Why you should like my perspective

[Doctordick]

Ok guys, no one seems to have been able to point out any great flaw in the geometric representation I have proposed in the thread "A Thought Experiment". That is, I believe I have presented a good case that the issue is representation only and not an issue of physical validity. If that is indeed the case, then please allow me to discuss the advantages of my perspective.

(If you seriously have no interest, please don't bother to read this!)

First let me say that I do not at all feel that Einstein's perspective should be laid aside. It should be studied and understood as a very powerful mechanism for expressing many constraints imposed by the necessity of the well known relativistic relationships. His development of the covariant representation of physical laws as a notation (which clearly guarantees that the represented laws are indeed the same in all reference frames) is a very powerful tool.

However, to regard his representation as the only possible way to represent the relativistic phenomena is very short sighted. There are many mathematical representations of phenomena which provide easy proof of what may otherwise be a difficult problem. Such things should not be taken as evidence that there are no other useful representations.

When it comes to understanding the physical universe, I believe my representation is greatly superior to the conventional perspective introduced by Einstein for the following specific reasons.

I. The geometry has a Euclidian metric with four "spatial" axes and thus many phenomena are much easier to mentally visualize in this presentation than they are in Einstein's perspective (Though it takes a little practice to get a few of the subtle issues straight).

II. The representation is fundamentally more symmetric than Einstein's representation as all four coordinates are totally equivalent. The $\tau$ axis is a spatial axis completely equivalent to x, y and z. The only thing which sets $\tau$ off as different is that the great majority of important entities exist in momentum quantized states in the $\tau$ direction. One could just as easily work with entities which were momentum quantized in any direction. That is, the asymmetry is a result of the problem being solved, not the geometry.

III. Time, being path length along the trajectories of the relevant events, is once more a parameter of motion and not a coordinate. This effect makes laying out valid quantum mechanical representation of phenomena straight forward.

IV. All possible lines within the geometry are legitimate possibilities for trajectories of entities of interest. Under Einstein's geometry, entities can not follow any space-time line elements along which Einstein's invariant interval is real; i.e., they must follow time like space-time lines as the invariant interval must be time like in the instantaneous rest frame of the entity ($d\tau$ must be real). Relaxing this external constraint (external to the geometry) leads to the idea of tachyons and time reversed actions (neither of which have ever been seen).

V. In my representation, uncertainty in rest mass is uncertainty in momentum in the $\tau$ direction. It follows that the extension of the wave function representing the entity has infinite extent. Two entities, both momentum quantized in the same direction can interact (changing their respective momentum perpendicular to $\tau$ without establishing a specific value for $\tau$). This is totally consistent with the $\tau$, rest mass uncertainty relationship. In Einstein's picture, proper time is path length in his geometry. As such, specific interactions can establish beginning and ending times which should conceptually constrain $\tau$ to a specific range. The result of such a measurement could be seen as requiring a non-zero uncertainty in rest mass. Generally I have noticed that physicists would rather deflect attention from this issue than answer it (it can be answered but it requires a little subtle argument).

VI. Negative mass would be momentum quantization in the minus $\tau$ direction and thus does not yield a negative value for the energy. This completely removes Dirac's infinite sea of negative energy particles. It also constrains mass conversion to energy to exactly the situations where it is seen to occur (the constraints come directly from the kinematics of conventional momentum conservation).

VII. In Einstein's perspective, conventional electro-magnetic phenomena can be shown to be a direct consequence of relativistic effects: i.e., a simple coulomb interaction cannot exist as relativistic shifts in one's coordinate system will create a magnetic interaction. The same thing is true in my perspective; however, when the detailed work is carried out, the resultant four component vector of momentum transfer is transformed into a scalar component related to the $\tau$ axis and a three component vector related to the x, y and z axes. The difference between the character of the two fields is a direct consequence of the momentum quantization in the direction of $\tau$. To make a long story short, magnetic monopoles (which have never been seen) are not a possibility.

VIII. Finally, the extension of quantum mechanics to general relativity is rather straight forward in my perspective (which is a quantum mechanical perspective from the get go) while an equivalent result from Einstein's perspective has yet to be accomplished.

Now, I am the only person who has ever gone deeply into this perspective and I have accomplished quite a little. It seems to me that, if I could interest others in examining the perspective, there could be a lot of other significant stuff still buried in there.

I also think Einstein's perspective is fundamentally invalid as it does not constitute the correct constraint on what can and cannot be seen. First, there exist solutions in his perspective which have never been seen. Now there are those who believe this is not a problem (people who think in compartmentized fashion); however, I hold that any answer to a question which gives the wrong result when pushed to the limit of definition is the wrong answer. And, secondly, it is, as yet, incomplete: i.e., no method has of yet been conceived of which can cast general relativistic quantum mechanics into his representation.

Furthermore, if anyone is interested, I can deduce my perspective from first principles and demonstrate that it is universally applicable to all possible universes.

Have fun -- Dick

 

[Antonio Lao]

I agree with you that magnetic monopoles cannot exist mainly for the reason that the divergence of the magnetic field is zero in vacuum and in matter (without having H as the field produced by the current density and the curl of the the electric field) and the fact that all magnetic field lines formed closed loops.

The reason why the electric and magnetic component of the vacuum cannot be separated is because their vector differences produce gravity and antigravity forces at the local infinitesimal region of the vacuum. Because of these differences, mass and charge can be defined macroscopically speaking (in relation to the effective distances of these vector differences). There might be no experimental way of detecting these effective distances. So we can just say it that this is the region of the Planck length.

The magnetic component of the vacuum is related to a timelike force. The electric component of the vacuum is related to a spacelike force.

 

[Doctordick]

Derivation from first principals!

If any of you who read this consider yourself to be a competent physicist or if you know of any competent physicists, I would seriously appreciate a little competent criticism on this presentation.

Derivation of Doctor Dicks Fundamental Equation -- Part I

What follows is a derivation of my Fundamental Equation of the Universe from first principals. The purpose of a fundamental equation of the universe would be to provide an explanation of everything known about the universe. For that reason, the subject of this paper is the creation of an abstract general model of any conceivable explanation of anything.

The first issue of such an endeavor is to define exactly what is meant by the phrase "an explanation". I will begin by pointing out that all "explanations" require something which is to be explained (in the case of the universe, that would be everything). Whatever it is that is to be explained, it can be thought of as information. It thus follows that "an explanation" is something which is done to (or for) information.

The question then is, if we are to model "explanation" in general, we must lay down exactly what it is that explanation does to (or for) information.

I will suggest that what an explanation does for information is that it provides expectations of subsets of that information. That is, it seems to me that if all the information is known, then any questions about the information can be answered. That could be regarded as the definition of "knowing". On the other hand, if the information is understood, then questions about the information can be answered given only limited or incomplete knowledge of the underlying information: i.e., limited subsets of the information. What I am saying is that understanding implies it is possible to predict expectations for information not known. The explanation constitutes a method which provides one with those rational expectations for unknown information consistent with what is known.

