Why you should like my perspective

[quddusaliquddus]

I think that is about as rude and inconsiderate that one can get!

The difference is that you deserve it.

 

[Doctordick]

Russell,

Sorry about the delay in my response to your last note but I wanted to try my best to do a decent job of communicating with you as you seem to be the only person who has begun to see the problem here. Plus that I have been very busy, first with issues around the house – plans for the summer – etc., etc..

It appears that you have reached a very high level of abstraction and that becomes the difficulty with communication IMHO. So your fellow physics forum participants must also endeavor to think ...abstractly. Communication is a two way street. We must also try harder to see what you are trying to communicate.

You have hit the nail exactly on the head. What I am trying to communicate is totally alien to the standard scientific approach. It stands by itself without any outside support and it can be refuted only with regard to itself: i.e., that there is something I am assuming can be done which cannot be done or one of the steps in my logic is flawed. To judge it because it does not jive with your current ideas is not a valid attack at all.

Now to say it is not worth looking at is another valid complaint. Perhaps it is not, but to make that judgment without understanding it can not be called a rational decision, it is nothing but an opinion. Personally, I think it is a very valuable observation and I think it has applications throughout science. But again, that is only an opinion; however, I do understand what I am trying to explain which puts me in a different boat.

I don't really think it is difficult to understand; not if it is taken one step at a time.

Thank you very much for the references:

I think Dr. Thooft is trying to do something very important and I wish him all the luck in the world. I also enjoyed your reference to Chaitin very much! I wasted a lot of time reading it (there are other things I should be doing). I sure wish someone like him would talk to me; he seems to be a very rational person.

Pardon me if I pull out one thing he said:

Let me give an example involving Fermat's ``last theorem'', namely the assertion that

xⁿ + yⁿ = zⁿ

has no solutions in positive integers x, y, z, and n with n greater than 2. Andrew Wiles's recent proof of this is hundreds of pages long, but, probably, a century or two from now there will be a one-page proof! But that one-page proof will require a whole book inventing a theory with concepts that are the natural concepts for thinking about Fermat's last theorem. And when you work with those concepts it'll appear immediately obvious---Wiles's proof will be a trivial afterthought---because you'll have imbedded it in the appropriate theoretical context.

I think the single most important phrase in that quote is "imbedded in the appropriate theoretical context". With regard to my work, it must be examined in the appropriate context or it cannot be understood. That is the major problem I have: trying to get people to lay aside what they "know is true".

A normal human being has a fundamentally complete mental image of the world long before even beginning any formal education. That image cannot possibly be characterized as well thought out.[/color] Clearly, one must admit the possibility that thousands upon thousands of insupportable presumptions could have already taken place.

Speaking of mathematics, I have never seen mathematics as a stagnant field. Mathematicians continually define new things and new relationships. And, physicists do also. Since math is the central language of communications in physics, physicists probably introduce more mathematical ideas than even professional mathematicians. Dirac produced quite a lot of opposition to his function \delta(x) when he first introduced it; however, mathematicians now regard it as a well defined mathematical object.

If you look at the thread, "A serious math question!", you will see that I am currently embroiled in the defense of a mathematical issue. The issue has to do with the fact that I use the chain rule of calculus to define the consequence of applying the derivative operator on \vec{\Psi_1}\vec{\Psi_2} when the product has not been defined! If you look at the thread, you will discover that the only response making any attempt to help me clarify the problem is from Hurkyl. I appreciate his comments very much but his help has come in the form of standard rules of mathematics and not from the perspective of logical analysis based on fundamentals.

I only brought that up because it is a very easy error to fall into. Physics and mathematics are both very complex subjects with much professional analysis already done. One problem with this is that people (for convenience sake) come up with shorthand notations which come close to looking logical on its face. (In fact, if that is not true of their shorthand representation, it is not really a good notation.) They use that notation because it is an uncluttered way of keeping track of very complex ideas. However, it must always be remembered that all shorthand notation suppresses much detailed information as understood.

