Showing posts with label Number Theory. Show all posts
Showing posts with label Number Theory. Show all posts

Sunday, February 15, 2015

RESPONSE TO COMMENTS BY A REVIEWER



Dear _____,

First of all, I want to thank you for your continuing interest in what Vernon and I are trying to do. As I think you know, we have asked a substantial number of people, scientists, mathematicians, philosophers, and serious thinkers of various kinds, to review our work. The most important of these reviewers, from my point of view, are those with sufficient training in mathematics and physics to be able to understand the basic concepts underlying Transcendental Physics and TDVP. These thinkers, one would hope, would be very open-minded and objective. However, based on the comments and statements of those who have responded to date, open-mindedness is quite rare. In, my opinion, those who have commented fall into of one the following categories:

1.)  Those who assume we don’t know what we are talking about. Their approach is to look for obvious errors and be done with us.
2.)  Those who have unconventional theories of their own. Their approach is to determine to what extent our ideas might support theirs. When they find at some point that they do not, they quickly lose interest.
3.)  Those with heavily vested interest in the so-called Standard Model. As with group #1, they search for any error at all to discredit our ideas because, if we are right, the paradigm they have invested their lives in must be wrong, and their life’s work is threatened. Our experience shows that they will do anything they can to defend the current paradigm.
4.)  Those who are truly open minded, as all scientists should be, and are willing to follow the logic of new ideas wherever it leads, even when the results conflict with their life’s work and/or their own belief system. So far, our experience is that such minds are very few and far between.

I have found that discussions with people in the first three categories are largely a waste of time. The first two have no interest in anything outside their own ideas, or ideas with which they are familiar, and people in the third group have no interest in anything outside the box of the current materialistic paradigm. I think you can probably identify some individuals in the discussions of the past couple of years who fall in to these categories. Two or three, for example, who sought to find flaws in the math, started by criticizing references to, and use of, some simple, basic mathematical concepts, but failed to understand the significance of these concepts in the new paradigm. Next, they offered counter examples to certain mathematical proofs and conclusions. When I pointed out flaws in their reasoning, they at first grudgingly admitted a mistake or two, and then got upset. One even told me that the discussion was not about criticizing his ideas. He even posted that he had “refuted” certain of my arguments, when it was easy to show that he had not.

I want to address your comments, but first, please permit me to recount a little more history to put the current discussions into proper perspective:

After studying the works of Planck, Einstein, Minkowski, Lorentz, Schrödinger, Bohr, and Heisenberg, while I was an undergrad physics student, I was convinced as early as 1956, that a theory of everything, even if it was defined only as a theory that would unify the known forces of nature, was not possible without including the actions of consciousness in the equations. I wrote about this around 1957 - 1959 or so. I also recognized that new math was needed, and that I needed to know more about number theory. I earned a degree in mathematics in 1962, and started in a graduate program in theoretical physics. I also found the basis for the new math I needed in George Spencer Brown’s ‘Laws of Form’ in 1962; coincidentally about the same time I studied John Bell’s inequality theorem and learned of Alain Aspect’s experimental resolution of the EPR paradox.

I developed the Calculus of Distinctions to deal with the interaction of consciousness and physical reality; and I first published some of the results of including consciousness in the equations in 1989 in “Infinite Continuity”. Prior to publication, I sent a copy of the manuscript to Stephen Hawking for review. He had a problem with the concept of three-dimensional time and rejected, out of hand the idea that consciousness had anything to do with reality at the quantum level.

I expanded some of the ideas, and published them again in ‘Transcendental Physics’ in 1996. My ideas were accepted and heralded as the new paradigm uniting relativity and quantum physics by several, including experimental physicist Dr. Henry Swift and astrophysicist Dr. Philip Anderson. It was discussed for months on the Karl Jaspers Forum and other internet forums and in the journal “Science within Consciousness” in the period 1996 – 1998. One participant suggested that I should be careful about sharing my ideas so freely on the internet, because “the ideas clearly represent a new paradigm, and unscrupulous individuals will steal them and call them their own.” Another participant quipped: “If you have something truly new, no one will steal it. You’ll have to cram it down their throats!” Unfortunately, the second comment proved to be the more accurate. Most people it seems, even scientists, believe that if they don’t understand something immediately, it must be wrong. As Max Planck said, “Science advances one funeral at a time.”