Thus I define "an explanation", from the abstract perspective, to be a method of obtaining expectations from given known information. It follows that a model of an explanation must possesses two fundamental components: the information to be explained and the mechanism used to generate expectations for possible additional information.

The first fundamental component is, "what is to be explained"; thus our first problem is to find an abstract way of representing anybody of information. Let "A" be what is to be explained and proceed with the following primitive definitions:

1. A is a set.
2. B is a set, defined to be an unordered finite collection of elements of A
3. C is defined to be a finite collection of sets B.
​

​

The specific problem is to create an abstract model which will model any explanation of A obtained from C. As an aside, it should be obvious that the necessity of defining C arises because, if all the elements of A are known, then A itself is a model of A and the problem posed is trivial. (Nevertheless, please note that the trivial case where C is identical to B which is identical to A is not excluded in this presentation.)

The second fundamental component is the definition of "an explanation" itself: we must establish an abstract definition of exactly what is meant by "an explanation of A". We will hold here that an explanation of A will consist of the following elements.

1. A set of reference labels for the elements of A (so that we may be able to reference those elements and thus know and discuss what it is that we are dealing with prior to achieving an understanding of those elements).
2. An algorithm which will yield the probability of any specific set B derived from A which is consistent with the distribution of B in C (this is required to assure the explanation yields rational expectations: i.e., so that our explanation will be consistent with the available information "C").
​

​

Construction of a model:

Since B is finite, its elements may be labeled.

1. Let label_i be the label of a particular element of B.
2. Let all label_i be mapped into the set of real numbers x_i.
3. Let all numbers x_i be mapped into points on the real x axis.
​

Thus it is seen that any set of labels for the elements of A available to the explanation (i.e., appearing in any set B) may be mapped into points on the real x axis; however a minor problem exists in any attempt to use this as a general model.

Sub Problem number 1:

Since all possible explanations must be modeled and B may contain the same element of A more than once: i.e., the points x_i need not be unique. There is a problem in modeling the elements of B as points on the real x axis. It should be clear that points with the same location can not represent multiple occurrences of the mapped label and information contained in B is lost in step three as put forth.
​

Solution to Sub Problem number 1:

1. Add to the model a real $\tau$ axis orthogonal to the real x axis.
2. Attach to every x_i an arbitrary $\tau_i$ such that every pair of identical x_i points have different $\tau_i$ attached. Our model can now display the fact of multiple occurrences of identical x_i.
​

​

The abstract model of any possible explanation is now a set of points (one set for each B) mapped into a set of (x,$\tau$) planes (one plane for each set B making up the set C).

We have now accomplished the first step: we have established a specific way of modeling all possible references to the elements in B in the set C; however, a second subtle problem arises here.

Sub Problem number 2:

The model is supposed to be able to model all possible references to the elements in A, not just to the elements found in the sets B contained in C.
​

Solution to Sub Problem number 2:

Since the elements of C are a finite collection of sets B_j, references to the elements of C may be mapped into any ordered set of real numbers t_j. Thus we may associate the specific t_j with all the (x,$\tau$)_j elements in B_j. If we then set up a real t axis perpendicular to the (x,$\tau$) plane, every element in the collection of B_j can be mapped to a point in the real (x,$\tau$,t) space. Since only a finite number of (x,$\tau$) planes are consumed by C, we have an uncountable number remaining to model the set of all possible collections B.
​

Providing for all possible sets B is equivalent to providing for all possible references to the elements in A as B is a collection of elements from A by definition.
​

We now have constructed a model capable of modeling all possible
reference labels for the elements of A.

The model consists of points in a real (x,$\tau$,t) space.

"Real" means that x, $\tau$ and t are taken from the set of real numbers.

In order to complete the problem, it is necessary to establish a general mechanism which is capable of yielding the probability of any specific set B derived from A which is absolutely one hundred percent consistent with the distribution of B in C (if it isn't consistent with the distribution of B in C, our explanation is invalidated by information already available to us) . This general mechanism must transform the distribution of B in C (a set of points in a real (x,$\tau$,t) space) into a probability (a number between zero and one) and thus can clearly be represented by a mathematical algorithm.

The first requirement of the required algorithm is that the result is a probability as our expectations of occurrence of any particular B can only be expressed as a probability. It may appear that only algorithms which yield an answer consisting of a positive real number (greater than or equal to zero) and (less than or equal to one) are applicable. However, any mathematical algorithm can be seen as an operation which transforms a given set of numbers into another set of numbers and any function of (x,$\tau$,t) may map to the desired algorithm, the desired probability being given by the "normalized" sum of the squares of the produced set of numbers.

It follows that our model may state that the Probability of any specific B is given by

$$P(\vec{x},t) = \vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)dv$$​

without introducing any limitations whatsoever on the nature of the explanation being modeled. The $\vec{x}$ stands for the complete collection of x and $\tau$ defining that specific B. The "dot" indicates a scalar product, $\vec{\Psi}$ is to be properly "normalized" and "dv" is dxd$\tau$. Since no constraint whatsoever has been placed on the problem by this notation, it follows that absolutely any explanation may be modeled by the function $\vec{\Psi}(\vec{x},t)$ where the argument is the collection of points which are mapped from the elements of the appropriate B (it should be understood that "B" is a reference to a specific expectation).

{The derivation will continue in the next post}

 

[Doctordick]

Derivation from first principals - part II

Derivation of Doctor Dicks Fundamental Equation -- Part II

There exist a couple of subtle aspects of the model so far described. Of very great significance is the fact that the goal was to create a model which will model any explanation of A obtained from C. The specific mapping of the labels for the elements of C are part of the model and not a given aspect of the phenomena to be modeled: i.e., not at all part of A. If follows that the $\vec{\Psi}(\vec{x},t)$ yielded by the model cannot be a function of that mapping procedure: i.e., all possible mappings must end up yielding exactly the same probability algorithm (the $\vec{\Psi}(\vec{x},t)$ must yield results consistent with the actual distributions of the elements of B in C independent of the chosen mappings). This fact can be used to prove that $\vec{\Psi}$ must satisfy some very simple partial differential relations.