I have noticed many times where students will manipulate this shorthand as if they know exactly what it all means when, in fact, all they are working on is the gross generalizations some paper has given them and they have no idea what the notation actually means and what kinds of errors can be made if one does not understand the details being suppressed. Feynman's diagrams for the expansion of terms in a scattering calculation are a good example. On occasion, I have asked students who give every appearance of understanding the field well (as taken from their facile use of the jargon), to write down the actual integral which has to be done as indicated by a particular Feynman graph. Only on very rare occasions will the student even begin to write down the terms in that integral. Most often they just look at me with their mouths open.

I could be wrong but you seem to have a penchant for using notation as if the meaning of the notation is well understood. Usually the notation is only well understood by the people working directly with the stuff on a daily basis. It's fine for internal communication but very seldom is of any use outside the particular group using it. It may take some work but people who do use it can usually explain in detail exactly what each element of the notations stands for and why it is there. Plus, they can point out all the stuff which is suppressed as understood.

If one ever wants to discuss the logic of the underlying aspects of the things represented by the shorthand, you must acquire a good understanding of what the shorthand stands for. Once you have done that, anyone is as qualified as anyone else to discuss the logic of the actual approach. Knowing the jargon is immaterial to the logic issue. You certainly know that jargon is not what makes an electric motor work. (I looked at your profile.)

This is exactly why Dr. Thooft makes so much of "what should be taught to the beginning student". One of the worst things a student can do is to go directly to advanced work (which is usually chock full of jargon) without learning the details of the underlying fundamentals. Knowing and understanding are very different things. And a facile familiarity with the jargon seldom assists understanding. It rather masks the subject so that one can have that emotional feeling that they understand it.

If you really want to understand something, you have to make good use of the KISS principle (Keep It Simple Stupid). I have tried to do that but everyone seems to want to lather what I say with all kinds of peripheral trash.

At the moment, these threads have become so lathered over with Trollish Trash that I am searching down the key posts so that I can quickly refer to them rather than repeating myself over and over.

Back to the point of the thread, do you now understand that all possible rules may be written in the form F=0. That is, do you have any questions about the following post?

https://www.physicsforums.com/showthread.php?p=213403#post213403

Sorry to be giving you so little attention lately. I had hoped that baffledMatt might have the wherewithal to follow me easily. But that effort was clearly a failure. I really can't blame him as he is deep in trying to understand other difficult things at the moment, but I am sorry it cut into our conversation.

Looking forward to hearing from you – I will try to be a little more attentive in the future.

Have fun -- Dick

 

[PFanalog57]

Now I get to that second issue. In the model for explanation I am building (through definition), the rules cannot depend upon t as t is a complete figment of my imagination. But I wanted t to map into the common conception of time used by scientists. Since a lot of phenomena discussed in physics are explained as time dependent phenomena, the specific time of an observation has to be recoverable from that observation: i.e., there must be a way of recovering the proper t from each and every observation. Essentially, this means that t must be implicitly defined by the observation itself (it cannot be explicitly defined as t is a complete figment of the model).

IMHO, you make a very good, if subtle, point about time Dr. D. There is an invariance with time, in that things only experience the "present" moment, while observing everything else, in varying "past" moments.

What I have really pointed out is the fact that there is a duality in common construction of theories. The rules are a consequence of the things which are conceived of as existing and the things which must exist are a consequence of the rules. Changing the rules changes what must exist. Changing what you allow to exist changes what rules these things must follow. If you are really after the simplest explanation, leaving both these issues open just complicates the problem. I have just shown that the rule F=0 can explain any arbitrary circumstance and F=0 is certainly a very simple rule. Can any of you give me a good reason why we should not simply say the rule is F=0 and consider what has to exist to make the rule true?

In fact, I can go through the effort of showing that any explanation with any rule can be mapped into an explanation relying on F=0. If that is true, then it seems to me that allowing any other rule does little more than complicate your explanation, particularly if that explanation is dependent on vague and ambiguous definitions.

If one ever wants to discuss the logic of the underlying aspects of the things represented by the shorthand, you must acquire a good understanding of what the shorthand stands for. Once you have done that, anyone is as qualified as anyone else to discuss the logic of the actual approach. Knowing the jargon is immaterial to the logic issue.

