language. During his life he will experience many interactions with reality, including the many experiences central to "learning the language" which he will eventually use to express his understanding of reality (an issue solved many many years later). The total number of experiences standing behind his knowledge may be unbelievably large but it is nonetheless finite. That means that the entire collection of his experiences (expressed via whatever language he has learned to use) can be seen as a finite collection of known facts.

The total number of "concepts" expressible via that language could certainly be listed. Once such a list of concepts were constructed, each and every one could be given a specific numerical index which could be used to refer to that specific concept (think of that index as a secret means of referring to a specific concept). Using that collection of numerical indices, any experience could be specified via the notation [math](x_1,x_2,\cdots,x_n)[/math] where each [math]x_i[/math] is the specific numerical index of a required concept.

Given the above notation, the scientist's explanation of his experiences (essentially his explanation of reality itself) can be represented by [math]P(x_1,x_2,\cdots,x_n)[/math], where P stands for the probability he holds that specific thought being represented by [math](x_1,x_2,\cdots,x_n)[/math] to be true. Note that "internal consistency" is a very simple aspect under this representation. Under the explanation being given, the truth of the specified thought is a function of the explanation and cannot change except by changing either the "thought" (what is being represented by [math](x_1,x_2,\cdots,x_n)[/math]) or the "explanation" itself.

One needs to comprehend that the specific collection of numerical indices used is entirely arbitrary. In essence there exists an infinite collection of such "secret codes" every one of which would be capable of expressing exactly the same knowledge expressed by that original collection of thoughts. For the sake of argument, consider a specific second "secret code" where exactly the same the specific concepts are represented by a totally different collection of numerical indices. In order to specify this second set, I will use [math]z[/math] instead of [math]x[/math]. In this case, I will use the notation [math](z_1,z_2,\cdots,z_n)[/math] to specify exactly the same thought originally expressed by [math](x_1,x_2,\cdots,x_n)[/math] in the original where each [math]z_i[/math] refers to exactly the same concept as does [math]x_i[/math].

In that case, the truth of a specific thought in this second "secret code", [math]P(z_1,z_2,\cdots,z_n)[/math] will be exactly the same as [math]P(x_1,x_2,\cdots,x_n)[/math]. The actual pattern of those indices has utterly no bearing on the result; however, one specific case stands out as quite interesting. If every [math]z_i[/math] index is exactly [math]x_i +a[/math] it must be true that [math]P(x_1+a,x_2+a,\cdots,x_n+a)\equiv P(x_1,x_2,\cdots,x_n)[/math].

This leads to another very interesting case. Suppose one considered two specific cases, one where [math]a=c+\Delta c[/math] and a second where [math]a=c[/math], another extremely interesting relationship appears.

[math]\lim_{\Delta c\rightarrow 0}\frac{P(x_1+c+\Delta c,x_2+c+\Delta c,\cdots,x_n+c+\Delta c,)-P(x_1+c,x_2+c,\cdots,x_n+c)}{\Delta c}[/math]

Anyone familiar with calculus will recognize the above expression is exactly the definition of the derivative of P with respect to c, the shift in the position of the origin. However, if [math]P(x_1,x_2,\cdots,x_n)[/math] is seen as a mathematical function one can make another rather astounding deduction. The derivative of P with respect to c can also be expressed via,

[math]\frac{dP}{dc}=\sum_{i=1}^{n}{\frac{\partial P}{\partial x_i}}\frac{d x_i}{dc}=0.[/math]

Since the expression we started with required [math]\frac{d x_i}{dc}=1[/math], this leads to the conclusion that in any internally consistent explanation of reality, expressed via [math]P(z_1,z_2,\cdots,z_n)[/math] requires that explanation (when seen as a mathematical function) must obey

[math]\sum_{i=1}^{n}{\frac{\partial P}{\partial x_i}}=0[/math]

over the entire range of applicable indices.

Now this assertion has a few flaws which are discussed in detail and resolved in my book. The result of that analyisi yields almost exactly the entire body of modern physics including some very interesting differences which I think amount to evidence that modern physics contains some serious errors.

Have fun --- Dick