The process yields three orthogonal differential constraints on $\vec{\Psi}$ in the three dimensional representational space defined by the x, $\tau$ and t axes of the model (if you need clarification on this issue, let me know).

$$\sum_i^n \frac{\partial}{\partial x_i}\vec{\Psi}\,=\, i \kappa_x \vec{\Psi}\,\,,\,\,\sum_i^n \frac{\partial}{\partial\tau_i}\vec{\Psi}\,=\, i\kappa_{\tau}\vec{\Psi}\,\,and\,\,\frac{\partial}{\partial t}\vec{\Psi}\,=\, im\vec{\Psi}$$
​

The final aspect of the model is to actually design a universal rule which is capable of yielding the distributions of the elements of B in C for every possibility. In this regard, it is quite easy to prove that, for any B (any distribution of points in the (x,$\tau$) plane) there exists a corresponding set D (a second distribution of points in the (x,$\tau$) plane), which, under the simple constraint that no two points can be the same, will constrain the distribution of B in C to exactly that distribution, no matter what that distribution might be (if you need clarification on this issue, let me know). The constraint that no two points can be the same is easily enforced by requiring:

$$F \, = \, \sum_{i\not= j}\delta (\vec{x_i}-{\vec{x_j}})\, =\, 0.$$
​

where $\vec{x_k}$ is defined to be the vector in the x, $\tau$ space defined by ($x_k,\tau_k$) and $\delta$ represents the Dirac delta function. This express constraint on the elements of B can be converted into an express constraint on $\vec{\Psi}$ by noting that the proper constraint on $\vec{\Psi}$ is that that $\vec{\Psi}$ must vanish whenever the above constraint on the elements is invalid; i.e., when F is not equal to zero, $\vec{\Psi}$ must be zero. Thus the product of the two must always be zero and the correct constraint on $\vec{\Psi}$ is given by:

$$\sum_{i\not= j}\delta (\vec{x_i}-{\vec{x_j}}) \vec{\Psi}\, =\, 0.$$
​

These four independent constraints on $\vec{\Psi}$ may be expressed in a very succinct form through the use of some very simple well known mathematical tricks.

If one defines a set of anti commuting matrices as follows:

$$[\alpha_{ix}\, , \,\alpha_{jx}]\,\,{\equiv}\,\,\alpha_{ix}\alpha_{jx} \, + \, \alpha_{jx}\alpha_{ix}\,=\,\delta_{ij}$$

$$[\alpha_{i\tau}\, , \,\alpha_{j\tau}]\,=\,\delta_{ij}$$

$$[\beta_{ij}\, , \, \beta_{kl}] \, = \, \delta_{ik} \delta_{jk}$$

$$[\alpha_{ix}\, , \, \beta_{kl}] \, = \, [\alpha_{i\tau}\, , \, \beta_{kl}]\, = 0\, ,\, \, \mbox{ where } \,\, \delta_{ij}\, = \,\left\{ \begin{array}{ll} 0 & \mbox{if i\noy=j}\\ 1 & \mbox{if i=j}.\end{array} \right.$$​

and defines two expressions ( $\vec{\alpha_i}$ = $\alpha_{ix}\hat{x}$ + $\alpha_{i\tau}\hat{\tau}$ and $\vec{\nabla_i} \,=\,\frac{\partial}{\partial x_i}\hat{x}\,+\,\frac{\partial}{\partial\tau_i}\hat{\tau}$ ), a small shift in perspective will allow the four constraints on $\vec{\Psi}$ to be written in a single equation as follows:

$$\left\{\sum_i\vec{\alpha_i}\,\cdot\,\vec{\nabla_i}\,+\, \sum_{i\not=j}\beta_{ij}\delta(\vec{x_i}\,-{\vec{x_j}})\right\} \vec{\Psi}\,\,=\,\,K\frac{\partial}{\partial t}\vec{\Psi}\,= \,iKm\vec{\Psi}$$
​

constrained by the requirement that

$$\sum_i\vec{\alpha_i}\,\vec{\Psi}\,=\,\sum_{i\not=j}\beta_{ij}\,\vec{\Psi}\, =\,0.$$
​

It follows that all explanations of anything may be directly modeled by a set of points in an (x,$\tau$) space moving through a t dimension and required to obey the fundamental equation given above. The probability of any particular set of elements in B being given by

$$P(\vec{x},t) = \vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)dv$$

​

And I have thus successfully created a model of all possible explanations of A consistent with C. The fact that no constraints of any kind were placed on A implies the solution has consequences of great significance to every science under study.

If anyone out there has the gray matter to follow the derivation and is interested in discussing the issues it raises, I am ready to discuss the following issues:

1. Possible errors in my derivation (I will have to leave finding them to you as I am not aware of any errors).
2. How to obtain solutions to the equation and the solutions that I have found.
3. The philosophical implications as to what impact the discovery has on one's mental image of reality.
4. Interpretation of the equation: just what the various parts of the derivation mean.

 

[Antonio Lao]

To understand the universe we simply need to understand three things:

1. Matter
2. Energy
3. Space

Their mutual interaction in spacetime creates different fundamental forces of nature. Matter (atomic theory) and energy (quantum theory), both, have been quantized. What we need to do now is to quantize space.

 

[Doctordick]

To understand the universe we simply need to understand three things:

1. Matter
2. Energy
3. Space

Their mutual interaction in spacetime creates different fundamental forces of nature. Matter (atomic theory) and energy (quantum theory), both, have been quantized. What we need to do now is to quantize space.

Antonio, do you understand the post which you have responded to?

That is a serious question -- Dick

 

[Russell E. Rierson]

The first fundamental component is, "what is to be explained"; thus our first problem is to find an abstract way of representing anybody of information. Let "A" be what is to be explained and proceed with the following primitive definitions:

1. A is a set.
2. B is a set, defined to be an unordered finite collection of elements of A
3. C is defined to be a finite collection of sets B.
​

​

It appears that you are defining the set "A" as a finite set, where the probability functions from "A" are limited to a finite number of choices?

According to Georg Cantor, for every set A, there is a choice function, f, such, that for any non-empty subset B of A, f(B) is a member of B.

The problem is that there may be infinitely many sets B, within A.

If A is a finite? collection, this problem could be resolved? But that leaves the problem of the need for a continuous causally connected manifold?

 

[Russell E. Rierson]

Doctordick, your scalar product probability function is extremely interesting and let me be the first to admit that I am not qualified to critique your intriguing ideas.

But what I do understand appears to be good.

 

[ZelmersZoetrop]

Although I must say I'm skeptical of any alteration of the Minkowski metric, this means of "Euclid-izing" normal SR space is vastly prefferable to multiplying by i the time co-ordinate. I'm curious, have you extended this concept into researching GR positive-definite metrics?

Also, I looked over your derivation of the qunatum mechanical probability density and it appears to be without flaw (though I might be missing something). Can you derive the probability density current this way as well?

 

[Antonio Lao]

Just looking in from a vantage point outside the physical universe where all the intimate details of its workings are a bit fuzzy.

 

[Doctordick]

It is not always easy to learn something new.

It appears that you are defining the set "A" as a finite set, where the probability functions from "A" are limited to a finite number of choices?

I get the feeling that we have a very long way to go. All I said in step #1 is that "A" is a set. I placed utterly no constraints on A whatsoever! If no constraints are placed on the definition of the set A, then A can be anything; A could be finite or A could be infinite. Furthermore, as there are no constraints on the definition of the set A, "the probability functions from 'A'" is a meaningless phrase.

According to Georg Cantor, for every set A, there is a choice function, f, such, that for any non-empty subset B of A, f(B) is a member of B.