Shorthand is a form of symbolism and if one knows the rules for manipulating the symbols, then the derivation will be correct? Eliminate the semantics as much as possible. That is what you are doing with your "x" references/associations onto the real numbers...? Tautologies of logic are non-semantical...

Back to the point of the thread, do you now understand that all possible rules may be written in the form F=0. That is, do you have any questions about the following post?

All equations can be arranged, such, that F = 0...

Please proceed...

 

[Doctordick]

IMHO, you make a very good, if subtle, point about time Dr. D. There is an invariance with time, in that things only experience the "present" moment, while observing everything else, in varying "past" moments.

I think you have seen a very important aspect of reality. Particularly if you go along with Newton ("action at a distance is clearly an impossible thing") and with Einstein ("One can give good reasons why reality cannot at all be represented by a continuous field"). If action at a distance is impossible and field theories are to be doubted, all we have left are "contact" interactions (Dirac's delta function). If that is the case, "time" only has meaning to any pair of entities in that, if they exist at the same time, they can interact. Any other meaning given to time is a construct of someone's theory.

Now I need to clear up a subtle issue here. I have not "assumed" that everything can be reduced to a Dirac type interaction; I have proved that, through the creation of suitable unknowable information, a Dirac type interaction can constrain "C" to whatever "C" happens to be. Quite a different statement and a very powerful proof.

Shorthand is a form of symbolism and if one knows the rules for manipulating the symbols, then the derivation will be correct? Eliminate the semantics as much as possible. That is what you are doing with your "x" references/associations onto the real numbers...? Tautologies of logic are non-semantical...

Exactly, but one must be very careful that they know exactly what the shorthand stands for. An error in interpretation can be a very serious error.

All equations can be arranged, such, that F = 0...

Your comment disturbs me slightly. The statement that "all equations can be arranged such that F=0" (though it is certainly true) is slightly askew of what I am saying. Perhaps what I am saying can be deduced from that statement; however, I have proved that the proper collection of "D" together with a Dirac type interaction term can always constrain "C" to exactly what is observed. Personally, I would have to assert that the proof is more to the point than your assertion.

It occurs to me that we actually haven't discussed that issue. In our conversation I have merely shown that there always exists an F=0 function which, together with a specific set of "unknowables" ("D") will constrain "C" to whatever is seen. We have not actually discussed the proof of the Dirac interaction. That proof may be found in Chapter 1, Part IV of my book at

http://home.jam.rr.com/dicksfiles/

Check out equations 1.21 through equation 1.25.

From your responses I am presuming that you have now accepted my proof of the constraints up to my comment in message #4 of this thread: "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". In order to understand that statement, one must understand "anti-commuting" operators and how to use them. I need to ask you if you understand the mechanics of manipulating anti-commuting entities.

The essence of the proof that \vec{\Psi} must satisfy my fundamental equation rests with a proof that the constraints already shown as necessary can be recovered from any solution to that equation: i.e., that any solution to my fundamental equation will satisfy the constraints already laid out and secondly, it must be shown that there exist no solutions satisfying the given constraints which will not be solutions to my fundamental equation. If you understand the nature of that circumstance, I will go directly to the proof that the fundamental equation must be true.

Thank you for making an attempt to follow my logic.

Have fun – Dick

PS I may be a little slow to answer future posts as I have just received a very interesting piece of software which will probably engross my interest greatly. I will try and check this forum at least once a day. Have fun everybody.

 

[PFanalog57]

...one must understand "anti-commuting" operators and how to use them. I need to ask you if you understand the mechanics of manipulating anti-commuting entities.

Commute:

AB = BA

Anti-commute:

AB = -BA

 

[Doctordick]

Proof of validity of the Fundamental Equation.

Hi Russell,

Hope you can follow this! If you have any questions, let me know.

The essence of the proof that \vec{\Psi} must satisfy my fundamental equation rests with a proof that the constraints already shown as necessary can be recovered from any solution to that equation: i.e., that any solution to my fundamental equation will satisfy the constraints already laid out and secondly, it must be shown that there exist no solutions satisfying the given constraints which will not be solutions to my fundamental equation.