Now, on to your comments:  I am thankful for your comments because they give me an opportunity to more fully explain the concepts underlying the mathematics of TDVP. I will copy from your email and then respond:

You wrote:
“Here´s some new feedback, specifically about theoretical physics (or at least its required methods) within your theories, but not about the *whole* TDVP theory (except physics, possibly extended to broader, non-materialist realms), and especially about QM (again) in relation to your (or Ed's) 9 dim. Spin model:

When I first mentioned to you in some mails years ago theories with hidden
variables in QM (David Bohm), and now when you have a 9D spin model with apparently more detailed variables, I point to the necessity of QM again, or at least consistency with experiments.”

My response:
You refer to ‘hidden variables’. This term, as used in QM, refers to attempts by some physicists, notably David Bohm, Eugene Wigner, and a few others, to explain the non-locality quantum entanglement of Bell’s inequality and the EPR paradox in terms of underlying, inaccessible variables which, if there, would validate Einstein’s opinion that QM as developed by Bohr and Heisenberg was incomplete, and eliminate, theoretically, the probabilistic uncertainty formalized by Heisenberg’s Uncertainty Principle.

The additional variables of TRUE units in TDVP are in no way hidden variables of this sort. They are hidden only in the sense that they are not directly measurable. The magnitudes of TRUE units, including mass, energy and gimmel (the third form) for specific sub-atomic entities are all indirectly determinable, like many things in science. The amount of gimmel in a given particle does not affect the quantum uncertainty between the measurements of location and angular momentum any more than the amount of mass or energy in the particle does. Heisenberg’s relationship of probabilistic uncertainty is not affected by Gimmel, an indirectly measurable variable combining with units of mass and energy to make up the TRUE quantum units of all stable particles, and thus they are not ‘hidden’ variables in the sense proposed by Bohm, et al.

You wrote:
“I do not see how the use of integers only will improve consistency with the known QM framework and the experiments; there needs to be some randomization as well i -strongly-suspect. The reason is, like I posted, because of the (statistical nature of the) measurements.

My response:
Let me explain the importance of using integers in the analysis of the combination of elementary particles to form stable compound particles like protons and neutrons: Planck’s discovery that elementary particles are always integer multiples of a basic unit means that we are dealing with discrete, as opposed to continuous values in the statistical analysis of collider data. A discrete random variable has a very different probability distribution than a continuous random variable, and functions representing compound entities formed by the combination of integral numbers of basic units can only have integer values. This means we are dealing with equations with integer variables, known to mathematicians as Diophantine equations. I’ll elaborate on this more as I respond to your further comments.

You wrote:
In some way with some quantum logic Ed or your other math assistant might
be able to add this to this spin-model, in order to generate the most common
QM experiments, but it won't be easy.

My response:
This has already been done. And, while it wasn’t as difficult as you might imagine, it may be hard to grasp at first. This is actually what Dimensional Extrapolation with unitary extensions and integer solutions to the Conveyance Equations in TRUE units are all about. The 9-D spin model is an outcome of the mathematics, not the other way around.

You wrote:
“For the rest when describing physics at the Planck scale, just a 9D spin model is not enough of course, because it's not only *particle* spin,  there also is QM involved with (mass-less) *photons*, and in fact with a  whole  of other particles (some with rapid decay); called the particle 'zoo'. In fact the existence of most of these particles seems to come out of the quantum field theories inherent in the Standard Model, but that's another -and slightly broader- subject.”

My response:
Actually, the mathematics of TDVP accurately encompasses all known QM processes. The derivation of TRUE units is fully consistent with, and actually dependent upon the statistical nature of the quantum measurements of collider data. TDVP is also consistent with the existence of mass-less photons and the entire ‘particle zoo’. All of the particles detected in the debris from high-energy collisions decay under ‘normal’ conditions into photons, electrons and up- and down-quarks, the four sub-atomic entities that make up the physical structures of our everyday world. The other particles are teased into existence by high-energy collisions here on Earth, or are naturally produced in extreme conditions of heat and pressure like those in stellar processes. This becomes clear in the 9-D integral model. TRUE units describe the total mass/energy/consciousness composition of sub-atomic particles under normal conditions. Only the particle combinations with the TRUE unit values that satisfy integer solutions of the Conveyance Equation for n = m = 3, dictated by Fermat’s Last Theorem achieve symmetric stability.