That's nice; but you will need to explain why you think it is applicable to what I am saying. I did not say B was a subset of A (to do so would put certain constraints on B which I have not suggested). What I said was that B was a set consisting of a finite collection of elements from the set A (a slightly different concept).

What is important here is that the set A is totally undefined and it is possible that no set B exists in A. In particular, I could define A as a set which contains no two identical elements. I could then define B to be a set of multiple identical elements consisting of a single element taken from A. In that case, B certainly would not be a subset of A. The important issue here is that absolutely no constraints be placed on A.

The problem is that there may be infinitely many sets B, within A.

Why do you think that is a problem?

If A is a finite? collection, this problem could be resolved? But that leaves the problem of the need for a continuous causally connected manifold?

Why do you need "a continuous causally connected manifold? It seems to me that you are trying to jump ahead of the derivation without understanding the derivation itself.

Doctordick, your scalar product probability function is extremely interesting and let me be the first to admit that I am not qualified to critique your intriguing ideas.

As I understood it, you felt that my derivation of general relativistic quantum mechanics sounded interesting. I took that to mean that you were interested in understanding it. That would mean that the purpose of this exchange would be to explain it to you. I certainly wouldn't expect you to critique something you do not understand (that is what the "trolls" on this forum are doing").

But what I do understand appears to be good.

Now here again I detect a sour note in the exchange. If all you want is a vague understanding of what I am doing then I don't think any great effort on my part is worthwhile. My purpose is not to "win adherents" to my position but rather to have my position understood so that understanding of it does not die when I die. The world has enough people who "adhere" to positions they do not understand.

Although I must say I'm skeptical of any alteration of the Minkowski metric, this means of "Euclid-izing" normal SR space is vastly prefferable to multiplying by i the time co-ordinate. I'm curious, have you extended this concept into researching GR positive-definite metrics?

I am an old man who has very little spare time to research anything. On top of that, I am fully aware of the decline in my mental abilities.

If you get deep into my work, you will find that I use the n dimensional Dalembertian operator. Now, forty years ago, when I first wrote the polar expansion of that operator down, it was absolutely obvious to me that the following statement was true.

$${\nabla}^2\,\equiv\,\sum_{i=0}^n\frac{\partial^2}{{\partial}x_i^2}$$
​

can be written in an n dimensional polar coordinate system as:

$$\left({\frac{1}{r}\right)}^n\frac{\partial}{\partial r}r^n\frac{\partial}{\partial r}+\frac{1}{r^2}\sum_{i=1}^n\left(\prod_{l=1}^{i-1}csc^2 \theta_l \right)(csc {\theta}_i)^{n-i}\frac{\partial}{\partial {\theta}_i} (sin {\theta}_i)^{n-i} \frac{\partial}{\partial {\theta}_i}}$$
​

Everything I did initially was all hand written. In 1987, I bought my first personal pc at a garage sale for a thousand dollars. It had one of the very early versions of word perfect which could type set equations. Well, I translated my paper into a word perfect document.

I remember getting to the above equation. It had been almost twenty years since I wrote the thing down and it was entirely possible that I had made an error. As a consequence, I proved it was true before I entered it in the document. It took me all afternoon to prove it to my satisfaction.

About five ago I ran across the old paper when cleaning up the attic, at the suggestion of my son-in-law, I converted the paper to HTML in order to post it on the internet. Since almost fifteen years had passed since the creation of the word perfect document, I again needed to prove the expression (I always worry that I have made an error). This time it took me six weeks and I could only do it by expanding the whole thing out completely (I had completely forgotten most all of the tricks which were such a big part of my repertoire forty years ago). I kept the work this time.

Thinking things out is a job for young people. All of you (if you don't die young) will eventually discover that things you find easy now you will find difficult when you are old.

Also, I looked over your derivation of the quantum mechanical probability density and it appears to be without flaw (though I might be missing something). Can you derive the probability density current this way as well?

Are you referring to the expression

$$P(\vec{x},t) = \vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)dv$$​

or to the equation further down in the derivation? If it is the second, I don't think you have been very careful in your examination. Surprise me and explain the "small shift in perspective" required to make that equation correct. As given, there is a very serious flaw in the presentation. I have not yet explained that "small shift in perspective" because it becomes quite clear what it must be when you attempt to prove that the equation is true: i.e., that you can recover the constraints given above it.

Again I will say, if you are going to take my word for things, then we are wasting our time. I hate to put such a burden on you all; but, if you don't understand it, why are you interested in it? There are certainly more important things to do with your life.

Have fun -- Dick

 

[Doctordick]

I am confused by your response!

Just looking in from a vantage point outside the physical universe where all the intimate details of its workings are a bit fuzzy.

Are you referring to your perspective or is this what you think I am doing?

If it is the second, you are entirely wrong. I made a serious effort to analyize exactly what we could say about the universe and came to some astounding conclusions. My work is very exact and not fuzzy in any way.

Have fun -- Dick

 

[KingNothing]

Doctordick, I suggest you take your work to a professor, or someone else who knows a ton about this stuff. You aren't going to find a ton of people capable of critiquing your work on a public forum.

 

[Russell E. Rierson]

I get the feeling that we have a very long way to go. All I said in step #1 is that "A" is a set. I placed utterly no constraints on A whatsoever! If no constraints are placed on the definition of the set A, then A can be anything; A could be finite or A could be infinite. Furthermore, as there are no constraints on the definition of the set A, "the probability functions from 'A'" is a meaningless phrase.


I did not say B was a subset of A (to do so would put certain constraints on B which I have not suggested). What I said was that B was a set consisting of a finite collection of elements from the set A (a slightly different concept).

What is important here is that the set A is totally undefined and it is possible that no set B exists in A. In particular, I could define A as a set which contains no two identical elements. I could then define B to be a set of multiple identical elements consisting of a single element taken from A. In that case, B certainly would not be a subset of A. The important issue here is that absolutely no constraints be placed on A.

I appreciate your reply sir.

[1.] If B is not a subset of A, then what is the correspondence from A to B? Is it a mapping? What is the state transition sequencing/relation from A to B? Of course, if A is undefined, it can have zero constraints.

[2.] Is A[in the physical sense] a form of primordial existence, tentatively speaking?

[3.] If A has no constraints then does A have infinite symmetry?

 

[Doctordick]

What part of "undefined" do you not understand?

I appreciate your reply sir.

[1.] If B is not a subset of A, then what is the correspondence from A to B? Is it a mapping? What is the state transition sequencing/relation from A to B? Of course, if A is undefined, it can have zero constraints.

A is undefined; the only purpose A serves is to be the definition of elements which go to make up B. Thus B is also completely open and unconstrained except for the fact that it is a finite set. C is also undefined except for the fact that it is a finite collection of sets B. Our problem is to explain A given C.

[2.] Is A[in the physical sense] a form of primordial existence, tentatively speaking?