The first step is to note that, from the definition of \alpha_{ix}, we know that \alpha_{kx}\alpha_{ix}\,=\,-\alpha_{ix}\alpha_{kx} + \delta_{ik}. We then left multiply the fundamental equation by \alpha_{kx} (left multiply means \alpha_{kx} is on the left of the expressions in the equation).

[Well, I just discovered a Latex error in the fundamental equation as shown in message #4 of this thread. I have corrected the error. If anybody sees any errors in anything I say, please point them out to me. I would appreciate it very much and it would do nothing but raise my opinion of whoever noticed it.]

Back to the issue at hand! Since the sum over i in the fundamental equation is over all events (both knowable and unknowable), i=k will occur exactly once in that sum and commuting \alpha_{kx} with the other \alpha and \beta yields a simple sign change. (Note that, since these matrices are not functions of x, \tau or t, \alpha_{kx} commutes with the various partial derivatives.) The result will be:

\frac{\partial}{\partial x_k}\vec{\Psi}-\left\{\sum_i\vec{\alpha_i}\,\cdot\,\vec{\nabla_i}\,+\,<br /> \sum_{i\not=j}\beta_{ij}\delta(\vec{x_i}\,-{\vec{x_j}})\right\}\alpha_{kx}<br /> \vec{\Psi}\,\,=\,\,K\frac{\partial}{\partial t}\alpha_{kx}\vec{\Psi}

<br /> =\,iKm\alpha_{kx}\vec{\Psi}
​

If the above expression is summed over all k, since \sum_k\alpha_k \vec{\Psi}\equiv0, only the first term survives. Thus we know that, if \vec{\Psi} is a solution to the fundamental equation, it is also a solution to the equation

\sum_k \frac{\partial}{\partial x_k}\vec{\Psi}\,=\,0.
​

This seems to be quite different from the original constraint. That difference is the source of the "small shift in perspective" which I mentioned in message #4. If \vec{\Psi}_0 is a solution to the above equation, simple substitution will confirm that

\vec{\Psi}_1\,=\,\displaystyle{e^{\frac{i}{n}{\sum_{i=1}^n}\kappa x_i}}\vec{\Psi}_0
​

is a solution to

<br /> \sum_{i=1}^n \frac{\partial}{\partial x_i}\vec{\Psi}_1\,=\, i \kappa\vec{\Psi}_1\,.
​

Exactly the same process will pull out the constraint on the \tau axis. The F=0 constraint is zero already so that the result of using the commutation properties of \beta_{ij} to isolate F yields exactly the correct constraint.

Anyone who is familiar with quantum mechanics will recognize this as essentially the mechanism to shift a many particle wave function into a new frame of reference moving with respect to the first. Of course, the partial differential corresponds to the momentum operator of standard quantum mechanics. This whole collection of relationships will be obvious to anyone with a basic education in beginning quantum.

In fact, it is precisely the presumption of shift symmetry [P(x+a) =P(x)] in quantum which is used to establish conservation of momentum. (The only real difference between my development of that constraint and the common physics notion is that my development does not constitute an assumption: it is instead a direct consequence of the arbitrary[/color] labeling of those as yet undefined references we started with.)

Since, in standard beginning quantum mechanics, the \kappa=0 solution of the many particle wave function only exists in the "center of mass" reference frame (when the total momentum of the system is zero), I will define my fundamental equation as valid only in the "center of mass" reference frame! Just as Newton's equation F=ma is valid only in an inertial frame, my equation is only valid in the frame where the partials with respect to x and \tau summed over all \vec{x_i} vanish.

Finally, general differential with respect to t may need to be a constant but there is no constraint that the constant be related to the left side of the fundamental equation. However, once again, if \vec{\Psi}_0 is a solution with m=0, simple substitution will confirm that

\vec{\Psi}_1\,=\,e^{i Mt}\vec{\Psi}_0
​

is a solution to for m=M no matter what M may be desired.

The other side of the coin is equally easy to defend. Any solution which fits the four constraints may be adjusted to one which is a solution to the fundamental equation. I have proved that any explanation of anything may be cast into a form which requires my fundamental equation to be valid. Except for the use of the term "The Universe" to represent "an explanation of anything" this is exactly the purpose of Chapter I of "The Foundation of Physical Reality".