You wrote:
“Now  I understand you or Ed have to start somewhere within the TDVP framework, i.e. with the 9D particle spin model, but then this would  only be a (minor) start, and certainly not a description or foundation of some 'new physics' or new paradigm in physics at large.”

My response:
As you might gather from my explanations above, I strongly disagree with this statement. While our presentations, as you say, must ‘start somewhere’, as a new paradigm, TDVP does not start with randomly chosen concepts. As a new paradigm must, it starts with proven fundamental mathematical and physical basics and expands them with new mathematics, new definitions and a new, more comprehensive theoretical framework, just as relativity and quantum mechanics did.in the early part of the last century.

Since 1935, there have been no paradigm-shifting new physics discoveries, only experimental and technological evidence of fields, particles and concepts that fit within the current materialistic paradigm. TDVP, on the other hand, with the inclusion of the action of consciousness, and detailed mathematical and dimensionometric applications of the Calculus of Distinctions, Dimensional Extrapolation and the Conveyance Equations, provides a new, expanded paradigm that not only encompasses and integrates known physics, chemistry, the life sciences, and verified paranormal phenomena, it provides answers and explanations for quantum and macro-scale phenomena not explained, or even explainable in the current paradigm.

You wrote:
Also i would like to come back on the subject of peer review (about stuff like
this 9D spin model) in the area of -theoretical-  *physics*.  … I would be more interested with which modern physicists you and-or Ed are talking in detail about the mathematical theories within your TDVP context.

My response:
We certainly agree about the importance of colleague review, and we have been eagerly seeking it for years. I have approached people like Stephen Hawking, Menos Kafatos, Henry Stapp, and Roger Penrose, and a number of mathematicians to get these ideas peer reviewed, and Vernon has approached many others. But finding qualified reviewers who are willing to spend their precious time reviewing something outside the box is easier said than done. See my comments above regarding the four categories of reviewers.

You continue:
This also because imho inventing workable validated theories in mathematical physics usually should not be much determined only by 'creativity' (although this may apply for generating hypotheses) but by having an understanding of experimental physics as w ell. Without the experiments, imho you are most of the  time  -in fact almost always-only  creating (highly) speculative 'theories' (in fact more  hypotheses  than theories); a well known fact in the philosophy of science btw, and mentioning things as new paradigms or being decades ahead of the others do not change such facts. NB it is not intended as (severe) criticism, but more as a suggestion how to continue the research and if also focus on the interconnections between your 'new physics' and the well-established older theories.

My response:
I certainly understand and appreciate this, as I’m sure Vernon does, but you apparently didn’t know that I’ve relied heavily on experimental physics in developing the mathematics.

You continued:
At least in your latest response on Ning you now seem to have acknowledged this, but then you also should admit that there is not much 'linkage' (yet?) between all the new ideas (including these TRUE units) with conventional 'fundamental' physics (apart from the periodic table, but that's not enough. Like i wrote earlier, in theoretical physics the quantum mechanics of the electron bands around the core (and the Pauli Exclusion Principle) are determining the periodic index; and also their reactivity with other elements. But that's another subject.  While it looks like an 'Eureka' experience finding such a new way of setting up the periodic table, together with some possible new findings, imho again more validation and verification is to be done to make it a workable theory instead of just a (wild) hypothesis.”

My response:
Again, you seem to be unaware of much of what we’ve published. As my previous discussion shows, there are multiple linkages between TDVP and fundamental physics, quantum mechanics and relativity. In addition to explaining why quarks combine in triads, the unique value of the Cabibbo angle, explaining the Periodic Table consistent with electron shell theory and Pauli’s exclusion principle, -but in much more detail-, explaining why fermions have an intrinsic spin number of ½, why photons, electrons, protons, and neutrons have the physical characteristics they do, and the quantization of angular momentum, as well as explaining non-locality and quantum entanglement, we are finding more links and explanations almost daily. If this doesn’t make TDVP “a workable theory instead of just a (wild) hypothesis”, I’d like to know what would.