A is undefined! It is what ever you wish it to be. You may define it anyway you want and the deduction I have put forth is valid. If the concept of abstract thought is over your head, you need to think about it a little. If I say one plus one is two, do you feel a need to ask the question "one what?"

[3.] If A has no constraints then does A have infinite symmetry?

A is undefined! Even more important than the fact that A is undefined is the fact that we don't know anything about A except what is contained in C.

Why does this theorem apply to reality? Why because we cannot define reality until we understand it and, no matter how much we know, we have to accept the fact that there may be things we do not know. Thus there is a great difference between what we are trying to explain and what we have to work with. The inherent nature of that difference is contained in the difference between A and C.

You are trying to work from the position that you know what reality is and you certainly do not! No one does!

Have fun -- Dick

 

[TeV]

VII. In Einstein's perspective, conventional electro-magnetic phenomena can be shown to be a direct consequence of relativistic effects: i.e., a simple coulomb interaction cannot exist as relativistic shifts in one's coordinate system will create a magnetic interaction. The same thing is true in my perspective; however, when the detailed work is carried out, the resultant four component vector of momentum transfer is transformed into a scalar component related to the $\tau$ axis and a three component vector related to the x, y and z axes. The difference between the character of the two fields is a direct consequence of the momentum quantization in the direction of $\tau$. To make a long story short, magnetic monopoles (which have never been seen) are not a possibility.

!
DocD,now this is curiosity.I've posted the question about possibility of detecting heavy mag. monopoles in low energy density universe such as we live in today (in quantum phys subforum ,but nobody responded).If you take a look at Maxwell equations they become even more symmetric if one considers the existence of the monopoles.
Also,only several years ago,many people would say that a stabile mm particle (rare or not- it doesn't matter) is must- postulated one since it is required in advanced high energy physics models beyond standard model.I don't have problems accepting their existence on high energy scales as we approach GUT level,but I believe there must be a mechanism that would make their life time very short and we cannot detect them in .As you said they have never been seen (despite great efforts in catching them on Earth wandering in universe ; or as indication from high energy production cosmic events..),and new wave of theoretical physicists seriously reconsider how to interpret 'sign' of mms in current candidates for TOEs ( string theories etc).

 

[Antonio Lao]

The magnetic monopole can only be found when the flow of time is stopped. Magnetic force is related to the existence of a velocity (such as sped of light). The force is a timelike force.

But since space and time are intimately connected, when time is zero, space is also zero and the both the spacelike force and the timelike force are all zero. This can happen at the singularity of the big bang or mini-bang black holes.

 

[TeV]

The magnetic monopole can only be found when the flow of time is stopped. Magnetic force is related to the existence of a velocity (such as sped of light). The force is a timelike force.

Antonio,
This is interpretation from the standpoint of classical electrodynamics and classical relativity which doesn't deal with elementary particles.
Maxwell ED perfectly works without any quantization ,without need for postulating particles that carry elementar charges (indeed it treats the source of EM fields in fashion of perfect charge fluid with +/- attributes ).
However,we know today that the our world is world of quanta (unfortunately or fortunatelly ).In 1932 Dirac showed that quantization of electrical charge in form of particle should necessary follow from the quantization of magnetic "charge" .Free elementar particle that carry electrical charge is electron and equivalent for magnetic charge is called magnetic monopole.
Mass of electron is small while mass of hypotetic mm is way way higher.
The "lightest" mm is classical Dirac's monoplole and its' mass is somewhere in GeV range or even TeV range.The heaviest one (heavy monopole) could be the relicts from Big Bang."Intermediate" ones are searched from events generated from cosmic ray bursts etc.
Noone has been found yet.
Current status:
http://arxiv.org/PS_cache/hep-ex/pdf/0302/0302011.pdf

 

[Antonio Lao]

The mass of magnetic monopoles is a different kind of mass. I am postulating two kinds of mass, the potential and the kinetic mass. Inertial and gravitational mass are both the same as potential mass while the mass of the photon (which I believed means its potential mas is zero) is kinetic mass. The momentum of the photon is equivalent to its kinetic mass.

 

[russ_watters]

Ok guys, no one seems to have been able to point out any great flaw in the geometric representation I have proposed in the thread "A Thought Experiment". That is, I believe I have presented a good case that the issue is representation only and not an issue of physical validity. If that is indeed the case, then please allow me to discuss the advantages of my perspective.

Your thought expermint seemed fine. The only problem is it didn't say anything new/different/useful.

 

[Doctordick]

If you take a look at Maxwell equations they become even more symmetric if one considers the existence of the monopoles.

Ah, I have at last reached someone actually working on a decent physics education. I sincerely hope I do not upset you. If I might quote myself in my answer to Russell E. Rierson this morning:

Why does this theorem apply to reality? Why because we cannot define reality until we understand it and, no matter how much we know, we have to accept the fact that there may be things we do not know. Thus there is a great difference between what we are trying to explain and what we have to work with. The inherent nature of that difference is contained in the difference between A and C.

You are trying to work from the position that you know what reality is and you certainly do not! No one does!

You are certainly right that Maxwell's equations are extremely symmetric and clearly admit of a solution amounting to a magnetic monopole; however, against this evidence you must keep in mind that those equations arose through phenomenological expression of known experimental results: i.e., they amount to a way of expressing what was known through experiments.

Maxwell's addition to the known equations of the time was done because he noticed the symmetry which appeared with that addition. Further experiment quickly defended the addition of the component he suggested. Yes, it was a brilliant "guess" of what might be real phenomena; however, the equation was still (after the guess was proved right) a phenomenological result.

My results are not phenomenological at all but are rather deduced from first principals. I have been trying to coach Russell into that deduction; however, I am afraid his familiarity with abstract deduction is severely limited at the moment. Perhaps you might find the post entitled "Derivation from first principals!" easier to understand than he did.

In that deduction, I produce a very fundamental equation. An equation which must apply to any explanation of anything. It turns out, after some serious work, that I can show that Maxwell's equations are an approximation to that equation; however, when Maxwell's equations are produced in that manner, the symmetry which allowed magnetic monopoles in his representation do not arise: i.e., the well known gauge transformations used in E&M are no longer strictly valid. Now, I am not saying that they are invalid but rather that their validity depends on some subtle assumptions which must be made.

To put it another way, deduction of Maxwell's equations from first principals require a specific gauge and include the issue that you are making some approximations in order to obtain that result. If, after you obtain the result, you assume your result is exactly correct (that is, pretend those approximations you made have no significant consequences, which in many cases they don't) then you get back all the gauge transformations ordinarily taught in standard E&M.

Thus it is my position that there is serious experimental evidence that my deduction from first principals is correct. Please, find an error in it if you can; but don't just point out that the academy disagrees with me. I already know that. I am an old man and I gave up on convincing them a long long time ago.

Have fun – Dick

PS – don't let this interfere with your graduate studies as learning standard physics is a very important thing if you want to understand the universe. You are severely limited if you don't understand exactly how the physicists came to the conclusions they did. Let our conversation be a simple personal discussion with no real significant consequences.