[QUOTE="The Foundation of Physical Reality", Chapter I]So, let us review exactly what has been accomplished in this opening chapter. First, I have constructed a mental model of "The Universe". It is admittedly an extremely simple model in that it consists of nothing more than points in a two dimensional Euclidean space who's position in that space is a function of time. It may be a simple model but it holds forth three very important aspects: first, it is very well defined and thus easy to understand; second, it is complete as there exists no communicable concept of reality which is not representable by this model and finally, we have a very specific method of answering any question asked together with the fact that the answer (i.e., the probability of any given answer) must obey an apparently simple equation.[/QUOTE]

At this point I have defined only thirteen concepts outside of mathematics itself.

-->"mathematics"; a set of logical relationships and definitions understood by enough people to provide decently unambiguous communication.
-->"A"; Whatever it is we wish to explain; the Universe, a problem, an explation…
-->"B"; That finite set of elements of A available to us which our explanation must absolutely explain.
-->"knowable"; elements of B which are elements of A.
-->"C"; A finite collection of sets B; all knowledge which is available to us from which we must create our model. ("C" is "knowable" information).
-->"D"; A finite collection of hypothetical sets analogous to B which are required by our explanation.
-->"unknowable"; elements attached to B which are not elements of A; hypothetical aspects of D.
-->"\vec{x_i}"; an arbitrary numerical label assigned to references to the elements of a given B_j plus those references in D attached to B_j
-->"time" an arbitrary numerical label attached to "B_j" plus the "unknowables" attached to that particular "B_j".
-->"observation"; A collection of references \vec{x_i}(t) which label all the "knowables" and "unknowables" of a particular B_j.
-->"past"; observations available to a test of the explanation.
-->"future"; observations not available to a test of the explanation.
-->"\vec{\Psi}(\vec{x},t)"; an arbitrary mathematical algorithm which will deliver a measure of the expectations for B_j given the associated observation via a normalized inner product with its adjoint {P(B_j)}.
-->"Center of mass coordinate system"; the abstract Euclidian coordinate system where the fundamental equation is valid.
​

If you can understand and accept the above, then all that is left is to find the solutions to the fundamental equation. Again, as I show you the solutions, I will define further concepts convenient to talking about those solutions.

Have fun -- Dick

 

[PFanalog57]

At this point I have defined only thirteen concepts outside of mathematics itself.

-->"mathematics"; a set of logical relationships and definitions understood by enough people to provide decently unambiguous communication.
-->"A"; Whatever it is we wish to explain; the Universe, a problem, an explation…
-->"B"; That finite set of elements of A available to us which our explanation must absolutely explain.
-->"knowable"; elements of B which are elements of A.
-->"C"; A finite collection of sets B; all knowledge which is available to us from which we must create our model. ("C" is "knowable" information).
-->"D"; A finite collection of hypothetical sets analogous to B which are required by our explanation.
-->"unknowable"; elements attached to B which are not elements of A; hypothetical aspects of D.
-->"\vec{x_i}"; an arbitrary numerical label assigned to references to the elements of a given B_j plus those references in D attached to B_j
-->"time" an arbitrary numerical label attached to "B_j" plus the "unknowables" attached to that particular "B_j".
-->"observation"; A collection of references \vec{x_i}(t) which label all the "knowables" and "unknowables" of a particular B_j.
-->"past"; observations available to a test of the explanation.
-->"future"; observations not available to a test of the explanation.
-->"\vec{\Psi}(\vec{x},t)"; an arbitrary mathematical algorithm which will deliver a measure of the expectations for B_j given the associated observation via a normalized inner product with its adjoint {P(B_j)}.
-->"Center of mass coordinate system"; the abstract Euclidian coordinate system where the fundamental equation is valid.
​

If you can understand and accept the above, then all that is left is to find the solutions to the fundamental equation. Again, as I show you the solutions, I will define further concepts convenient to talking about those solutions.

The solutions for "quantum gravity" would be especially interesting.

Please continue