You wrote:
About the methods used in general in your physics theories as part of your
Toe: maybe this '' C.O.D.' theory by Ed indeed is innovative new method which can be used in mathematical physics, to be recognized as such it should  be studied more in detail by others i suppose, and only then later it might be acknowledged as such.”

My response:
Unless you’ve read the published articles associated with “Reality Begins with Consciousness” and/or the posts on my Transcendental Physics blog, located at www.ERCloseTPhysics.com, you wouldn’t know that over the years, I have discussed the mathematical basis of Transcendental Physics and TDVP with a substantial number of professional mathematicians and mathematical physicists; I have approached at least fifty or sixty. I have documentation of many of these discussions in the form of letters and emails. Of these, only a handful, I believe 5 or 6 actually took the time to look at my work in any detail. The problem, as with getting reviewers for TDVP, is few are willing to invest much time to review anything outside the mainstream paradigm, especially if it involves new math. One professional mathematician, Dr. Vladimir Brandin, has endorsed CoD and used it in his studies of intelligence. We published one paper together:

Brandin V, Close ER: The calculus of dimensional distinctions: Elements of mathematical theory of intellect. Moscow: 2003.

Details of CoD and applications have been published in journal articles. We can supply copies if you want to see them.

I’d like to elaborate a bit more on the mathematical and dimensionometric bases of Transcendental Physics and TDVP for you by pointing out the difference between classical Aristotelian and Platonic reasoning as it pertains to mathematics and scientific research: Aristotelians see mathematics simply as a man-made tool, while Platonists see mathematics as symbolic reflections of an underlying reality. As such, the imperfect tools of human formulation can always be improved to more and more closely mimic and reveal the perfectly logical patterns of reality. I see the value of the Aristotelian point of view in technological and engineering applications, but I also subscribe to the Platonic point of view as valid in constructing a paradigm to illustrate the nature of reality.

To understand TDVP and the use of the CoD, I think it will be helpful for you to know that there are three basic concepts behind the mathematics of TDVP:

1.) There is a direct correlation between the structures of number theory and the structures of the universe. This is why even the most abstract mathematical theorem finds application in the real world sooner or later.
2.) The experimental resolution (Aspect, et al) of the EPR paradox implies consciousness involvement and non-locality. These features are explainable within the framework of a universe with more dimensions than the four of the space-time of Minkowski and Einstein (3S – 1T).
3.) Max Planck discovered that we live in a quantized universe, but mathematical physics has not been properly adjusted to accommodate this fact.

You may agree or disagree with basic concept #1. If you are primarily Aristotelian in your thinking, as many scientists are, you may see the correlation between the types of numbers and the measures of dimensions, as shown by Dimensional Extrapolation, as a remarkable coincidence. If you accept basic concept #1, you will agree that the correlations we’ve discovered are not coincidental.

Basic concept #2 by itself does not imply any specific number of discrete dimensions, but when combined with #1, a maximum number of nine finite orthogonal dimensions are derived.

Concerning basic concept #3, to adjust mathematical physics to a quantized universe, we must first recognize that the calculus of Newton and Leibniz does not apply at the quantum level because, for applications of differential and integral calculus to yield valid results, the domains of the variables involved must be continuous. In a quantized universe, distinctions of content, like mass, energy and consciousness, exist only in finite, discrete integer amounts, and, as we have shown in TDVP, the distinctions of extent, like space and time, are also limited to finite, discrete volumes due to the relativistic light-speed limitation on velocity.
So the dimensional domains of a quantized universe are not continuous. No variable in a quantized universe can approach zero infinitesimally closely, as it must be able to do for Newtonian calculus to yield valid results at the quantum scale. In TDVP, the infinitesimals of Newtonian calculus are replaced by the minimal distinctions of TRUE units, and the Calculus of Distinctions is the mathematical system I’ve developed to extend calculus to the sub-quark level. To be clear, the CoD does not replace Newtonian calculus at the macro scale; it extends calculation to the quark scale, analogous to the way relativity does not replace Newtonian physics at normal scales of measurement, and only comes to play in the vicinity of extremely massive objects, or when relative velocities are near light-speed.