 

[TeV]

The momentum of the photon is equivalent to its kinetic mass.

Hmm,how about a little dimensional analizing here.
You probably wanted to say "proportional" instead of "equivalent".
In my language word equivalent =the same,equal.
Certainly,dimensionaly mass and momentum aren't equivalent.

 

[Antonio Lao]

TeV,

Yeah. You are right. This needs dimensional analysis. This was my problem since the beginning. The two kinds of mass: potential and kinetic that I'm surmising can only be described by the use of matrices. When these matrices are mutliplied together numbers can be factored that seem to or be forced to agree with experimental values. The only evidence I have is the mass ratio of proton and electron. I got a number of 1832, the experiment is 1836.

In one other part of my research, I am making another assertion that force is equivalent to spacetime.

 

[Doctordick]

In one other part of my research, I am making another assertion that force is equivalent to spacetime.

And could you explain exactly why you would make such an assertion?

Have fun -- Dick

 

[Doctordick]

Back to the original issue!

There exist a couple of subtle aspects of the model so far described. Of very great significance is the fact that the goal was to create a model which will model any explanation of A obtained from C. The specific mapping of the labels for the elements of C are part of the model and not a given aspect of the phenomena to be modeled: i.e., not at all part of A. If follows that the $\vec{\Psi}(\vec{x},t)$ yielded by the model cannot be a function of that mapping procedure: i.e., all possible mappings must end up yielding exactly the same probability algorithm (the $\vec{\Psi}(\vec{x},t)$ must yield results consistent with the actual distributions of the elements of B in C independent of the chosen mappings). This fact can be used to prove that $\vec{\Psi}$ must satisfy some very simple partial differential relations.

The process yields three orthogonal differential constraints on $\vec{\Psi}$ in the three dimensional representational space defined by the x, $\tau$ and t axes of the model (if you need clarification on this issue, let me know).

$$\sum_i^n \frac{\partial}{\partial x_i}\vec{\Psi}\,=\,i \kappa_x \vec{\Psi}\,\,,\,\,\sum_i^n \frac{\partial}{\partial\tau_i}\vec{\Psi}\,=\, i\kappa_{\tau}\vec{\Psi}\,\,and\,\,\frac{\partial}{\partial t}\vec{\Psi}\,=\, im\vec{\Psi}$$
​

Well, no one has asked me for clarification so either you all understand why what I wrote is true or have no understanding of the issue "why is it true?" Actually, the issue is quite simple and should be understandable to any high school student of calculus. All you really need to understand is the definition of a partial derivative and the chain rule of calculus. Under the presumption that the second possibility is the most probable, I will exactly explain the rational behind the result. If you are interested in theoretical physics, you should know this kind of thing.

P(B) cannot be dependent on the labeling procedure (the $\vec{\Psi}(\vec{x},t)$ must yield results consistent with the actual distributions of the elements of B in C independent of the chosen mappings). It follows that, since adding a number "a" to the value of every x_i reference label does not alter the reference relationship between any x_i and its associated element of B in any way at all, it cannot change the function P in any way. Thus if we replace every x_i in that expression of $\vec{\Psi}$ with (x_i+a) and look at the resultant calculated value of the probability as a function of a, we know that P(a+$\Delta$a) = P(a). This implies that:

$$\frac{P(a+\Delta a) - P(a)}{\Delta a}\,\,=\,\,0.$$
​

That clearly implies that $\frac{dP}{da}$ is exactly zero. Now, if one understands that a partial derivative is defined to be exactly the same as a regular derivative (if you treat all other variables as constants), the result shown in message 4 is exactly the consequence of the chain rule of calculus.

If one considers a change of variables from (x+a)_i to z_i, the chain rule of calculus allows us to write:

$$\frac{d}{da}\,\,=\,\,\sum_i^n \frac{\partial z_i}{\partial a}\frac{\partial}{\partial z_i}$$
​

but the partial of zi[/sup] with respect a is just 1, a trivial result. Since we cannot change the result of a mathematical algorithm just by changing the name of the variable (which is all substitution of z for x would actually do) we know that

$$\sum_i^n \frac{\partial}{\partial x_i} P\,\,=\,\,0$$
​

Simple substitution will confirm that the expressed constraint on $\vec{\Psi}$ given in message 4 is a solution to the above equation.

I hope you all understood that and found it interesting. It is a very powerful underpinning concept of quantum mechanics. (Note to others, you can stop me from posting such things by either explaining it yourselves or at least commenting that it is common knowledge; anything to let me know you are aware of such things.)

Have fun -- Dick

 

[Antonio Lao]

First hint I got is from the equivalence principle of general relativity. The equivalence of inertial mass and gravitational mass. The spacetime curvature is the same as the gravity force. So that in general relativity the concept of force is replaced by the description of a curvature in spacetime.

The maximum value of the spacetime curvature seems to be found only at the local infinitesimal region of spacetime at the domain of Planck length. So that the intrinsic Gaussian curvature K is given by:

$$K = \frac{1}{ds^2}$$

where $ds^2$ is the spacetime interval. Coincidentally, at this local region, the inner product of two nearly orthogonal forces (timelike force and spacelike force) is also zero along with the spacetime interval being zero.

When this happens, space is splitted into two regions, for want of more appropriate words, we can just call them positive and negative region of space. Each is controlled by what I call the true quantum of square of energy. A positive square and a negative square.

 

[Doctordick]

First hint I got is from the equivalence principle of general relativity. The equivalence of inertial mass and gravitational mass.

One of the worst things one can do in theoretical physics is to try to intuitively extend the mathematics to new presumed results without understanding exactly what specific definitions of the terms in the mathematical model are.

Mathematics is a very powerful tool but it only applies to reality when specific things defined in the mathematics bear an exact one to one mapping into physical reality. Most of the common translations of relativity into English discussion of consequences tend to be somewhat loose in definition.

So that the intrinsic Gaussian curvature K is given by:

$$K = \frac{1}{ds^2}$$

where $ds^2$ is the spacetime interval.

The expression you give is not a spacetime interval. You also misuse the term "force" in the extention of your argument.

Could I ask if you can follow the mathematics in my posts? At this point, what I have said is mathematics only and has no bearing on reality as I have made no mapping between that mathematics and reality. These are no more than important mathematical relations I intend to use.

Think of it as a map maker telling you that he is going to use various colors, line types (thin, broad, or dotted). That would be a quick and obvious step in map making but in laying out the mathematics one is going to use, the process is a little longer as mathematics is a complex and extensive mechanism of notation.

Have fun -- Dick

 

[Antonio Lao]

Dick,

Is it correct to say that it is a quadratic form of a metric (distance and length are defined)?

 

[Antonio Lao]

Dick,

The timelike force is related to the magnetic force and the spacelike force is related to the electric force. These forces exist prior to the definition of what is an electric charge? When charge is defined then electric and magnetic properties are also defined. Properties such as the permeability and permittivity of matter and vacuum.

 

[Doctordick]

Dick,

Is it correct to say that it is a quadratic form of a metric (distance and length are defined)?

Physics is supposed to be an "exact science"; if you cannot define your terms "exactly" then we are discussing psudo science, not physics.

 

[Doctordick]

Dick,

The timelike force is related to the magnetic force and the spacelike force is related to the electric force. These forces exist prior to the definition of what is an electric charge? When charge is defined then electric and magnetic properties are also defined. Properties such as the permeability and permittivity of matter and vacuum.

Again, I am afraid these are just vague allusions to definition. You seem to be basing your discussion on popular notions of physics and not on succinct examinable definitions. Physics is not a simple subject. When you follow something like Dr. Feynman's lectures, you are hearing vague generalizations; however, behind those vague generalizations are very specific thoughts.

The problem is that the important specific thoughts in physics are, for the most part, only communicable with mathematics. Just as maps are only meaningful when you can tell the difference between various lines and icons. In physics, you need to be able to put your thoughts into well defined mathematical expressions before you can talk about relations between those ideas.

I think you are in way over your head. You need to learn basic physics before going off into flights of fancy. I notice that you have not responded to my question about your ability to understand my post on partial derivatives and the validity of the resultant expressions given in post #4:

$$\sum_i^n \frac{\partial}{\partial x_i}\vec{\Psi}\,=\, i \kappa_x \vec{\Psi}\,\,,\,\,\sum_i^n \frac{\partial}{\partial\tau_i}\vec{\Psi}\,=\, i\kappa_{\tau}\vec{\Psi}\,\,and\,\,\frac{\partial}{\partial t}\vec{\Psi}\,=\, im\vec{\Psi}$$
​

If you cannot understand that mathematical step, you cannot understand the theoretical underpinnings of modern physics.

Is there anyone out there reading this forum who can help me with this?

Have fun -- Dick

 

[Russell E. Rierson]

The timelike force is related to the magnetic force and the spacelike force is related to the electric force. These forces exist prior to the definition of what is an electric charge? When charge is defined then electric and magnetic properties are also defined. Properties such as the permeability and permittivity of matter and vacuum.

Interesting explanation Antonio. It seems that elctromagnetism is spacelike and gravitation is timelike.

 

[Russell E. Rierson]

Derivation of Doctor Dicks Fundamental Equation -- Part II

There exist a couple of subtle aspects of the model so far described. Of very great significance is the fact that the goal was to create a model which will model any explanation of A obtained from C. The specific mapping of the labels for the elements of C are part of the model and not a given aspect of the phenomena to be modeled: i.e., not at all part of A. If follows that the $\vec{\Psi}(\vec{x},t)$ yielded by the model cannot be a function of that mapping procedure: i.e., all possible mappings must end up yielding exactly the same probability algorithm (the $\vec{\Psi}(\vec{x},t)$ must yield results consistent with the actual distributions of the elements of B in C independent of the chosen mappings). This fact can be used to prove that $\vec{\Psi}$ must satisfy some very simple partial differential relations.

The process yields three orthogonal differential constraints on $\vec{\Psi}$ in the three dimensional representational space defined by the x, $\tau$ and t axes of the model (if you need clarification on this issue, let me know).

$$\sum_i^n \frac{\partial}{\partial x_i}\vec{\Psi}\,=\, i \kappa_x \vec{\Psi}\,\,,\,\,\sum_i^n \frac{\partial}{\partial\tau_i}\vec{\Psi}\,=\, i\kappa_{\tau}\vec{\Psi}\,\,and\,\,\frac{\partial}{\partial t}\vec{\Psi}\,=\, im\vec{\Psi}$$
​

The final aspect of the model is to actually design a universal rule which is capable of yielding the distributions of the elements of B in C for every possibility. In this regard, it is quite easy to prove that, for any B (any distribution of points in the (x,$\tau$) plane) there exists a corresponding set D (a second distribution of points in the (x,$\tau$) plane), which, under the simple constraint that no two points can be the same, will constrain the distribution of B in C to exactly that distribution, no matter what that distribution might be (if you need clarification on this issue, let me know). The constraint that no two points can be the same is easily enforced by requiring:

$$F \, = \, \sum_{i\not= j}\delta (\vec{x_i}-{\vec{x_j}})\, =\, 0.$$
​

where $\vec{x_k}$ is defined to be the vector in the x, $\tau$ space defined by ($x_k,\tau_k$) and $\delta$ represents the Dirac delta function. This express constraint on the elements of B can be converted into an express constraint on $\vec{\Psi}$ by noting that the proper constraint on $\vec{\Psi}$ is that that $\vec{\Psi}$ must vanish whenever the above constraint on the elements is invalid; i.e., when F is not equal to zero, $\vec{\Psi}$ must be zero. Thus the product of the two must always be zero and the correct constraint on $\vec{\Psi}$ is given by:

$$\sum_{i\not= j}\delta (\vec{x_i}-{\vec{x_j}}) \vec{\Psi}\, =\, 0.$$
​

These four independent constraints on $\vec{\Psi}$ may be expressed in a very succinct form through the use of some very simple well known mathematical tricks.

If one defines a set of anti commuting matrices as follows:

$$[\alpha_{ix}\, , \,\alpha_{jx}]\,\,{\equiv}\,\,\alpha_{ix}\alpha_{jx} \, + \, \alpha_{jx}\alpha_{ix}\,=\,\delta_{ij}$$

$$[\alpha_{i\tau}\, , \,\alpha_{j\tau}]\,=\,\delta_{ij}$$

$$[\beta_{ij}\, , \, \beta_{kl}] \, = \, \delta_{ik} \delta_{jk}$$

$$[\alpha_{ix}\, , \, \beta_{kl}] \, = \, [\alpha_{i\tau}\, , \, \beta_{kl}]\, = 0\, ,\, \, \mbox{ where } \,\, \delta_{ij}\, = \,\left\{ \begin{array}{ll} 0 & \mbox{if i\noy=j}\\ 1 & \mbox{if i=j}.\end{array} \right.$$​

and defines two expressions ( $\vec{\alpha_i}$ = $\alpha_{ix}\hat{x}$ + $\alpha_{i\tau}\hat{\tau}$ and $\vec{\nabla_i} \,=\,\frac{\partial}{\partial x_i}\hat{x}\,+\,\frac{\partial}{\partial\tau_i}\hat{\tau}$ ), a small shift in perspective will allow the four constraints on $\vec{\Psi}$ to be written in a single equation as follows:

$$\left\{\sum_i\vec{\alpha_i}\\,\dot\,\vec{\nabla_i}\,+\, \sum_{i\not=j}\beta_{ij}\delta(\vec{x_i}\,-{\vec{x_j}})\right\} \vec{\Psi}\,\,=\,\,K\frac{\partial}{\partial t}\vec{\Psi}\,= \,iKm\vec{\Psi}$$
​

constrained by the requirement that

$$\sum_i\vec{\alpha_i}\,\vec{\Psi}\,=\,\sum_{i\not=j}\bata_{ij}\,\vec{\Psi}\, =\,0.$$
​

It follows that all explanations of anything may be directly modeled by a set of points in an (x,$\tau$) space moving through a t dimension and required to obey the fundamental equation given above. The probability of any particular set of elements in B being given by

$$P(\vec{x},t) = \vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)dv$$

​

And I have thus successfully created a model of all possible explanations of A consistent with C. The fact that no constraints of any kind were placed on A implies the solution has consequences of great significance to every science under study.