In summary, contrary to the impressions you have portrayed in your email of Feb. 3, 2015, TDVP is, in fact a comprehensive new paradigm with new mathematics, allowing consciousness to be included in the equations of mathematical physics for the first time. This paradigm has explained a number of empirical observations not explained by the current paradigm. The new mathematics, rigorously defined in several published books and articles, reveals an existential nine-dimensional finite domain embedded in an infinite substrate which contains the blueprints of all of the stable forms that support life and consciousness in the universe. I have tried repeatedly since 1989 to obtain competent peer review, and Vernon and I have sought colleague review in every venue available to us over the past six years as we’ve continued to develop the new paradigm. If you have any questions or concerns, or require more detailed explanations, please let me know.

Sincerely,

Edward R. Close, PhD, PE, DISPE




Wednesday, December 31, 2014

UNIFYING QUANTUM PHYSICS AND RELATIVITY

Unifying Quantum Physics and Relativity
The full unification of quantum physics and relativity is brought about in TDVP by applying the tools of CoDD and Dimensional Extrapolation to the mathematical expressions of three well-established features of reality, recognized in the current scientific paradigm: 1.) quantization of mass and energy as two forms of the same essential substance of reality; 2.) introduction of time as a fourth dimension, and 3.) the limitation of the velocity of rotational acceleration to light speed, c. In this process, the need for a more basic unit of quantization is identified, and when it is defined, the reason there is something rather than nothing becomes clear.

Einstein recognized that mass and energy are interchangeable forms of the physical substance of the universe, and discovered that their mathematical equivalence is expressed by the equation E=mc2. In TDVP, accepting the relativistic relationship of mass and energy at the quantum level, we proceed, based on Planck’s discovery, to describe quantized mass and energy as the content of quantized dimensional distinctions of extent. This allows us to apply the CoDD to quantum phenomena as quantum distinctions and describe reality at the quantum level as integer multiples of minimal equivalence units. This replaces the assumption of conventional mathematical physics that mass and energy can exist as dimensionless points analogous to mathematical singularities.

The assumption of dimensionless physical objects works for most calculations in practical applications because our units of measurement are so extremely large, compared to the actual size of elementary quanta, that the quanta appear to be existing as mathematical singularities, i.e. dimensionless points. (The electron mass, e.g., is about 1x10-30 kg, with a radius of about 3x10-15 meter.) Point masses and point charges, etc. are simply convenient fictions for macro-scale calculations. The calculus of Leibniz and Newton works beautifully for this convenient fiction because it incorporates the fiction mathematically by assuming that the numerical value of a function describing the volume of a physical feature of reality, like a photon or an electron, can become a specific discrete finite entity as the value of a real variable, like the measure of distance or time approaches zero asymptotically (i.e. infinitely closely). This is a mathematical description of a non-quantized reality. But we exist in a quantized reality.

Planck discovered that the reality we exist in is actually a quantized reality. This means that there is a “bottom” to physical reality; it is not infinitely divisible, and thus the calculus of Newton and Leibniz does not apply at the quantum level. This is one reason scientists applying Newtonian calculus to quantum mechanics declare that quantum reality is ‘weird’. The appropriate mathematical description of physical reality at the quantum level is provided by the calculus of distinctions with the relationships between the measureable minimum finite distinctions of elementary particles defined by integral solutions of the appropriate Diophantine equations. The mathematics of quanta is the mathematics of integers.

In TDVP we find that, for quantized phenomena, existing in a multi-dimensional domain consisting of space and time, embedded in one or more additional dimensional domains, the fiction of dimensionless objects, a convenient mathematical expedient when we did not know that physical phenomena are quantized, is no longer appropriate. We can proceed with a new form of mathematical analysis, the calculus of dimensional distinctions (CoDD), and treat all phenomena as finite, non-zero distinctions. Replacing the dimensionless points of conventional mathematical physics with distinctions of finite unitary volume, we can equate these unitary volumes of the elementary particles of the physical universe with integers. We can then relate the integers of quantum reality to the integers of number theory and explore the deep relationship between mathematics and reality.