If anyone out there has the gray matter to follow the derivation and is interested in discussing the issues it raises, I am ready to discuss the following issues:

1. Possible errors in my derivation (I will have to leave finding them to you as I am not aware of any errors).
2. How to obtain solutions to the equation and the solutions that I have found.
3. The philosophical implications as to what impact the discovery has on one's mental image of reality.
4. Interpretation of the equation: just what the various parts of the derivation mean.

A spacetime manifold could have a probability in which it embeds a three dimensional, simply connected manifold, that has locally Euclidean metric h_ab.
The simply connected manifold will divide into M^+ and M^- .

It becomes factorized as the product of psi^+ and psi^-

Partial derivatives construct the momentum constraints.

 

[Doctordick]

If anyone out there has the gray matter to follow the derivation and is interested in discussing the issues it raises, I am ready to discuss the following issues:

1. Possible errors in my derivation (I will have to leave finding them to you as I am not aware of any errors).
2. How to obtain solutions to the equation and the solutions that I have found.
3. The philosophical implications as to what impact the discovery has on one's mental image of reality.
4. Interpretation of the equation: just what the various parts of the derivation mean.

You seem to have neglected following the derivation as a prerequisite to a serious discussion. I have some strong suspicions that you did not follow the deduction as, if you had, I think you would have understood why the discussion topics are listed in the order given. You appear to be jumping to #4 without even considering what comes before.

A spacetime manifold could have a probability in which it embeds a three dimensional, simply connected manifold, that has locally Euclidean metric h_ab.
The simply connected manifold will divide into M^+ and M^- .

It becomes factorized as the product of psi^+ and psi^-

Partial derivatives construct the momentum constraints.

What are you trying to say here? Is this supposed to indicate to me that you understood what I wrote down? I have not mentioned a "spacetime manifold" and you have not defined what you mean by the term "spacetime manifold". I have not brought up or defined any concept referred to as "connected" nor have you! Just what does the symbol M^+ refer to and/or the symbol M^-.

It appears to me that you do not understand the difference between fact and theory. Mathematics is a tool! A very valuable tool when it comes to theory development. You, russ_waters and many others on this forum seem to think that I am presenting a theory. Nothing could be further from the truth. What I am setting before you are facts. What I would like you to do is to understand these facts. If you could see them, we could have something to talk about.

I feel a strong kinship with Galileo Galilei. Around 1609 his use of the telescope (which, by the way, he didn't invent) opened his eyes to facts not known to those around him. Some seven years later, he brought down the churches wrath when he attacked the followers of Aristotle, the scientific god of his era. Though he worked very hard to get the church to look through his telescope, and see what he saw, he failed utterly. He died over twenty five years later, a convicted heretic. He was lucky as what he was saying did not die with him and today we enjoy the consequences of his thoughts.

My telescope is advanced mathematics. I have pointed it in a direction alien to the practitioners of that field and seen things no one else has seen. I have also incurred the wrath of the academy by arguing against the followers of Einstein, the scientific god of our era. Though I have worked hard to get the academy to look through my telescope, I have also utterly failed. All I get is reasons why what I see cannot possibly be so; exactly the same reason the church wouldn't look through Galileo's telescope.

Please examine what I have put forth on this forum. I haven't presented any theories; I have pointed out facts. Facts you will see if you follow my mathematics. But, if you cannot follow the mathematics, then you can no more see those facts than those who refuse to look. Go look! Examine the truth of the mathematical deduction I have set down. Either it is correct or it is in error. If you don't understand it, tell me what you do not understand and I will do my best to clarify it.

What I have proved is that my "fundamental equation" is true for any collections of theoretical expectations one might have and has utterly nothing to do with the theory behind those expectations or the interpretation of the concepts central to that theory. It is a tool to look at what is reasonable and what is unreasonable regarding probable expectations. How does one look at the universe through my telescope? One looks at the solutions to my fundamental equation and the relations which those solutions require. Without the solutions you have nothing to look at and nothing to argue about.

One of the problems endemic to this forum is that everyone seems to think that they can ignore the facts while they think about their esoteric theories. I suspect most all the mentors know that most every theory put forth here is easily destroyed by the simple expedient of looking at the facts. The problem is that lacking education, most of the posters are simply ignorant of the facts.

Einstein's theories of relativity, both special and general, are "theories", not facts (that is why they are called theories). But the facts that defend his theories are facts. If you are to come up with a theory which is to be seen as reasonable, then you must come up with a specific detailed procedure for deducing exactly the observed facts from that theory. It must agree with the known facts! And it must be consistent with all facts known: i.e., it must not require ignoring any specific facts. And, in addition, you better point out a flaw in the theory you are trying to replace!

This is why very few professional physicists come up with new theories! It is not a trivial endeavor.

In order to think about theories, you must first know and understand the facts. Failure to understand this is exactly the reason the "Theory Development" forum is considered "crackpots are us" heaven. You need to have an education as to what the facts are and popular generalizations of hard scientific results do not qualify as facts even if they are promulgated by recognized authorities!

Have fun but think about it -- Dick

 

[Antonio Lao]

Dick,

For my lack of mathematical knowledge, I will still willing to respond to your math expressions.

1. The sum of all partial derivatives of a certain function with respect to 1-dim space is proportional to the imaginary part of this same function.

2. The sum of all partial derivatives of a certain function with respect to timelike independent variable is proportional to the imaginary part of this same function.

3. the partial with respect to time of this function is proportional to the imaginary part of same function.

Now to say what I intended to do as far as the use of math is concerned are the following:

1. I am getting rid of all uses of derivative (partial or exact). These were partly Newton's doing. We are now beyond that. The partial derivative is a way of dealing with continuous change of continuous functions such as a wave function. All wave functions depend on two keys properties, the wavelength and the frequency. The wavelength is a vector. The frequency is a scalar and it is the inversely proportional of time. I have more to say here but will defer for the time being.

2. I am getting rid of the numeral "zero" in the math I'm using. I am using only Hadamard matrices with elements consist of 1 and -1.

3. There are functions that can only be added together. I call them Hamiltonian functions. To me, the true Hamiltonian is a function that gives the square of energy. Only Hamiltonian possesses a quantum.

4. There are functions that can only be subtracted. I call them Lagrangian functions. These do not have a quantum.

More to say on all of these working principles of my research.