In TDVP, we have also developed the procedure of Dimensional Extrapolation using dimensional invariants to move beyond three dimensions of space and one of time. Within the multi-dimensional domains defined in this way, mass and energy are measures of distinctions of content. If there are other dimensions beyond the three of space and one of time that are available to our physical senses, how are they different, and do they contain additional distinctions of content? If so, how is such content different from mass and energy? We know that mass and energy are two forms of the same thing. If there are other forms, what is the basic “stuff” that makes up the universe? Is it necessarily a combination of mass and energy, - or something else? For the sake of parsimony, let’s begin by assuming that the substance of reality, whatever it is, is multi-dimensional and uniform at the quantum level, and that mass and energy are the most easily measurable forms of it in the 3S-1t domain. This allows us to relate the unitary measure of inertial mass and its energy equivalent to a unitary volume, and provides a multi-dimensional framework to explore the possibility that the “stuff” of reality may exist in more than two forms.

The smallest distinct objects making up the portion of reality apprehended by the physical senses in 3S-1t, i.e. that which we call physical reality, are spinning because of asymmetry and the force of the natural universal expansion that occurs as long as there is no external resistance. If there were no additional dimensions and/or features to restore symmetry, and no limit to the acceleration of rotational velocity, physical particles would contract to nothingness, any finite universe would expand rapidly to maximum entropy as predicted by the second law of thermodynamics for finite systems. But, due to the relativistic limit of light speed on the accelerated rotational velocity of elementary particles in 3S-1t, the quantized content of the most elementary particle must conform to the smallest possible symmetric volume, because contraction to a smaller volume would accelerate the rotational velocity of the localized particle to light speed in 3S-1t, making its mass (inertial resistance) infinite. That minimal volume occupied by the most elementary of particles is the finite quantum distinction replacing the infinitesimal of Newton/Leibniz calculus, and it provides the logical volumetric equivalence unit upon which to base all measurements of the substance of reality.

We can define this minimal volume as the unitary volume of extent, and its content as the unitary quantity of mass and energy. The mass/energy relationship (E=mc2) is linear, since in the 3S-1t context, c2 is a constant, allowing us to define unitary mass and unitary energy as the quantity of each that can occupy the finite rotational unitary volume. This fits nicely with what we know about elementary particles: All elementary particles behave in the same way prior to impacting on a receptor when encountering restricting physical structures like apertures or slits. A particle of unitary mass occupying a unitary volume could be an electron, and a particle of unitary energy occupying a unitary volume before expansion as radiant energy, could be a photon. Einstein explained this equivalence between electrons and photons and Planck’s constant in a paper published in 1905. 

This brings us to a very interesting problem: what happens when we combine multiples of the unitary volumes of mass/energy to form more complex particles? How do we obtain protons and neutrons to form the stable elemental structures of the physical universe?

When we view the spinning elementary particles of the 3S-1T physical universe from the perspective of a nine-dimensional reality, we can begin to understand how Planck was quite correct when he said “there is no matter as such”. What we call matter, measured as mass, is not really “material” at the quantum level. What is it then that we are measuring when we weigh a physical object? The real measurement of mass is not weight, which varies with relative velocity and location and can be zero without any loss of substance; it is inertia, the resistance to motion. The illusion of solid matter arises from the fact that elementary particles resist accelerating forces due to the fact that they are spinning like tiny gyroscopes, and they resist any force acting to move them out of their planes of rotation. An elementary particle spinning in all three orthogonal planes of space resists lateral movement equally in any direction, and the measurement of that resistance is interpreted as mass.


Mass and energy, the two known forms of the substance of the physical universe, embedded in a nine-dimensional domain, form stable structures only under very specific mathematical and dimensionometric conditions. Without these conditions, no physical universe could exist because of the second law of thermodynamics23, which dictates that any finite physical system always decays toward maximum entropy, i.e. total disorder, lacking structure of any kind. If our universe were composed of random debris from an explosion originating from a mathematical singularity, because of the continuous operation of the second law of thermodynamics in an expanding debris field, simple particles accidentally formed by random mass/energy encounter, would decay before a new random encounter could occur and form a more complex combination, because the number random encounters would decrease as the debris field expands. If our physical universe is embedded in the nine-dimensional reality described by TDVP, it escapes this fate of dissolution. While it may change and evolve, its form, and even the way it evolves, will always reflect the intrinsic logical order and patterns of the transfinite substrate within which it is embedded. If this is correct, we have the answer to the question Leibniz regarded as the first and most important metaphysical question of all: We can explain why there is something instead of nothing.